Answer:
x² + 10x - 12
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
x(2x - 2) + 6(2x - 2) ← distribute both parenthesis
= 2x² - 2x + 12x - 12 ← collect like terms
= 2x² + 10x - 12
Answer:
m = 
Step-by-step explanation:
m - 
= 1 - 
Multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions
6m - 3(m - 1) = 6 - 2(m - 2) ← distribute parenthesis on both sides
6m - 3m + 3 = 6 - 2m + 4 , that is
3m + 3 = - 2m + 10 ( add 2m to both sides )
5m + 3 = 10 ( subtract 3 from both sides )
5m = 7 ( divide both sides by 5 )
m =
3x + 2y = 39
5x - y = 13
Multiplying the last by two:
10x - 2y = 26
Adding to the first
13x = 65
x = 5
y = 5x-13 =25-13=12
Check:
3(5)+2(12)=39 good
5(5)-12=13 good
Answer: x=5, y=12
Answer:
12π in³
Step-by-step explanation:
The right triangle formed by the radius (r), height (x), and slant height (y) is a 3-4-5 right triangle, with the dimension 4 inches being the perpendicular height from the base to the apex. That is, the Pythagorean theorem tells us ...
r² + x² = y²
x = √(y² -r²) = √(25 -9) = 4 . . . inches
The formula for the volume of a cone is ...
V = (1/3)πr²h . . . . . . . . h is the height, what you call x
Your cone has r = 3 in, h = 4 in. Filling in these numbers and simplifying, we get ...
V = (1/3)π(3 in)²(4 in) = 12π in³
The volume of the cone is 12π cubic inches.
