Answer:
x = - 2 ± 
Step-by-step explanation:
To solve the equation using the method of completing the square.
Given
x² + 4x - 7 = 0 ( add 7 to both sides )
x² + 4x = 7
add ( half the coefficient of the x- term )² to both sides
x² + 2(2) x + 4 = 7 + 4
(x + 2)² = 11 ( take the square root of both sides )
x + 2 = ± ( subtract 2 from both sides )
x = - 2 ± ← exact solution
r(x) / s(x)
= r/s (x)
= (3x - 1)/ (2x + 1)
so if r/s (6)
= [3(6) - 1] / [(2(6) + 1]
Answer is the first option
3(6) - 1
--------------
2(6) + 1
9514 1404 393
Answer:
3) D
4) D
5) B
6) B
Step-by-step explanation:
3) A "Pythagorean triple" is a set of 3 integers that could be the sides of a right triangle. The only triangle shown with integer side lengths is choice D.
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5) The only triangle for which the square of the hypotenuse is the sum of the squares of the other two sides is choice D.
11² +2² = (5√5)²
121 + 4 = 125
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6) The lengths of sides of each right triangle are 2/3 of those of choice D in problem 4. That is, they are a 7-24-25 triangle, multiplied by 2. That means the height is 24·2 = 48, and the area is ...
A = 1/2bh
A = 1/2(28 m)(48 m) = 672 m² . . . . matches choice B
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7) The side lengths of a 30-60-90 triangle have the ratios 1 : √3 : 2. That is, the short leg is half the hypotenuse, a fact stated in A and D. Those true statements make it clear that statement B is false.
Answer:
The polynomial will be 
.
Step-by-step explanation:
The three degree polynomial function f(x) has zeros at x = 0 and at x = 4 having multiplicity 2.
Therefore, (x - 0) and (x - 4)² will be factors of the polynomial f(x).
Hence, the polynomial will be f(x) = Ax(x - 4)² .............. (1), where A is any constant that we have to evaluate.
Now, given that f(5) = 20
So, from the equation (1) we have
20 = A(5)(5 - 2)²
⇒ 
Therefore, the polynomial will be (Answer)
