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andrezito [222]
3 years ago
14

Write a quadratic function in standard form with a leading coefficient of 1 for the given set of zeros. 7 and 4

Mathematics
1 answer:
Viefleur [7K]3 years ago
6 0

We are given : Zeros x=7 and x=4 and leading coefficent 1.

In order to find the quadratic function in standard form, we need to find the factors of quadratic function first and the multiply by given leading coefficent.

For the given zeros x=7 and x=4, we get the factors (x-7) and (x-4).

So, we need to multiply (x-7) and (x-4) by foil method.

We get

(x-7)(x-4) = x*x + x* -4 -7*x -7*-4

x^2 -4x -7x +28.

Combining like terms, we get

-4x-7x = -11x

x^2 -4x -7x +28 = x^2 -11x +28.

Now, we need to multiply x^2 -11x +28 quadratic by leading coefficent 1.

We get

1(x^2 -11x +28) = x^2 -11x +28.

Therefore, the required quadratic function in standard form is x^2 -11x +28.


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Answer:

1.5 feet

Step-by-step explanation:

V = base area x height

divide the two members by the base area

height = V/ base area

height = 13.5 / 9 = 1.5 feet

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2 years ago
Please select the best answer from the choices provided.
Dominik [7]

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Five friends want to rent a go-cart track that costs $100. Each friend intends to contribute the same about.
jasenka [17]
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2 years ago
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What is the product of -5x^3 + 2x - 4 and 2x^3 - 4x^2 + 6?
irina1246 [14]

Answer:

-10x⁶+20x⁵+4x⁴-46x³+16x²+12x-24

Step-by-step explanation:

(-5x³ + 2x - 4)(2x³ - 4x² + 6)

= -10x⁶ + 4x⁴ - 8x³ + 20x⁵ - 8x³ + 16x² - 30x³ + 12x - 24

= -10x⁶+20x⁵+4x⁴-46x³+16x²+12x-24

(-5x³ + 2x - 4)(2x³ - 4x² + 6)

Is same as

(2x³ - 4x² + 6)(-5x³ + 2x - 4)

Because multiplication is commutative.

a×b = b×a

7 0
3 years ago
An airline finds that if it prices a cross-country ticket at $300, it will sell 200 tickets per day. It estimates that each $10
Rom4ik [11]

Answer:

Ticket price = $170

Number of tickets sold = 850

Step-by-step explanation:

Let X= the number of $10 price reduction and the number of 50 tickets increase

Let p= price per ticket

Let q= number of tickets sold

Let R= revenue

Let p(x) = price of ticket now sold

Let q(x) = number of tickets now sold

R(x) = p(x) * q(x)

P(x) = 300 - 10x

q(x)= 200 + 50x

R(x) = (300 -10x) (200 - 50x)

= 60000 + 15000x - 2000x - 500x^2

= 60000 + 13000x - 500x^2

Differentiate with respect to x

dR(x)/dx = 13000-1000x

Put dR(x)/dx = 0

0= 13000 - 1000x

1000x = 13000

Divide through by 1000

1000x/1000 = 13000/1000

x = 13

Therefore x = 13 for $10 price reduction and 50 tickets increase

p(x) = 300 - 10x

= 300 - 10*13

= 300 - 130

= $170

q(x) = 200 + 50x

= 200 + 50*13

= 200 + 650

= 650

Maximum Revenue = p(x) * q(x)

= 170 * 850

= $144,500

For 13 reductions, we have $170 price reduction and 850 ticket sales

8 0
3 years ago
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