Solving for a Variable
3. A rectangle has length $(3 x+7) \mathrm{cm}$ and width $(2 x-1) \mathrm{cm}$. What is the area of the rectangle? $\mathrm{K}$
A) $(5 x+6) \mathrm{cm}^{2}$
C) $\left(6 x^{2}+11 x-7\right) \mathrm{cm}^{2}$
B) $\left(6 x^{2}-7\right) \mathrm{cm}^{2}$
D) $\left(6 x^{2}-11 x-7\right) \mathrm{cm}^{2}$
Solving by Graphing
Solve the system of equations by graphing: \(y = 2x + 3\) and \(y = -x + 1\)
Arithmetic Operations
Simplify the expression \(2x^2 + 5x - 3 + 3x^2 - 2x + 1\).
Combining Like Terms
Simplify the expression \(3x - 7 + 2x + 5\)
Simple Exponents
Solve for the value of \( x \) in the following equation: \(2^{x+3}=32\).
Distributive Property
Simplify the expression \(4x(3x - 7) + 2(5x - 3)\) using the distributive property.
Prime Factorizations
Find the prime factorization of the number 315.
Finding the Factors
Find the factors of the algebraic expression \(2x^2 - 5x - 3\).
Finding the LCM of a List of Expressions
Find the Lowest Common Multiple (LCM) of the expressions \(2x^2y\), \(8xy^2\), and \(16x^2y^3\).
Finding the LCD of a List of Expressions
Find the least common denominator (LCD) of the list of expressions: \(\frac{1}{x^2-4}, \frac{1}{x^2-1}, \frac{1}{x^2-9}\)
Determining if the Number is a Perfect Square
Is the number 49 a perfect square?
Evaluate
Evaluate the expression \(5x^2 - 3x + 7\) for \(x = -2\)
Evaluate the Expression Using the Given Values
Evaluate the expression \(2x^2 - 3y + 4z\) when \(x = -1\), \(y = 2\), and \(z = -3\).
Evaluating the Difference Quotient
(1 point)
State sales tax $y$ is directly proportional to retail price $x$. An item that sells for 186 dollars has a sales tax of 10.22 dollars. Find a mathematical model that gives the amount of sales tax $y$ in terms of the retail price $x$.
Your answer is $y=$
What is the sales tax on a 340 dollars purchase.
Your answer is:
Dividing
Points: 0.5 of 1
Use long division to find the quotient $Q(x)$ and the remainder $R(x)$ when $P(x)$ is divided by $d(x)$ and express $P(x)$ in the form $d(x) \cdot Q(x)+R(x)$.
\[
\begin{array}{l}
P(x)=x^{3}+2 x^{2}-9 x+183 \\
d(x)=x+7
\end{array}
\]
\[
P(x)=(x+7)
\]
Combining
Combine the algebraic expressions: \(3x^2 + 2x - 7\) and \(-2x^2 + 5x +4\).
Evaluating Radicals
Evaluate the expression \( 2\sqrt{8} + 3\sqrt{18} \)
Solving Using the Square Root Property
Solve the equation \(x^{2}=16\) using the square root property.
Determining if True
If \(x = 3\) and \(y = 2\), is the following statement true? \( 2x + 3y = 12 \)
Finding the Holes in a Graph
Find the hole in the graph of the function \( f(x) = \frac{(x - 2)(x + 3)}{(x - 2)(x + 4)} \)
Finding the Common Factors
Find the common factors of the expressions \(15x^3y^2z\) and \(45x^2y^4z^2\).
Expand a Trinomial with the Trinomial Theorem
Perform the indicated operations.
3) $3(4 x+2 y)(4 x-6 y)$