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2 years ago

Evaluate the function for x =2 and x = 6 f(x) = 4x −3

Mathematics

1 answer:

Nadusha1986 [10]2 years ago

5 0

F(2) = 4(2) -3
f(2) = 8-3
f(2) = 5

f(6) = 4(6) -3
f(6) = 24-3
f(6)= 21

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Which set of numbers could represent the lengths of the sides of a right triangle?

DiKsa [7]

Answer:

The first set: 8, 15, and 17.

Step-by-step explanation:

By the pythagorean theorem, a triangle is a right triangle if and only if

$\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2$ .

In this case,

$\text{longest side}^2 = 17^2 = 289$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}$ .

In other words, indeed $\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2$ . Hence, 8, 15, 17 does form a right triangle.

Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two

Factor out the common factor $2$ to simplify the calculations.

$\text{longest side}^2 = 20^2 = 400$

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121$ .

$\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}$ .

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

$\text{longest side}^2 = 11^2 = 121$ .

<h3> $\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}$ .</h3>

$\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2$ .

Hence, by the pythagorean theorem, these three sides don't form a right triangle.

6 0

4 years ago

Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. S

Georgia [21]

Answer:

Step-by-step explanation:

Total number of boxes of cookies that Kendal bought to bring to the party is x.

Each box contains 12 cookies. This means that total number of cookies in x boxes would be

12 × x = 12x

She decides to keep two boxes for herself. This means that the total number of cookies that she kept for herself would be

12 × 2 = 24 cookies

She brings 60 cookies to the party.

The equation that can be used to find the number of boxes, x, Kendal bought would be

12x = 24 + 60

12x = 84

x = 84/12 = 7 boxes

6 0

3 years ago

What x values would be good to use so she does not get fractions for her y values when making the table of ordered pairs.

Ber [7]

Answer:

-3, 0, 3

Step-by-step explanation:

Given, $y = -\frac{4}{3}x + 2$ , the set of x values that will make Kayda not to get y values that are not fraction are -3, 0, 3.

This is so, because,

when x = -3, $y = -\frac{4}{3}(-3) + 2 = \frac{12}{3} + 2 = 4 + 2 = 6$

when x = 0, $y = -\frac{4}{3}(0) + 2 = -0 + 2 = 2$

when x = 3, $y = -\frac{4}{3}(3) + 2 = \frac{-12}{3} + 2 = -4 + 2 = -2$

The correct response is -3, 0, 3

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3 years ago

A map using a scale of 1 inch:5 miles shows a section of land with an area of 3.2 inches what is the actual area of the section

Firlakuza [10]

Answer:

16 miles

Step-by-step explanation:

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

the scale drawing is usually reduced at a constant dimension

scale of the drawing = original dimensions / dimensions of the scale drawing

Actual area = 3.2 x 5 = 16 miles

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3 years ago

You are choosing between two health clubs. Club A offers membership for a fee of $24plus a monthly fee of $11. Club B offers mem

Kay [80]

24 + 11 = 35 + 11 = 46 + 11 = 57 + 11 = 68 +11 = 79 + 11 = 90 + 11 = 101
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$101, 7 months

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3 years ago