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2 years ago

How do you solve equations with fractions like this? I'm v v confused -3x + 4/5 = -2/3x + 12

Mathematics

1 answer:

sasho [114]2 years ago

7 0

Answer:

Step-by-step explanation:

You first collect isolate all the variables

-3x+4/5=-2/3x+12

Subtract 4/5 from both side and add2/3x from both sides

-7/3x=56/5

You then multiply both sides by the reciprocal of the coefficient of the variable, in this case -3/7

-7/3x*(-3/7)=(56/5)*(-3/7)

x=-168/35

x=-24/5

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2 years ago

A boy owns 7 pairs of pants, 3 shirts, 2 ties, and 6 jackets. How many different outfits can he wear to school if he must wear o

lutik1710 [3]

Answer:

252.

Step-by-step explanation:

We use the Multiplication Rule:

Number of outfits = 7 * 3 * 2 * 6 = 252.

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2 years ago

Read 2 more answers

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love history [14]

Answer:

B. $450

Step-by-step explanation:

The amount of commission is the commission rate (3%) times the amount of sales to which it is applied ($5000). Garrett's commission last week would be ...

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He is also paid $300 each week in addition to his commission, so his total pay last week was ...

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2 years ago

You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along

sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

$d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}$

Then, the time (speed divided by distance) is:

$t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1$

To optimize this function we have to derive and equal to zero:

$\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\ \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\$

$x$

As $d_b=x$ , the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

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3 years ago

Up to 12 people, p, can ride in the van.

Masteriza [31]

Answer:

12 people can fit so the van had enough sests

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3 years ago

How do you solve equations with fractions like this? I'm v v confused -3x + 4/5 = -2/3x + 12​

How do you solve equations with fractions like this? I'm v v confused -3x + 4/5 = -2/3x + 12