The cost of a taxi ride starts with a $P$ dollar pickup fee plus $c$ dollars per kilometer. If a journey is $k$ kilometers long and a 15\% service tax is applied to the total cost (including pickup), which equation correctly models the total cost $T$?
Solve for $x$: $3(2x - 5) - 4 = 5x - 2(1 - 3x)$.
A pattern is defined by the rule for the number of elements in the $n$-th figure: $S_n = 2n^2 - n$. What is the difference in the number of elements between the 10th figure and the 9th figure?
If the expression $2(3x - 1) + 5$ is algebraically equivalent to $A(x + 1) + B$, what are the values of $A$ and $B$?
Evaluate the expression $E = \frac{3a^2 - b}{2a + 3}$ when $a = -2$ and $b = -5$.
A cyclist travels $20 \text{ km}$ at a speed of $v \text{ km/h}$. If they increased their speed by $5 \text{ km/h}$, they would save 20 minutes on the same journey. Which equation correctly models this situation?
Solve the inequality: $5 - 3(x + 2) \ge 4x - 10$.
A functional relationship is defined by the following points: $(1, 3), (2, 8), (3, 15), (4, 24)$. Which rule describes this relationship?
Rearrange the formula $A = \frac{x}{y} + 4$ to make $y$ the subject.
The cost function for Company A is $C = 5n + 50$ and for Company B is $C = 8n + 20$, where $n$ is the number of units. The graphs of these two functions intersect at the point $(10, 100)$. What does this intersection point represent?
Determine the $n$-th term rule for the sequence: $\frac{3}{1}, \frac{5}{4}, \frac{7}{9}, \frac{9}{16}, \dots$
Which scenario describes a linear functional relationship between quantity $Q$ and time $t$?
Solve for $x$: $\frac{x-1}{2} + \frac{2x+3}{5} = 4$.
Which algebraic inequality represents all numbers $k$ that are greater than $-4$ (excluding $-4$) and less than or equal to $7$?
If the expression $4(x+2) - 3x$ is algebraically equivalent to $Ax + B$, what is the value of $A+B$?
Calculate the exact value of the expression $P = (3\frac{1}{3} - \frac{5}{6}) \times (\frac{11}{14} \div 0.88)$. Give your answer as an improper fraction in its simplest form.
A value $X$ is increased by $10\%$. The resultant value is then decreased by $10\%$. If the final value achieved is $198$, what was the original value $X$?
A sum of money is divided among P, Q, and R. The ratio of P's share to Q's share is $2 : 1$. The ratio of Q's share to R's share is $3 : 1$. If R receives $100 less than P, what is the total sum shared?
Identify the largest value among the following quantities: $P = 0.\overline{8}$, $Q = \frac{19}{24}$, $R = 83\%$, $S = 2\frac{1}{3} \div 2.8$.
The ratio of flour to sugar in a cake recipe is $3:0.5$. If a baker uses $1\frac{1}{2}$ cups of flour, how many cups of sugar does she use?
Angle $A$ and Angle $B$ are supplementary. Angle $A$ has a measure of $(7x - 5)^\circ$ and Angle $B$ has a measure of $(3x + 25)^\circ$. What is the measure of the smaller angle?
Calculate the area of the triangle with vertices $A=(-1, 3)$, $B=(5, -1)$, and $C=(2, 6)$.
A rectangular swimming pool is designed such that its length is $1.5$ times its width. If the total area of the pool is $1350$ square meters, what is the perimeter of the pool?
A rectangular prism has dimensions such that the length ($L$) is twice the width ($W$), and the height ($H$) is 2 meters greater than the width. If the space diagonal ($D$) of the prism is $\sqrt{70}$ meters, what is the volume of the prism?
A map uses a scale of $1:500$. If a school building measures $10$ cm on the map, what is the actual length of the building in meters?
Which equation matches the graph?
Simplify the ratio $\left(\frac{5}{6}\right) : 0.45 : \left(1 \frac{1}{3}\right)$ to its simplest form involving only integers.
Alice, Ben, and Chloe share a total of $360$. Alice receives $\frac{2}{3}$ of the total amount shared by Ben and Chloe combined. Ben and Chloe share the remainder in the ratio $3:5$. How much money does Chloe receive?
Which option represents the 'Best Buy' (lowest unit price)? Option A: $3$ kg of apples for \$9.60. Option B: $2$ kg of apples for \$6.80.
A stationary supplier sells specialized paper in bulk. If $2\frac{1}{2}$ dozen reams cost $240, how much will 40 reams cost, assuming the price is directly proportional to the quantity purchased?
Three workers can complete a task in $6$ hours. Assuming the work rate is constant, how long would it take $4$ workers to complete the same task?
A map uses a scale of $1:50,000$. If the distance measured between two landmarks on the map is $4$ cm, what is the actual ground distance in kilometers?
Convert a speed of $72$ kilometers per hour ($km/h$) into meters per second ($m/s$).
A $36$-litre drink mixture uses water and cordial concentrate in the ratio $5:4$. To adjust the taste, $A$ litres of water are added and $2A$ litres of cordial concentrate are removed. If the new ratio of water to cordial concentrate is $5:2$, what is the total amount of cordial concentrate that was removed?
Two geometrically similar shapes have corresponding side lengths in the ratio $1:3$. What is the ratio of their corresponding areas?