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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #411 : High School Math

Solve for if x-.16=.32 .

Possible Answers:

x=4.8

x=.44

x=48

x=.48

x=.16

Correct answer:

x=.48

Explanation:

We need to isolate x so that it is the only term on the left side of the equation.

To do this, add .16 to both sides of the equation:

x-.16+.16=.32+.16

The numbers on the left side cancel to leave by itself.

.32+.16=.48

The answer is therefore x=.48 .

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Example Question #1 : How To Find The Perimeter Of Kite

Find the perimeter of the following kite:

Kite

Possible Answers:

$18+\sqrt{10} m$

$10+6\sqrt{10} m$

$16+\sqrt{10} m$

$8+6\sqrt{10} m$

$10+9\sqrt{10} m$

Correct answer:

$10+6\sqrt{10} m$

Explanation:

In order to find the length of the two shorter edges, use a Pythagorean triple:

3-4-5

3m-4m-5m

In order to find the length of the two longer edges, use the Pythagorean theorem:

A^2+B^2=C^2

(9)^2+(3)^2=C^2

C^2=90

$C=3\sqrt{10}m$

The formula of the perimeter of a kite is:

$P = 2(side_{short})+2(side_{long})$

Plugging in our values, we get:

$P = 2(5m)+2(3\sqrt{10}m) = 10+6\sqrt{10}m$

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Example Question #1 : How To Find The Perimeter Of Kite

Find the perimeter of the following kite:

Screen_shot_2014-03-01_at_9.16.34_pm

Possible Answers:

$12\sqrt{2}m + 12m$

$12\sqrt{2}m - 12m$

24m

$12\sqrt{3}m - 12m$

$12\sqrt{3}m + 12m$

Correct answer:

$12\sqrt{2}m + 12m$

Explanation:

The formula for the perimeter of a kite is:

$P = 2(s_{long}) + 2(s_{short})$

Where $s_{long}$ is the length of the longer side and $s_{short}$ is the length of the shorter side

Use the formulas for a 45-45-90 triangle and a 30-60-90 triangle to find the lengths of the longer sides. The formula for a triangle is $a-a-a \sqrt{2}$ and the formula for a triangle is $a-a \sqrt{3}-2a$ .

Our 45-45-90 triangle is: $3 \sqrt{2}m-3 \sqrt{2}m-6m$

Our 30-60-90 triangle is: $3 \sqrt{2}m-3 \sqrt{6}m-6\sqrt{2}m$

Plugging in our values, we get:

$P = 2(6\sqrt{2}m) + 2(6m)$

$P = 12\sqrt{2}m + 12m$

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Example Question #1 : How To Solve Two Step Equations With Integers In Pre Algebra

24=2X-6

X=?

Possible Answers:

Correct answer:

Explanation:

This is a two-step equation. First simplify the whole numbers by adding 6 to both sides:

$24+\left ( 6\right )=2X-6+\left ( 6\right )$

30=2X

Then divide both sides by 2

$\frac{30}{2}=\frac{2X}{2}$

15=X

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Example Question #2 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for .

4x-3=13

Possible Answers:

x=64

x=2.5

x=4

x=12

Correct answer:

x=4

Explanation:

Perform the same operation on both sides of the equation.

4x-3=13

Add 3 to both sides.

4x-3+3=13+3

4x=16

Divide both sides by 4 and simplify the fraction.

$\frac{4x}{4}=\frac{16}{4}$

x=4

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Example Question #3 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve the following equation for .

3m + 5 = 17

Possible Answers:

$\frac{22}{3}$

Correct answer:

Explanation:

3m + 5 = 17

To solve a two step equation, we want to isolate the variable. This means first "getting rid of" the number which is being added to the variable, in this case . To get rid of the , we first recognize that it is being added, then we do the inverse and subtract from both sides.

3m+5-5=17-5

3m=12

Now, we want to do the inverse of multiplying by , which is dividing by on both sides.

$\frac{3m}{3}=\frac{12}{3}$

m=4

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Example Question #1 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve the following equation for .

$8 - \frac{k}{7} = 5$

Possible Answers:

Correct answer:

Explanation:

$8 - \frac{k}{7} = 5$

We want to first isolate the variable, thus we first try to get rid of the constants being added to the variable, in this case the . To eliminate , we do the inverse of addition, and subtract from both sides.

$8-\frac{k}{7}-8=5-8$

$- \frac{k}{7} = -3$

Then, we want to do the inverse of dividing by , which is multiplying by . Remember that multiplying two negative terms results in a positive term.

$(-7)(-\frac{k}{7})=(-7)(-3)$

k=21

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Example Question #2 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve the equation for .

$\small 7p+3=10p$

Possible Answers:

$\small p=-\frac{13}{10}$

$\small p=1$

$\small p=-1$

$\small p=\frac{13}{10}$

Correct answer:

$\small p=1$

Explanation:

$\small 7p+3=10p$

Subtract from both sides to get the variables on the same side, and simplify.

$\small 7p+3-7p=10p-7p$

$\small 3=3p$

Divide both sides by .

$\small \frac{3}{3}=\frac{3p}{3}$

$\small 1=p$

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Example Question #2 : How To Solve Two Step Equations With Integers In Pre Algebra

Solve for :

4x-2=14

Possible Answers:

Correct answer:

Explanation:

We have two steps to this problem. Remember our end result is to get isolated on one side of the equation.

First we add to each side, cancelling out the on the left side. This brings the equation to 4x =16 .

Remember to get rid of a number we perform the opposite operation. The is multiplied with the , therefore to cancel it out we will divide by .

divided by equals . What we do to one side we must do to the other, therefore we divide by also. This becomes x=4 .

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Example Question #3 : How To Solve Two Step Equations With Integers In Pre Algebra

Simplify:

$(2x^{2}+5) (3x^{3}+ 3)$

Possible Answers:

$5x^{6} + 8$

$6x^{5} +15$

$6x^6 +6x^{2} + 15x^{3} +15$

$6x^{5}+15x^{3}+6x^{2}+15$

6x^6 +15

Correct answer:

$6x^{5}+15x^{3}+6x^{2}+15$

Explanation:

The requires the FOIL method (first, outside, inside, last).

Multiplying the first two monomials $2x^2 \cdot 3x^3$ equals $6x^{5}$ .

The outside two are $2x^{2} \cdot 3$ which equals $6x^{2}$ .

The two inside monomials are $5 \cdot 3x^3$ which equals 15x^3 .

The last two are $5\cdot 3$ which is .

All together this becomes $6x^{5}+15x^{3}+6x^{2}+15$ .

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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #411 : High School Math

Example Question #1 : How To Find The Perimeter Of Kite

Example Question #1 : How To Find The Perimeter Of Kite

Example Question #1 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #2 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #3 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #1 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #2 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #2 : How To Solve Two Step Equations With Integers In Pre Algebra

Example Question #3 : How To Solve Two Step Equations With Integers In Pre Algebra

All High School Math Resources

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