Solve the linear equation for $x$: $3x + 7 = 22$.
Linear Algebra Functions
Question · Easy
Flip it: the negative swing
Short
Given the linear function $f(x) = 4x - 5$, what is the value of $f(3)$?
What is the slope of the line passing through the points $(2, 3)$ and $(6, 11)$?
What are the coordinates of the y-intercept of the line $y = -3x + 8$?
Simplify the expression $(x^4)(x^7)$.
Exponential Models
Stats test: find the median
Evaluate the exponential function $f(x) = 3 \cdot 2^x$ for $x = 4$.
Point $P(3, -2)$ is translated 4 units right and 5 units up. What are the coordinates of the image point $P'$?
Geometric Transformations
What are the coordinates of point $(5, -4)$ after a reflection across the x-axis?
Calculate the mean of the data set: $\{4, 8, 12, 16, 20\}$.
Data Analysis Statistics
Find the median of the data set: $\{3, 7, 9, 15, 21\}$.
Solve the inequality: $2x - 4 < 10$.
What is the slope of the horizontal line $y = 5$?
Simplify the monomial expression $(2x^3)^4$.
In the exponential decay function $A(t) = 500(0.85)^t$, what is the initial value?
Find the distance between the origin $(0, 0)$ and the point $(6, 8)$ in the coordinate plane.
What is the midpoint of the line segment connecting $(2, 8)$ and $(10, 4)$?
Identify the mode of the data set: $\{2, 5, 5, 8, 9, 12\}$.
What is the range of the data set: $\{14, 22, 9, 31, 18\}$?
Solve for $x$: $5x - 15 = 0$.
Find the common difference of the arithmetic sequence: $4, 9, 14, 19, 24, \dots$
Evaluate the algebraic expression $2a + 3b$ when $a = 4$ and $b = 5$.
Point $A(4, -3)$ is rotated $180^\circ$ about the origin. What are the coordinates of $A'$?
What is the slope of any line parallel to $y = -4x + 9$?
A rental company charges a flat fee of $15 plus $3 per hour. Which equation represents total cost $C$ for $h$ hours?
What is the percent rate of growth for the exponential function $f(t) = 200(1.06)^t$?
In a data summary, the first quartile $Q_1 = 12$ and the third quartile $Q_3 = 28$. What is the Interquartile Range (IQR)?
What is the x-intercept of the line $2x + 4y = 12$?
For the geometric sequence defined by $a_n = 3 \cdot 2^{n-1}$, what is the 4th term ($a_4$)?
What is the slope of a line perpendicular to $y = \frac{1}{3}x + 2$?
Simplify by combining like terms: $4x + 7y - 2x + 3y$.
Solve the multi-step equation for $x$: $4(x - 3) + 2x = 30$.
Question · Medium
Solve the system of linear equations using substitution: $y = 2x + 1$ $3x + y = 16$
Solve the system of equations using elimination: $2x + 3y = 12$ $2x - y = 4$
Solve the linear inequality for $x$: $-3x + 5 \ge -10$.
What is the domain of the square root function $f(x) = \sqrt{x - 4}$?
A phone plan charges a monthly fee of $25 plus $0.10 per text message. The total cost is $C(m) = 0.10m + 25$. What is $C(150)$?
Write the equation of the line passing through $(3, 5)$ with a slope of $-2$ in slope-intercept form.
Find the standard form equation $Ax + By = C$ of the line passing through $(0, 4)$ and $(2, 0)$.
An arithmetic sequence has first term $a_1 = 5$ and common difference $d = 4$. Find the 15th term ($a_{15}$).
A sequence is defined recursively by $a_1 = 8$ and $a_n = a_{n-1} + 3$. What is $a_5$?
A population of bacteria is modeled by $P(t) = 1000(1.05)^t$, where $t$ is in hours. What is the population after 3 hours (rounded to the nearest whole number)?
A car purchased for $24,000 depreciates in value by 20% each year ($V(t) = 24000(0.80)^t$). What is its value after 2 years?
Find the 4th term of a geometric sequence where $a_1 = 5$ and the common ratio $r = 3$.
Compare $f(x) = 10x + 5$ and $g(x) = 2^x$. For which integer value of $x$ does $g(x)$ first exceed $f(x)$ for positive $x$?
An investment of $1,000 earns 4% interest compounded annually ($A = 1000(1.04)^t$). How much money is in the account after 2 years?
Under the translation vector $(x, y) \rightarrow (x - 3, y + 4)$, what is the image of preimage point $A(-1, 2)$?
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