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3 years ago

Factor the polynomial 4x^2 + 12 + 9

Mathematics

1 answer:

Anuta_ua [19.1K]3 years ago

7 0

Answer:

The answer is $(2x+3)^2$ .

Step-by-step explanation:

Multiply the coefficient of the squared term and the constant. Then, find the factors that add up to 12:

$4*9=36\\36:\{1*36,2*18,3*12,4*9,6*6\}\\6+6=12$

Split the middle term:

$4x^2+6x+6x+9$

Factor by grouping:

$[4x^2+6x]+[6x+9]\\2x(2x+3)+3(2x+3)\\(2x+3)(2x+3)\\(2x+3)^2$

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Solve for x. <br> 8x^2 - 5 = 11

GenaCL600 [577]

Answer:

x = ±sqrt(2)

Step-by-step explanation:

8x^2 - 5 = 11

Add 5 to each side

8x^2 - 5+5 = 11+5

8x^2 = 16

Divide each side by 8

8x^2 = 16/8

x^2 = 2

Take the square root of each side

sqrt(x^2) = ±sqrt(2)

x = ±sqrt(2)

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The sum of the three angles in a triangle is 180 degrees. One of the angle measures 30 degrees, and the second angle measures 75

Molodets [167]

Answer:

75 degrees

Step-by-step explanation:

30 + 75 = 105

180 - 105 = 75

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4 years ago

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3 years ago

How do you solve this

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3 years ago

Select the quadratic function with a graph that has the following features. x-intercept at (8,0) y-intercept at (0,-32) maximum

Basile [38]

Answer:

The correct option is C.

Step-by-step explanation:

The function has axis of symmetry at $x=6$ , it represents that the parabola is along the x-axis and the standard form of parabola is

$y=a(x-h)^2+k$

Where, a is scale factor and (h,k) is vertex.

The maximum or minimum value of a quadratic function is the vertex of parabola. So, vertex of parabola is (6,4).

$y=a(x-6)^2+4$

The y-intercept of the function is (0,-32)

$-32=a(0-6)^2+4$

$-32-4=36a$

$-36=36a$

$a=-1$

Therefore required equation of parabola is

$y=-(x-6)^2+4$

$y=-(x^2-12x+36)+4$

$y=-x^2+12x-36+4$

$y=-x^2+12x-32$

Therefore option C is correct.

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3 years ago