Answer:
Step-by-step explanation:
We can use trigonometry to find the angle between the slant height and the base of the cone.
The base of the cone is a circle with radius 1.65 cm. The slant height is the hypotenuse of a right triangle whose other two sides are the height (which we don't know) and the radius (1.65 cm).
Using the Pythagorean theorem, we can find the height of the cone:
height^2 = (slant height)^2 - (radius)^2
height^2 = (4.70 cm)^2 - (1.65 cm)^2
height^2 = 19.96 cm^2 - 2.72 cm^2
height^2 = 17.24 cm^2
height = sqrt(17.24) cm
height = 4.15 cm (rounded to two decimal places)
Now we can use trigonometry to find the angle between the slant height and the base of the cone.
tan(angle) = opposite / adjacent
tan(angle) = height / radius
tan(angle) = 4.15 cm / 1.65 cm
tan(angle) = 2.515
Taking the inverse tangent (or arctan) of both sides, we get:
angle = arctan(2.515)
angle = 70.32 degrees (rounded to two decimal places)
Therefore, the angle between the slant height and the base of the cone is 70.32 degrees.
If i have a 97% grade and i get a 75% on a quiz that counts 7% of my grade, how much is my grade? (37 points)
Answer: 90.32%
Step-by-step explanation:
To calculate your updated grade after receiving a 75% on a quiz that counts 7% of your overall grade, you can use the following formula:
New grade = (Old grade * (100 - weight of quiz)) + (Quiz grade * weight of quiz)
Plugging in your values, we get:
New grade = (97 * (100 - 7)) + (75 * 7)
New grade = (97 * 93) + (5.25)
New grade = 903.16
Therefore, your new grade is 90.32%.
Answer: The sum of the weight of all your coursework plus your final is equal to 14.00
Step-by-step explanation:
not sure
please help with these 2 questions in math
The correct answer is E (-1,-3). Reflection across the x-axis is a transformation that flips the object across an imaginary line that runs through the center of the x-axis.
What is transformation?Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.
In this case, the x-axis is the line y = 0. The figure ABCD is reflected across this line, resulting in point A being reflected to E.
When a figure is reflected, the x-coordinates remain the same, while the y-coordinates change sign. This means that the x-coordinate of point A (-1) remains the same, but the y-coordinate (3) changes to its opposite (-3). Therefore, the resulting coordinates of point A are (-1,-3).
Reflection across the x-axis is an example of a transformation. Transformations involve changing the position, size or orientation of a figure, but not its shape. This means that the figure ABCD is still the same shape after being reflected, but its position has changed. After being reflected, the figure is now located on the opposite side of the x-axis.
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A line has a slope of 5/6
and passes through the point (7,6). Write its equation in slope-intercept form.
Answer:
y = 5/6x + 1/6
Step-by-step explanation:
m = 5/6, x = 7, y = 6
y = mx + b
6 = 5/6(7) + b
b = 6 - 35/6
b = 36/6 - 35/6 = 1/6
y = 5/6x + 1/6
Answer:
Below
Step-by-step explanation:
Here is another way:
Start with point ( 7,6) slope ( m= 5/6) form :
(y-6) = 5/6 ( x-7) expand
y-6 = 5/6 x - 35/6 add 6 to both sides
y = 5/6 x + 1/6 Done.
Write a quadratic function for the area of the figure. Then, find the area for the given value of x. x = 20 A quadratic function for the area of the figure is A(x) = (Simplify your answer.) ... X
answer: x= 20x
Step-by-step explanation: 2+2 is 4, 4+4 is 8, quick maths
In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
Answer:
This should be a permutation
Step-by-step explanation:
P (n, r) = n!/(n-r)!
P (12,5) = 12!/(12-5)!
P (12,5) = 12!/7!
P(12,5) = 95040
Just curious to know
Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.
what is percentage ?Since "percent" is a slang term for "per hundred," when we discuss percentages, we are speaking to a fraction of a hundred. In a variety of contexts, including math, science, finance, and daily living, percentages are used. The percent sign (%) is commonly used to denote percentages. As an illustration, to determine what proportion of 50 apples are red, you would split the number of red apples by the total number of apples and multiply the result by 100.
given
If Jane had phoned 1,000 times and you had allowed 67% of those calls to go to voicemail, then 67% of those calls would have left voicemails for you.
You can multiply the overall number of calls by the proportion of calls that went to voicemail to determine how many voicemails you would have received:
1000 x 67% = 670
Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.
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The complete question is :-
Jane called one thousand times to tell you she's sorry. If you saw she was calling and let your phone go to voicemail 67% of the time, how many voicemails would you have received if she left one each time?
Possible Answers:
3,700
57,000
67
None of the given answers
670
In PQR, PQ= 5.4, QR= 3.6, and PR=6.2. To the nearest Tenth, what is M∠R
Therefore , the solution of the given problem of angles comes out to be M∠R measured at 45.4 degrees, to the closest tenth.
An angle meaning is what?The intersection of the lines that form a skew's ends determines the size of its biggest and smallest walls. There's a possibility that two paths will intersect at a junction. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by placing two line beams in various configurations between their ends.
Here,
To determine the size of angle R in triangular PQR, we can apply the Law of Cosines:
=> cos(R) = (PQ₂ + PR₂ - QR₂) / (2 * PQ * PR)
=> cos(R) = (5.4₂ + 6.2₂ - 3.6₂) / (2 * 5.4 * 6.2)
=> cos(R) = 0.6960917
When we calculate the inverse cosine of both sides, we obtain:
=> R = cos⁻¹(0.6960917)
=> R equals 45.4 degrees
Angle R in triangle PQR is therefore measured at 45.4 degrees, to the closest tenth.
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ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST
A) The completed table is given as follows:
L D(L)
0 0
3 1
4 1
6.5 2
10 2
11.9 2
15 3
B) the graph is attached accordingly.
C) In the context of the given problem, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).
What is the explanation for the above response?a) To complete the table, we need to use the given function D(L) to determine the number of beverage dispensers needed to hold different amounts of coffee.
We know that each beverage dispenser can hold 6 liters of coffee, so we can start by dividing the amount of coffee needed by 6 and rounding up to the nearest integer to get the number of dispensers needed.
D(L) = ceil(L/6)
Using this formula, we can complete the table as follows:
L D(L)
0 0
3 1
4 1
6.5 2
10 2
11.9 2
15 3
Note that for L=0, we don't need any dispensers, so the value of D(L) is 0. For all other values of L, we divide by 6 and round up to get the corresponding value of D(L).
b) The graph is attached.
c) In the context of the given problem, the function D(L) gives the minimum number of beverage dispensers needed to hold L liters of coffee, assuming each dispenser can hold 6 liters.
So, D(43) = 8 means that if Giada needs to brew and store 43 liters of coffee, she will need at least 8 beverage dispensers. Each dispenser can hold 6 liters, so the first 7 dispensers will be completely filled, and the last dispenser will be partially filled with the remaining coffee.
In other words, if Giada fills 7 dispensers completely, she will have used 42 liters of coffee, and the remaining 1 liter of coffee will be stored in the 8th dispenser. Therefore, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).
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Increase the number 15/16 by 3/5 of it of it. Then increase the resulting number by 3/5 of it
The resulting number is 12/5
What are arithmetical operations?Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it
So, performing the operations,
15/16+15/16×3/5
= 15/16(1+3/5)
= 15/16(8/5)
= 120/80
= 3/2
Now,
3/2+3/2×3/5
= 3/2(1+3/5)
= 3/2(8/5)
= 24/10
= 12/5
Hence, the resulting number is 12/5
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Write numbers to make an expression equivalent to 5x - 4
Expression equivalent to 5x - 4 are 5(x - 4/5), 5x - 20/5, 10x/2 - 8/2 and 3(5x/3) - 4
How numbers to make an expression equivalent to 5x - 4To create an expression equivalent to 5x - 4, we need to use arithmetic operations such as addition, subtraction, multiplication, and division, along with numbers and variables. The goal is to manipulate the numbers and variables in a way that results in the same value as 5x - 4.
Here are some examples of how we can do this:
5(x - 4/5)
In this expression, we start with x and subtract 4/5 from it. Then we multiply the result by 5. This is equivalent to distributing the 5 to x and -4/5, which gives us 5x - 4.
5x - 20/5
Here, we simply subtract 20/5 (which simplifies to 4) from 5x. This gives us 5x - 4.
(25x - 20)/5
In this expression, we start with 25x and subtract 20 from it. Then we divide the result by 5. This is equivalent to simplifying the expression to 5x - 4.
10x/2 - 8/2
This expression might look a bit different, but it's still equivalent to 5x - 4. Here, we start with 10x and divide it by 2, which gives us 5x. Then we subtract 8/2 (which simplifies to 4) from it, giving us 5x - 4.
3(5x/3) - 4
In this expression, we start with 5x and divide it by 3. Then we multiply the result by 3, which gives us 5x. Finally, we subtract 4 from it, giving us 5x - 4.
