Answer: triangle sum , x= 9
Step-by-step explanation:
The triangle angle sum theorem states that the 3 interior angles of a triangle sum to 180 degrees. Add all of the angle measures together and set equal to 180. (3x-4)+(5x-7)+(13x+2) = 180. Combine like terms. 21x -9 = 180. Add 9 to both sides. 21x= 189. Divide both sides by 21. X = 9
Answer:
![\fbox{y = 8/5 }](https://tex.z-dn.net/?f=%20%5Cfbox%7By%20%3D%208%2F5%20%7D%20)
Explanation:
[to solve for y, first use the properties of equality to simplify the equation]
5y + 3 = 8y − 5 + 2y
5y + 3 = (8y + 2y) – 5
[regroup the like terms of y together: commutative property of equality ; adding in a different order will still give you the same result]
5y + 3 = 10y – 5
[combine like terms]
5y + 3 = 10y – 5
![\: \: \: \: \: \: -3 \: \: \: \: \: \: \: \: \: \: \: -3](https://tex.z-dn.net/?f=%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20%5C%3A%20-3%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%20-3)
[subtract 3 from both sides in order to eliminate the constant term on the left side: subtraction property of equality]
5y = 10y – 8
–10y –10y
[subtract 10 from both sides in order to eliminate the variable term: subtraction property of equality]
-5y = -8
÷(-5) ÷(-5)
[divide both sides by -5 to cancel out the coefficient of y: division property of equality]
y = 8/5
Answer: 15.3 in
Step-by-step explanation:
First, the formula for the volume is: ![V=\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2h)
If you solve for h,
![h=\frac{V}{\pi r^2}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7BV%7D%7B%5Cpi%20r%5E2%7D)
![h=\frac{1200in^3}{(3.14)(5in)^2}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B1200in%5E3%7D%7B%283.14%29%285in%29%5E2%7D)
![h=15.3in](https://tex.z-dn.net/?f=h%3D15.3in)
<em>The x and y intercept of 5x + 5y = -30 are (-6, 0) and (0, -6) respectively.</em>
<h2 /><h2>
Explanation:</h2>
The Standard Form of the equation of a line is given by:
![Ax+By=C \\ \\ A,B,C \ Real \ Constants \ and \ A>0](https://tex.z-dn.net/?f=Ax%2BBy%3DC%20%5C%5C%20%5C%5C%20A%2CB%2CC%20%5C%20Real%20%5C%20Constants%20%5C%20and%20%5C%20A%3E0)
So:
![5x+5y=-30](https://tex.z-dn.net/?f=5x%2B5y%3D-30)
is written in Standard Form. The x and y intercepts are:
![x-intercept: \ (x,0) \\ \\ y-intercept: \ (0,y)](https://tex.z-dn.net/?f=x-intercept%3A%20%5C%20%28x%2C0%29%20%5C%5C%20%5C%5C%20y-intercept%3A%20%5C%20%280%2Cy%29)
So:
FOR X-INTERCEPT:
![Let's \ set: \\ y=0 \\ \\ 5x+5(0)=-30 \\ \\ Isolating \ x: \\ \\ 5x=-30 \\ \\ x=-\frac{30}{5} \\ \\ \boxed{x=-6}](https://tex.z-dn.net/?f=Let%27s%20%5C%20set%3A%20%5C%5C%20y%3D0%20%5C%5C%20%5C%5C%205x%2B5%280%29%3D-30%20%5C%5C%20%5C%5C%20Isolating%20%5C%20x%3A%20%5C%5C%20%5C%5C%205x%3D-30%20%5C%5C%20%5C%5C%20x%3D-%5Cfrac%7B30%7D%7B5%7D%20%5C%5C%20%5C%5C%20%5Cboxed%7Bx%3D-6%7D)
FOR Y-INTERCEPT:
![Let's \ set: \\ x=0 \\ \\ 5(0)+5y=-30 \\ \\ Isolating \ x: \\ \\ 5y=-30 \\ \\ y=-\frac{30}{5} \\ \\ \boxed{y=-6}](https://tex.z-dn.net/?f=Let%27s%20%5C%20set%3A%20%5C%5C%20x%3D0%20%5C%5C%20%5C%5C%205%280%29%2B5y%3D-30%20%5C%5C%20%5C%5C%20Isolating%20%5C%20x%3A%20%5C%5C%20%5C%5C%205y%3D-30%20%5C%5C%20%5C%5C%20y%3D-%5Cfrac%7B30%7D%7B5%7D%20%5C%5C%20%5C%5C%20%5Cboxed%7By%3D-6%7D)
Finally,<em> the x and y intercept of 5x + 5y = -30 are (-6, 0) and (0, -6) respectively.</em>
<h2>Learn more:</h2>
Parallel lines: brainly.com/question/12169569
#LearnWithBrainly
Answer:
x = 5 or x = 1
Step-by-step explanation:
x² - 6x + 7 = 0
x² - 6x = -7
x² - 6x + 9 = -7 + 9 1/2 of the x term than square it and add it the both sides.
(x - 3)(x - 3) = 2
( x -3)² = 2
= ![\sqrt{2}](https://tex.z-dn.net/?f=%5Csqrt%7B2%7D)
(x - 3) = ± 2
x - 3 = 2 or x - 3 = -2
x = 5 or x = 1