Answer:
x = - 5 , x = 
Step-by-step explanation:
the values of x that make f(x) zero are the zeros
to find the zeros let f(x) = 0 , that is
3x² + 13x - 10 = 0
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × - 10 = - 30 and sum = + 13
the factors are + 15 and - 2
use these factors to split the x- term
3x² + 15x - 2x - 10 = 0 ( factor the first/second and third/fourth terms )
3x(x + 5) - 2(x + 5) = 0 ← factor out (x + 5) from each term
(x + 5)(3x - 2) = 0
equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
3x - 2 = 0 ⇒ 3x = 2 ⇒ x =
Answer:
- (√30 - 1, 0)
- (-√30 - 1, 0)
Step-by-step explanation:
Making the equation of the parabola :
⇒ y = a(x - h)² + k
⇒ y = (x + 1)² - 17 - 13
⇒ y = (x + 1)² - 30
x-intercepts have y = 0 :
- 0 = (x + 1)² - 30
- (x + 1)² = 30
Taking the square root on each side :
- √(x + 1)² = √30
- x + 1 = ±√30
- x = ±√30 - 1
The x-intercepts are :
- (√30 - 1, 0)
- (-√30 - 1, 0)
( 'x' is not 144 .)
The supplement of an angle is (180 - x) .
The problem says that (2/3) of 'x' is equal to (180 - x) .
180 - x = 2/3 x
Multiply each side by 3 :
( Note: 3 x 180 = 540 .)
540 - 3x = 2x
Add 3x to each side:
540 = 5x
Divide each side by 5 :
<u>x = 108°</u> .
Answer: the volume of a rectangular prisim with lenths (12ft , height 14 ft , and width 17 ft ) is
V=2856ft³
