Enter the unknown value that makes this statement true. 25% of is 35

The absolute value function can be defined using piecewise notation.

den301095 [7]

<h3>Answers:</h3>

A(10) = 10
A(0) = 0
A(-3) = 3
A(3.14159) = 3.14159
A(x) = 7 leads to either x = 7 or x = -7
A(x) = -5 has no solutions

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Explanations:

The piecewise function has two identities based on what the x input is.

If x = 0 or larger, then A(x) = x based on the top row.

Or, if x < 0, then A(x) = -x based on the second row.

So for an input like x = 10, we have A(10) = 10. The input is identical to the output. The same goes for x = 0 and x = 3.14159

Each output tells us how far away the input is from zero on the number line.

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For a negative input, we'll use the second row

A(x) = -x

A(x) = -(x)

A(-3) = -(-3)

A(-3) = 3

Showing that the number -3 is exactly 3 units away from zero on the number line. In other words, |-3| = 3.

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To solve A(x) = 7, we have to think what input(s) will lead to an output of 7.

What two numbers are 7 units away from zero on the number line? That would be -7 and 7.

If you plugged x = 7 into the piecewise function, you'll use the top row to get A(7) = 7. The bottom row will have A(-7) = 7.

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There are no solutions to A(x) = -5 because the result of an absolute value is never negative. Negative distances do not make sense, so that's why absolute value is defined this way.

If you tried x = 5 then A(5) = 5

Trying x = -5 leads to A(-5) = 5

There's no way to get a negative output.

8 0

2 years ago

Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k.

Firdavs [7]

Answer:

k = -5

Step-by-step explanation:

The function f(x) passes through the points (-4,0) and (-2,2).

Therefore, the equation of the straight line is given by

$\frac{y-2}{2-0} =\frac{x-(-2)}{-2-(-4)}$

⇒ $\frac{y-2}{2} =\frac{x+2}{2}$

⇒ y = x + 4

⇒ f(x) = x + 4 ......... (1)

Now, g(x) passes through the points (-4,0) and (-2,-10).

Then the equation will be

$\frac{y-(-10)}{-10-0} =\frac{x-(-2)}{-2-(-4)}$

⇒ $\frac{y+10}{-10} =\frac{x+2}{2}$

⇒ y = - 5x - 20 = - 5 (x + 4)

⇒ g(x) = -5 (x + 4) ....... (2)

Therefore, from equations (1) and (2) we get k = -5 (Answer)

5 0

3 years ago

Read 2 more answers

How can a triangular prism have a greater volume than a rectangular prism?

nevsk [136]

Answer:

If the triangular prism is bigger than the rectangular prism, it will have a greater volume. There are also many other reasons listed below:

Possible reasons:

If the triangular prism is bigger than the rectangular prism, it will have a greater volume
The rectangular prism could have less width than the triangular prism
The rectangular prism could have less depth than the triangular prism
The rectangular prism could have less length than the triangular prism

<em>Please mark Brainliest if correct.</em>

<em>Sorry if it is not correct.</em>

4 0

3 years ago

Read 2 more answers

Write an inequality to describe the region. The solid upper hemisphere of the sphere of radius 5 centered at the origin

dusya [7]

Answer:

$x^2 + y^2 + z^2 \le 25$ for $z \ge 0$

Step-by-step explanation:

Given

$r = 5$ --- radius

Required

Determine the inequality of the region

The inequality of a region of a sphere is determined using:

$x^2 + y^2 + z^2 \le r^2$

Substitute 5 for r

$x^2 + y^2 + z^2 \le 5^2$

$x^2 + y^2 + z^2 \le 25$

Solving further: <em>The question says only the upper hemisphere is considered.</em>

This implies that:

$z \ge 0$

<em>So, the equation is:</em>

$x^2 + y^2 + z^2 \le 25$

$z \ge 0$

5 0

3 years ago

The annual tuition at a specific college was $20,500 in 2000, and $45,4120

allochka39001 [22]

Answer:

Step-by-step explanation:

Assuming the rate of increase in the cost of tuition fee per year is linear. We would apply the formula for determining the nth term of an arithmetic sequence which is expressed as

Tn = a + (n - 1)d

Where

a represents the first term of the sequence.

d represents the common difference.

n represents the number of terms in the sequence.

From the information given,

a = $20500(amount in 2000)

From 2000 to 2018, the number of terms is 19, hence,

n = 19

T19 = 454120

Therefore,

454120 = 20500 + (19 - 1)d

454120 - 20500 = 18d

18d = 433620

d = 433620/18

d = 24090

Therefore, the equation that can be used to find the tuition y for x years after 2000 is expressed as

y = 20500 + 24090(x - 1)

To to estimate the tuition at this college in 2020, the number of terms between 2000 and 2020 is 21, hence

x = 21

y = 20500 + 24090(21 - 1)

y = 20500 + 481800

y = $502300

8 0

3 years ago