Answer: a = 2
Step-by-step explanation: 2.5 x 2 = 5 5 + 4.2 = 9.2
[tex]4.2+2.5a=9.2[/tex]
Rearrange:
[tex]2.5a+4.2=9.2[/tex]
Subtract 4.2 from both sides:
[tex]2.5a+4.2-4.2=9.2-4.2[/tex]
[tex]2.5a=5[/tex]
Divide both sides by 2.5:
[tex]\dfrac{2.5a}{2.5} =\dfrac{5}{2.5}[/tex]
[tex]\fbox{a = 2}[/tex]
help please all 4 problems
The equation of the slope is y = -5x + 72.
What is slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
Given that:
72 inches is the depth of the liquid level in water tank.
Water drains at a rate of 5 inches per minute.
Let y represent the tank's height, which is given as 72.
Let x be the total number of minutes, here x = 0.
Therefore, the slope's equation is the rate at which the water drains, that is:
m = -5
The equation of the line is given by the formula:
y = mx + c
Substitute the values:
72 = -5(0) + c
c = 72
And the equation is:
y = -5x + 72
Hence, the equation of the slope is y = -5x + 72.
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Help I need the answer
Answer:
9
Step-by-step explanation:
make them equal to each other
15x = 14x + 9
x = 9
6/7 of a number is 5400. find 7/9 of the same money
Answer:
7/9 of the same money is 4900
Step-by-step explanation:
If 6/7 of a number is 5400, we can set up an equation to find the value of the number:
(6/7)x = 5400
To solve for x, we can multiply both sides by 7/6:
x = 5400 * (7/6)
x = 6000
Now that we know the number is 6000, we can find 7/9 of that value:
(7/9) * 6000 = 4900
So 7/9 of the same money is 4900.
HELPPPPPPPPPPPP DUE IN 20 MIN
Answer: D
Step-by-step explanation: the amount per cashews (c) is $2.45. Therefore, its 2.45c
The amount per pounds of sugar is $0.61. Therefore, its 0.61s
And, since its "buying" (basically, adding), you gotta add them. So, the answer would be: 2.45c+0.61s
find an equation of a plane containing the three points (3, -1, -2), (1, -6, -4), (1, -5, -2) in which the coefficient of is -8.
A 2-column table with 3 rows. The first column is labeled time (t) with entries negative 2, 3.5, 30. The second column is labeled Elevation(e) with entries a, b, c.
Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water’s edge. The equation of her average change in elevation over time is e = 300 – 10t, where t is the time in minutes since she left the cabin, and e is her elevation with regard to sea level. Which values are viable points, and what are their values in the table relating t and e?
a =
b =
c =
Answer:
a = not viable
b = 265
c = 0
good?
Answer: a = not viable b= 265 c = 0
Step-by-step explanation:
solve (4+8x) over 12x
Answer:
C
Step-by-step explanation:
(4+8x)/12 simplifies to (1+2x)/3x
the long leg of a right triangle is 71 feet longer than the short leg. the hypotenuse is 85 feet long. how long are the legs of the right triangle?
The right triangle Short leg: 14 feet and Long leg: 85 feet.
Because you have a right triangle, and you know the hypotenuse, you can use the Pythagorean Theorem:
x2 + y2 = 852
You are told the difference between the 2 sides:
x = y + 71
Now you have 2 equations. Use the expression for x in the 2nd equation, and substitute into the first:
(y + 71)2 + y2 = 852
Originally known as a rectangle triangle , a right triangle or right-angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle), i.e., It has two perpendicular sides.
The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
The hypotenuse is the side that is opposite the right angle (side c in the figure). Legs are the sides that are close to the correct angle (or catheti, singular: cathetus).
The side b that is adjacent to angle B and opposite to angle A is known as side a, while the side a that is adjacent to angle A and opposite to angle B is known as side b.
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The value of the short leg of the right angle triangle is 14 feet while the value of the long leg will be 85 feet.
