Answer: We can use trigonometry to solve this problem.
Let x be the length of the ladder, and h be the height of the ladder.
We can use the tangent function to relate the angle of elevation, the length of the ladder, and the height of the ladder:
tan(74°) = h / x
We know that x = 12 ft and we can find h.
We can cross multiply and solve for h:
x * tan(74°) = h
12 * tan(74°) = h
We can use a calculator to find the value of h, this will give us the height of the ladder.
Finally, we can use the Pythagorean theorem to find the length of the ladder:
x^2 = h^2 + 12^2
x = √(h^2 + 12^2)
Round your answer to the nearest tenth, we have x = √(h^2 + 12^2)
We can use the value of h to find the length of the ladder.
However, without the value of h it is not possible to find the length of the ladder.
Step-by-step explanation:
A 54-foot long wire will be attached to the top of a pole for support, and will be pulled tight and anchored to the ground.
If the wire makes a 13 degree angle with the ground, how tall is the pole?
The height of the pole used in the question is; 12.15 ft
How to use trigonometric ratios?The 3 main trigonometric ratios are;
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
Now, since the guy wire makes an angle of 13 degrees with the ground, it means the guy wire will be the hypotenuse of the right angle triangle and the height of the pole which we will label as h will be the opposite side of the triangle. Thus;
height/54 = sin 13
height = 54 * sin 13
height = 54 * 0.225
Height = 12.15 ft
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Compute the probability of being dealt at random and without replacement a 13-card bridge hand consisting of: (a) 6 spades, 4 hearts, 2 diamonds, and 1 club; (b) 13 cards of the same suit.
The probabilities are found to be 0.00196 in case- 1 and
1 / 158753389900 in case - 2.
Note that there are a total of 52 cards in bridge, so by combinations that there are a total of
(13
52) numbers to deal 13 cards. There are a total of 13 spades, hearts, diamonds and clubs, respectively, so there are
(13
6) ways to get spades, etc., so that by multiplication principle the probability in we're looking for:
( a ) ( 13 (13 (13 (13
6) 4) 2) 1)
(52
13)
= 1716x715x78x13 / 635013559600
= 0.00196.
( b) there are a total of 4 drawings where all 13 cards are are of the same suit, corresponding to a choice of either spades, hearts, diamond, or clubs. Therefore the probability here is given by :
4 / ( 52 = 4/ 635013559600
13)
= 1 / 158753389900 .
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Whats BD? Please help. Thanks
The value of side BD of the kite is 12 units
How to find the value of side BD of the kite?
In mathematics, kite is a quadrilateral which has two pairs of congruent adjacent sides.
A kite is a geometric shape which is symmetrical. It has two pairs of congruent adjacent sides, and two pairs of congruent opposite angles. The diagonals of a kite are perpendicular bisectors of each other.
Using Pythagoras theorem:
BC² = CE² + BE²
BE = √(BC² - CE²)
BE = √(10² - 8²) = 6 units
Since ΔCDE is identical to ΔBCE.
Thus, DE = BE
DE = 6 units
Since BD = BE + DE
Thus, BD = 6 + 6 = 12 units
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 - Tanner's beaker had 45 milliliters of water in it at first. After each of his friends poured in 8 milliliters, the
beaker contained 93 milliliters. How many friends poured water into Tanner's beaker?
Answer:
x=6
Step-by-step explanation:
hope this helps you with your question
Select the correct answer from each drop-down menu.
Consider the function f(x) = |₂³| − 1.
The piecewise functions that coincide with the given function are
[(x + 3)-1, when x is greater than or equal to 3,
[(x-3)/2] -1, when x is less than 3,
[(x+3)/2] -1, when x is greater than -3,
[-(x+3)/2] -1, when x is greater than or equal to -3,
and
Yes, the piecewise functions that coincide with the given function are [(x + 3)-1, when x is greater than or equal to 3, [(x-3)/2] -1, when x is less than 3, [(x+3)/2] -1, when x is greater than -3, and -(x+3)/2] -1, when x is greater than or equal to -3.
Piecewise functionThe piecewise functions that coincide with the given function are as follows: when x is greater than or equal to 3, the piecewise function is (x + 3)-1; when x is less than 3, the piecewise function is (x-3)/2 -1; when x is greater than -3, the piecewise function is (x+3)/2 -1; and when x is greater than or equal to -3, the piecewise function is -(x+3)/2 -1.This means that, depending on the value of x, the resulting value of the function f(x) = |₂³| − 1 will be different.For example, when x is equal to 3, then f(x) = 0; when x is equal to -3, then f(x) = -2; and when x is equal to 1, then f(x) = -1.Thus, the piecewise functions correctly express the given function, as they correctly capture the different values of f(x) for different values of x.No, the piecewise functions that coincide with the given function are[(x + 3)-1, when x is greater than or equal to 3,[(x-3)/2] -1, when x is less than 3,[-(x-3)/2] -1, when x is less than or equal to -3,[(x-3)/2] -1, when x is greater than -3.To learn more about Piecewise function refer to:
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How do you factor and simplify 4x^2+ 25
Answer:
(4x + 5)(4x + 5)
Step-by-step explanation:
4x * 4x = 4x^2, and 5 * 5 = 25. Thus being 4x^2 + 25
1. Is G (cost) a function of t (time)? Explain your reasoning
2. Is t (time) a function of G (cost)? Explain your reasoning.
{G} is the function of {t} and vice - versa is also true.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a graph as shown in the image.
{ 1 } -
Yes, the given function G{t} is the function of {t}. It is a piecewise function.
{2} -
Let the given function is -
y = G{t}
We can find the inverse as -
t = G⁻¹{y}
Yes, {t] is also the function of {G}.
Therefore, it can be concluded that {G} is the function of {t} and vice - versa is also true.
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Let U = {(q, r, s, t, u, v, w, x, y, z)
A = {q, s, u, w, y}
B = {q, s, y, z)
C = {v, w, x, y, z).
List the elements in the set.
AL(BNC)
A. {q, s, u, w, y, z)
B. q, r, w, y, z}
C. {q, y, z)
D. {q, w, y}
PLEASE HELP!
The elements of the set A'(B∩C)is { r, t , v, x, y, z}
How to determine the setIt is important to note that the universal set is the set containing all the elements for a given event.
From the information given, we have that;
U = {(q, r, s, t, u, v, w, x, y, z)A = {q, s, u, w, y}B = {q, s, y, z)C = {v, w, x, y, z)The signs used to represent sets are;
∩ - Intersection of sets used to represent the common elements of two or more sets∪- Union of sets used to represent the sum of sets without repetitionTo determine the set,
A'(B∩C)
A' = { r, t, v, x, z}
B∩C = { y, z}
Now, the set A'(B∩C)
A'(B∩C) = { r, t , v, x, y, z}
Hence, the set is { r, t , v, x, y, z}
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Order the steps to solve the equation
log(x2-15) = log(2x) form 1 to 5.
x²-2x-15=0
Potential solutions are -3 and 5
x²-15 = 2x
x-5=0 orx+3=0
(x - 5)(x + 3) = 0
A logarithm is an operation used to determine the exponent of a given base number.
What is logarithm?
A logarithm is a mathematical function that describes the relationship between the power to which a number (called the base) must be raised, and the resulting value. The logarithm of a number is the power to which the base must be raised to produce that number.
Start by moving the logarithm to the left-hand side of the equation: log(x²-15) = log(2x)
Next, use the property of logarithms that log(a/b) = log(a) - log(b) to get x²-15 = 2x
then you can simplify the equation by subtracting 2x from both sides x²-2x-15=0
then factor the equation to get (x - 5)(x + 3) = 0
Finally, use the Zero Product Property to solve for x. The solutions will be x = 5 or x = -3
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Write the following ratio using two other notations.
6:5
Use only the numbers above (not any others).
Notation one:
Notation two:
0.
3
0=0
0:00 to
0<0 0>
The ratio may be written if it is a component of a percentage.
6 is to 5 is 12 is to 10 .
What is a ratio notation?Ratios can be expressed as a notation, like 1/2, or as a ratio, like 6:5. A ratio's value is determined by dividing the first and second numbers. Consider the ratio 12:10 as an example. "6 to 5" should be read as the ratio. Any fraction, like 6/5, can also be expressed as a ratio, which is written as 6:5.
A colon or a fraction bar are two typical symbols representing ratios. You can also use words.
6 : 5 = 6/5 = 6 to 5
The ratio may be written if it is a component of a percentage.
6 is to 5
as in ...
12 is to 10 what 6 is to 5, and vice versa.
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What are the dimensions of the product?
[2 1 0] x [1 -1 2 -1 -2 1 0 1 1] =
The resulting vector has the same dimensions as the original, 1 x 3.
What is a matrix?A rectangular array of numbers, symbols, or expressions set up in rows and columns is known as a matrix. They are employed in a wide variety of mathematical disciplines and contexts, including calculus, statistics, physics, and engineering, as well as linear algebra. Matrices are an essential tool for solving systems of linear equations and representing linear transformations since they may be added, subtracted from, and multiplied by other matrices.
The matrix multiplication of [2 1 0] and [1 -1 2 -1 -2 1 0 1 1] is:
[2 1 0] x [1 -1 2 -1 -2 1 0 1 1] = [2(1) + 1(-1) + 0(2), 2(-1) + 1(-2) + 0(1), 2(0) + 1(1) + 0(1)]
= [2 -3 1]
Therefore, the product of the two matrices is a row vector [2 -3 1], which has the dimensions 1 x 3.
If we subtract 1 from each element of this row vector, we get:
[2 -3 1] - 1 = [1 -4 0]
So, the resulting vector has the same dimensions as the original, 1 x 3.
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A parabola can be drawn given a focus of ((7,6) and a directrix of y=-8y=−8. What can be said about the parabola?
The parabola has a vertex at (7 , -1) has a p-value of -0.5 and it opens downwards.
How to interpret the equation of a parabola?The axis of symmetry of a parabola is basically perpendicular to the directrix and contains the focus and vertex.
Thus, the axis of symmetry is the vertical line x = 7.
The vertex lies halfway between the focus and directrix. Thus, we can say that the vertex is (7, (6 - 8)/2) = (7, -1)
Due to the fact that the vertex lies above the focus and the directrix is horizontal, then it means that the parabola opens downward.
Therefore, the focus is (7 - 8)/2 = -0.5 units below the vertex, so, p = -0.5
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Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant.
sin(t), cos(t); Quadrant II
sin(t)=_____________
If the terminal point determined by t is in the given quadrant.sin(t), cos(t); sin(t)= -cos(t) in Quadrant II.
In Quadrant II, the sine function is positive and the cosine function is negative. The sine and cosine functions are related by the Pythagorean identity, which states that sin^2(t) + cos^2(t) = 1.
Since the sine is positive and the cosine is negative in Quadrant II, we can square the sine function and subtract it from 1 to get:
1 - sin^2(t) = cos^2(t)
We can then take the square root of both sides to get:
cos(t) = sqrt(1 - sin^2(t))
And since the cosine is negative in Quadrant II, we can then multiply the equation by -1 to get:
sin(t) = -cos(t)
This equation is only valid in Quadrant II.
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Find the total surface area
The total surface area is 3994ft sq.
How to find the volume and base's area of a right rectangular pyramid?Suppose the base of the pyramid has length = l units, and width = w units.
Surface area of rectangular prism = 2lb +2lh+2bh
Suppose that the height of the pyramid is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]
is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, so its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
Given;
Length= 32ft
Breadth= 21ft
Height= 25ft
Now,
Surface area of rectangular prism = 2lb +2lh+2bh
=2*32*21+2*32*25+2*21*25
=1344+1600+1050
=3994
Therefore, the area will be 3994ft sq.
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The sum of the differences between sample observations and the sample mean is
a. Zero
b. The range
c. The mean deviation
d. The standard deviation
The sum of the differences between sample observations and the sample mean is zero.
Statistics is a science that deals with methods of collecting data, processing data, presenting data, analyzing data, drawing conclusions, and making reasonable decisions based on existing facts.
There are some terms that are frequently used in statistics:
Range is the difference between the largest and the smallest values in a data set;Mean is the average of the sample values;Mean deviation is the average deviation of the data from the mean;Variance is a measure of how far the data is spread from its average value, which is equal to the average distances of the sample observations from the sample mean;Standard deviation is a value used to determine the distribution of data in a sample and see how close the data is to the mean value. The standard deviation is equal to the square root value of the variance.The sum of the differences between sample observations and the sample mean can be denoted as ∑(xi - mean), where n is the size of the sample and i = 1,2,3,...,n
∑(xi - mean) = ∑xi - n*mean,
= n*mean - n*mean
= 0
Thus the sum of the differences between sample observations and the sample mean is zero.
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solve this system of equations by using the elimination method.
x+2y=4 x+3y=10
Answer: The elimination method is a method for solving a system of equations by eliminating one of the variables. One way to do this is to multiply one equation by a constant and then add or subtract it from the other equation to cancel out one of the variables.
We will start by multiplying the first equation by -1:
x + 2y = 4 ----> -x - 2y = -4
Now we will add the second equation to the modified first equation:
-x - 2y = -4
(x + 3y = 10)
0x + 1y = 6
Now we can solve for y:
y = 6
Now that we know y = 6, we can substitute this back into one of the original equations, for example the first one:
x + 2y = 4
x + 2(6) = 4
x = -8
So the solution to the system of equations is x = -8 and y = 6
Therefore, the solution is (-8,6)
Step-by-step explanation:
What are m and b in the linear equation, using the common meanings of m and b?
2 + 3x + 5 - 2x = y
The values of m and b on the linear equation:
2 + 3x + 5 - 2x = y
are
m = 1
b = 7
How to find the values of m and b?A general linear equation can be written as in the slope-intercept form as:
y = m*x + b
Where m is the slope and b is the y-intercept.
Here we have the linear equation
2 + 3x + 5 - 2x = y
Now we want to write this in the slope-intercept form, to do so, we just need to simplify the left side, then we will get:
2 + 3x + 5 - 2x = y
(2 + 5) + (3x - 2x) =y
7 + x = y
Then the linear equation is:
y = 1*x + 7
So the values are:
a = 1
b = 7
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which statement is true? a. the graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g. b. the graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g. c. the graph of
The graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g.
The graph of a function is a visual representation of the function's mathematical relationship between inputs and outputs. When a function is said to be "stretched", this means that the graph is being transformed in some way. In this case, the graph of function f is being stretched vertically by a factor of 3 to create the graph of function g. This means that the vertical distance between each point on the graph of function f will be 3 times as great on the graph of function g. For example, if the graph of function f has a point (1,2) then the corresponding point on the graph of function g would be (1, 6). This transformation will change the shape of the graph and the values of the inputs and outputs of the function. The graph of the transformed function g will be wider, taller, and have different values for the inputs and outputs.
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The table shows the balance of Rob’s checking account at the end of the day. This is $95.50 less than the amount he had the beginning of the day.
Which of the following equations can be used to determine Rob’s account balance at the beginning of the day?
What expression is equivlent to -4(3x-5)?
The answer to this question is -12x+20
FILL IN THE BLANK for a positive angle, the rotation from the initial side to the terminal side takes place in a ______direction. For a negative angle, the rotation takes place in a _______direction. (?;?)
For a positive angle, the rotation from the initial side to the terminal side takes place in a counter clockwise where as for a negative angle, the rotation takes place in a clockwise.
In math the term angle is defined as a figure in which two rays emerge from a common point and this is called the vertex of the angle and the two rays forming the angle are called its arms or sides.
Here we have to know that the angle which is greater than 180 degrees but less than 360 degrees is called a reflex angle.
Here we need to find the missing term in the given statement.
According to the definition of angle we have know that the rotation is measured from the initial side to the terminal side of the angle.
If it has Positive angles result from counterclockwise rotation, and negative angles result from clockwise rotation.
Here we have know that the angle with its initial side on the x‐axis is said to be in standard position.
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Step It Out 12 Find the product. Identify any properties that you used. A. (4)(-0.5)(-3) (-3) Turn Tused the order of operations and multiplied from The product is even / odd. B. (-)(-7X(-9) =) (-)(-9) because the number of negative factors is -O) -00 (3) = -21 89 to I used the the order of the factors, and then I used the Property of Multiplication to group factors to make the multiplication easier. The product is because the number of negative factors is even / odd Property of Multiplication to switch
The solution to the product is -18 and the property is negative factors
How to determine the productFrom the question, we have the following parameters that can be used in our computation:
(4)(-0.5)(-3) (-3)
Using the property of negative factors, we have
(4)(-0.5)(3) (3)
Next, we remove the brackets
This gives
4 * -0.5 * 3 * 3
Evaluate the product
-18
Hence, the solution is -18
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What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place.
0.11 to 0.21
0.10 to 0.23
0.16 to 0.17
0.11 to 0.16
The 95% confidence interval for this population proportion is (0.10,0.23).
sample size n = 125
number of people planned to take an extended vacation = 21
sample proportion (p) = 21/125 = 0.168
Confidence level = 0.95
significance level (α) = 1-0.95 = 0.05
Z score = Z(0.05) = 1.96, from the Z table.
confidence interval for a population proportion is-
p±Zα/2 *[tex]\sqrt{\frac{p(1-p)}{n} }[/tex] = 0.168± 1.96[tex]* \sqrt{\frac{0.168(1-0.168)}{125} }[/tex]
= 0.168 ± 1.96*0.334
= 0.168 ± 0.0655
= (0.1025, 0.2335)
= (0.10,0.23)
Hence, the confidence interval is (0.10,0.23).
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Find IJ and JK in parallelogram HIJK.
h 6p
i 7p+17
j 9p+11
K
The values of IJ and JK in parallelogram HIJK are 52 and 80 respectively
How to find the values?Recall that in every parallelogram, the opposite sides are equal and parallel.
This implies that IJ ║ HK and HI ║ JK
⇒ 5s - 88 = 3s - 32
Collecting the like terms we have
5s-3s = -32 +88
2s = 56
This implies that s = 28
By substitution we have s as 3(28) -32
= 84-32 = 52 and and 4(28)-32 = 80
The sides of the parallelogram are 80 and 52 respectively
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a. x has an average of 5 and a standard deviation of 80. b. x has a bell shaped distribution with an average of 5 and a standard deviation of 80. c. x has a uniform distribution with an average of 80 and a standard deviation of 5. d. x has a bell shaped distribution with an average of 80 and a standard deviation of 5. e. secret statisticians code meaning that ohio state graduates are morons. 10 points question 2 what is the notation for the following (in matching order): standard deviation of a population, average of a sample, a set of sample averages, mean of a population, standard deviation of a sample, is distributed, bell shape a. s, mu, sampling distribution, x-bar, sigma, ~, n b. sigma, x-bar, sampling distribution, mu, s, n, ~ c. sigma, x-bar, sampling distribution, mu, s, ~, n d. s, x-bar, sampling distribution, mu, sigma, ~, n 10 points question 3 what is the meaning of x-bar ~ n(80,1) a. the random variable x is distributed with a bell shape, an average of 80 and a standard deviation of 1. b. the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1. c. the random variable x is distributed with a bell shape, an average of 1 and a standard deviation of 80. d. the set of x-bars is distributed with a bell shape, an average of 1 and a standard deviation of 8
The answer to question 1 is not a statistical question. The answer to question 3 is that the notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.
Question 1: e. secret statisticians code meaning that ohio state graduates are morons.
This is not a statistical question and does not have a correct answer.
Question 2: c. sigma, x-bar, sampling distribution, mu, s, ~, n
The notation for the following (in matching order) is: sigma (standard deviation of a population), x-bar (average of a sample), sampling distribution (a set of sample averages), mu (mean of a population), s (standard deviation of a sample), ~ (is distributed), n (bell shape).
Question 3: b. the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.
The notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.
The answer to question 1 is that it does not have a correct answer as it is not a statistical question. The answer to question 2 is that the notation for the following (in matching order) is: sigma (standard deviation of a population), x-bar (average of a sample), sampling distribution (a set of sample averages), mu (mean of a population), s (standard deviation of a sample), ~ (is distributed), n (bell shape). The answer to question 3 is that the notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.
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The number 1465 rounded to its highest place value is?
Frank rented a unicycle at the circus. He paid a flat rental fee of $15 plus $2 and hour. The total cost was $23. Write and solve an equation you can use to find the number of hours he rented the unicycle.
Answer:
4 hrs
Step-by-step explanation:
let x = # of hours he rented the unicycle
$15 + ($2/hr)x = $23
($2/hr)x = $23 - $15 = $8
x = ($8) / ($2/hr) = 4 hours
The three interior angles of a triangle measure x°, (x-4)°, and (x+16)°. Which is the measure of one of the three angles?
OA) 48°
O B) 52°
O C) 60°
OD) 70°
=======================================================
Explanation:
Every triangle has the rule where the inside angles add to 180.
(angle1)+(angle2)+(angle3) = 180
x + (x-4) + (x+16) = 180
3x+12 = 180
3x = 180-12
3x = 168
x = 168/3
x = 56
Then we can determine each angle.
angle1 = x = 56 degreesangle2 = x-4 = 56-4 = 52 degrees (choice B)angle3 = x+16 = 56+16 = 72 degreesAs a check:
angle1+angle2+angle3 = 56+52+72 = 180
This confirms the answer is correct.
y varies jointly with x and the square of z
The equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 is Y= 11/14 xz^2.
How can the equation of variation be determined?The concept that will be used here is variation.
since Y varies jointly with respect to z^2 and x the we will introduce K which is the proportionality constant, then we have:
Y= Kxz^2.
The we can introduce Y, x and z to solve for the single unknown and have the answer for the equation of variation.
231=K (6) (7^2)
231=6*49*K
231=(K*294)
231/294=K.
K = 11/14
We can have Y= 11/14 xz^2 which is the equation of variation.
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complete question:
Find an equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 the equation of varation is y
What is the measure of AC
Side AC of the similar triangle system has a length of 6 units. (Correct choice: C)
How to determine the missing length in a system of two similar right triangles
Two triangles are similar when both have congruent angles but sides are not congruent though proportional. In this problem we find the case of two similar right triangles, whose relationship is shown below:
AD / AC = CD / BC = AC / AB
If we know that AD = 4 and AB = 9, then the length of side AC is:
4 / AC = AC / 9
AC ² = 36
AC = 6
The length of side AC is equal to 6 units.
To learn more on similar triangles: https://brainly.com/question/14926756
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