Solving Expressions - Algebra 2

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Question

If and , what is the value of $-a^{-2}-b^{-2}$ ?

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Answer

Substitute the values into the expression.

$-(6)^{-2}-(-6)^{-2}$

In order to evaluate this expression, we will need to rewrite the negative exponents into fractions.

$-(6)^{-2}-(-6)^{-2}= -\frac{1}{6^2}-\frac{1}{(-6)^2}$

Simplify the fractions.

$-\frac{1}{36}-\frac{1}{36} =- \frac{2}{36}$

Reduce this fraction.

The answer is: $-\frac{1}{18}$

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Question

If and , what is the value of $\frac{b}{\sqrt a}$ ?

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Answer

Substitute the values in the expression.

$\frac{b}{\sqrt a} = \frac{2}{\sqrt 3}$

Rationalize the denominator by multiplying square root of three on the top and bottom of the fraction.

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

Simplify the top and bottom.

The answer is: $\frac{2\sqrt{3}}{3}$

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Question

Solve for x.

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Answer

a. Simplify each side of the equation using the distributive property.

b. Add 6x to both sides of the equation to move all terms with "x" to the left side of the equation.

c. Add 5 to both sides of the equation to move all constants to the right side of the equation.

d. Divide both sides of the equation by 30 to isolate the variable. Simplify the resulting fraction

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Question

Emily buys a rose plant when it is inches tall. The tag indicates that it will grow inches every year. She also buys a tulip plant when it is inches tall. The tag indicates that it will grow inches a year. After how many years are the two plants the same height?

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Answer

We can express each plant's growth as a function of years in the following equations:

Rose height after x years =

Tulip height after x years =

Since we are looking for the year when the two plants are of equal height, we set these expressions for height equal to each other, and solve for x:

Combining like terms by subtracting 2x from both sides and subtracting 5 from both sides gives us:

The plants will reach the same height after 6 years of growth.

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Question

If , simplify $x^{2}+3x-4$ .

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Answer

First, you substitute for : $(4^{2})+3(4)-4$

Next, use PEMDAS (Parentheses, Exponents, Multiplication, Dividion, Addition, and Subtraction) to preform the algebraic operations in the correct order. When we apply this rule to simplify we get the following:

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Question

Solve for if . $3z+y^{2}=22$ .

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Answer

First, substitute 2 for z: $3(2)+y^{2}=22$ .

Then, simplify: $6+y^{2}=22$ .

Next, you must isolate y by moving all other numbers and variables to the other side of the equation: $6+y^{2}-6=22-6$ , which gives you $y^{2}=22-6$ .

And simplify: $y^{2}=16$ .

Here, we then take the square root of both sides: $\sqrt{y^{2}}=\sqrt{16}$ .

Simplfy: $y=\pm 4$ , because both $-4\cdot-4=16$ and $4\cdot4=16$ .

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Question

Simplify $z^{3}+x^{4}y^{2}-y^{3}+13$ given and .

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Answer

First, substitute 1 for z, 2 for x and 3 for y: $1^{3}+2^{4}3^{2}-3^{3}+13$ and simplify: $1+16\cdot9-27+13$ .

Using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction), we simplify the multiplication: .

Then add and subtract from left to right: .

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Question

Evaluate the expression if , , and

$\frac{(y+z)^2}{xw}$

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Answer

After you plug in all of your given values the expression is as followed;

$\frac{(-2+2)^2}{8\cdot3}=\frac{0}{24}=0$

Since the numerator is zero, therefore, the entire fraction equals zero.

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Question

Evaluate the expression if , , and

$\frac{12w-6y}{z^2}$

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Answer

When you plug in your given values the expression should read as followed;

$\frac{12(3)-6(-2)}{2^2} = \frac{36+12}{4}=\frac{48}{4}=12$

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Question

Simplify the expression

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Answer

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Question

Evaluate the expression $b^{4}+3a-9$ when and .

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Answer

First, you subsitute for and for : $(5)^{4}+3(6)-9$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

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Question

Evaluate the expression $a^{2}-7a+4b$ when and .

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Answer

First, substitute for and for : $(2)^{2}-7(2)+4(7)$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

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Question

Evaluate the expression $-5+15-x-3x^{2}$ given .

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Answer

First, you substitute for : $-5+15-(5)-3(5)^{2}$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

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Question

Evaluate the expression $3b-2a^{2}+c$ when , , and .

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Answer

First, substitute for , for , and for : $3(8)-2(4)^{2}+(25)$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

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Question

Evaluate the expression $5^{x}-2x+6x-b$ when and .

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Answer

First, substitute for and for : $5^{3}-2(3)+6(3)-(8)$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

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Question

Evaluate the expression when and .

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Answer

First, substitute for and for :

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

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Question

Evaluate the expression $4(5-x)^{y}-24x$ when and .

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Answer

First, substitute for and for : $4(5-(2))^{(3)}-24(2)$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

$4(3)^{3}-24(2)$

Leaving you with,

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Question

Evaluate the expression $(3b^{2}-5a^{3})+31$ when and .

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Answer

First, substitute for and for : $(3(5)^{2}-5(4)^{3})+31$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

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Question

Evaluate the expression $x^{y}-z^{x}+x^{z}$ when , , and .

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Answer

First, substitute for , for , and for : $(2)^{3}-(4)^{2}+(2)^{4}$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

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Question

Evaluate the expression $x(a+b)-x^{a}$ when , , and .

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Answer

First, substitute for , for , and for : $(3)(2+10)-(3)^{2}$

Now, using the order of operations (Parentheses, Exponents, Multiplication, Division, Addittion, Subtraction), begin to simplify the expression:

Leaving you with,

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