Which of the following numbers is an irrational number?
Real Number System And Exponents
Question · Easy
Would you rather: marbles
Short
Between which two consecutive integers does $\sqrt{53}$ lie on a number line?
Convert the repeating decimal $0.444...$ ($0.\bar{4}$) to a fraction in simplest form.
Question · Medium
Simplify the expression $3^4 \cdot 3^5$.
Simplify $\frac{x^8}{x^{-3}}$ for $x \neq 0$.
Simplify $(2x^3 y^{-2})^3$ and express with exponents.
Express $0.00045$ in scientific notation.
Evaluate $(3 \times 10^4) \times (5 \times 10^6)$ and express the result in scientific notation.
Evaluate $\frac{8.4 \times 10^8}{2.1 \times 10^3}$ and express the answer in scientific notation.
Calculate $(4.2 \times 10^5) + (3.8 \times 10^4)$ and express the result in scientific notation.
Question · Hard
Solve $x^2 = 144$ for all real solutions.
Solve $x^3 = -64$ for $x$.
Which set of real numbers is correctly ordered from smallest to largest value?
A microscopic cell measures $2.5 \times 10^{-6}$ meters long. If 4,000 of these cells are placed end-to-end in a straight line, what is the total length in scientific notation?
Approximate the value of $\sqrt{75}$ to the nearest tenth.
Evaluate the multi-step radical expression: $\sqrt{64} + \sqrt[3]{125} - 2^3$.
Solve for positive $x$: $3x^2 - 12 = 135$.
Simplify $\frac{4^{-2} \cdot 4^5}{4^1}$.
The mass of Earth is approximately $5.97 \times 10^{24}$ kg and the mass of the Moon is approximately $7.35 \times 10^{22}$ kg. Approximately how many times heavier is Earth than the Moon?
Simplify the expression $\frac{(x^2 y^{-3})^2 \cdot (x y^4)^{-1}}{x^{-3} y^{-2}}$ and express with positive exponents.
Solve for $x$: $3(x - 4) + 2x = 18$.
Expressions And Linear Equations
Solve for $x$: $5x - 7 = 2x + 14$.
Solve for $x$: $\frac{2}{3}x - 5 = \frac{1}{2}x + 1$.
Which of the following linear equations has infinitely many solutions?
Which of the following linear equations has NO solution?
Find the slope of the line passing through the points $(2, 5)$ and $(6, 17)$.
A car travels at a constant speed, covering 150 miles in 3 hours. What is the slope of the line representing distance (y) versus time (x)?
Write the equation of a line with slope $-2$ and y-intercept $5$ in slope-intercept form.
What is the equation of the line passing through the points $(1, 4)$ and $(3, 10)$?
Convert the standard form equation $3x + 4y = 12$ into slope-intercept form.
Find the x-intercept of the line $2x - 5y = 10$.
Solve the system of equations by substitution: $y = 2x + 1$ and $3x + y = 11$.
Solve the system of equations by elimination: $2x + 3y = 12$ and $2x - 3y = 0$.
Mateo bought 4 notebooks and 2 pens for $14. Sofia bought 2 notebooks and 3 pens for $11. What is the cost of one notebook?
Solve the system of linear equations: $\frac{1}{2}x + \frac{1}{3}y = 4$ and $x - y = 3$.
How many solutions does the system of equations $y = 4x - 3$ and $2y = 8x + 6$ have?
Where do the linear graphs $y = x + 2$ and $y = -x + 6$ intersect?
Solve for $x$: $4(2 - x) - 3(x + 1) = 12$.
Plan A for a phone costs $20 per month plus $0.15 per minute. Plan B costs $35 per month plus $0.10 per minute. For how many call minutes $m$ will both plans cost the exact same amount?
For what value of $k$ will the system of equations $3x - y = 6$ and $6x - 2y = k$ have infinitely many solutions?
A gym charges an initial registration fee of $50 plus a monthly fee of $25. Which linear equation models the total cost $C$ after $m$ months?
Given the points $(0, 2)$, $(2, 8)$, and $(4, 14)$ on a linear graph, what is the rate of change?
What is the equation of a vertical line passing through the point $(-4, 7)$?
Line $L_1$ has equation $y = 4x - 7$. Line $L_2$ is parallel to $L_1$ and passes through point $(3, 2)$. What is the equation of line $L_2$?
A ticket office sold 250 tickets for a concert. Adult tickets cost $12 and child tickets cost $8. Total ticket sales were $2,440. How many adult tickets were sold?
Which set of ordered pairs represents a function?
Functions And Linear Models
The vertical line test is used to determine whether:
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