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aniked [119]
3 years ago
15

Line $1$ represents the graph of $3x + 4y = -14$. Line $2$ passes through the point $(-5,7)$, and is perpendicular to line $1$.

If line $2$ represents the graph of $y=mx +b$, then find $m+b$.
Mathematics
1 answer:
Sophie [7]3 years ago
8 0

Answer:

15

Step-by-step explanation:

First, solve for Line 1

3x + 4y = -14

<em>move the x to the right of the equation</em>

4y = -3x - 14

<em>divide the whole equation by 4 </em>

y = -3/4x - 14/4

<u>Line 1 is y = -3/4x - 7/2 </u>

Then, solve for Line 2

Since Line 2 is perpendicular, change the sign of the slope of Line 1 and then get the reciprocal of that.

-3/4 to 3/4 to 4/3

4/3 is the slope of Line 2.

Now, we want to find what the b of the equation is, so we can plug in our x (-5) and our y (7) into the y=mx+b equation to find b. The 4/3 is the m or the slope.

y = mx + b

<em>plug in the y, m, and x into the equation</em>

7 = (4/3)(-5) + b

<em>multiply the m and x together </em>

7 = -20/3 + b

<em>add 20/3 to both sides so it will cancel out on the right of the equation and be added to the 7 on the left of the equation</em>

<u>41/3 = b </u>

So, m = 4/3 and b = 41/3

Add them together and you get 45/3 or 15.

I hope this helped!

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Which pair shows equivalent expressions?
seraphim [82]

Given:

The pair of expressions in the options.

To find:

The pair that shows equivalent expressions.

Solution:

We have,

2\left(\dfrac{2}{5}x+2\right)

By using distributive property, we get

2\left(\dfrac{2}{5}x+2\right)=2\left(\dfrac{2}{5}x\right)+2(2)

2\left(\dfrac{2}{5}x+2\right)=\dfrac{4}{5}x+4

So, option A is incorrect and option B is correct.

We have,

2\left(\dfrac{2}{5}x+4\right)

By using distributive property, we get

2\left(\dfrac{2}{5}x+4\right)=2\left(\dfrac{2}{5}x\right)+2(4)

2\left(\dfrac{2}{5}x+4\right)=\dfrac{4}{5}x+8

So, options C and D both are incorrect.

Therefore, the correct option is B.

6 0
2 years ago
Read 2 more answers
One angle of a right triangle measures 19∘. What is the measure of the other angle?
MArishka [77]

Answer:

71°

Step-by-step explanation:

The equation should be 19+90+x=180

Step 1: Add 19+90=109

Step 2: Subtract 180-109=71

So, you're answer is 71°

7 0
3 years ago
I got c which is 100 but I don’t know how jerry got A
Anna007 [38]

Choice C is the correct answer because

\frac{(6+2)^3-12}{5}\\\\\frac{(8)^3-12}{5}\\\\\frac{512-12}{5}\\\\\frac{500}{5}\\\\100\\\\

So in short, \frac{(6+2)^3-12}{5}=100\\\\

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

The mistake Jerry likely made was that he only cubed the 2 and didn't realize the 6 was part of that cubing process. It seems he didn't add first and decided to cube before adding.

This is probably what steps Jerry did

\frac{6+2^3-12}{5}\\\\\frac{6+8-12}{5}\\\\\frac{14-12}{5}\\\\\frac{2}{5}\\\\

But as mentioned, those steps are incorrect because the 6 is part of the cubing operation. In other words, Jerry should have added the 6+2 first before cubing afterward (due to PEMDAS determining the order of operations).

Or you could think of it like this

\frac{(6+2)^3-12}{5}\\\\\frac{(6+2)(6+2)(6+2)-12}{5}\\\\\frac{(8)(8)(8)-12}{5}\\\\\frac{512-12}{5}\\\\\frac{500}{5}\\\\100

4 0
2 years ago
About 250 million drivers are registered in the United States. While on a trip with her family, a student counted the number of
Lilit [14]
She could estimate that there would be about 148 million female drivers.

From her data, she found there were 118 females drivers out of the total 200 drivers that she counted.

That is 118 out of 200 or 0.59 or 59%.

Now, just take 59% of 250.

0.59 x 250 = 147.5 which rounds to 148.
4 0
3 years ago
Order decimals from least to greatest .. 1.09, 1.901,1.9,1.19
Nuetrik [128]
The easiest way to do this is to write the decimals with equal amount of places after the dot and you'll see it more clearly:

1.09 = 1.090
1.901 = 1.901
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1.19 = 1.190

So from the least to the greatest:

1.090
1.190
1.900
1.901

In a form you gave at the beginning:

1.09 < 1.19 < 1.9 < 1.901
7 0
2 years ago
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