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2 years ago

Values that represent a linear function are shown in the table below.

Mathematics

1 answer:

Olegator [25]2 years ago

8 0

Answer:

A.4

explanation:

you can find the slope using this formula

m=(y2-y1)/(x2-x1)

(-16--8)/(-7--5)= 4

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Graphs and equations of lines

dmitriy555 [2]

Answer:

a) $y = -\frac{3}{4} x + 5$

b) $y = 6x-18$

c) $y = \frac{4}{5} x+\frac{19}{5}$

Step-by-step explanation:

a) The slope / gradient is the coefficient of $x$ , so for a) it will be $y=-\frac{3}{4} x + C$ .

C is the y-intercept, so the full equation will be $y = -\frac{3}{4} x + 5$ .

b) Again, since the slope is 6, we know the coefficient of $x$ will be 6.

Now, we have a point on the line and so far, we know the equation is $y=6x+c$ . The coordinates of the point are (2,-6). So now we substitute the y and x values into the equation in order to find C.

$-6 = 6(2)+C$

$-6 = 12+C$

$C = -18$

$y = 6x-18$

c) To find the gradient we must use the formula $\frac{rise}{run}$ .

rise = change in y value

run = change in x value

so, the gradient $= \frac{7-3}{4-(-1)} = \frac{4}{5}$

Now the equation is $y = \frac{4}{5} x +C$

Again, to find C we substitute any of the coordinates into the equation. I will use (-1,3).

$3 = \frac{4}{5} (-1) +C$

$3 + \frac{4}{5} =C$

$C =\frac{19}{5}$

so c) is $y = \frac{4}{5} x+\frac{19}{5}$

6 0

3 years ago

What is the surface area of a rectangular prism that has a height of 5 cm, a width of 10 cm, and a depth of 4 cm?

Ket [755]

Option C: $220 \ cm^2$ is the surface area of the rectangular prism

Explanation:

The height of the rectangular prism is 5 cm

The width of the rectangular prism is 10 cm

The depth of the rectangular prism is 4 cm

We need to determine the surface area of the rectangular prism.

The surface area of the rectangular prism can be determined using the formula,

$A=2(w l+h l+h w)$

Substituting $w=10$ , $h=5$ and $l=4$ in the formula, we get,

$A=2 \cdot(10 \cdot 4+5 \cdot 4+5 \cdot 10)$

Multiplying the terms within the bracket, we have,

$A=2 \cdot(40 +20+5 0)$

Adding all the values within the bracket, we get,

$A=2 \cdot(110)$

Multiplying, we have,

$A=220$

Thus, the surface area of the rectangular prism is $220 \ cm^2$

Hence, Option C is the correct answer.

4 0

3 years ago

Read 2 more answers

(8, 1) and (-1, 10)<br> Slope

gizmo_the_mogwai [7]

Answer:

<h2>The answer is 1</h2>

Step-by-step explanation:

The slope of the line between two points can be found by using the formula

$m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1}$

where

(x1 , y1) and (x2 , y2) are the points

From the question is points are

(8, 1) and (-1, 10)

Substitute the values into the above formula and solve for the slope

That's

$m = \frac{10 - 1}{8 + 1} \\ = \frac{9}{9} = 1$

We have the final answer as

Hope this helps you

7 0

3 years ago

What are two consecutive numbers whose cube differs by 271

valentina_108 [34]

Answer:

Two consecutive numbers cubes differ by 271. Let the two consecutive numbers be x and x + 1. The difference of the two consecutive numbers is 271. ( x + 1 ) ^3 - x ^3 = 271. 1 + 3 x ^ 2 + 3 x - 271 = 0.

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Last year direct marketing had $122,222 in sales. This year direct marketing's sales are down by 9%. What are direct marketings

Mashutka [201]

Answer:

$111222.02

Step-by-step explanation:

This year = Last year * (100%-9%)

This year = 122222 * 91% = 111222.02

7 0

1 year ago