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2 years ago

Fit a quadratic function to these three points: (-2,8), (0, -4), and (4, 68) Respuesta

Mathematics

1 answer:

zloy xaker [14]2 years ago

3 0

Answer:

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

Step-by-step explanation:

Let the quadratic function be y = f(x) = ax^2 + bx + c.

For the point (-2, 8) ( x = -2 when y = 8) we have:

a(-2)^2 + (-2)b + c = 8

4a - 2b + c = 8 For (0, -4) we have:

0 + 0 + c = -4 so c = -4. For (4, 68) we have:

16a + 4b + c = 68

So we have 2 systems of equations in a and b ( plugging in c = -4):

4a - 2b - 4 = 8

16a + 4b - 4 = 68

4a - 2b = 12

16a + 4b = 72 Multiplying 4a - 2b = 12 by 2 we get:

8a - 4b = 24

Adding the last 2 equations:

24a = 96

a = 4

Now plugging a = 4 and c = -4 in the first equation:

4(4) - 2b - 4 = 8

-2b = 8 - 16 + 4 = -4

b = 2.

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castortr0y [4]

Answer: 72 cars.

Step-by-step explanation:

Let be "x" the number of toys that Moby had to start with.

According to the information given in the exercise, Moby sold half his toy car collection. This can be represented with the following expression:

$\frac{1}{2}x$

Then he bought 12 more cars, giving a total amount of 48 toy cars.

Therefore, the equation that represents this situation is the equation shown below:

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Now you must solve for "x" in order to find its value.

You get that this is:

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3 years ago

A political pollster wants to know what proportion of voters are planning to vote for the incumbent candidate in an upcoming ele

balandron [24]

Answer:

$1.\ \ np\geq 10\\\\2.\ \ n\geq 10x$

Step-by-step explanation:

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$n\geq 10x\\\\n=2000\\x=150\\10x=1500\\\therefore n\geq 10x$

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3 years ago

6. a semicircle has as its diameter the hypotenuse of a right triangle shown below. determine the area of the semicircle to the

jeyben [28]

Answer:

$A = 137.3cm^2$

Step-by-step explanation:

Given

See attachment

Required

The area of the semicircle

First, we calculate the hypotenuse (h) of the triangle

Considering only the triangle, we have:

$\cos(68) = \frac{7}{h}$ --- cosine formula

Make h the subject

$h = \frac{7}{\cos(68)}$

$h = \frac{7}{0.3746}$

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The area of the semicircle is then calculated as:

$A = \frac{\pi h^2}{8}$

This gives:

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$A = 137.3cm^2$

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2 years ago

When do we flip an inequality?

tatuchka [14]

Answer:

When multiplying and dividing it by a negative

Step-by-step explanation:

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2 years ago

Read 2 more answers

Solve the equation E = v + Ir for r

iren [92.7K]

Answer:

A. $\text{r} = \frac{\text{E}-\text{v}}{\text{I}}$

Step-by-step explanation:

E = v + Ir

E - v = Ir (subtract by v on both sides)

(E-v)/I = r (divide by I on both sides)

$\therefore \text{r} = \frac{\text{E}-\text{v}}{\text{I}}$

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1 year ago