Answer:
120 cm cubed
Step-by-step explanation:
first we need to find the size of the triangular face. we can do this by taking the height and with of the base, multiplying them, then dividing by two (3*8)/2
which gives us 12, so now we multiply by 10 to get the volume of the full prism. 12*10=120
Answer:
![3x-5y=-20](https://tex.z-dn.net/?f=3x-5y%3D-20)
Step-by-step explanation:
We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have two standard form equations which we will get a slope and a y-intercept from. We will convert each to slope intercept form to get the information. We will then write a new slope-intercept equation and convert to standard form.
3x-5y=7 has the same slope as the line. Let's convert.
![3x-5y=7\\3x-3x-5y=7-3x\\-5y=7-3x\\\frac{-5y}{-5}=\frac{7-3x}{-5} \\](https://tex.z-dn.net/?f=3x-5y%3D7%5C%5C3x-3x-5y%3D7-3x%5C%5C-5y%3D7-3x%5C%5C%5Cfrac%7B-5y%7D%7B-5%7D%3D%5Cfrac%7B7-3x%7D%7B-5%7D%20%5C%5C)
![y=\frac{3}{5}x -\frac{7}{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B5%7Dx%20-%5Cfrac%7B7%7D%7B5%7D)
The slope is
.
2y-9x=8 has the same y-intercept as the line. Let's convert.
![2y-9x=8\\2y-9x+9x=8+9x\\2y=8+9x\\\frac{2y}{2}=\frac{8+9x}{2}](https://tex.z-dn.net/?f=2y-9x%3D8%5C%5C2y-9x%2B9x%3D8%2B9x%5C%5C2y%3D8%2B9x%5C%5C%5Cfrac%7B2y%7D%7B2%7D%3D%5Cfrac%7B8%2B9x%7D%7B2%7D)
![y=\frac{8}{2}+\frac{9x}{2} \\y=4+\frac{9}{2}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B8%7D%7B2%7D%2B%5Cfrac%7B9x%7D%7B2%7D%20%20%5C%5Cy%3D4%2B%5Cfrac%7B9%7D%7B2%7Dx)
The y-intercept is 4.
We take
and b=4 and substitute into y=mx+b.
![y=\frac{3}{5}x+4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B5%7Dx%2B4)
We now convert to standard form.
![-\frac{3}{5}x+y=\frac{3}{5}x-\frac{3}{5}x+4\\-\frac{3}{5}x+y=4](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B5%7Dx%2By%3D%5Cfrac%7B3%7D%7B5%7Dx-%5Cfrac%7B3%7D%7B5%7Dx%2B4%5C%5C-%5Cfrac%7B3%7D%7B5%7Dx%2By%3D4)
For standard form we need the coefficients of x and y to be not zero or fractions. We need integers but the coefficient of x cannot be negative. So we multiply the entire equation by -5 to clear the denominators.
![-5(-\frac{3}{5}x+y=4)\\3x-5y=-20](https://tex.z-dn.net/?f=-5%28-%5Cfrac%7B3%7D%7B5%7Dx%2By%3D4%29%5C%5C3x-5y%3D-20)
Answer:
∠U=103°
∠V=77°
∠T=103°
∠S= 77°
Step-by-step explanation:
:)
Answer:
[6 , 18]
Step-by-step explanation:
Answer:
13t+5
Step-by-step explanation: