Answer:
![m=\frac{3}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B3%7D%7B4%7D)
Step-by-step explanation:
We can use the slope formula in order to find the slope of the line
![m=\frac{-2-2}{0-(-3)} \\m=\frac{-4}{3}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-2-2%7D%7B0-%28-3%29%7D%20%5C%5Cm%3D%5Cfrac%7B-4%7D%7B3%7D)
For a line to be perpendicular, it must have a slope that is the negative reciprocal, so that means that we swap the numerator and denominator and then multiply it by -1, this means that
![m=\frac{-4}{3}\\\\m=\frac{3}{-4} \\\\m=\frac{-3}{-4} \\\\m=\frac{3}{4}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-4%7D%7B3%7D%5C%5C%5C%5Cm%3D%5Cfrac%7B3%7D%7B-4%7D%20%5C%5C%5C%5Cm%3D%5Cfrac%7B-3%7D%7B-4%7D%20%5C%5C%5C%5Cm%3D%5Cfrac%7B3%7D%7B4%7D)
Answer:
The number is -1.
Step-by-step explanation:
Let the number be represented by n.
Then "9 is added to twice a number and this sum is multiplied by 6" is represented by 2n + 9, and
" the number is multiplied by 7 and 14 is added to the product" is
7n + 14.
Then the complete equation is 2n + 9 = 7n + 14.
We must solve this for n. To accomplish this, subtract 2n from both sides, obtaining 9 = 5n + 14. Then subtract 14 from both sides, obtaining
-5 = 5n. Then n must be -1.
1080/90 = 12
2250/150 = 15
There would be a higher rate on the 2250 labels on 150 sheets.
Answer: For the sum of 130
First: $90
Second: $40
Step-by-step explanation:
We write equations for each part of this situation.
<u>The Total Charge</u>
Together they charged 1550. This means 1550 is made up of the first mechanics rate for 15 hours and the second's rate for 5 hours. Lets call the first's rate a, so he charges 15a. The second's let's call b. He charges 5b. We add them together 15a+5b=1550.
<u>The Sum of the Rates</u>
Since the first's rate is a and the second is b, we can write a+b=130 since their sum is 130.
We solve for a and b by substituting one equation into another. Solve for the variable. Then substitute the value into the equation to find the other variable.
For a+b=130, rearrange to b=130-a and substitute into 15a+5b=1550.
15a + 5 (130-a)=1550
15a+650-5a=1550
10a+650-650=1550-650
10a=900
a=$90 was charged by the first mechanic.
We substitute to find the second mechanic's rate.
90+b=130
90-90+b=130-90
b= $40 was charged by the second mechanic
the equation in the slope-intercept of the side of triangle ABC that is perpendicular to segment EF is y = x + 1
<h3>How to determine the equation</h3>
From the figure given, we can deduce the coordinates of the sides
For A
A ( 4,2)
For B
B ( 4, 5)
C ( 1, 2)
D ( 2, -4 )
E ( 5, -4)
F ( 2, -1)
The slope for BC
Slope = ![\frac{y2 - y1}{x2 - x1}](https://tex.z-dn.net/?f=%5Cfrac%7By2%20-%20y1%7D%7Bx2%20-%20x1%7D)
Substitute the values for both B and C coordinates, we have
Slope = ![\frac{2- 5}{1 - 4}](https://tex.z-dn.net/?f=%5Cfrac%7B2-%205%7D%7B1%20-%204%7D)
Find the difference for both the numerator and denominator
Slope = ![\frac{-3}{-3}](https://tex.z-dn.net/?f=%5Cfrac%7B-3%7D%7B-3%7D)
Slope = 1
We have the rotation for both point ( 0, 1)
y - y1 = m ( x - x1)
The values for y1 and x1 are 1 and 0 respectively and the slope m is 1
Substitute the values
y - 1 = 1 ( x - 0)
y - 1 = x
Make 'y' the subject of formula
y = x + 1
Thus, the equation in the slope-intercept of the side of triangle ABC that is perpendicular to segment EF is y = x + 1
Learn more about linear graphs here:
brainly.com/question/4074386
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