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savvas realize topic 5 assesment
Finally, express the solution as an interval of real numbers or as a set of values that make the inequality. x<10.4, x>3.3, x≥32 and x≤-15.
How to solve inequality?To solve an inequality, you need to find the set of values that make the inequality true. The process for solving an inequality depends on the type of inequality and the variables involved. Here are the general steps:
Determine the type of inequality: Is it a greater than (>), less than (<), greater than or equal to (≥), or less than or equal to (≤) inequality?Simplify both sides of the inequality as much as possible using algebraic operations such as addition, subtraction, multiplication, and division. Remember to apply the same operation to both sides of the inequality.If you multiplied or divided both sides of the inequality by a negative number, you need to reverse the direction of the inequality. For example, if you multiplied both sides of x < 3 by -1, you would get -x > -3.If there are variables on both sides of the inequality, move them all to one side of the inequality and simplify.If there are absolute values in the inequality, you may need to split the inequality into two separate cases, one for when the quantity inside the absolute value is positive, and one for when it is negative.Finally, express the solution as an interval of real numbers or as a set of values that make the inequality true. If the inequality is strict (> or <), use an open interval (e.g., (a, b)). If the inequality includes equality (≥ or ≤), use a closed interval (e.g., [a, b]).
by the question.
a. x-3.5>6.9
x>6.9+3.5
x>10.4
b. 6.4>x+3.1
x[tex]\geq 32[/tex]
c. x/4≤8
x≤32
d. 2/3x≤-10
x≤-15
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Jacque bought 2.5 pounds of dark chocolate covered pecans at $0.30 per ounce. In dollars and cents, what was the cost of these pecans?
Answer:
$12.00
Step-by-step explanation:
We know that 1 pound = 16 oz. Thus, we can create a proportion to find how many ounces (x) is 2.5 pounds:
[tex]\frac{1}{16}=\frac{2.5}{x}\\ x=(2.5*16)\\ x=40[/tex]
Since 2.5 pounds = 40 oz, we can now multiply 40 by 0.30 to find the price of 40 ounces of peacans priced at $0.30/ounce:
40 * 0.30 = $12.00
K
Add the fractions. Simplify if possible.
2
9x
+
10
9x
The sum of the given fractions is (2x + 10)/x.
What is fraction ?
A fraction is a way of representing a part of a whole or a ratio between two quantities. It is written in the form of a numerator and a denominator separated by a horizontal line. The numerator represents the number of equal parts under consideration, while the denominator represents the total number of equal parts that make up the whole. For example, the fraction 3/4 represents three equal parts out of a total of four equal parts. Fractions can be added, subtracted, multiplied, and divided to perform various mathematical operations.
According to the question:
The given fractions can be added if they have a common denominator. In this case, the common denominator is 9x.
So, we need to write the fractions with 9x as the denominator:
2/1 * (9x/9x) = 18x/9x
10/1 * (9/9x) = 90/9x
Now, we can add these two fractions:
18x/9x + 90/9x = (18x + 90)/9x = 9(2x + 10)/9x = 2x + 10/ x
Therefore, the sum of the given fractions is (2x + 10)/x.
Q: Find K by Adding the fractions and simplify if possible k=(2*(9x))+(10*(9x))
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is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 26 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
x is first angle
y is second angle
and z is third angle
Step-by-step explanation:
This question is solved by a system of equations. We have that:x is the first angle.y is the second angle.z is the third angle.Doing this, we get that:The first angle measures 30º.The second angle measures 67º.The third angle measures 83º.The sum of the measures of the angles of a triangle is 180. This means that The sum of the measures of the second and third angles is five times the measure of the first angle.This means that:From this, the first angle can be found:The measure of the first angle is of 30º.The third angle is 16 more than the second.This means that:Since We get that the second angle is:The second angle measures 67º.For the third angle:The third angle measures 83º.
please help immediately
please go to my profile and answer the other I need them asap.
10³•10⁵•10³
Step-by-step explanation:
10³means 10×3,10⁵means 10×5and 10³means 10×3 30+50+30=110
2. Solve based on the diagram below.
What is the value of angle x? How do you know (what type of angle pairs are they)?
Answer: 160
Step-by-step explanation: The straight line or line X is 180 degrees. So subtracted 20. This is because X is intersected by another line which makes the upper notch 20 degrees.
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 29 feet up. The ladder makes an angle of 71 degrees with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
Answer:
30.7
Step-by-step explanation:
sin(71) = 29/x
x = 29/sin71
≈ 30.7
Perry's patio is 6 meters long and 53 meters wide. What is the area of his patio?
PLEASE HELP! Find missing side lengths of B and C. Explain
Answer:
b=7 & c=7√2
Step-by-step explanation:
b=7 as it is an isosceles triangle
now using Pythagoras theorem,
(c)^2= (7)^2+(7)^2
⇒(c)^2= 49+49
⇒(c)^2= 98
⇒c= √98
⇒c=7√2
Answer:
b = 7c = 7√2Step-by-step explanation:
You want the missing side lengths in an isosceles right triangle with one side given as 7.
Isosceles right triangleThe two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:
b = 7
The hypotenuse of an isosceles right triangle is √2 times the side length:
c = 7√2
__
Additional comment
You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.
c² = 7² + b²
c² = 7² +7² = 2·7²
c = √(2·7²) = 7√2
The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.
The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.
Jen is studying how years of drought conditions have caused the water level of Richland Reservoir to drop. At the start of the study, the water in the reservoir was 65 meters deep. Jen observed that the depth of the water dropped by about 0.8 meters the first month of the study. She wants to know what the depth of the water will be if it continues dropping at the same rate. You can use a function to approximate the depth of the water in the reservoir x months after the start of the study. Write an equation for the function.
The equation for the function is D(x) = 65 - 0.8x. Where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
What is a linear function?
A linear function is a mathematical function that has a constant rate of change or slope between the independent variable (x) and the dependent variable (y). It is a function that can be graphically represented as a straight line.
We can use a linear function to approximate the depth of the water in the reservoir x months after the start of the study, since the depth is dropping at a constant rate of 0.8 meters per month. Let D(x) be the depth of the water in meters x months after the start of the study. Then we have:
D(x) = 65 - 0.8x
where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
Therefore, the equation for the function is D(x) = 65 - 0.8x.
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1/4 x5/3 as a fraction
The product of the fraction 1/4 x5/3 is 4/12
What are fractions?Fractions are defined as the part of a whole number, variable or element.
The different types of fractions in mathematics are;
Simple fractions.Proper fractions.Improper fractions.Complex fractions.Mixed fractions.Examples of simple fraction; 1/4, 2/3
Examples of improper fractions; 3/2. 4/3
Examples of proper fractions; 1/2, 2/3
From the information given, we have that;
1/4 x5/3
To determine the product, we need to multiply the numerator, then multiply the denominator
5/12
We can no longer divide the values as there is no common divisor.
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A line has the equation y - 6 = 5x + 9 . work out the gradient and the y intercept of the line.
The gradient of the line is 5, and the y-intercept of the line is 15.
EquationsThe given equation is in the form of y = mx + c, where m is the gradient (slope) of the line and c is the y-intercept of a straight line represented in 2D plane.
Rearranging the given equation, we get:
y - 6 = 5x + 9
Adding 6 to both sides, we get:
y = 5x + 15
Now we can see that the equation is in the required form of y = mx + c. The gradient (slope) of the line is 5, which is the coefficient of x in the equation. The y-intercept is 15, which is the constant term in the equation.
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(1 − cos 0) (1 + cos 0)= 1/csc²0
Step-by-step explanation:
lol sorry for untidy work
Are quadrilaterals LMNO and PQRS similar?
Yes, quadrilaterals LMNO and PQRS are similar because a translation and a dilation map quadrilateral LMNO onto PQRS.
Yes, quadrilaterals LMNO and PQRS are similar because a rotation and a dilation map quadrilateral LMNO onto PQRS.
Yes, quadrilaterals LMNO and PQRS are similar because a reflection and a dilation map quadrilateral LMNO onto PQRS.
No, quadrilaterals LMNO and PQRS are not similar because their corresponding segments are not proportional.
The correct answer is (d) No, quadrilaterals LMNO and PQRS are not similar because their corresponding sides are not proportional.
What are quadrilaterals?A quadrilateral is a geometric shape with four sides and four corners.
To be classified as a quadrilateral, its shape must be a closed figure with four straight sides and four interior angles.
To determine quadrilaterals are similar, we need to check if corresponding angles are congruent and corresponding sides are proportional.
Checking corresponding angles are congruent:
∠ L to ∠P.
∠M to ∠Q.
∠ N to ∠ R.
∠O to ∠S.
All corresponding angles are congruent. Therefore, quadrilaterals have the same shape.
Check if corresponding sides are proportional.
