Algebra

What is the coefficient of $x$ in the expression $x + 1$?

Evaluate $50 - a^2$ for $a = 5$.

Simplify $3 \times 4 \times k$.

Which expression represents 'the square of $x$ plus $4$'?

What is the value of $x^3 + 1$ when $x = -2$?

Simplify the expression: $2(3n - 4) - 2n$.

Identify the coefficient of $y$ in the expression $\frac{y}{5} - 10$.

A rectangular swimming pool has a width of $w$ meters and a length that is twice its width. A tiled deck of uniform width $2$ meters is constructed around the entire outer edge of the pool, as shown in the diagram. Find the simplified algebraic expression that represents the area of the tiled deck in square meters.

Simplify the expression: $4(x - 2)^2 - 4(x^2 - 4x + 4)$.

Simplify $\frac{x^2 - 9}{x + 3}$ given $x \neq -3$.

Simplify: $y + 10 + 2y - 5$.

Simplify the expression by collecting like terms: $5x + 2 - 3x + 4$.

Simplify: $12b - 6b + b$.

Simplify the expression: $p + q + p + q + p$.

Simplify the expression: $7 - (2x - 3) + x$.

Expand and simplify: $2(3m - 1) + 4$.

Simplify the expression: $x^2 + 4x - 2x + 3$.

Simplify the highly nested expression: $10 - \{3x - [2x - (5 - x)]\}$

Simplify the following expression: $3xy^2 - 2x^2y + 5xy^2 + 2x^2y$

Simplify the following expression: $\frac{2}{3}(6x - 9) - \frac{1}{4}(8x + 12)$

If $B = a \times b \times c$, find $B$ when $a = 1$, $b = 5$, and $c = 10$.

Calculate speed $S = \frac{d}{t}$ when distance $d = 100$ km and time $t = 4$ h.

Calculate the mean $N = \frac{x + y + z}{3}$ if $x = 2$, $y = 4$, and $z = 6$.

Find the value of $Z = 3(x + y)$ when $x = 2$ and $y = 3$.

The perimeter of a specialized polygon is $P = 4s + 2w$. Calculate $P$ if $s = 10$ and $w = 5.5$.

A combined resistance $R$ is found by $R = \frac{xy}{x + y}$. Find $R$ if $x = 12$ and $y = 4$.

The Body Mass Index (BMI) is calculated as $M = \frac{w}{h^{2}}$. Calculate $M$ for a mass $w = 80$ kg and height $h = 2$ m.

Find the value of $w$ in $w = \sqrt[3]{x + y}$ when $x = 120$ and $y = 5$.

Calculate $z = \frac{a + b + c}{3}$ for $a = -12.5$, $b = 7.5$, and $c = 20$.

Given $E = mgh + \frac{1}{2}mv^{2}$, find $E$ when $m = 2$, $g = 10$, $h = 5$, and $v = 4$.

Solve for $g$: $\frac{g}{6} - 2 = 4$

Find the value of $f$: $9f - 9 = 72$

Solve for $e$: $10e + 20 = 100$

Solve for $d$: $\frac{d}{15} = 4$

Solve for $x$: $7x - 4 = 52$

Find the value of $x$: $0.5x + 0.5 = 2.5$

Solve for $x$ in: $12 = \frac{x + 10}{2}$

A number machine follows a specific sequence of algebraic operations to transform an input value $x$ into an output value. The process is illustrated in the flowchart below. If the machine produces a final output of $-6.3$, what was the original input value $x$?

A laboratory technician uses a specialized sensor to monitor the cooling process of a chemical sample. The relationship between the sensor's voltage reading $V$ and the sample's actual temperature $T$ (in $^{\circ}$C) is modeled by the linear equation:

$V = 14.2 - 3.5T$

If the sensor currently displays a voltage reading of $59.7$, find the actual temperature $T$ of the sample.

A rectangle has an area of $48 \text{ cm}^2$. Its width is $6 \text{ cm}$ and its length is given by the expression $\frac{2x + 4}{3}$ cm. Based on the geometric properties provided, find the value of $x$.

What are the first three terms of a sequence with the rule $T_n = 2n$?

What is the next term in the sequence: $1000, 100, 10, \dots$?

Find the difference between terms in the sequence: $1, 8, 15, 22, \dots$

Calculate the $1^{st}$ term for the sequence $T_n = n + 99$.

What is the $15^{th}$ term of the sequence $u_n = 100 - 2n$?

Find the rule for the sequence: $10, 19, 28, 37, \dots$

A library fine starts at $2.00$ and increases by $0.50$ per day. What is the fine after $10$ days?

What is the sum of the first $10$ terms of the sequence $2, 4, 6, 8, \dots$?

A sequence of shapes uses squares. Pattern 1 has 1 square, Pattern 2 has 4, Pattern 3 has 7. How many squares are in Pattern $50$?

Find the common difference of an arithmetic sequence where $u_1 = -12$ and $u_{15} = 30$.

If $y = x + x$, what is $y$ when $x = 4$?

What are the coordinates of a point $4$ units to the right of the $y$-axis and $2$ units below the $x$-axis?

If you move the point $(2, 3)$ down by $5$ units, what is the new $y$-coordinate?

If $y = \frac{20}{x}$, what is $y$ when $x = 2$?

What is the perimeter of a triangle with vertices $(1, 1), (1, 4),$ and $(5, 1)$?

A set of points $(1, 6), (2, 7), (3, 8)$ follows a pattern. What is the $y$-coordinate when $x = 10$?

The point $(4, 10)$ is on the line $y = mx + 2$. What is the value of $m$?

A triangle has vertices $(0, 0)$, $(a, 0)$, and $(0, b)$. If the midpoint of the hypotenuse is $(3, 4)$, what is the area of the triangle?

If the point $(x, y)$ is in the second quadrant, then the point $(y, x)$ must be in which quadrant?

The distance between point $(x, 3)$ and $(2, 3)$ is 7 units. What are the possible values of $x$?