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3 years ago

Write a rule for the linear function in the graph.

Mathematics

2 answers:

labwork [276]3 years ago

6 0

3=4m+ b
-1=3m+b

m=4
plug in to either equation,
3=16+ b
b=-13

Thus, C would be the answer.

Darya [45]3 years ago

4 0

Answer: The correct option is (C) $y=4x-13.$

Step-by-step explanation: We are given to write a rule for the linear function given in the graph.

Since the graph is a straight line, so we are to find the equation of the line to find the rule.

From the graph, we note that

the points (3, -1) and (4, 3) lie on the straight line.

So, the slope of the line will be

$m=\dfrac{3-(-1)}{4-3}\\\\\\\Rightarrow m=4.$

Since the line passes through the point (4, 3), so the equation of the line is given by

$y-3=m(x-4)\\\\\Rightarrow y-3=4(x-4)\\\\\Rightarrow y=4x-16+3\\\\\Rightarrow y=4x-13.$

Thus, the required rule for the linear function is

$y=4x-13.$

Option (C) is correct.

You might be interested in

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the

devlian [24]

Answer:

The rocket will reach its maximum height after 6.13 seconds

Step-by-step explanation:

To find the time of the maximum height of the rocket differentiate the equation of the height with respect to the time and then equate the differentiation by 0 to find the time of the maximum height

∵ y is the height of the rocket after launch, x seconds

∵ y = -16x² + 196x + 126

- Differentiate y with respect to x

∴ y' = -16(2)x + 196

∴ y' = -32x + 196

- Equate y' by 0

∴ 0 = -32x + 196

- Add 32x to both sides

∴ 32x = 196

- Divide both sides by 32

∴ x = 6.125 seconds

- Round it to the nearest hundredth

∴ x = 6.13 seconds

∴ The rocket will reach its maximum height after 6.13 seconds

There is another solution you can find the vertex point (h , k) of the graph of the quadratic equation y = ax² + bx + c, where h = $-\frac{b}{2a}$ and k is the value of y at x = h and k is the maximum/minimum value

∵ a = -16 , b = 196

∴ $h=-\frac{196}{2(-16)}$

∴ h = 6.125

∵ h is the value of x at the maximum height

∴ x = 6.125 seconds

- Round it to the nearest hundredth

∴ x = 6.13 seconds

4 0

3 years ago

Can someone help with this problem please.

Solnce55 [7]

The area of the shaded triangle formed as the result of the overlap is = 62.35 inches ²

<h3>Calculation of the equilateral triangle</h3>

After folding the rectangle with length of 12 inches and width of 18 inches, an equilateral triangle was formed.

An equilateral triangle is a type of triangle where by all the three sides are equal.

To determine the value of one of the sides, CB or CD is used because the folding didn't affect these sides.

Using the formula for the area of an equilateral triangle,

A = √¾ a²

a= 12 inches

A = √¾ ×12²

A = 62.35 inches ²

Learn more about triangle here:

brainly.com/question/1058720

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3 0

1 year ago

4t - 2 + t2 = 6 + t^2

aliya0001 [1]

Answer:

t = 2 , t = 4

Explanation:

The equation has two solutions.

3 0

2 years ago

A local company makes a candy that is supposed to weigh 1.00 ounces. A random sample of 25 pieces of candy produces a mean of 0.

AysviL [449]

Answer:

$n=(\frac{2.58(0.004)}{0.001})^2 =106.50 \approx 107$

So the answer for this case would be n=107 rounded up to the nearest integer

Step-by-step explanation:

Information given

$\bar X= 0.996$ the sample mean

$s=0.004$ the sample deviation

$n =25$ the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =0.001 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

We can use as estimator of the real population deviation the sample deviation for this case $\hat \sigma = s$ / The critical value for 99% of confidence interval is given by $z_{\alpha/2}=2.58$ , replacing into formula (b) we got: