Your answer is 5.
On the first triangle ABC, the answers are all divided by 7, to the triangle DEF. So 35/7 is 5. Hope this helps.
132=5x-8
5x=-132-8
5x=-140
X=
Hey there!
To find the equation of a line, we first have to determine its slope knowing that parallel lines have the same slope.
Let the line that we are trying to determine its equation be
and the line that is parallel to
be
.
passes through the points (9 , 2) and (3 , -5) which means that we can find its slope using the slope formula:
⇒Subtitute the values :
![\implies \sf{m = \dfrac{\Delta y}{\Delta x} = \dfrac{\green{-5} - \orange{2}}{\red{ \: \: 3} - \blue{9 }} = \dfrac{ - 7}{ - 6} = \boxed{ \bold{\dfrac{7}{6} }}}](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Csf%7Bm%20%3D%20%5Cdfrac%7B%5CDelta%20y%7D%7B%5CDelta%20x%7D%20%3D%20%5Cdfrac%7B%5Cgreen%7B-5%7D%20-%20%5Corange%7B2%7D%7D%7B%5Cred%7B%20%5C%3A%20%5C%3A%203%7D%20-%20%5Cblue%7B9%20%7D%7D%20%3D%20%5Cdfrac%7B%20-%207%7D%7B%20-%206%7D%20%3D%20%5Cboxed%7B%20%5Cbold%7B%5Cdfrac%7B7%7D%7B6%7D%20%7D%7D%7D)
.
Assuming that we want to get the equation in Slope-Intercept Form, let's substitute m = 7/6:
Slope-Intercept Form:
We know that the coordinates of the point (0 , -3) verify the equation since it is on the line
. Now, replace y with -3 and x with 0:
![\implies \sf{\overbrace{-3}^{y} = \dfrac{7}{8} \times \overbrace{0}^{x} + b} \\ \\ \implies \sf{-3 = 0 + b} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies \sf{\boxed{\bold{b = -3}} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:](https://tex.z-dn.net/?f=%20%5Cimplies%20%5Csf%7B%5Coverbrace%7B-3%7D%5E%7By%7D%20%3D%20%5Cdfrac%7B7%7D%7B8%7D%20%5Ctimes%20%5Coverbrace%7B0%7D%5E%7Bx%7D%20%2B%20b%7D%20%5C%5C%20%5C%5C%20%5Cimplies%20%5Csf%7B-3%20%3D%200%20%2B%20b%7D%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%5C%20%5C%5C%20%5Cimplies%20%5Csf%7B%5Cboxed%7B%5Cbold%7Bb%20%3D%20-3%7D%7D%20%7D%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20)
Therefore, the equation of the line
is ![\green{\boxed{\red{\bold{\sf{y = \dfrac{7}{6}x - 3}}}}}](https://tex.z-dn.net/?f=%20%5Cgreen%7B%5Cboxed%7B%5Cred%7B%5Cbold%7B%5Csf%7By%20%3D%20%5Cdfrac%7B7%7D%7B6%7Dx%20-%203%7D%7D%7D%7D%7D%20)
▪️Learn more about finding the equation of a line that is parallel to another one here:
↣brainly.com/question/27497166
For these questions you’re distributing.
When multiplying exponents it’s quite simple
(x)(x)= x^2
(x^3)(x^3)= x^6
Raising a function with an exponent with another exponent
(x^4)^4 is x^16
So when two functions to a power are multiplied the exponents add. Then a function with an exponent is raised to another exponent, the exponents multiply.
b. 15h^2-10h
c. 12p^4-15pm
d. 12h^3+8h^2g
e. h^4+7h