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2 years ago

12

One-fourth of a number increased by thirteen is less than two.

1 answer:

finlep [7]2 years ago

3 0

Answer: x < -44

Step-by-step explanation:

alright my fellow dude gamer, i want you to know that "a number" is basically just x

so lets do this

$\frac{1}{4}x + 13 < 2$

ok now we are going to solve for x, no?

$\frac{1}{4}x < -11$

i just subtracted 13 from both sides

now we divide -11 by 1/4

$x < -44$

MAGIC! ABSOLUTELY FANTASTIC! OH MY GOODNESS AHHHHHHH

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If a car makes a trip of 422 miles in 8 hours, what is its average speed per hour?

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52.75 miles per hour (MPH)

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In Colorado Springs, a local newspaper ran a full page of nearly 100 mug shots of people the police wanted to arrest for serious

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2 years ago

Leila puts an integer into the "In" box of each machine.

kykrilka [37]

The machines represent equivalent expressions.

The output produced by both machines is 372

The equation represented on machine A is:

$\mathbf{y = 2(5x + 3) - 24}$

The equation represented on machine B is:

$\mathbf{y = 4(2(x + 11) - 7)}$

Where: x and y represent the inputs and the outputs, respectively

When the outputs are the same, it means:

$\mathbf{y = y}$

So, we have:

$\mathbf{2(5x + 3) - 24 = 4(2(x + 11) - 7)}$

Open brackets

$\mathbf{10x + 6 - 24 = 8x + 88 - 28}$

$\mathbf{10x - 18 = 8x + 60}$

Collect like terms

$\mathbf{10x - 8x = 18 + 60}$

$\mathbf{2x = 78 }$

Divide both sides by 2

$\mathbf{x = 39 }$

Substitute 39 for x in $\mathbf{y = 2(5x + 3) - 24}$

$\mathbf{y = 2 \times (5 \times 39 + 3) - 24}$

$\mathbf{y = 372}$

Hence, the output produced by both machines is 372

Read more about equivalent expressions at:

brainly.com/question/15715866

4 0

2 years ago

For the following pair of functions, find (f+g)(x) and (f-g)(x).

ch4aika [34]

Given:

The functions are

$f(x)=4x^2+7x-5$

$g(x)=-9x^2+4x-13$

To find:

The functions $(f+g)(x)$ and $(f-g)(x)$ .

Solution:

We know that,

$(f+g)(x)=f(x)+g(x)$

$(f+g)(x)=4x^2+7x-5-9x^2+4x-13$

$(f+g)(x)=(4x^2-9x^2)+(7x+4x)+(-5-13)$

$(f+g)(x)=-5x^2+11x-18$

And,

$(f-g)(x)=f(x)-g(x)$

$(f-g)(x)=(4x^2+7x-5)-(-9x^2+4x-13)$

$(f+g)(x)=4x^2+7x-5+9x^2-4x+13$

$(f+g)(x)=(4x^2+9x^2)+(7x-4x)+(-5+13)$

$(f-g)(x)=13x^2+3x+8$

Therefore, the required functions are $(f+g)(x)=-5x^2+11x-18$

and $(f-g)(x)=13x^2+3x+8$ .

7 0

3 years ago