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High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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

Example Questions

Example Question #12 : How To Multiply Polynomials In Pre Algebra

Combine into a single simplified fraction:

$\frac{x+3}{x+2}+\frac{x+5}{x^{2}-1}$

Possible Answers:

$\frac{4x^{3}-5x^{2}+3x-7}{-x^{3}+2x^{2}-x+2}$

$\frac{3x^{3}-2x^{2}-5x+6}{x^{3}-2x^{2}+x-2}$

$\frac{5x^{3}+3x^{2}-2x+1}{x^{3}+2x^{2}-x+2}$

$\frac{2x^{3}+2x^{2}+3x+8}{x^{3}+2x^{2}+x+2}$

$\frac{x^{3}+4x^{2}+6x+7}{x^{3}+2x^{2}-x-2}$

Correct answer:

$\frac{x^{3}+4x^{2}+6x+7}{x^{3}+2x^{2}-x-2}$

Explanation:

Multiply to get a common denominator:

$\frac{x+3}{x+2}+\frac{x+5}{x^{2}-1} = \frac{(x+3)(x^{2}-1)+(x+5)(x+2)}{(x+2)(x^{2}-1)}$

Next, using FOIL (first, outer, inner, last) remove the parantheses and then combine like terms to get:

$\frac{x^{3}+4x^{2}+6x+7}{x^{3}+2x^{2}-x-2}$

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Example Question #11 : How To Multiply Polynomials In Pre Algebra

Simplify $ax(bx-ca^{2})$ .

Possible Answers:

$abx^{2}-a^{3}cx$

$abx^{2}-ca^{2}$

$abx^{2}+ca^{3}x$

$ax-ca^{3}x$

2abx-3acx

Correct answer:

$abx^{2}-a^{3}cx$

Explanation:

Use the distributive property:

$ax(bx-ca^{2})= ax\cdot bx-ax\cdot ca^{2}= abx^{2}-a^{3}cx$

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Example Question #12 : How To Multiply Polynomials In Pre Algebra

Multiply to find the polynomial.

(2x+2)(x-4)

Possible Answers:

2(x^2+2x+3)

2x^2-6x+8

2x^2+6x-8

2x^2-6x-8

2x^2+6x+8

Correct answer:

2x^2-6x-8

Explanation:

Multiply using the FOIL method.

First: (2x)(x)=2x^2

Outside: (2x)(-4)=-8x

Inside: (x)(2)=2x

Last: (2)(-4)=-8

Add the terms together to get the final expression.

2x^2-8x+2x-8=2x^2-6x-8

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Example Question #13 : How To Multiply Polynomials In Pre Algebra

Multiply to find the polynomial.

(x+2)(-x-7)

Possible Answers:

-x^2+9x+14

-x^2+9x-14

x^2-9x-14

x^2+9x+14

-x^2-9x-14

Correct answer:

-x^2-9x-14

Explanation:

Multiply using the FOIL method.

First: (x)(-x)=-x^2

Outside: (x)(-7)=-7x

Inside: (2)(-x)=-2x

Last: (2)(-7)=-14

Add the terms to get the final expression.

-x^2-7x-2x-14=-x^2-9x-14

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Example Question #14 : How To Multiply Polynomials In Pre Algebra

What is $10\%$ of ?

Possible Answers:

Correct answer:

Explanation:

Convert % to a decimal, which is .

Then multiply by to get .

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Example Question #15 : How To Multiply Polynomials In Pre Algebra

What is the product of and $4x^{2}-3xy+y^{2}$ ?

Possible Answers:

$8x^{3}-6x^{2}y+2xy^{2}$

$2x^{3}-x^{2}y-xy^{2}$

$6x^{3}-5x^{2}y+2xy^{2}$

$-8x^{3}+6x^{2}y-2xy^{2}$

$6x^{3}-x^{2}y+xy^{2}$

Correct answer:

$8x^{3}-6x^{2}y+2xy^{2}$

Explanation:

In order to simplify this problem distribute to each component of $4x^{2}-3xy+y^{2}$ .

