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3 years ago

1. Find the distance between the two numbers on a number line. Write your awnser as a mixed number.

Mathematics

1 answer:

guapka [62]3 years ago

6 0

Answer:

3 1/4
10.6
3 1/3

Step-by-step explanation:

The distance = number to the right - number to the left

1..................................................................

-2 1/2 - (-5 3/4) = -5/2 + 23/4 = - 10/4 + 23/4 = 13/4 = 3 1/4

2...................................................................

8.4 - (-2.2) = 8.4 + 2.2 = 10.6

3...................................................................

-3 2/3 - (- 7) = -11/3 + 7 = - 11/3 + 21/3 = 10/3 = 3 1/3

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Answer:

$\huge\boxed{y=-\frac{1}{7}x+ 10}$

Step-by-step explanation:

In order to find the equation of this line, we need to note two things.

A) The slope of two lines that are perpendicular will be opposite reciprocals (that is, multiplying them gets us -1.)
B) We can substitute a point inside an incomplete equation to try and find a missing value.

So first, let's find the opposite reciprocal of 7 which will be the slope to this equation.

Reciprocal of 7: $\frac{1}{7}$
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So the slope of this line will be $-\frac{1}{7}$ . The y-intercept will change, and we can substitute what we know into the equation $y=mx+b$ .

$y = -\frac{1}{7}x+b$

Now, we can substitute a point on the graph (14, 8) into this equation to find b.

$8 = -\frac{1}{7} \cdot 14 + b$
$8 = -\frac{14}{7} + b$
$8 = -2 + b$
$b = 10$

Now that we know the y-intercept, we can finish off our equation by plugging that in.

$y = -\frac{1}{7}x + 10$

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