You may apply the Pythagorean Theorem since you have a right triangle and know the hypotenuse:
x^2 + y^2 = 852
You are told the difference between the 2 sides:
x = y + 71
Now we have 2 equations.
Now, we will use the expression for x in the 2nd equation, and substitute into the first:
Thus we will get it as:
(y + 71)^2+y^2=852
A right triangle, also known as a right-angled triangle, is a triangle with one angle that is a right angle (that is, a 90-degree angle), i.e., it has two perpendicular sides.
The connection between the sides and angles of a right triangle is the basis of trigonometry.
The hypotenuse is the opposite side of the right angle.
Legs are the sides that are nearly at the right angle
The side b that is adjacent to angle B and opposite to angle A is known as side a, while the side a that is adjacent to angle A and opposite to angle B is known as side b.
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For the following right traingle, find the side length x. Round your answer to the nearest hundredth
Answer:
20
Step-by-step explanation:
(Hypotenuse)²=(Opposite)²+(Adjacent)²
(25)²=(15)²+(A)²
A²=625-225
A=✓400
A=20.00
A large school district employs 3,461 teacher. If there are 28 students per teacher, how many students are there?
Answer: To find the number of students, you can multiply the number of teachers by the number of students per teacher.
3,461 teachers * 28 students/teacher = 96,668 students
So, there are 96,668 students in the school district.
Step-by-step explanation:
Write the explicit formula for each geometric sequence.
Then determine the 8th term of each sequence.
Show work below.
Part A) 4, 16, 64, 256,...
Answer: The explicit formula for a geometric sequence is given by:
an = a1 * r^(n-1)
Where a1 is the first term, r is the common ratio, and n is the term number.
Part A) In this sequence, the first term is 4, and the common ratio is 4/1 = 4.
So the explicit formula for this sequence is:
an = 4 * 4^(n-1)
To find the 8th term of this sequence, we can substitute n = 8 into the formula:
a8 = 4 * 4^(8-1)
a8 = 4 * 4^7
a8 = 4 * 16,384
a8 = 65,536
Therefore, the 8th term of this sequence is 65,536.
Step-by-step explanation:
the nine horizontal and nine vertical lines on an $8 \times 8$ checkerboard form $r$ rectangles, of which $s$ are squares. the number $s/r$ can be written in the form $m/n$, where $m$ and $n$ are relatively prime positive integers. find $m n$.
By using the combination theorem, it can be concluded that the value of m + n = 125
Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.
nCr = n! / (n - r)! r!
Let's denote the number of rectangles as r, and the number of squares as s:
r = ⁹C₂ x ⁹C₂
= (9! / (9 - 2)! 2!) x (9! / (9 - 2)! 2!)
= (9! / 7! 2!) x (9! / 7! 2!)
= 36 x 36
= 1296 rectangles
s = 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8²
= 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64
= 204 squares
Then we get the ratio of s : r as follows:
s / r = 204 / 1296
= 17 / 108
Since m represents the horizontal lines and n represents the vertical lines, then m + n = 17 + 108 = 125.
Thus, it can be concluded that the value of m + n = 125
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Trina must spend at least 45 minutes, m, studying for her test
The inequality that describes that Trina must spend at least 45 minutes studying for her test at x ≥ 45 min.
How to write the inequality ?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance. In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions.
Trina is to spend at least 45 minutes studying for her test which means that she can either spend 45 minutes studying, or more than 45 minutes.
The inequality for this is therefore:
x ≥ 45
Assuming that the minutes she spends studying is x.
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Full question is:
Trina must spend at least 45 minutes studying for her math test. (find the inequality)
Write your answer as a fraction or whole number without exponents.
4 ^–1 =
The index form 4 ^–1 as a fraction or whole number without exponents is 1/4
What are index forms?The index form of a number described as the number that is written as an exponential expression
Index forms are also described as a single number that is raised to another number or variable.
The index or exponent of an exponential expression shows how many times to multiply the base by itself in the expression.
From the information given, we have the index form as;
4^-1
This is represented as a fraction;
1/4^1
Note that any number that is raised to 1 is equal to the number
1/4
Hence, the value is 1/4
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Nolan invested $5,300 in an account paying an interest rate of 3.8% compounded annually. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $6,880?
With compound interest of 3.8% compounded annually it will take 7 years for the value of the account to reach $6,880.
What is Compound interest?
Compound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.
Formula to find compound interest:
A=P(1+r/n)^nt
Where,
A = amount
P = principal
r = rate of interest
n = number of times interest is compounded per year
t = time (in years)
Alternatively, we can write the formula as given below:
CI = A – P
Where CI=Compound Interest
Now,
As given
A=$6880
P=$5300
r=3.8%
n=1
t=?
Therefore,
The time it would take to become $6880 will be
6880=5300(1+3.8/100)^t
From here t=7 years
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Calcula la fuerza resultante de un avión que viaja 24 km al sur y 17 km al oeste.
La ecuación de la fuerza resultante es el vector R = F · cos 234.689° i + F · sin 234.689° j.
¿Cómo determinar la fuerza resultante de un avión?
Los vectores se caracterizan por tener magnitud y dirección, sea F la magnitud de la fuerza resultante del avión (nótese que la magnitud es un valor no negativo por regla general), cuya fórmula es la siguiente:
R = F · cos θ i + F · sin θ j
Donde:
F - Magnitud de la fuerza, en newtons. θ - Dirección del vector con respecto a la dirección este, en grados.La dirección del vector se determina mediante la siguiente función trigonométrica inversa:
θ = tan⁻¹ (Fy / Fx)
Donde:
Fx - Componente horizontal, en kilómetros. Fy - Componente vertical, en kilómetros.Si sabemos que Fx = - 17 km y Fy = - 24 km, entonces la ecuación de la fuerza resultante es:
θ ≈ 234.689°
R = F · cos 234.689° i + F · sin 234.689° j
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Solve by using a proportion. Round answer to the nearest hundredth of necessary.
A map scale designates 0.75 inch = 50 miles. If the distance between two towns on the map is 2.75 inches, how many miles must you drive
to go from the first town to the second town?
Answer:
miles
To go from the first town to the second town, you must drive 137.5 miles.
What is an proportion?
A proportion is a mathematical equation that compares two ratios. It is usually written as two equal fractions or ratios, one on each side of the equation. A proportion can be used to compare the relationship between different quantities, such as measurements, rates, or even time.
We can use proportion to solve this problem. The proportion relates the map scale to the actual distance:
0.75 inch / 50 miles = x / distance
where x is the actual distance we want to find.
We can cross-multiply and solve for x:
0.75 inch * distance = 2.75 inches * 50 miles
x = (2.75 inches * 50 miles) / 0.75 inch
x = (137.5 miles)
To go from the first town to the second town, you must drive 137.5 miles.
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Given the measure of arc(ABC) = 7x + 20 and arc(AC) = 4x + 10, find x.
Answer:
Step-by-step explanation:
Ahh hell nah
Convert 36 pounds to kilograms. (1 pound = 0.454 kilogram)
79 kilograms
7.9 kilograms
163.44 kilograms
16.344 kilograms
36 pounds is equal to 16.344 kilograms.
Given that we need to convert 36 pounds to kilograms.
We have 1 pound = 0.454 kilogram,
To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.454 kilogram.
Given that we have 36 pounds, we can multiply this value by the conversion factor to find the equivalent weight in kilograms:
36 pounds x 0.454 kilogram/pound = 16.344 kilograms
Therefore, 36 pounds is equal to 16.344 kilograms.
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What is the probability of flipping a coin 8 times and getting heads 2 times?
Round your answer to the nearest tenth of a percent.
OA. 21.9%
OB. 27.3%
OC. 3.1%
OD.
