The triangle has sides; a = 11.3 ft, b = 9.03 ft, and c = 12.9 ft. 1
Angles of approximately A = 59°, B = 51°, and C = 70°
What is a triangle?Triangle is a shape of three line segments these segments have three points which crosses it.
The Law of Cosines states that;
c² = a² + b² - 2ab Cos(C)
put values;
12.9² = 11.3² + b² - 2(11.3)(b) Cos(C)
166.41 = 127.69 + b² - 22.6b Cos(C)
b² - 22.6b Cos(C) - 38.72 = 0
We know the quadratic formula, solve it for value of b:
b = [-22.6 Cos(C) ± [tex]\sqrt{(22.6Cos(C))^2 - 4*1*(-38.72)))[/tex]] / (2×1)
b = -11.3 Cos(C) ± [tex]\frac{\sqrt{510.76 Cos^2(C) + 154.88}}{2}[/tex]
To solve for the angles A and C, we can use the Law of Sines, which states that for any triangle with sides of lengths a, b, and c, and its opposite angles which are A, B, and C, So the equation is:
sin(A)/a = sin(B)/b = sin(C)/c
We know that c = 12.9 ft and a = 11.3 ft, and we have just found b, so we can use the Law of Sines to solve for the angles A and C.
sin(A)/11.3 = sin(C)/12.9
sin(A) = (11.3/12.9)sin(C)
sin(A) = 0.875969
A = [tex]Sin^{-1}(0.875969)[/tex]
A ≈ 59° (rounded to the nearest minute)
Now we can use the fact that the sum of the angles in a triangle is 180° to solve for C:
C = 180° - A - B
C = 180° - 59° - [tex]Sin^{-1}[/tex]([22.6cos(C) ± [tex]\sqrt{(511.56 - 154.88 Cos^2(C)) }[/tex]] / 2)
We can use a numerical solver to find the value of C that satisfies this equation. One possible value for C is:
C ≈ 70° (rounded to the nearest minute)
Finally, we can use the Law of Sines again to find the other angle B:
Sin(B)/b = sin(C)/c
Sin(B) = (b/12.9)sin(C)
Sin(B) = (b/12.9)sin(70°)
B = [tex]Sin^{-1}[/tex]((b/12.9)sin(70°))
By putting the value of b,
B ≈ 51° (rounded to the nearest minute)
Therefore, the triangle has sides of lengths 11.3 ft, approximately 9.03 ft, and 12.9 ft, and angles of approximately 59°, 51°, and 70°.
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5 Ahmid used the total number of people who bought a
hot dog and the total number of people who did not
buy a hot dog to make the relative frequency table
below. Does it provide evidence that there is an
association between buying a hot dog and buying a
drink at a baseball game? Explain why or why not.
Drink
No Drink
Total
Hot Dog
70.2%
29.8%
100%
No Hot Dog
38.5%
61.5%
100%
The frequency table shows that there is a relationship between buying a hot dog and buying a drink at a baseball game. The huge 70.2% is evidence of this.
What does the table show?The frequency table is meant to show the relationship between variables. Of all the values provided, the relationship with the highest percentage is 70.2%.
This shows that the number of people who purchased a hot dog while also purchasing a drink constituted the highest number. None of the figures come close to this one. So, there is a strong relationship between the variables.
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What is the mode of this data set?
The line graph is titled Amount of Rainfall. The Y axis is labeled inches. The X axis is labeled weeks. Week 1 has a dot at 2 inches. Week 2 has a dot at 3 inches. Week 3 has a dot at 1 inch. Week 4 has a dot at 3 inches. Week 5 has a dot at 5 inches. Week 6 has a dot at 4 inches. The dots are connected one to the next by a line to show a change in the amount of rainfall.
2
3
4
There is no mode.
The mode of this data set is 3 inches.
In the given data set, the values of rainfall in inches for each week are as follows:
Week 1: 2 inches
Week 2: 3 inches
Week 3: 1 inch
Week 4: 3 inches
Week 5: 5 inches
Week 6: 4 inches
The mode is the value that appears most frequently, which in this case is 3 inches. Therefore, the mode of this data set is 3 inches.
