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tankabanditka [31]
3 years ago
10

Solve the following equation by factoring: 9x^2 – 3x – 2 = 0

Mathematics
2 answers:
maks197457 [2]3 years ago
6 0

Answer:

A

Step-by-step explanation:

Given

9x² - 3x - 2 = 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 = 9 × - 2 = - 18 and sum = - 3

The factors are - 6 and + 3

Use these factors to split the x- term

9x² - 6x + 3x - 2 = 0 ( factor the first/second and third/fourth terms )

3x(3x - 2) + 1(3x - 2) ← factor out (3x - 2) from each term

(3x - 2)(3x + 1) = 0

Equate each factor to zero and solve for x

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = \frac{2}{3}

3x + 1 = 0 ⇒ 3x = - 1 ⇒ x = - \frac{1}{3}

crimeas [40]3 years ago
5 0
The answer is A. X=-1/3 or x=2/3
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3 years ago
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A seat on a Ferris wheel is level with the center of the wheel. The diameter of the wheel is 210 feet (ft). If the wheel
frutty [35]

Answer:

The change in the height of the seat of the Ferris wheel is a reduction in height of approximately 74.25 feet

Step-by-step explanation:

The given information are;

The position of the seat on the Ferris wheel = The center level of the wheel

The diameter of the Ferris wheel = 210 feet

The angle of rotation of the wheel = 45° counterclockwise

The height of a point on the Ferris wheel is given by the relation;

h = A·cos(b·x + c) + d

With regards to the question, we have;

h = The height of the seat of the Ferris wheel

A = The amplitude = 1/2 × The diameter of the wheel = 210/2 = 105 feet

360/b = The period

c = The phase shift = 90°

d = The mid line = 0

For a rotation of 45° counterclockwise or-45° clockwise, we have;

b·x = 45°, therefore;

h  = 105 × cos(45° + 90°) + 0 = 105 × cos(135°) + 0

h = 105 × cos(135°) ≈ -74.25 feet

Therefore, the height of the seat of the Ferris wheel reduces by 74.246 feet.

6 0
3 years ago
Consider the function f(x)=x3+15x2+74x+120. If f(x)=0 for x=−6, for what other values of x is the function equal to 0? List the
jasenka [17]

Answer:

other x values are -5,-4

Step-by-step explanation:

f(x)=0 for x=−6

Apply synthetic division to get the quotient . using that we find other two values of x

-6                1           15             74          120

                   0          -6           - 54          -120                    

                  -------------------------------------------------

                    1           9             20         0

the quotient is x^2+9x+20=0

now factor the left hand side, product is 20 and sum is 9

x^2+9x+20=0\\(x+5)(x+4)=0\\x+5=0 , x=-5\\x+4=0, x=-4

So  other x values are -5,-4

8 0
3 years ago
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Let the number total slices = x

He ate (1/4) x

He has x - 1/4 x = 3/4 x slices left.

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T = (8*3/4) x

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3 years ago
A rectangle has a perimeter of 24 inches and a width of 4 inches. What is the length?
Svetradugi [14.3K]

Answer: the length is 8

Step-by-step explanation:

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