10.9%
SUBMIT
Answer:
10.9%
Step-by-step explanation:
You want to do the number of ways that can happen, which is [tex]_8C_2 = 28[/tex] divided by the total number of possibilities which is [tex]2^8[/tex] to get 10.9%
if x, y, and z are integers and xy z is an odd integer, is x an even integer? (1) xy xz is an even integer. (2) y xz is an odd integer. a) statement (1) alone is sufficient, but statement (2) alone is not sufficient. b) statement (2) alone is sufficient, but statement (1) alone is not sufficient. c) both statements together are sufficient, but neither statement alone is sufficient. d) each statement alone is sufficient. e) statements (1) and (2) together are not sufficient.
c) both statements together are sufficient, but neither statement alone is sufficient.
According to the question
The query asks if statements (1) and (2) by themselves are sufficient to determine whether x is an even number. The answer is that neither assertion by itself is adequate to ascertain what x is worth. However, when both claims are taken into account, they are adequate to decide whether or not x is an even number. This is due to the fact that if xyz is even and yz is odd, x must be even. If x were odd, both xy xz and y xz would be strange as well. Due to this, the proper response is "c) neither statement is adequate when read alone, but both assertions taken together are sufficient."
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A linear function passes through the points (-3, 14)
and (2, -1). What is the rate of change of the
function?
The rate of change of the linear function is the third option which is -3.
The linear function runs through the points (-3,14) and is specified in question (2,-1).
The function's rate of change must be determined.
Having said that,
The slope of a linear function determines how quickly it changes.
A line's slope
By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.
In light of this, the slope of a line passing through the points (-3,14) and (2,-1) is
(-1-14)/(2-(-3)) = -15/5 = -3.
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In which number does the digit 8 have a value that is 1/10 10 1 start fraction, 1, divided by, 10, end fraction times as great as the digit 888 in the number 2{,}980. 72,980. 72, comma, 980, point, 7?
The digit 8 has a value that is 1/10 times as great as the digit 8 in the number 2,980.7 will be 548
The 8 in our number, 2,980.7, is in the tens place and hence represents an 80.
The value of the digit 8 is equal to 1/10 of 10 divided by 1, which is 10 times greater than the value of the digit 888.
We need a number that contains an 8 and has a value that is 1/10 of the previous number, hence we need:
1/10*80 = 8
So, the number we're seeking has an 8 in the position of the one.
Option C: 548 would be this.
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Suppose you spend $500. 00 on an oven to bake bread. Each loaf of bread costs 0. 20 to bake. You sell the loaves for 1. 00 each. How many loaves of bread must you sell for you to break even? (Use a system of equations to model each situation. Solve by any method. ) (PLEASE SHOW ANSWER AND WORK. SERIOUS APPLICANTS ONLY, THIS IS A MATH TEST, I FAILED THE LAST ONE. )
We must sell 625 loaves of bread to break even.
If it is a solution of equations, fill all the information of your solution into the equations you are working on to ensure that all equations are satisfied by your solution. And then, solve these equations to find the answer to your problem.
Let N be the number of loaves you sell.
Your cost would be,
C = 500 + 0.2N
Your revenue would be,
R = 1. N
Now, find out when is C = R
⇒500 + 0.2N = N
⇒500 = 0. 8 N
⇒N = 500/0. 8
⇒N = 625
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Which of these triangle pairs can be mapped to each other using both a translation and a reflection across the line containing AB?
Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A B C. It is also slightly higher than triangle A B C.
Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C.
Triangles A B C and X Y Z are congruent. Triangle X Y Z is slightly higher and to the right of triangle A B C.
Triangles A B C and X Y Z are congruent. Triangle A B C is rotated to the right to form triangles X Y Z. Triangle X Y Z is also higher and to the right of triangle A B C.
( the answer is not B )
The triangle pairs that can be mapped to one another using both a translation and a reflection across the line containing AB will be A based on the provided information. Triangles A B C and X Y Z are similar. Triangle A is created by reflecting triangle X, Y, and Z across a line. The correct option is A.
