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3 years ago

Find f(-2) for the function: f(x)= 3x^2-1, x<1 x+2, x> 1

1 answer:

azamat3 years ago

8 0

F(x) = 3x² - 1
f(-2) = 3(-2)² - 1
f(-2) = 3(4) - 1
f(-2) = 12 - 1
f(-2) = 11

f(x) = x < 1
f(-2) = -2 < 1

f(x) = x + 2
f(-2) = -2 + 2
f(-2) = 0

f(x) = x > 1
f(-2) = -2 > 1
f(-2) = -2 < 1

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Simplify each product using the Distributive Property.

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4 years ago

A maple tree in the backyard of a home has a height of 0.75 meters. How many times as tall (t) is a nearby hickory tree that is

anygoal [31]

Answer: 12

Step-by-step explanation:

Since we are informed that a maple tree in the backyard of a home has a height of 0.75 meters.

To know the jow many times tall (t) is a nearby hickory tree that is 9 meters tall, we've to divide the height of the hickory tree by the height of the maple tree. This will be:

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3 years ago

Find the circumferences of the two circles circle a has a radius of 21 meters and circle b has a radius of 28 meters Is the rela

Feliz [49]

Answer:

The circumference for circle a is $\\ C = 131.9430$ m.

The circumference for circle b is $\\ C = 175.9240$ m.

The relationship between the radius of a circle and the circumference (the distance around the circle) is constant and is the same for all circles and can be written as $\\ \frac{C}{r} = 2\pi$ or, in a less familiar form, $\\ \frac{r}{C} = \frac{1}{2\pi}$ . The number $\\ \pi$ is constant for all circles and has infinite digits, $\\ \pi = 3.14159265358979....$ .

Step-by-step explanation:

The circumference of a circle is given by:

$\\ C = 2*\pi*r$ [1]

Where

$\\ C$ is the circle's circumference.

$\\ r$ is the radius of the circle.

And

$\\ \pi = 3.141592....$ is a constant value (explained below)

We can say that the distance around the circle is the circle's circumference.

The circumferences of the two circles given are:

Circle a, with radius equals to 21 meters ( $\\ r = 21m$ ).

Using [1], using four decimals for $\\ \pi$ , we have:

$\\ C = 2*\pi*r$

$\\ C = 2*3.1415*21$ m

$\\ C = 131.9430$ m

Then, the circumference for circle a is $\\ C = 131.9430$ m.

Circle b, with radius equals to 28 meters ( $\\ r = 28m$ ).

$\\ C = 2*3.1415*28$ m

$\\ C = 175.9240$ m

And, the circumference for circle b is $\\ C = 175.9240$ m.

We know that

$\\ 2r = D$

That is, the diameter of the circle is twice its radius.

Then, if we take the distance around the circle and we divided it by $\\ 2r$

$\\ \frac{C}{2r} = \frac{C}{D} = \pi$

This ratio, that is, the relationship between the distance around the circle (circumference) and the diameter of a circle is $\\ \pi$ and is constant for all circles. This result is called the $\\ \pi$ number, which is, approximately, $\\ \pi = 3.141592653589793238....$ (it has infinite number of digits).

We can observe that the relationship between the radius of a circle and the circumference is also constant:

$\\ \frac{C}{2r} = \frac{C}{D} = \pi$

$\\ \frac{C}{2r} = \pi$

$\\ \frac{C}{r} = 2\pi$

However, this relationship is $\\ 2\pi$ .

We can rewrite it as

$\\ \frac{r}{C} = \frac{1}{2\pi}$

And it is also constant.

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3 years ago

Two mechanics worked on a car. The first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. Together they

kogti [31]

Let's define variables:
x = Rate in $ / hr of the mechanic working 15hr
y = Rate in $ / hr of the mechanic working 5hr
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x + y = 130
15x + 5y = 1400
Solving the system we have:
x = $ 75 / hr
y = $ 55 / hr
Answer:
the rate charged per hour by mechanics was:
x = $ 75 / hr
y = $ 55 / hr

5 0

4 years ago