$=(2x)(4x^{2}-3xy+y^{2})$

Distribute.

$=(2x*4x^{2})+(2x*-3xy)+(2x*y^{2})$

Multiply and simplify.

$=8x^{3}-6x^{2}y+2xy^{2}$

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Example Question #18 : How To Multiply Polynomials In Pre Algebra

The length of a particular rectangle is greater than the width of the rectangle. If the perimeter of the rectangle is , what is the area of the rectangle?

Possible Answers:

Correct answer:

Explanation:

If the width is , then the length is x + 4 . The perimeter equals , so x + x + x+4 + x+4 = 16 .

solving for , we have 4x + 8 = 16

x = 2 , the width, so the length is .

Then, to find the area we multiply times , which equals .

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Example Question #1 : How To Find The Height Of An Equilateral Triangle

Equilateral_triangle

An equilateral triangle has a side length of $\sqrt{3}$ . What is the triangle's height $\dpi{100} h$ ?

Possible Answers:

$\frac{3}{2}$

Not enough information to solve

$\sqrt{3}$

$\frac{\sqrt{3}}2{}$

Correct answer:

$\frac{3}{2}$

Explanation:

The altitude, $\dpi{100} h$ , divides the equilateral triangle into two $30^{\circ}-60^{\circ}-90^{\circ}$ right triangles and divides the bottom side in half.

In a $30^{\circ}-60^{\circ}-90^{\circ}$ right triangle, the sides of the triangle equal , $x\sqrt{3}$ , and . In these equations equals the length of the smallest side, which in our triangle is $\frac{s}{2}$ or $\frac{\sqrt{3}}{2}$ .

In this scenario:

$h=x\sqrt{3}$

and

$x=\frac{\sqrt{3}}2{}$

Therefore,

$h=\frac{\sqrt{3}}{2}*\frac{\sqrt{3}}{1}$

$\rightarrow\frac{3}{2}$

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Example Question #2 : How To Find The Height Of An Equilateral Triangle

Equilateral_triangle

An equilateral triangle has a side length of s=4 cm . What is its height, ?

Possible Answers:

5.19cm

4.36cm

1.73cm

Not enough information to solve

3.46cm

Correct answer:

3.46cm

Explanation:

An altitude slices an equilateral triangle into two $30^{\circ}-60^{\circ}-90^{\circ}$ triangles. These triangles follow a side-length pattern. The smallest of the two legs equals and the hypotenuse equals . By way of the Pythagorean Theorem, the longest leg or $h=x\sqrt{3}$ .

Therefore, we can find the height of the altitude of this triangle by designating a value to . The hypotenuse of one of the $30^{\circ}-60^{\circ}-90^{\circ}$ is also the side of the original equilateral triangle. Therefore, one can say that 2x=s=4cm and x=2cm .

$h=x\sqrt{3}$

$h=2\sqrt{3}cm$

$\rightarrow3.46cm$

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Example Question #12 : Equilateral Triangles

What is the height of an equilateral triangle with side 6?

Possible Answers:

$3\sqrt{3}$

$6\sqrt{2}$

Correct answer:

$3\sqrt{3}$

Explanation:

When you draw the height in an equilateral triangle, it makes two 30-60-90 triangles. Because of that relationship, the height (which is across from the $60^{\circ}$ ) is $3\sqrt{3}$ .

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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 #12 : How To Multiply Polynomials In Pre Algebra

Example Question #11 : How To Multiply Polynomials In Pre Algebra

Example Question #12 : How To Multiply Polynomials In Pre Algebra

Example Question #13 : How To Multiply Polynomials In Pre Algebra

Example Question #14 : How To Multiply Polynomials In Pre Algebra

Example Question #15 : How To Multiply Polynomials In Pre Algebra

Example Question #18 : How To Multiply Polynomials In Pre Algebra

Example Question #1 : How To Find The Height Of An Equilateral Triangle

Example Question #2 : How To Find The Height Of An Equilateral Triangle

Example Question #12 : Equilateral Triangles

All High School Math Resources

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