What is the Triangles about?The first triangle pair is a pair that can be mapped to one another using both translation and reflection across a line containing AB.
The first figure is made up of the coordinates XYZ and ABC, which are translations and reflections of one another across the line AB.
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Answer: it is A
Step-by-step explanation: just took the test
PLEASE HELP!! GIVING 50 POINTS. NEED DONE ASAP
Answer:
1. T, W, E, G
2. C, B, D, A
Step-by-step explanation:
For question 1:
G passes through (2, 3) and (0, -1). So, the slope is [tex]\frac{-1-3}{0-2}[/tex] = 2.
T passes through (0, 3) and (4, 4) so the slope is (4-3)/(4-0) = [tex]\frac{1}{4}[/tex].
E has a slope of [tex]\frac{5}{3}[/tex] because the equation is y = mx+b where m is the slope.
W has a slope of [tex]\frac{1}{3}[/tex] since slope is increase in y divided by increase in x.
The order of these from least to greatest is [tex]\frac{1}{4}[/tex], [tex]\frac{1}{3}[/tex], [tex]\frac{5}{3}[/tex], and 2.
Therefore, the answer is T, W, E, G.
For question 2:
A passes through (0, -1) and (2, 2), so the slope is (2- -1)/(2-0) = [tex]\frac{3}{2}[/tex].
B passes through (2, 0) and (4, 1), so the slope is (1-0)/(4-2) = [tex]\frac{1}{2}[/tex].
C has a slope of [tex]\frac{1}{4}[/tex] since the equation is y=mx+b where m is the slope.
D has a slope of [tex]\frac{3}{4}[/tex] since the slope is increase in y divided by increase in x.
The order of these from least to greatest is [tex]\frac{1}{4}[/tex], [tex]\frac{1}{2}[/tex], [tex]\frac{3}{4}[/tex], and [tex]\frac{3}{2}[/tex].
Therefore, the answer is C, B, D, A.
I hope this helps! :)
Didn't understand something? Some important formulas/things to remember that I used:
The equation of a linear function can be written as y=mx+b. m represents the slope.
The slope is the change/increase (decrease, in some cases), in y, divided by the change/increase in x.
The formula for the slope is [tex]\frac{Y2 - Y1}{X2 - X1}[/tex], where Y2 is the y coordinate of the second point, Y1 is the y coordinate of the first point, X2 is the x coordinate of the second point, and X1 is the x coordinate of the first point.
Which sentence uses correct punctuation?
A. Exercise and diet; these are the keys to living a long life.
O
B. There are three places I want to visit: Japan, India, and France.
C. Mara wished she could visit the stars: she often dreamed of it.
D. Dr. Chu has this to say about sugar; "Only eat small amounts."
Answer:
C. Mara wished she could visit the stars: she often dreamed of it.
I'm a bit Confused on this math problem could someone help me please? thanks if you do! :D
Answer:
Step-by-step explanation:
Alright so let me try and explain this as best as I can:
So the graph isn't linear because the graph shows a parabola (a boomerang kind of shape that happens if you use an exponent somewhere in a y=mx+b formula if I remember correctly) and not a straight line. Linear graphs cannot curve, and this one does. Not sure why it it would be a function though. Assuming the answer chosen is correct, my best guess as to why it might be a function is because it continues to go in the same direction forever, there is a predictable amount of change between each point and you can follow a formula to find every point on the graph.
I really hope this helps a little!
The group of linear function is shown on the coordinate grid. What is the slope of the line?
Answer:
what grid
Step-by-step explanation:
I think of a number. I halve it and multiply it by 4. my answer is 40. What is the number? pls it's needed urgently due in 10mins
Answer:
The number is 20
Step-by-step explanation:
First we have n, then n/2, then 4n/2, which equals 40. Thus, we have 2n=40, or n=20 which is the number.
Answer:
20
Step-by-step explanation: