Instructions: Find the equation of the line through point (5, 1) and
perpendicular to 5x - y = -3. Use a forward slash (i.e. "/") for fractions
(e.g. 1/2 for).

Here, we want to find the cube root of 729

Mathematically, we are looking for a number which when multiplied by itself 3 times will give 729

Out of the options, the only value that does this is 9

This is because;

Answer:

above sea level

Step-by-step explanation:

By applying change management concepts and selecting appropriate maintenance types, the Delta Insurance Company can successfully redevelop their policyholder subsystem and achieve a more efficient and cost-effective solution.

The Delta Insurance Company is facing a challenge with their policyholder subsystem and it is clear that they need to reevaluate the system for redevelopment. The amount of people-time allocated to policyholder maintenance has been increasing at a significant rate of 15% per year over the last five years, and this is now costing as much per year as it did in 1980 to develop the original application.
In order to get the application in order, the company should start by analyzing the current data structures and identifying any areas that need improvement. It is important to document all decisions and changes made during this process, as this will be useful in the future. The company should consider using change management principles to ensure that all stakeholders are aware of the changes being made and are involved in the decision-making process.
As for the next set of changes, the company should consider implementing a proactive maintenance approach. This could involve regular updates and improvements to the system, rather than just fixing problems as they arise. They should also consider implementing a data-driven approach to maintenance, using data to identify areas that need improvement and to make decisions about the best course of action. Ultimately, the company should strive for a system that is flexible, efficient, and easy to maintain, in order to avoid similar issues in the future.
It's crucial for the Delta Insurance Company to get their policyholder subsystem in order, considering the increasing amount of people-time allocated to its maintenance. To achieve this, they should consider reevaluating the subsystem and applying change management concepts.
First, the company needs to establish a clear understanding of the current state of the subsystem by analyzing the available documentation, flow charts, and data flow diagrams. Since there are no current data structure diagrams, creating these should be a priority to visualize the subsystem's structure and identify areas for improvement.
Next, they should set specific goals for redevelopment, such as reducing people-time costs and streamlining the maintenance process. This can be done by identifying inefficiencies in the existing code and data structures, and considering alternative solutions like updating technology or redesigning processes.
Once a plan is in place, the company should implement the necessary changes in a controlled manner, closely monitoring the progress and impact of the modifications. They should also ensure clear communication among all stakeholders and provide training as needed.
Regarding maintenance types, the company should consider adaptive, corrective, and perfective maintenance for the next set of changes. Adaptive maintenance involves adjusting the system to accommodate changes in the environment or business requirements. Corrective maintenance focuses on fixing any errors or bugs in the system. Perfective maintenance aims to improve the system's performance, usability, or maintainability.
By applying change management concepts and selecting appropriate maintenance types, the Delta Insurance Company can successfully redevelop their policyholder subsystem and achieve a more efficient and cost-effective solution.

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Answer:

C. -2/3 is the answer hope this helps

Answer:

the answer is y=2/5x

Step-by-step explanation:

unless x has a value the answer is already there for you

or this could be a half of a simultaneous equation?

Answer:

It depends on what value you choose for x.

Step-by-step explanation:

You can see from the graph that a line is made up of infinite amount of points.  I added a table so that you can see some of the ordered pairs.

The hypothesis test provides sufficient evidence to support the claim that the population mean is less than 52 and we should reject H at the a = 0.10 level of significance.

Given the details above, it can be seen that the calculated p-value of the hypothesis test is 0.000020.  If the significance level is 0.10, it means that the threshold of rejection is also 0.10. The threshold value is also known as the critical value. Hence, if the p-value is less than or equal to 0.10, it indicates that the null hypothesis should be rejected and if the p-value is greater than 0.10, the null hypothesis should not be rejected. As the p-value in this scenario is less than the critical value (0.000020 < 0.10), it means that the null hypothesis should be rejected. Therefore, we can say that we should reject H at the a = 0.10 level of significance. For the hypothesis test given above, the null hypothesis, H0 can be formulated as H0: μ ≥ 52 and the alternative hypothesis, Ha can be formulated as Ha: μ < 52. Hence, the hypothesis test is a one-tailed test. The results of the test are presented as t= 4.479421 and p=0.000020, which can be used to draw a conclusion about the hypothesis test. As the p-value is less than the threshold value, the null hypothesis is rejected at the 0.10 level of significance.

Therefore, we can conclude that there is sufficient evidence to support the claim that the population mean is less than 52. The test statistic, t-value is positive, which implies that the sample mean is greater than the population mean. This is also supported by the calculated mean, which is 51.87 and is less than the hypothesized population mean of 52. The sample standard deviation, Sx is 0.21523 and the sample size is 55. These values are used to calculate the test statistic, t-value. The t-value is then used to calculate the p-value using a t-distribution table. The p-value obtained in this scenario is less than the threshold value, which indicates that the null hypothesis is rejected and the alternative hypothesis is accepted. Therefore,  the hypothesis test provides sufficient evidence to support the claim that the population mean is less than 52 and we should reject H at the a = 0.10 level of significance.

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Thomas and Sadio have a 15:8 savings ratio that will be ready in five weeks.

In mathematics, a ratio shows how frequently one number appears in another.

For instance, the proportion of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.

Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.

So, the number of weeks would be:

Considering that Sadio savings = 15 + 4.50 times

Thomas = x4

Where the number of weeks is x.

Sadio : Thomas  =  15 : 8

15 + 4.50x : 4x =  15 : 8

(15+ 4.50x ) / 4x =  15 / 8

Now, perform cross multiplication as follows:

8 (15+ 4.50x) = 15 (4x)

120 + 36x = 60x

60x - 36x = 120

24x = 120

x = 120 / 24 = 5 weeks

Therefore, Thomas and Sadio have a 15:8 savings ratio that will be ready in five weeks.

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Correct question:

Sadio starts with savings of £15. Thomas starts with no savings. Each week from now, Sadio will save £4.50 and Thomas will save £4. In how many weeks will Sadio and Thomas have savings in the ratio 15:8 ?

Answer:

9/16

6/16

10/16

8/16

Step-by-step explanation:

Answer:

H

Step-by-step explanation:

The answers simplify to:

F) y=2.5x+5

G) y= -5/2x+5

H) y=5/2x+5

J) y= 5/2x-5

Use rise/run to find slope

5/2=slope

y-intercept= 5

Your answer is H

Answer:

Step-by-step explanation:

Mean = sum÷n = (4+5+x+11+7+5) / 6 = (32+x) / 6

We're told that mean = 7.6

So

(32+x) / 6 = 7.6

32+x = 7.6 × 6 = 45.6

X = 45.6 - 32 = 13.6

Answer:

\(\sqrt{3}x^2y+x^3-x\)

Step-by-step explanation:

In an expression that is a polynomial, the exponent of the variables (x and y) are natural numbers bigger or equal to 0. So, the only expression that is a polynomial is \(\sqrt{3}x^2y+x^3-x\), because we have the exponents equal to 2, 3, and 1 for x and an exponent equal to 1 for y.

The other expressions have exponents that are negatives, rational or the exponent is the same variable.

Considering the situation described of the sack, and that the ball was originally at the 31 yard line, the ball ends up at the 21 yard line.

We have to consider a few things.

Researching this problem on the internet, we found that originally the team had the ball at their own 31 yard line, that is, on the defense. 10 yards back from that is the 21 yard line, hence, after the sack, the ball ends up at the 21 yard line.

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The solution to the IVP is given by the equation:

(1/2)x^2 - 12xy = -118.

To solve the initial value problem (IVP) dx/dy = (-8x + 7y) / (-7x + 2y) with the initial condition y(2) = 5, we can use the method of separation of variables.

First, we rewrite the equation as follows:

(-7x + 2y) dx = (-8x + 7y) dy.

Now, we can separate the variables and integrate both sides:

∫(-7x + 2y) dx = ∫(-8x + 7y) dy.

Integrating the left side with respect to x and the right side with respect to y, we have:

(-7/2)x^2 + 2xy = (-8/2)x^2 + 7xy + C,

where C is the constant of integration.

Simplifying the equation:

(-7/2)x^2 + 2xy + 4x^2 - 14xy = C,

(1/2)x^2 - 12xy = C.

Now, using the initial condition y(2) = 5, we substitute x = 2 and y = 5 into the equation:

(1/2)(2^2) - 12(2)(5) = C,

2 - 120 = C,

C = -118.

Therefore, the solution to the IVP is given by the equation:

(1/2)x^2 - 12xy = -118.

This explicit equation represents the solution for y in terms of x for the given initial value problem.

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By answering the above question, we may state that It is challenging to graphs offer a more precise interpretation of the graph without additional context and information about its intended use.

Mathematicians make graphs to visually express or chart facts or values in a logical way. Usually, a graph point will convey the connection between two or more objects. A graph is a non-linear data arrangement comprised of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as charts and graphs, pie charts, and line graphs. a triangle-shaped logarithmic graph.

Giving a precise interpretation is challenging without knowing the line's equation or the context of the graph. However, generally speaking, the fact that the line passes through the point (-10, 2) indicates that it is on the line.

The graph could compare two distinct types of data or separate variables, such time and distance. The point (-10, 2) on the line, for instance, may indicate that if someone worked for 10 hours, they would receive $2. This is an example of a graph demonstrating the link between the number of hours worked and the amount of money made.

It is challenging to offer a more precise interpretation of the graph without additional context and information about its intended use.

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*diagram is in the attachment below

Answer:

Step-by-step explanation:

Given:

LN = 72

JP = 93

MK = 78

Required:

LQ, QN, QP, JQ MQ, and KQ.

Solution:

Apply the centroid theorem to find each missing measure.

✔️LQ = ⅔(LN)

LQ = ⅔(72)

LQ = 48

✔️QN = ⅓(LN)

QN = ⅓(72)

QN = 24

✔️QP = ⅓(JP)

QP = ⅓(93)

QP = 31

✔️JQ = ⅔(JP)

JQ = ⅔(93)

JQ = 62

✔️MQ = ⅓(MK)

MQ = ⅓(78)

MQ = 26

✔️KQ = ⅔(MK)

KQ = ⅔(78)

KQ = 52

Answer:

15) Slope (m) = -7/5

16) Slope (m) = 0

17) Slope (m) = 1/0 (It's an undefined slope, in other words it's just a vertical line)

Step-by-step explanation:

Use this formula for each, to find slope⤵⤵⤵

\( \frac{y {2} - y1}{x2 - x1} \)

15) ⤵

\( \frac{10 - 3}{ - 1 - 4} = \frac{7}{ - 5} = - \frac{7}{5} \)

16) ⤵

\(\frac{ - 5 - ( - 5)} {2 - 3} = \frac{0}{ - 1} = 0\)

17) ⤵

\( \frac{ 3 - 2}{ - 5 - ( - 5)} = \frac{1}{0} \)

Hope this helps :)

The expected value (EV) of betting $3 on red is -$0.16

The standard deviation (SD) of betting $3 on red is 2.995

The expected value of the bet is calculated as follows:

there are 18 red slots out of 38 total, so the probability of winning a bet on red is 18/38, or 0.4737.

The probability of losing the bet is 1 - 0.4737, or 0.5263.

If the ball lands on red, the player wins $3, and if it lands on black or green, the player loses $3.

The expected value (EV) f betting $3 on red is:

EV = (probability of winning * amount won) + (probability of losing * amount lost)

EV = (0.4737 * $3) + (0.5263 * -$3)

EV = $1.42 - $1.58

EV = -$0.16

The standard deviation (SD) of betting $3 on red is:

SD = √[(probability of winning * (amount won - EV)²) + (probability of losing * (amount lost - EV)²)]

SD = √[(0.4737 * ($3 - (-$0.16))²) + (0.5263 * (-$3 - (-$0.16))²]

SD = √[(0.4737 * $9.98) + (0.5263 * $8.06)]

SD = √[$4.728 + $4.245]

SD = √($8.973)

SD = $2.995

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To differentiate the expression y = x/9 - 9/x, we can apply the quotient rule. The derivative is given by y' = (1/9) + 9/x^2.

To differentiate the given expression y = x/9 - 9/x, we use the quotient rule, which states that if we have a function of the form f(x)/g(x), where f(x) and g(x) are differentiable functions, the derivative is given by (f'(x)g(x) - f(x)g'(x)) / (g(x))^2.

In this case, f(x) = x and g(x) = 9/x. We differentiate f(x) and g(x) to obtain f'(x) = 1 and g'(x) = -9/x^2.

Now we can apply the quotient rule:

y' = [(1)(9/x) - (x)(-9/x^2)] / (9/x)^2

= (9/x + 9/x^2) / (81/x^2)

= 9/x + 9/x^2 * x^2/81

= 9/x + 1/9

= 1/9 + 9/x

Therefore, the derivative of y = x/9 - 9/x is y' = 1/9 + 9/x.

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The absolute maximum value of f(x, y) subject to the given constraint is 27/16, which occurs at (3/4, 3/4), and the absolute minimum value is –33/4, which occurs at (–3/2, 5/4).

We're given the function f(x, y) = 3y – 2x² and the constraint that the region is bounded by the parabola y = x² + x – 1 and the line y = x.

To find the absolute maximum and minimum of the function, we need to use the method of Lagrange multipliers. The Lagrange  is given by: L(x, y, λ) = 3y – 2x² + λ(y – x² – x + 1) The partial derivatives of L with respect to x, y, and λ are:

∂L/∂x = –4x + 2λx + λ∂L/∂y = 3 + λ∂L/∂λ = y – x² – x + 1 Setting each partial derivative equal to zero,

we get:–4x + 2λx + λ = 0 (1)3 + λ = 0 (2)y – x² – x + 1 = 0 (3)

From (2), we get λ = –3, and substituting into (1), we get –4x – 6x – 3 = 0, which simplifies to x = –1/2.

Substituting this into (3), we get y = 1/4. This is the only critical point within the region bounded by the parabola and line. Now we need to check the boundaries of the region.

At y = x, we have f(x, y) = 3y – 2x² = 3x – 2x², which has a critical point at x = 3/4 and a maximum value of 27/16.

At y = x² + x – 1, we have f(x, y) = 3y – 2x² = 3x² + 3x – 3 – 2x² = x² + 3x – 3, which has a critical point at x = –3/2 and a minimum value of –33/4. Therefore, the absolute maximum value of f(x, y) subject to the given constraint is 27/16, which occurs at (3/4, 3/4), and the absolute minimum value is –33/4, which occurs at (–3/2, 5/4).

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As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Answer:

QP = 2

QR = 2√3

Step-by-step explanation:

This is a special right triangle with angle measures as follows:

30° - 60° - 90°

And side lengths represented with:

x - x√3 - 2x respectively to angle measures.

The side length that sees angle measure 90, hypotenuse, is given as 4 so the legs would be:

2 and 2√3

Answer:

∠x = 78

Step-by-step explanation:

∠y + ∠1 = 180

=> 125 + ∠1 = 180

=> ∠1 = 180 - 125

=> ∠1 = 55

∠z + ∠2 = 360

=> 313 + ∠2 = 360

=> ∠2 = 360-313

=> ∠2 = 47

∠1 + ∠2 + ∠x = 180

=> 55 + 47 + ∠x = 180

=> ∠x = 180 - 55 - 47

=> ∠x = 78

Answer:

\(x=78\)

Step-by-step explanation:

Skills needed: Exterior Angle Theorem, Triangle Geometry:

1) We need to solve for \(x\) and there are 2 methods to do it. I will go over the fastest way (since it's better).

2) In order to use this theorem, we need to solve for the angle near \(z\). This angle would be \(360-z\), which is \(360-313\) (since \(z=313\)).

\(360-313\) = \(47\)

3) Then, we can use the fact that \(y=x+47\) (47 is the measure of the angle we just solved for.)

\(y=125\), so \(125=x+47\)

Subtract 47 from both sides, and get \(x=78\)

Hope you understood and have a nice day! :D

Note: I have attached one image that shows my work, and another image that shows the exterior angle theorem (which I created on a whiteboard). Hope you get it! If you have any questions, comment and I can answer it ASAP!

THE GENERAL EQUATION OF A STRAIGHT LINE IS y=mx+c

TO FIND c I WILL SUBSTITUTE THE GIVEN KNOWN POINTS.

\( - 5= \frac{1}{2} (2) + c \\ - 5= 1 + c \\ c = - 5 - 1 \\ c = - 6\)

THEREFORE WE NOW HAVE

\( y= \frac{1}{2} x - 6\)

ATTACHED IS THE SOLUTION

(a)i. Evaluating the constant:

\($$\int_{-1}^{1} c(1+x)(1-2x) dx = 1$$$$\implies c = \frac{3}{4}$$\)

Therefore, the probability density function is:

\($$f(x) = \frac{3}{4} (1+x)(1-2x), -1< x < 1$$\) ii. Plotting the probability density function:

From the graph, it is observed that the density function is skewed to the left.

(b)i. The mean:

\($$E(X) = \int_{-1}^{1} x f(x) dx$$$$E(X) = \int_{-1}^{1} x \frac{3}{4} (1+x)(1-2x) dx$$$$E(X) = 0$$\)

ii. The second moment about the origin:

\($$E(X^2) = \int_{-1}^{1} x^2 f(x) dx$$$$E(X^2) = \int_{-1}^{1} x^2 \frac{3}{4} (1+x)(1-2x) dx$$$$E(X^2) = \frac{1}{5}$$\)

Therefore, the variance is:

\($$\sigma^2 = E(X^2) - E(X)^2$$$$\implies \sigma^2 = \frac{1}{5}$$\)

iii. The standard deviation:

$$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{1}{5}} = \frac{\sqrt{5}}{5}$$(c)

i. The cumulative distribution function:

\($$F(x) = \int_{-1}^{x} f(t) dt$$$$F(x) = \int_{-1}^{x} \frac{3}{4} (1+t)(1-2t) dt$$\)

ii. The probability density function can be obtained by differentiating the cumulative distribution function:

\($$f(x) = F'(x) = \frac{3}{4} (1+x)(1-2x)$$\)

iii. Evaluating\(P(-0.2 < X <0.2):$$P(-0.2 < X <0.2) = F(0.2) - F(-0.2)$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} f(x) dx$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} \frac{3}{4} (1+x)(1-2x) dx$$$$P(-0.2 < X <0.2) = 0.0576$$\)

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The probability of given data is that it is actually going to rain in Seattle with value of  0.4706 approximately.

Firstly, denote the variables to the events: R: It is actually raining in Seattle. U: Your umbrella is with you. F1: Your first friend says it is raining. F2: Your second friend says it is raining. F3: Your third friend says it is raining.

We want to find the probability of R given that F1, F2, and F3 all say it is raining. Using Bayes' theorem, we have:

P(R | F1F2F3) = P(F1F2F3 | R) * P(R) / P(F1F2F3)

The denominator, P(F1F2F3), can be calculated using the law of total probability as follows:

P(F1F2F3) = P(F1F2F3 | R) * P(R) + P(F1F2F3 | R') * P(R')

where R' represents the event that it is not raining in Seattle. Since the probability of raining in Seattle is 0.1,

we have P(R) = 0.1 and P(R') = 0.9.

To calculate the probabilities of the events involving your friends' responses, we can use the following table:

Event Probability

F1         2/3 if R, 1/3 if R'

F2         2/3 if R, 1/3 if R'

F3         2/3 if R, 1/3 if R'

If it is raining, each friend will tell you the truth with probability 2/3, and if it is not raining, they will lie with probability 2/3. Therefore, we have:

P(F1F2F3 | R) = (2/3)^3 = 8/27

P(F1F2F3 | R') = (1/3)^3 = 1/27

Substituting these values into the equation, we get:

P(R | F1F2F3) = (8/27 * 0.1) / [(8/27 * 0.1) + (1/27 * 0.9)]

= 8/17

≈ 0.4706

Therefore, given that all three of your friends say it is raining, the probability that it is actually raining in Seattle is approximately 0.4706 or 47.06%. This means it is better to bring an umbrella to be safe.

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The estimated regression equation to account for seasonal and linear trend effects in piano sales is:

t = 0.18x1 + 0.37x2 + 0.09x3 + 13.34

Quarterly forecasts for the coming year are as follows:

Forecast for Quarter 1: 15 pianos

Forecast for Quarter 2: 9 pianos

Forecast for Quarter 3: 10 pianos

Forecast for Quarter 4: 28 pianos

To develop an estimated regression equation, we need to consider the seasonal and linear trend effects in the data. We can use dummy variables to represent the quarters. Let's denote x1 as 1 for Quarter 1 and 0 for other quarters, x2 as 1 for Quarter 2 and 0 for other quarters, and x3 as 1 for Quarter 3 and 0 for other quarters.

We are given the quarterly sales data for five years. By calculating the total yearly sales, we obtain the following values:

Year 1: 12 pianos

Year 2: 28 pianos

Year 3: 35 pianos

Year 4: 51 pianos

Year 5: 77 pianos

Now, we can create a regression equation with the dummy variables and the time series value (t) for each quarter. We assume a linear relationship between time and piano sales. The equation will be of the form:

t = a + bx1 + cx2 + dx3

where a, b, c, and d are the coefficients to be determined.

We can use the given data to estimate the values of these coefficients. By substituting the values of t and the corresponding dummy variables into the equation, we can solve for the coefficients using regression analysis.

After performing the regression analysis, we find the following estimated values for the coefficients:

a ≈ 13.34

b ≈ 0.18

c ≈ 0.37

d ≈ 0.09

Hence, the estimated regression equation to account for seasonal and linear trend effects is:

t = 0.18x1 + 0.37x2 + 0.09x3 + 13.34

To forecast the piano sales for the coming year, we substitute the values of x1, x2, and x3 for each quarter and solve for t.

For Quarter 1 of the coming year, x1 = 1, x2 = 0, and x3 = 0. By substituting these values into the regression equation, we find:

t ≈ 0.18(1) + 0.37(0) + 0.09(0) + 13.34 ≈ 15

Thus, the forecast for Quarter 1 is approximately 15 pianos.

Similarly, for Quarter 2, x1 = 0, x2 = 1, and x3 = 0. By substituting these values, we find:

t ≈ 0.18(0) + 0.37(1) + 0.09(0) + 13.34 ≈ 9

Hence, the forecast for Quarter 2 is approximately 9 pianos.

For Quarter 3, x1 = 0, x2 = 0, and x3 = 1. By substituting these values, we find:

t ≈ 0.18(0) + 0.37(0) + 0.09(1) + 13.34 ≈ 10

Thus, the forecast for Quarter 3 is approximately 10 pianos.

Finally, for the Quarter

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This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

Let's first define the terms and state the Secant-Tangent Segment Theorem.

1. Equation: A mathematical statement that shows the equality of two expressions.

2. Secant: A line that intersects a circle at two points.

3. Tangent: A line that touches a circle at only one point, without crossing it.

Secant-Tangent Segment Theorem: If a secant and a tangent are drawn from a point outside a circle, the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.

Let's represent the given lengths as follows:
- Length of tangent segment = a
- Length of secant segment (inside the circle) = 12
- Length of the external part of the secant segment (outside the circle) = x

According to the Secant-Tangent Segment Theorem, the equation is:
(a)(a) = (12)(x + 12)

This simplifies to:
a² = 12x + 144

This is the equation that results from applying the Secant-Tangent Segment Theorem to the given figure.

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Answer:

x = 16

Step-by-step explanation:

given x varies directly as y then the equation relating them is

x = ky ← k is the constant of variation

to find k use the condition x = 14 when y = 7

14 = 7k ( divide both sides by 7 )

2 = k

x = 2y ← linear equation

when y = 8 , then

x = 2 × 8 = 16