Note that a data set can have more than one mode if there are two or more values that appear with the same frequency and are more frequent than any other value in the data set.
However, in this data set, there is only one mode, which is 3 inches.
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The difference between numbers tell you how far apart they are on the number line 8 and -16 our units apart because 8 -6 = 14
The answer of the given question based on the number line is the difference between 8 and -16 is not 14, it is 24. and 8 and -16 are 24 units apart on the number line.
What is the use of number line?A number line is a visual representation of the real number system, where numbers are placed in order from left to right, with zero in the center. The number line is an important mathematical tool used in a variety of ways, including:
Understanding and comparing numbers: By plotting numbers on a number line, we can visually see the relative size and position of numbers in relation to each other.
Performing arithmetic operations: The number line can be used to add, subtract, multiply, and divide numbers.
Graphing functions: The number line can be used as the horizontal axis of a graph to plot functions and other mathematical relationships.
Actually, the difference between 8 and -16 is not 14, it is 24.
To find the difference between two numbers on a number line, you need to subtract the smaller number from the larger number. In this case, 8 is larger than -16, so we subtract -16 from 8:
8 - (-16) = 8 + 16 = 24
Therefore, 8 and -16 are 24 units apart on the number line.
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GUYS PLEASE HELP
* I’LL GIVE YOU BRAINLIEST
Write and simplify a polynomial expression to find the area of 4 circles. Each circle has a radius of (4a-6)
π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .
what is polynomial ?When variables and coefficients are combined using arithmetic procedures like addition, subtraction, multiplication, and non-negative integer exponents, the result is a mathematical expression known as a polynomial. Any numerical value may be represented by the variables, and the expression's coefficients are constants that combine the variables.
given
A = πr², where r is the circle's radius, is the method for calculating a circle's surface area. The area of one circle can be expressed as follows if the radius of each circle is (4a–6):
A₁ = π(4a-6)²
If we condense this phrase, we get:
A₁ = π(16a² - 48a + 36)
A₂ = π(4a-6)²
A₂ = π(16a² - 48a + 36)
A₃ = π(4a-6)²
A₃ = π(16a² - 48a + 36)
A₄ = π(4a-6)²
A₄ = π(16a² - 48a + 36)
We can add up the areas of each of the four circles to determine their combined area:
A1 + A2 + A3 + A4 Equals A total
A total is equal to π (16a2 - 48a + 36) + π(16a2 - 48a + 36) + π(16a2 - 48a + 36).
π(64a2 - 192a + 144) = A total
π(64a2 - 192a + 144) is the polynomial expression to find the area of 4 circles where circle has a radius of (4a-6) .
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what is the center of dilation
The center of a dilation is a fixed point in the plane about which all points are expanded or contractedAnswer:
Step-by-step explanation:
Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
Question 6(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the cost of used books in dollars.
A horizontal line starting at 1 with tick marks every one unit up to 9. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There are two dots above 1, 2, 3, 5, and 6. There are four dots above 7.
Which measure of center is most appropriate to represent the data in the graph, and why?
The median is the best measure of center because there are no outliers present.
The median is the best measure of center because there are outliers present.
The mean is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are outliers present.
Therefore, the correct answer is: The range is the best measure of variability, and it equals 78.
What is range?Range is a measure of variability that represents the difference between the maximum and minimum values in a dataset. It gives an indication of how spread out the data is. To find the range of a dataset, you simply subtract the minimum value from the maximum value. Range is often used as a quick and simple measure of variability, but it can be sensitive to outliers and extreme values.
Here,
1. For question 5, the appropriate measure of variability for the given data set is the range, which is the difference between the maximum value and the minimum value in the data set.
To find the maximum and minimum values from the given stem-and-leaf plot, we can look at the highest and lowest digits in each row. The highest value is 83 and the lowest value is 5, so the range is:
Range = 83 - 5 = 78
2. For question 6, the appropriate measure of center to represent the data in the given line plot is the median, because the data is skewed to the right and there are outliers present. The median is less sensitive to outliers than the mean.
Therefore, the correct answer is: The median is the best measure of center because there are outliers present.
