Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model.
Sheila swam \displaystyle 5 \mathrm{~km} .
Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model. Ursula walked an unknown distance,
three times.
Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model.
Tasnia drove \displaystyle 5 \mathrm{~km} plus an unknown distance.
Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model. Susu read a book twice.
a) Build a volume model to represent a cube with side length \displaystyle 4 \mathrm{~cm} . Sketch the model and label the length,
width, and height.
b) What is the volume of the cube?
Write this as a power.
c) Write an expression for the area of
one face of the cube as a power.
Evaluate the area of one face.
d) Write an expression for the surface
area of the cube. Evaluate the surface
area of the cube.
Evaluate.
\displaystyle 5^{3}
Evaluate.
\displaystyle (-2)^{6}
Evaluate.
\displaystyle \left(\frac{3}{4}\right)^{3}
Evaluate.
\displaystyle 1.06^{5}
Write as a single power. Then, evaluate the expression.
\displaystyle 3^{2} \times 3^{3} \times 3
Write as a single power. Then, evaluate the expression.
5^6 \div 5 \div 5^2
Write as a single power. Then, evaluate the expression.
4^6 \div 4^5 \times 4^2
Write as a single power. Then, evaluate the expression.
4^6 \div 4^5 \times 4^2
Write as a single power. Then, evaluate the expression.
[(-3)^2]^3
Write as a single power. Then, evaluate the expression.
\dfrac{(5^4)^3}{5^5 \times 5^4}
E. coli is a type of bacteria that can cause dangerous health problems. It doubles every 20 min. The initial population of a sample of E. coli is 400.
a) Copy and complete this table.
\displaystyle
\begin{array}{|c|c|}
\hline Time (min) & \text{Population of E. coli} \\
\hline 0 & 400 \\
\hline 20 & 800 \\
\hline 40 & \\
\hline 60 & \\
\hline 80 & \\
\hline 100 & \\
\hline 120 & \\
\hline
\end{array}
b) Construct a graph of population versus time. Use a smooth curve to connect the points. Describe the shape of the graph.
c) What will the population be after
5 h?
8 h?
Simplify.
a^5b^4 \times a^3b^2
Simplify.
\dfrac{d^6 \times d^5}{d^7}
Simplify.
\dfrac{m^{10}}{m^3 \times m^5}
Simplify.
\dfrac{(y^6)^3}{(y^5)^2}
Identify the coefficient and variable part of each term.
6x
Identify the coefficient and variable part of each term.
-5y
Identify the coefficient and variable part of each term.
7
Identify the coefficient and variable part of each term.
4a^5b^3
Identify the coefficient and variable part of each term.
dm
Identify the coefficient and variable part of each term.
\dfrac{2}{3}x^2y^3
In a hockey tournament, teams are awarded 4 points for a win and 2 points for an overtime win.
a) Write an expression that describes the number of points a team has.
b) Use your expression to find the number of points earned by a team that has five wins and two overtime wins.
State the degree of each term.
5x^4
State the degree of each term.
-7m^5
State the degree of each term.
a^3b^2c
State the degree of each term.
5
State the degree of each polynomial.
5x+4
State the degree of each polynomial.
3y^4-2
State the degree of each polynomial.
5m^2+3m+6
State the degree of each polynomial.
6a^3-5a^2+4a-3
Classify each pair of terms as either like or unlike.
3x and -7x
Classify each pair of terms as either like or unlike.
4y and 5z
Classify each pair of terms as either like or unlike.
4ab and -2ab
Classify each pair of terms as either like or unlike.
3x^2y and 4xy^2
Classify each pair of terms as either like or unlike.
5xy and 3yx
Classify each pair of terms as either like or unlike.
5m^2 and 8m^2
Identify the like terms in each set.
5a^2, -3b, 2d, 6x^2, 7b^3, -5x^2, 4a, 6c
Identify the like terms in each set.
6y^2, 5y^2, -4y^3, 3, -4y^2, -2y^3
Simplify by collecting like terms.
3x+5y+4x+6y
Simplify by collecting like terms.
5d+3m-4d-5m
Simplify by collecting like terms.
2a^2-5a+3-a^2+2a-6
Simplify by collecting like terms.
3w^2+2wy-y^2-2w^2-2wy+4y^2
Simplify by collecting like terms.
4d-8e-6f+3d+5e-10f
Simplify by collecting like terms.
6a^3-4ab+5b^2-3+5a^3-3ab
Simplify.
(5x+3)+(6x-4)
Simplify.
(4y-3)+(5y-2)
Simplify.
(3p^2+5p+4)+(7p^2-4p-3)
Simplify.
(4m^2-3mn-2n^2)-(m^2+mn-5n^2)
Simplify.
(6a+8b)+(3a-4b)-(5a-3b)
A rectangular cake has dimensions 4x by 3x+2. Find a simplified expression for its perimeter.
Expand.
5(x+2)
Expand.
-4(y-3)
Expand.
2m(3m+4)
Expand.
-4g(2g-3)
Expand and simplify.
4(2x+3y)+5(3x+6y)
Expand and simplify.
3(4y-2w)-3(2y+1)
Expand and simplify.
4(3a+2b)+3(2a-3b)-(a+2b)
Expand and simplify.
-4[3-2(c+5)-4c]