Answer:
Step-by-step explanation:
13.
<h3>Given</h3>
<u>Quadratic equation</u>
- 4x² - 3x - 4 = 0
- With the roots of α and β
<h3>To Find </h3>
- The quadratic equation with roots of 1/(3α) and 1/(3β)
<h3>Solution</h3>
<u>The sum and the product of the roots of the given equation:</u>
- α + β = -b/a ⇒ α + β = -(-3)/4 = 3/4
- αβ = c/a ⇒ αβ = -4/4 = - 1
<u>New equation is:</u>
- (x - 1/(3α))(x - 1/(3β)) = 0
- x² - (1/(3α) + 1/(3αβ))x + 1/(3α3β) = 0
- x² - ((3α + 3 β)/(3α3β))x + 1/(3α3β) = 0
- x² - ((α + β)/(3αβ))x + 1/(9αβ) = 0
- x² - (3/4)/(3(-1))x + 1/(9(-1)) = 0
- x² + 1/4x - 1/9 = 0
- 36x² + 9x - 4 = 0
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14.
<h3>Given</h3>
<u>Quadratic equation</u>
- 3x² +2x + 7 = 0
- With the roots of α and β
<h3>To Find </h3>
- The quadratic equation with roots of α + 1/β and β + 1/α
<h3>Solution</h3>
<u>The sum and the product of the roots of the given equation:</u>
- α + β = -b/a ⇒ α + β = -2/3
- αβ = c/a ⇒ αβ = 7/3
<u>New equation is:</u>
- (x - (α + 1/β))(x - (β + 1/α)) = 0
- x² - (α + 1/β + β + 1/α)x + (α + 1/β) (β + 1/α) = 0
- x² - (α + β + (α + β)/αβ )x + αβ + 1/αβ + 2 = 0
- x² - (-2/3 - (2/3)/(7/3))x + 7/3 + 1/(7/3) + 2 = 0
- x² - (-2/3 - 2/7)x + 7/3 + 3/7 + 2 = 0
- x² + (14 + 6)/21x + (49 + 9 + 42/21) = 0
- x² + 20/21x + 100/21 = 0
- 21x² + 20x + 100 = 0
Answer:
There are no enough information to determine the length of the fence, assuming we were given the perimeter of the fence, and say, the dimension of the fence, then we can easily find the length.
Perimeter of the fence, P = 2(L + B).. If the fence is a rectangular.
L = (P/2) - B
If the fence is square, P = 4L
L = P/4
Answer:
B. 4 7/8 x 5 x 12 1/2
Step-by-step explanation:
volume = L x H x W
Answer:
Red balls 2/14
Green balls 1/14
Step-by-step explanation:
I hope that helped.