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the concentration of a drug in a patient's bloodstream is monitored over 10-minute intervals for two hours. t (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 c (mg) 0 2 17 37 55 72 89 103 111 113 113 103 68 a.) how fast is the concentration of the drug changing at 50 minutes? 1.7 mg/min b.) how fast is the concentration of the drug changing at 85 minutes? 1 mg/min c.) is the drug's concentration increasing or decreasing at 115 minutes? decreasing
a) The rate of change of the drug's concentration at 50 minutes is 1.7 mg/min.
b) The rate of change of the drug's concentration at 85 minutes is 0.2 mg/min.
c) The drug's concentration is decreasing at 115 minutes.
a) The central difference approach can be used to calculate the rate of medication change after 50 minutes.
f'(x) = (f(x+h) - f(x-h))/2 × h ....(1)
As per the question, we have h = 10 and x = 50
Substitute the values of h = 10 and x = 50 in (1),
f'(40) = (f(50+10) - f(50-10))/2 × 10
f'(40) = (89-55)/20
f'(40) = 1.7 mg/min
b) For the rate of change of concentration at 85 minutes:
Here, f(80) = 111 mg and f(90) = 113.
The concentration at 90 minutes is 113 mg.
Rate of change = (f(90) - f(80)) / h
= (113 - 111) /10
= 2 / 10
= 0.2 mg/min
c) Since the concentration at 120 minutes (68 mg) is lower than the concentration at 110 minutes (103 mg), the drug's concentration is decreasing.
Therefore, the drug's concentration is decreasing at 115 minutes.
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IXL
An equilateral triangle with center C is shown below.
(HELP!!)
The area of the equilateral triangle is 36√3 square units
What is area of the equilateral triangle?
Area of an equilateral triangle is equal to(√3/4)a², where an is the length of the triangle's side.
In an equilateral triangle, the center, the centroid, and the circumcenter coincide.
The distance between the center and a vertex is 6cm, which is also the radius of the circumcircle.
The side length is [tex]6(3)^{1/2}[/tex], which is twice the length of the radius.
So, the radius of the circumcircle is 6 cm, and the length of each side of the equilateral triangle is 12 cm.
The area of an equilateral triangle with side length s is given by:
A = (s² * √3) / 4
Substituting s = 12, we get:
A = (12² * √3) / 4
= 36√3
Therefore, the area of the equilateral triangle is 36√3 square units.
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The plane traveled 6 mores miles after passing the George Washington Bridge, descending at a 2° angle before landing in the Hudson River.
5a) At what altitude (in feet) did the airplane cross over the G.W. Bridge (e)?
The altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.
What is altitude?Altitude refers to the height of an object or location above a specific reference point, usually the Earth's sea level. In aviation, altitude is often used to describe the height of an aircraft above sea level, and is measured in feet or meters.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It involves the study of trigonometric functions, which are functions of an angle, and are used to relate the angles and sides of a right triangle.
In the given question,
To solve this problem, we need to use trigonometry and the fact that the plane descended at a 2° angle. Let's assume that the altitude of the plane at the George Washington Bridge is h feet.
Using trigonometry, we know that the tangent of the angle of descent is equal to the difference in altitude divided by the horizontal distance traveled. In this case, we have:
tan(2°) = (h - e) / 6
To solve for h, we need to isolate it on one side of the equation. Multiplying both sides by 6, we get:
6 tan(2°) = h - e
Adding e to both sides, we get:
h = 6 tan(2°) + e
We can use a calculator to find the tangent of 2°, which is approximately 0.03492. Substituting this value and the given distance of 6 miles into the equation, we get:
h = 6(0.03492) + e
h = 0.2095 + e
Therefore, the altitude of the plane at the George Washington Bridge is approximately 0.2095 miles (or 1,106 feet) above sea level, plus whatever the height of the bridge is.
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how many ways can you select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer?
There are 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.
To calculate this, we can use a combination formula. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the size of the group and r is the number of people in the committee.
In this case, n = 15 and r = 3.
Using this formula, we can calculate that there are 15! / (3! * (15 - 3)!) = 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.
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how many acres are in a government rectangular survey that consists of the sw 1/4, ne 1/4, and nw 1/4 of section 13, blendon township?
The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.
We have,
In the Government Rectangular Survey System, a section is a square tract of land measuring 1 mile by 1 mile, covering an area of 640 acres.
Each section is divided into quarters.
If we consider the SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township, the total acreage can be calculated as follows:
SW 1/4:
This represents one-fourth of the section.
The SW 1/4 of Section 13 is 640 acres / 4 = 160 acres.
NE 1/4:
The NE 1/4 of Section 13 is also 160 acres.
NW 1/4:
The NW 1/4 of Section 13 is 160 acres.
To find the total acreage, add up the individual acreages:
160 acres (SW 1/4) + 160 acres (NE 1/4) + 160 acres (NW 1/4)
= 480 acres
Therefore,
The government rectangular survey consisting SW 1/4, NE 1/4, and NW 1/4 of Section 13 in Blendon Township covers 480 acres.
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suppose the first and the last page of the document must be printed in color, and only two printers are able to print in color. the two color printers can also print black-and-white. how many ways are there for the 100 pages to be assigned to the four printers?
If the first and last pages of a document must be printed in color, and only two printers can print in color, then there are a total of 4⁹⁹ ways that 100 pages can be assigned for printing to four printers.
The fundamental principle of counting says that if there are p ways to do one thing and q ways to do another thing, then there are p×q ways to do both things. Number of printers that is able to print in color = 2
Number of colors printed by printers = 2
We have to determine the number of ways are there for the 100 pages to be assigned to the four printers. Now, consider there are no restrictions. Let's break this problem into two parts. First, we have to print 2 pages in color and there are only two color printers. So, number of ways to print the first and the last page of the document = 2²
= 4
Number of remaining pages of document = 98
Number of avaliabile printers = 4
Now, second part, we have only 98 pages (out of 100 pages, 2 colors pages are already printed). Each of these 98 pages can be assigned to a printer in 4 ways. So, number of ways to print remaining 98 pages of document = 4⁹⁸.
Using the counting principle, number of ways for printing the 100 pages by four printers = 2² × 4⁹⁸
= 4 × 4⁹⁸ = 4⁹⁹
Hence, required number of ways are 4⁹⁹.
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Jessica went deep sea diving. She make the first stop on her descent at 25 meters below the surface of the water. From that point she dives down further, stopping every 5 meters. If she makes 4 additional stops, which number represents her position, relative to the surface of the water?
*
A 45
B 20
C -20
D -45
Answer:
-45
Step-by-step explanation:
Please help with #10 and #13!!
The angle of rotation in standard form is 251.5651 degrees.
The length of arc S is approximately 20.94 feet.
How do we solve this?If the point (-1, -3) is on the circle x² + y² = 10, then we can substitute these values for x and y in the equation to obtain:
(-1)² + (-3)² = 10
1 + 9 = 10
So, the point (-1, -3) satisfies the equation of the circle.
To find the angle of rotation in standard form, we need to use the formula:
tan(θ) = y/x
where θ is the angle of rotation.
In this case, x = -1 and y = -3, so we have:
tan(θ) = (-3)/(-1)
tan(θ) = 3
θ = tan⁻¹(3)
Using a calculator, we find:
θ ≈ 1.2490 radians or 71.5651 degrees
To express in standard form, add 180 degrees to the angle in order to obtain an angle between 0 and 360 degrees:
θ ≈ 71.5651 + 180 ≈ 251.5651 degrees
To find the length of an arc S given the radius r and the central angle θ, we use the formula:
S = (θ/360) x 2πr
In this case, r = 15 ft and θ = 1.396 radians
Substituting the values:
S = (1.396/2π) x 2π(15 ft)
S ≈ 1.396 x 15 ft
S ≈ 20.94 ft
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Complete question:
Consider the point (-1, -3), which is on the circle x² + y² = 10. Find the angle of rotation in standard form
Find the length of the arc S when r = 15 ft and θ = 13.96°
state the meaning of the central limit theorem in your own words. how important is it to the development and use of statistical quality control techniques?
The central limit theorem is a statistical theory that specifies the probability distribution of a sum or average of several random variables whose distribution is not known.
It is an important theorem since it is utilized to help forecast or estimate the behavior of a specific set of data.
This theorem holds that when you take repeated samples of the same size from a population with a finite standard deviation, the means of those samples will be normally distributed, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Further more, the theorem indicates that the larger the sample size, the more closely the sample mean distribution will approximate a normal distribution.
This is why it is vital in the development and use of statistical quality control techniques, since they rely on correct assumptions about the population’s normality.
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A walkway forms one diagonal of a square playground. The walkway is 22m long. How long is a side of the playground?
Answer:
15.556
Step-by-step explanation:
The length of the diagonal of a square is equal to the length of one side of the square multiplied by the square root of 2
22=x√2
solve ABC subject to the given conditions if possible. Round the lengths of the sides and measures of the angles (in degrees) to one decimal place it necessary.
B=64 degrees, a=25, b=41
To solve triangle ABC, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:
c^2 = a^2 + b^2 - 2ab*cos(C)
We are given B, a, and b, so we can solve for c as follows:
c^2 = 25^2 + 41^2 - 2(25)(41)cos(64)
c^2 = 625 + 1681 - 2135cos(64)
c^2 = 1829 - 2135*cos(64)
c^2 = 311.90
Taking the square root of both sides, we get:
c ≈ 17.7
So the length of side c is approximately 17.7 units.
To find the measures of angles A and C, we can use the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:
a/sin(A) = b/sin(B) = c/sin(C)
We know a, b, and c, and we just solved for c, so we can use the Law of Sines to solve for angles A and C:
a/sin(A) = c/sin(C)
sin(A) = asin(C)/c
A = sin^{-1}(asin(C)/c)
A = sin^{-1}(25*sin(C)/17.7)
Similarly,
b/sin(B) = c/sin(C)
sin(B) = bsin(C)/c
B = sin^{-1}(bsin(C)/c)
B = sin^{-1}(41*sin(C)/17.7)
To find angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:
C = 180 - A - B
Using a calculator, we get:
A ≈ 41.6 degrees
B ≈ 74.1 degrees
C ≈ 64.3 degrees
Therefore, the measures of the angles in triangle ABC are approximately:
A ≈ 41.6 degrees
B = 64 degrees
C ≈ 64.3 degrees
And the lengths of the sides are approximately:
a = 25
b = 41
c ≈ 17.7
p(x) = 4x; Find p(-6)
p(x)= (x-4)²-(x-6)². ... 4X - 20 = 0 => X = 20/4 => X= 5.
HELP** complete the problem by creating two binomials that represent that sides of the shape . Then multiply to get a quadratic equation . Draw a picture to help set up the problem . 6. Albert installs swimming pools . While the pools can come in different sizes, Albert only offers rectangular pools that are always twice as wide as they are long. He also puts a deck around the entire pool, and the deck is always 4ft wide on each side. Write an equation to represent the total area of the pool and deck.
Let's denote the width and length of the pool by “w” and “l” respectively. Then, the width of the pool and deck combined would be:So the equation that represents the total area of the pool and deck as binomials is [tex]: A = 2(L + 8)(2L + 8)[/tex]
What binomials that represent that sides of the shape?Let's start by drawing a diagram of the rectangular pool and the surrounding deck:
___________ Pool Length (L)
| |
| |
| |
| |
W|___________|
| Deck Width|
| = 4ft |
|___________|
We know that the width of the pool (W) is twice its length (L), so we can write:
[tex]W = 2L[/tex]
We also know that the deck is 4ft wide on each side, so the total width of the pool and deck is:
[tex]W_total = W + 8 = 2L + 8[/tex]
And the total length of the pool and deck is:
[tex]L_total = L + 8[/tex]
The total area of the pool and deck can be found by multiplying the total width by the total length:
[tex]A = W_total \times L_total[/tex]
Substituting our expressions for W_total and L_total, we get:
[tex]A = (2L + 8) * (L + 8)[/tex]
Expanding the brackets, we get:
[tex]A = 2L^2 + 24L + 64[/tex]
So the equation that represents the total area of the pool and deck is:
2L^2 + 24L + 64
To represent the sides of the shape as binomials, we can factor out a common factor of 2 from the quadratic expression:
[tex]A = 2(L^2 + 12L + 32)[/tex]
Then we can write the sides of the shape as:
[tex]L + 8[/tex] and [tex]2L + 8[/tex]
Therefore, So the equation that represents the total area of the pool and deck as binomials is: [tex]A = 2(L + 8)(2L + 8)[/tex]
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Find the volume of the triangular prism below
We can claim that after answering the above question, the As a result, the triangular prism has a volume of 240 cubic centimetres.
what is prism?A prism is a polyhedron with an n-sided polygonal basis, a second base that is a shifted copy of the first base, and n extra faces (necessarily all parallelograms), with two connecting the corresponding sides of the base. All cross sections that are parallel to the base are translations of it. A prism is a two-sided, solid, three-dimensional object with two faces. It has the same cross-sections, flat sides, and similar bases. Faces of a prism are parallelograms or rectangles with no bases. A prism is a refracting item that is homogeneous, solid, and transparent, contained by two planes that are obliquely oriented to one another. A typical prism has two triangular faces and three parallel rectangular faces. They are made of either glass or metal.
To calculate the volume of a triangular prism, multiply the area of the triangular base by the prism's height.
Triangle area = 1/2 * base * height
Triangle area = 1/2 * 8 cm * 6 cm
Triangle area = 24 cm2
We must now determine the prism's height. The diagram shows that the prism has a height of 10 cm.
Finally, the volume of the triangular prism can be calculated by multiplying the area of the triangle base by the prism's height:
Prism volume = base area * The prism's height
Prism volume = 24 cm2 * 10 cm
Prism volume = 240 cm3
As a result, the triangular prism has a volume of 240 cubic centimeters.
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there is a three term arithmetic sequence with the first term 9. if you add 2 to the second term and 20 to the third term it forms a geometric sequence. what is the smallest number the third term in the geometric sequence could be?
The geometric sequence is 9 + 2 + 20 = 29.
The smallest number the third term in the geometric sequence can be is 29.
This is because when you add 2 to the second term and 20 to the third term of the three-term arithmetic sequence with a first term of 9,
the third term of the geometric sequence is 9 + 2 + 20 = 29.
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Tanya painted a mural that was 8 feet tall. The area of the mural was 224 square feet. What is the length of Tanya’s mural?
The length of Tanya's mural is 28 feet.
What is the length of Tanya’s mural?A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.
Area of a rectangle is expressed as;
Area = length × width
We know that the area of Tanya's mural is 224 square feet, and the height of the mural is 8 feet.
So we can use these values to find the length of the mural:
Area = length × width
224 = length × 8
To solve for the length, we can divide both sides of the equation by 8:
length = 224 ÷ 8
length = 28 feet
Therefore, the dimension of the length is 28 feet.
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Which statements about this system of equations are true? Check all that apply
2 x minus 7 y = negative 13. Negative 2 x + 11 y = 1.
The x-variable will be eliminated when adding the system of equations.
The y-variable will be eliminated when adding the system of equations.
The sum of the system of equations is 4 y = negative 12.
x = 17
y = negative 3
There are infinitely many solutions to the system of equations.
As a result, (x, y) = is the answer to a set of equations. (-17, -3). There aren't an endless number of answers because there is a single one.
What sort of equation would that be?The meaning of an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are split by the 'equal' symbol.
The statements that are true about this system of equations are:
The x-variable will be eliminated when adding the system of equations.
There are infinitely many solutions to the system of equations.
To eliminate the x-variable, we can add the two equations as follows:
(2x - 7y) + (-2x + 11y) = -13 + 1
Simplifying the left-hand side and the right-hand side gives:
4y = -12
Dividing both sides by 4 yields:
y = -3
Substituting y = -3 into either of the original equations gives:
2x - 7(-3) = -13
Simplifying this equation yields:
2x + 21 = -13
Subtracting 21 from both sides yields:
2x = -34
Dividing both sides by 2 yields:
x = -17
Therefore, the solution to the system of equations is (x, y) = (-17, -3). Since there is a unique solution, there are not infinitely many solutions.
The statement "The sum of the system of equations is 4y = -12" is false since the sum of the equations does not simplify to that expression.
The statement "x = 17" is false since the correct solution is x = -17.
The statement "The y-variable will be eliminated when adding the system of equations" is false since adding the equations only eliminated the x-variable.
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In a car park,
the number of cars: the number of vans = 7:4
the number of vans: the number of lorries = 3:2
The total number of cars, vans and lorries in the car park is 205
How many vans are in the car park?
Therefore , the solution of the given problem of unitary method comes out to be the parking lot has 60 trucks.
What is an unitary method?It is possible to accomplish the objective by using this widespread convenience, pre-existing variables, or all significant components from the initial Diocesan adaptable survey that adhered to a specific methodology. If it doesn't, both of the essential components of a term confirmation outcome will undoubtedly be lost, but if it is, there is going to be another opportunity to contact the entity.
Here,
Let's begin by giving the unknowns variables:
x = number of vehicles
Van count = 4 times
Since there are 205 cars overall, the number of lorries is equal to (205 - 11x).
The value of x can be determined using the second bit of knowledge:
=> 4x/3 = (205 - 11x)/2
When we simplify this solution, we obtain:
=> 8x = 3(205 - 11x)
=> 8x = 615 - 33x
=> 41x = 615
=> x = 15
We can now determine the quantity of vans:
Van count = 4x = 4(15) = 60
Consequently, the parking lot has 60 trucks.
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a company conducted a marketing survey for families with young children and found that 113 113 families own a nintendo ds and 192 192 families own a nintendo wii. if 22 22 own a wii and a ds, how many own either a wii or ds, but not both?
out of the families that have DS, 20 have both, so subtract them from the absolute to get 124 - 20 = 104.
out of the families that have WII, 20 have both, so subtract them from the all-out to get 186 - 20 = 166.
you presently have 3 classifications that are unadulterated.
104 own DS in particular.
266 own WII in particular.
20 own both.
the complete that possesses either a DS or a WII however not both is equivalent to 104 + 266 = 370.
you need to subtract 20 from every classification since it is remembered for both.
it is remembered for DS and it is remembered for WII.
Market surveys are apparatuses to straightforwardly gather criticism from the interest group to grasp their qualities, assumptions, and prerequisites. Marketers foster previously unheard-of techniques for impending items/benefits however there can be no affirmation about the outcome of these methodologies.
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the complete question is:
A company conducted a marketing survey for families with young children and found that 124 families own a Nintendo DS and 186 families own a Nintendo Wii. If 20 own a Wii and a DS, how many own either a Wii or DS, but not both?
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Part 1
The granular fertilizer 12-12-12 is composed of 12% nitrogen, 12% phosphate, and 12% potassium. Similarly, the fertilizer 16-17-0 is composed of 16% nitrogen, 17% phosphate, and 0% potassium. If a gardener mixes a 10 pound bag of 12-12-12 with a 5 pound bag of 16-17-0, what are the concentrations of nitrogen, phosphate, and potassium in the mixture? Express the answers as percents
the concentrations of nitrogen, phosphate, and potassium in the mixture are 13.33%, 13.67%, and 8%, respectively. To find the concentrations of nitrogen, phosphate, and potassium in the mixture, we need to calculate the total amount of each nutrient in the two bags and then divide by the total weight of the mixture.
First, let's calculate the amount of each nutrient in the 10 pound bag of 12-12-12:
Nitrogen: 12% of 10 pounds = 1.2 pounds
Phosphate: 12% of 10 pounds = 1.2 pounds
Potassium: 12% of 10 pounds = 1.2 pounds
Next, let's calculate the amount of each nutrient in the 5 pound bag of 16-17-0:
Nitrogen: 16% of 5 pounds = 0.8 pounds
Phosphate: 17% of 5 pounds = 0.85 pounds
Potassium: 0% of 5 pounds = 0 pounds
Now, let's add up the total amount of each nutrient in the two bags:
Nitrogen: 1.2 + 0.8 = 2 pounds
Phosphate: 1.2 + 0.85 = 2.05 pounds
Potassium: 1.2 + 0 = 1.2 pounds
Finally, let's divide the total amount of each nutrient by the total weight of the mixture (10 + 5 = 15 pounds) and express the answers as percentages:
Nitrogen: (2 / 15) x 100% = 13.33%
Phosphate: (2.05 / 15) x 100% = 13.67%
Potassium: (1.2 / 15) x 100% = 8%
Therefore, the concentrations of nitrogen, phosphate, and potassium in the mixture are 13.33%, 13.67%, and 8%, respectively.
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HELP ME ASAPPPPP!!!!
Thus, the explicit formula for the simple interest sequence A(n) = P + (n-1)(i.P) is: A(n) = P * (1 + i * (n-1)).
What is simple interest?Simple interest is a method of calculating interest on a loan or investment where interest is charged only on the initial principal amount. In simple interest, the interest rate is applied to the original principal amount, and the interest earned remains the same throughout the entire term of the loan or investment.
by the question.
The formula for a simple interest sequence A(n) = P + (n-1) (i.P) represents the value of an investment that earns simple interest over n periods, where:
A(n) is the value of the investment after n periods.
P is the principal or initial investment
i is the interest rate per period as a decimal fraction (e.g. 0.05 for 5%)
n is the number of periods
To derive the explicit formula for A(n), we can use the formula for simple interest:
I = P * i * n
where I am the total interest earned over n periods. We can then express A(n) as:
A(n) = P + I
Substituting the expression for I, we get:
A(n) = P + P * i * (n-1)
Simplifying, we can factor out P to get:
A(n) = P * (1 + i * (n-1))
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The figure below is composed of a regular hexagon and three congruent triangles. What is the area of the figure rounded to the nearest square meter?
The area of the figure rounded to the nearest square meter is 97 m². So correct option is A.
Describe regular pentagon?With five equal sides and five equal angles, a regular pentagon is a polygon. In other words, a regular pentagon's sides and angles are all congruent. It is a closed, two-dimensional object that is categorized as a sort of polygon since it is constructed of straight line segments.
Regular pentagons have a number of distinctive features, including:
A regular pentagon has 108 degree internal angles that are all equal.
A standard pentagon's outside angles are all 72 degrees in angle.
A regular pentagon is divided along its diagonals into three smaller triangles, two of which are congruent.
Regular pentagons are prevalent in a variety of fields, including geometry, architecture, and the arts.
First, you would need to determine the side length of the regular hexagon. This can be done using the radius of the circumscribed circle, which is given as 5 meters. The side length of the hexagon can be calculated using the formula:
s = r * √(3)
where s is the side length and r is the radius of the circumscribed circle. Plugging in the given value for r, we get:
s = 5 * √(3)
simplifying, we get:
s ≈ 8.7 meters
Next, you would need to calculate the area of one of the congruent triangles. This can be done using the formula:
A = (1/2) * b * h
where A is the area of the triangle, b is the base, and h is the height. The base of the triangle is equal to one side of the hexagon, which we just calculated to be approximately 8.7 meters. To find the height, we can draw an altitude from one vertex of the triangle to the opposite side, creating a 30-60-90 right triangle. The height is equal to the shorter leg of this triangle, which can be calculated using the formula:
h = (1/2) * s * √(3)
Plugging in the value for s, we get:
h ≈ 7.5 meters
Now we can calculate the area of one of the triangles:
A = (1/2) * 8.7 * 7.5 ≈ 32.6 square meters
Finally, we can calculate the total area of the figure by adding the area of the hexagon to three times the area of one of the triangles:
A = 6 * (s²) * √(3)/4 + 3 * A
Plugging in the values we calculated, we get:
A ≈ 96.9 square meters
Rounding to the nearest square meter, we get:
A ≈ 97 square meters
Therefore, the answer is A. 97 m².
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please help me solve this i’ll mark brainliest
Answer:
measure of angle MPQ is 125
Step-by-step explanation:
1) Corresponding angles are congruent
5x=3x+50
2x=50
x=25
2) Substitute back into the equation
3(25)+50 = 125
help my math math math
Pr(total)=pr(blue)+pr(green)+pr(red)=4+1+2
=7
a) pr(blue)= pr(blue)/pr(total)=4/7
b) pr(green)= pr(green)/pr(total)=1/7
c) pr(not green)= pr(blue)+pr(red)= 4/7+2/7=6/7
d)pr(not purple)= ???
e)pr(red)=pr(red)/pr(total)=2/7
Question d seems like it is a problem cause we were not told that a purple ball was in the bag.