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belka [17]
1 year ago
12

35 POINTS please help asap

Mathematics
1 answer:
andrezito [222]1 year ago
7 0

The quadratic equation given in the graph can be represented in these two following ways:

  • Factored: f(x) = 2x(x - 4).
  • Vertex form: y = 2(x - 2)² - 8.

<h3>What is the Factor Theorem?</h3>

The Factor Theorem states that a polynomial function with roots x_1, x_2, \codts, x_n is given by:

f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)

In which a is the leading coefficient.

In this graph, the roots are x_1 = 0, x_2 = 4, hence the factored form of the polynomial is:

f(x) = ax(x - 4).

When x = 5, y = 10, hence the leading coefficient is found as follows:

10 = 5a(5 - 4)

5a = 10

a = 2.

Hence the factored form of the polynomial is:

f(x) = 2x(x - 4).

<h3>What is the equation of a parabola given it’s vertex?</h3>

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the vertex is at point (2,-8), hence h = 2, k = -8 and:

y = a(x - 2)² - 8

When x = 5, y = 10, hence the leading coefficient is found as follows:

10 = a(5 - 2)² - 8

9a = 18

a = 2.

Hence the equation in vertex-form is:

y = 2(x - 2)² - 8

More can be learned about quadratic functions at brainly.com/question/24737967

#SPJ1

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Answer:

(a)\ Area = 3765.32

(b)\ Area = 4773

Step-by-step explanation:

Given

A_1 = 169in^2 --- area of each square

Shade = 4in

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

L^2 = A_1

L^2 = 169

L = \sqrt{169

L=13

The length of two squares make up the radius of the semicircle.

So:

r = 2 * L

r = 2*13

r = 26

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

A_2 = 16 * 169

A_2 = 2704

The area of the semicircle is:

A_3 = \frac{\pi r^2}{2}

A_3 = \frac{3.14 * 26^2}{2}

A_3 = 1061.32

So, the area of the window is:

Area = A_2 + A_3

Area = 2704 + 1061.32

Area = 3765.32

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

Length = 4 * 13 + 8

Length = 60

Height = 4*13 + 4

Height = 56

The area is:

A_1 = 60 * 56 = 3360

The radius of the semicircle becomes initial radius + 4

r = 26 + 4 = 30

The area is:

A_2 = \frac{3.14 * 30^2}{2} = 1413

The area of the shade is:

Area = A_1 + A_2

Area = 3360 + 1413

Area = 4773

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Answer:

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<u />

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Step-by-step explanation:

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Find the measure of angle CED in the figure below. Enter only the number.
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Answer:

∠ CED = 58°

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Which polynomial can be simplified to a difference of squares
Mrrafil [7]
<h2>Hello!</h2>

The answer is:

The polynomial that can be simplified to a difference of squares is the second polynomial:

16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}=(4-1)(4+1)

<h2>Why?</h2>

To solve this problem, we need to look for which of the given quadratic terms given for the different polynomials can be a result of squaring (elevating by two).

So,

Discarding, we have:

The quadratic terms of the given polynomials are:

First=10a^{2}

Second=16a^{2}

Third=25a^{2}

Fourth=24a^{2}

We have that the coefficients of the quadratic terms that can be obtained by squaring are:

16a^{2} =(4a)^{2} \\\\25a^{2} =(5a)^{2}

The other two coefficients are not perfect squares since they can not be obtained by square rooting whole numbers.

So, the first and the fourth polynomial are discarded and cannot be simplified to a difference of squares at least using whole numbers.

Therefore, we need to work with the second and the third polynomial.

For the second polynomial, we have:

16a^{2} -4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2} =(4-1)(4+1)

So, the second polynomial can be simplified to a difference of squares.

For the third polynomial, we have:

25a^{2} +6a-6a+36=16a^{2}+36=(5a)^{2}+(6)^{2}

So, the third polynomial cannot be simplified to a difference of squares since it's a sum of squares.

Hence, the polynomial that can be simplified to a difference of squares is the second polynomial:

16a^{2}-4a+4a-1=16a^{2}=(4a)^{2}-(1)^{2}

7 0
3 years ago
Read 2 more answers
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