LM =√((-1 - (-2))² + (4 - 2)²) = √(2² + 2²) = 2√2
MN = √((3 - (-1))² + (4 - 4)²) = √(4²) = 4
NO = √((4 - 3)² + (2 - 4)²) = √(2² + 2²) = 2√(2)
OL = √((-2 - 4)² + (2 - (-6))²) = √(6² + 8²) = 10
PQ = √((4 - 2)² + (-2 - (-6))²) = √(2² + 4²) = 2√5
QR = √((12 - 4)² + (-2 - (-2))²) = √(8²) = 8
RS = √((15 - 12)² + (-6 - (-2))²) = √(3² + 4²) = 5
SP = √((2 - 15)² + (-6 - (-6))²) = √(13²) = 13
LM / PQ = (2√2) / (2√5) = √(8/5)
MN / QR = 4 / 8 = 1/2
NO / RS = (2√(2)) / 5√(1) = (2/5)√(2)
OL / SP = 10 / 13
The corresponding sides are not proportional because they are not all equal or proportional to each other. Therefore, we can conclude that the quadrilaterals LMNO and PQRS are not similar.
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Compute the probability that a randomly selected person does not have a birthday on the 1st day of the month.
Answer:
0.9973 or 364/365
Step-by-step explanation:
Assuming that every day of the year is equally likely to be someone's birthday, the probability that a randomly selected person has a birthday on the 1st day of the month is 1/365, since there are 365 possible birthdays in a year.
Therefore, the probability that a randomly selected person does not have a birthday on the 1st day of the month is:
P(not on 1st day) = 1 - P(on 1st day)
P(not on 1st day) = 1 - 1/365
P(not on 1st day) = 364/365
So, the probability that a randomly selected person does not have a birthday on the 1st day of the month is 364/365 or approximately 0.9973.
What is the value of x in (x+3)^2=49 show your work
Answer:
x = 4,-10Step-by-step explanation:
(x+3)^2=49
x+3=√(49)
x+3=√(7^2)
x+3=7
x+3-3=7-3
x=4x+3=-√(49)
x+3=-7
x+3-3=-7-3
x=-10x = 4,-10
In a recent survey, 60% of the community favored building a supermarket in their neighborhood. If 25 citizens are chosen, what is the variance of the number favoring the supermarket?
The variance of the number of citizens favoring the supermarket is 6.
To find the variance of the number of citizens favoring the supermarket, we need to use the binomial distribution formula:
Variance = n × p × (1 - p)
where n is the number of trials (25 in this case), p is the probability of success (0.6 in this case), and (1 - p) is the probability of failure.
Plugging in the values, we get:
Variance = 25 × 0.6 × (1 - 0.6)
Variance = 25 × 0.6 × 0.4
Variance = 6
The binomial distribution is a probability distribution that models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes, success or failure. In this case, the trials are the 25 citizens who were chosen, and the success is the event of favoring the supermarket, which has a probability of 0.6.
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Your tank has a volume of 10 L at the surface (1 atm pressure). You reach a depth of 66 ft. What is the
pressure? What is the volume?
the pressure at a depth of 66 ft is 197,580 Pa, and the volume of the tank at this depth is 0.000505 L.
EquationsTo find the pressure at a depth of 66 ft in a liquid, we can use the formula:
pressure = density x gravity x depth
Assuming the liquid in the tank is water, the density is 1000 kg/m³, and gravity is 9.81 m/s².
First, we need to convert 66 ft to meters:
66 ft x 0.3048 m/ft = 20.1168 m
Then, we can find the pressure at this depth:
pressure = 1000 kg/m³ x 9.81 m/s² x 20.1168 m = 197,580 Pa
To find the volume of the tank at this depth, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume (1 atm and 10 L, respectively), and P₂ and V₂ are the final pressure and volume.
We can rearrange this equation to solve for V₂:
V₂ = (P₁ x V₁) / P₂
Substituting the values, we get:
V₂ = (1 atm x 10 L) / (197,580 Pa / 1 atm) = 0.000505 L
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How many feet of fencing will be needed to enclose this dog pen? 4.8ft by 4yd
Answer:
19.2 ft
Step-by-step explanation:
rx+sy=24
4x+16y=120
In the system of equations above, r and s are
constants. If the system has an infinite number of
solutions, what is the value of rs
?
The values of r and s, considering that the system has an infinite number of solutions, are given as follows:
r = 4/5.s = 16/5.How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.The number of solutions of a system of two linear functions is given as follows:
Infinity solutions: same slope and intercept.Zero solutions: same slope, difference intercepts.One solution: different slopes.For this problem, the system has an infinite number of solutions, meaning that the equations are multiples, thus the values of r and s are given as follows:
120/24 = 5.r = 4/5.s = 16/5.More can be learned about linear functions at https://brainly.com/question/24808124
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