Answer:
Slope Intercept form of the equation is ![y = \frac{1}{3} x - 9](https://tex.z-dn.net/?f=y%20%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%209)
Step-by-step explanation:
Here, the two point line are given as is A(-6,-3) and B(6,-7)
The slope of the line AB = ![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
![m = \frac{-7-(-3)}{6-(-6)} = \frac{-7 + 3}{6 + 6} = \frac{4}{12} \\\implies m = \frac{1}{3}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-7-%28-3%29%7D%7B6-%28-6%29%7D%20%20%20%3D%20%5Cfrac%7B-7%20%2B%203%7D%7B6%20%2B%206%7D%20%20%20%3D%20%5Cfrac%7B4%7D%7B12%7D%20%5C%5C%5Cimplies%20m%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
⇒ the slope of AB is m = (4/3)
By SLOPE INTERCEPT FORMULA:
The equation of a line with slope m and a point (x0, y0) is given as
(y-y0)= m (x-x0)
⇒ The equation of line with point (6,-7) is:
![y + 7 = \frac{1}{3} (x-6) \implies 3y + 21 - x + 6 - 0\\or, -x + 3y + 27 = 0](https://tex.z-dn.net/?f=y%20%2B%207%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%28x-6%29%20%20%5Cimplies%20%203y%20%2B%2021%20%20-%20x%20%2B%206%20-%200%5C%5Cor%2C%20-x%20%2B%203y%20%2B%2027%20%3D%200)
Now, the given equation is -x + 3y = -27
Convert it in the SLOPE INTERCEPT FORM y = mx + c
We get, 3y = x - 27
or, ![y = \frac{1}{3} x - \frac{27}{3} \\\implies y = \frac{1}{3} x - 9](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%5Cfrac%7B27%7D%7B3%7D%20%5C%5C%5Cimplies%20y%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%209)
Hence, the Slope Intercept form of the equation is ![y = \frac{1}{3} x - 9](https://tex.z-dn.net/?f=y%20%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%209)
Answer:
270
Step-by-step explanation:
37 % of a number is the same as divide by 100 and multiply by 37. To get this number we do the opposite: divide 99.9 by 37 which gives us 27 and then multiply by 100 which will give us 270.
if we check this: 270 /100 *37 = 99,9
Using the Pythagorean theorem:
a^2 + 24^2 = 26^2
a^2 + 576 = 676
a^2 = 676 - 576
a^2 = 100
a = SQRT(100)
a = 10
Answer:
B. 7.967
Step-by-step explanation: