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3 years ago

What is the rate of change of the linear relationship modeled in the table (-2,5) (-1,4) (0,3) (1,2)

Mathematics

1 answer:

poizon [28]3 years ago

8 0

The rate of change of the linear relationship is -1.

Explanation:

It is given that there is a linear relationship between all these points, these points lie on a straight line.

The equation to find the slope passing through two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the points $(-2,5)$ and $(-1,4)$ , we get,

$\begin{aligned}m &=\frac{4-5}{-1+2} \\&=\frac{-1}{1} \\&=-1\end{aligned}$

Thus, the slope is -1.

Thus, the rate of change of the linear relationship is -1.

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Write the expression as a single logarithm

viva [34]

We have to use the following log rules here

$a log (b) = log b^a , log(a) + log(b) = log(ab), log (a)-log(b) = log(a/b)$

So for the given question , that is

$18log \sqrt x +9 log \sqrt [3]{x}-log 10 = log(x^{18/2}) + log(x^{9/3})-log 10$

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3 years ago

Which inequality correctly compares Five-sixths, One-half, Three-ninths, and 1?

enot [183]

Answer:

Three-ninths < One-half < Five-sixths < 1

Step-by-step explanation:

We are supposed to compares Five-sixths, One-half, Three-ninths, and 1

$\frac{5}{6} , \frac{1}{2},\frac{3}{9} , 1$

Take LCM of denominators

LCM of 6,9,2,1 = 18

$\frac{5}{6} \times \frac{3}{3}=\frac{15}{18}$

$\frac{1}{2} \times \frac{9}{9}=\frac{9}{18}$

$\frac{3}{9} \times \frac{2}{2}=\frac{6}{18}$

$1 \times \frac{18}{18} = \frac{18}{18}$

$\frac{6}{18}$

$\frac{3}{9}$

Three-ninths < One-half < Five-sixths < 1

7 0

3 years ago

Is 32k+24=8(4k+3) true? a.True b.False

melisa1 [442]

Answer:

a. True.

Step-by-step explanation:

32k + 24 = 8(4k + 3)

32k + 24 = 32k + 24

32k - 32k = 24 - 24

0 = 0

Since 0 does equal 0, the statement is a. True.

Hope this helps!

6 0

3 years ago

Read 2 more answers

Point R is located at (3, 2) and point S is located at (8, 15) .

Ulleksa [173]

Answer: (4, 4.6)

=======================================

The x coordinates of the points (3,2) and (8,15) are x = 3 and x = 8 respectively. The distance between these x values is 8-3 = 5 units. So we move 5 units to the right to go from the first point to the second point.

Imagine we had 5 blocks. If 1 of them is colored red and the other four are green, then the ratio of red to green is 1:4. We have 1 part red, 4 parts green. So 1+4 = 5 total. The "red block" in the metaphor mentioned basically tells us how far to move over the total distance 5. So we move 1/5th of the way along the horizontal distance of 5.

1/5 of 5 = (1/5)*5 = 1

So we move exactly one unit along the x direction. Therefore, we add 1 to to the x coordinate of (3,2) to end up with (3+1,2) = (4,2). This isn't the final answer, but it helps get us closer.

---------------

For the y coordinates of the given points we see that the y difference is 15-2 = 13. Multiply this by 1/5 to get

(1/5)*13 = 13/5 = 2.6

We follow effectively the same steps as before, but now we're dealing with the y values this time. So we move 2.6 units in the y direction (ie move 2.6 units up)

Add 2.6 onto the y value of that last point we found to get (4,2+2.6) = (4,4.6)

So that explains why the answer is (4, 4.6)

A visual might help so I've posted one below in the attached images. In that image, the location of point T is the final answer.