PSAT: Advanced Math - Nonlinear equations in one variable and systems of equations in two variables - Matt Wheeland | Library

1

$|p| + 61 = 65$
Which value is a solution to the given equation?

$\dfrac{65}{61}$

$4$

$126$

$130$

1

$p = 20 + \dfrac{16}{n}$
The given equation relates the numbers $p$ and $n$, where $n$ is not equal to $0$ and $p > 20$. Which equation correctly expresses $n$ in terms of $p$?

$n = \dfrac{p - 20}{16}$

$n = \dfrac{p}{16} + 20$

$n = \dfrac{p}{16} - 20$

$n = \dfrac{16}{p - 20}$

1

The graph of a system of a linear equation and a nonlinear equation is shown. What is the solution $(x, y)$ to this system?

$(0, 0)$

$(0, 2)$

$(2, 4)$

$(4, 0)$

1

$57x^2 + (57b + a)x + ab = 0$
In the given equation, $a$ and $b$ are positive constants. The product of the solutions to the given equation is $kab$, where $k$ is a constant. What is the value of $k$?

$\dfrac{1}{57}$

$\dfrac{1}{19}$

$1$

$57$

1

The solutions to $x^2 + 6x + 7 = 0$ are $r$ and $s$, where $r < s$. The solutions to $x^2 + 8x + 8 = 0$ are $t$ and $u$, where $t < u$. The solutions to $x^2 + 14x + c = 0$, where $c$ is a constant, are $r + t$ and $s + u$. What is the value of $c$?

1

During a 5-second time interval, the average acceleration $a$, in meters per second squared, of an object with an initial velocity of 12 meters per second is defined by the equation
where $v_f$ is the final velocity of the object in meters per second. If the equation is rewritten in the form $v_f = xa + y$, where $x$ and $y$ are constants, what is the value of $x$?

1

If $u - 3 = \dfrac{6}{t - 2}$, what is $t$ in terms of $u$?

$t = \dfrac{1}{u}$

$t = \dfrac{2u + 9}{u}$

$t = \dfrac{1}{u - 3}$

$t = \dfrac{2u}{u - 3}$

1

$w^2 + 12w - 40 = 0$
Which of the following is a solution to the given equation?

$6 - 2\sqrt{19}$

$2\sqrt{19}$

$\sqrt{19}$

$-6 + 2\sqrt{19}$

1

$|x - 2| = 9$
What is one possible solution to the given equation?

1

$3x(x-4)(x+5)=0$
What is one of the solutions to the given equation?

$-4$

$0$

$3$

$5$

1

$x^2 = (22)(22)$
What is the positive solution to the given equation?

1

The equation $12t + b = c$ relates the variables $t$, $b$, and $c$. Which of the following correctly expresses the value of $c - b$ in terms of $t$?

$\dfrac{t}{12}$

$t$

$t + \dfrac{1}{12}$

$12t$

1

$\dfrac{4x^2}{x^2-9}-\dfrac{2x}{x+3}=\dfrac{1}{x-3}$
What value of $x$ satisfies the equation above?

$-3$

$-\dfrac{1}{2}$

$\dfrac{1}{2}$

$3$

1

The total revenue from sales of a product can be calculated using the formula $T = PQ$, where $T$ is the total revenue, $P$ is the price of the product, and $Q$ is the quantity of the product sold. Which of the following equations gives the quantity of product sold in terms of $P$ and $T$?

$Q = \dfrac{P}{T}$

$Q = \dfrac{T}{P}$

$Q = PT$

$Q = T - P$

1

$6r = 7s + t$
The given equation relates the variables $r$, $s$, and $t$. Which equation correctly expresses $s$ in terms of $r$ and $t$?

$s = 42r - t$

$s = 7(6r - t)$

$s = \dfrac{6}{7}r - t$

$s = \dfrac{6r - t}{7}$

1

What are the solutions to the given equation?

(-5 ± √(25 + 168)) / 12

(-6 ± √(25 + 168)) / 12

(-5 ± √(36 - 168)) / 12

(-6 ± √(36 - 168)) / 12

1

In the $xy$-plane, the graph of $y = x^2 - 9$ intersects line $p$ at $(1,a)$ and $(5,b)$, where $a$ and $b$ are constants. What is the slope of line $p$?

$6$

$2$

$-2$

$-6$

1

$P = \dfrac{W}{t}$
The power $P$ produced by a machine is represented by the equation above, where $W$ is the work performed during an amount of time $t$. Which of the following correctly expresses $W$ in terms of $P$ and $t$?

$W = Pt$

$W = \dfrac{P}{t}$

$W = \dfrac{t}{P}$

$W = P + t$

1

$y = x^2$
$2y + 6 = 2(x + 3)$
If $(x, y)$ is a solution of the system of equations above and $x > 0$, what is the value of $xy$?

1

2

3

9

1

$\dfrac{14x}{7y} = 2\sqrt{w + 19}$
The given equation relates the distinct positive real numbers $w$, $x$, and $y$. Which equation correctly expresses $w$ in terms of $x$ and $y$?

$w = \sqrt{\dfrac{x}{y}} - 19$

$w = \sqrt{\dfrac{28x}{14y}} - 19$

$w = \left( \dfrac{x}{y} \right)^2 - 19$

$w = \left( \dfrac{28x}{14y} \right)^2 - 19$

1

In the given equation, $c$ is a positive constant. Which of the following is one of the solutions to the given equation?
$\dfrac{x^{2}}{\sqrt{x^{2}+c^{2}}} = \dfrac{c^{2}}{\sqrt{x^{2}-c^{2}}} + 39$

$-c$

$-c^{2} - 39^{2}$

$- \sqrt{39^{2} - c^{2}}$

$- \sqrt{c^{2} + 39^{2}}$

1

$|-5x + 13| = 73$
What is the sum of the solutions to the given equation?

$-\dfrac{146}{5}$

$-12$

$0$

$\dfrac{26}{5}$

1

$14j + 5k = m$
The given equation relates the numbers $j$, $k$, and $m$. Which equation correctly expresses $k$ in terms of $j$ and $m$?

$k = \dfrac{m - 14j}{5}$

$k = \dfrac{1}{5}m - 14j$

$k = \dfrac{14j - m}{5}$

$k = 5m - 14j$

1

$5(x + 7) = 15(x - 17)(x + 7)$
What is the sum of the solutions to the given equation?

1

$-x^{2} + bx - 676 = 0$
In the given equation, $b$ is a positive integer. The equation has no real solution. What is the greatest possible value of $b$?

1

$8j = k + 15m$
The given equation relates the distinct positive numbers $j$, $k$, and $m$. Which equation correctly expresses $j$ in terms of $k$ and $m$?

$j = \dfrac{k}{8} + 15m$

$j = k + \dfrac{15m}{8}$

$j = 8(k + 15m)$

$j = \dfrac{k + 15m}{8}$

1

$2x^2 - 8x - 7 = 0$
One solution to the given equation can be written as $\frac{8 - \sqrt{k}}{4}$, where $k$ is a constant. What is the value of $k$?

1

$y = 5x + 4$
$y = 5x^2 + 4$
Which ordered pair $(x, y)$ is a solution to the given system of equations?

$(0, 0)$

$(0, 4)$

$(8, 44)$

$(8, 84)$

1

$7m = 2(n + p)$
The given equation relates the positive numbers $m$, $n$, and $p$. Which equation correctly gives $m$ in terms of $n$ and $p$?

$m = \dfrac{2(n+p)}{7}$

$m = 2(n + p)$

$m = 2(n + p) - 7$

$m = 2 - n - p - 7$

1

$x = 49$
$y = \sqrt{x} + 9$
The graphs of the given equations intersect at the point $(x, y)$ in the $xy$-plane. What is the value of $y$?

16

40

81

130

1

$x = 8a(b + 9)$
The given equation relates the positive numbers $a$, $b$, and $x$. Which equation correctly expresses $a$ in terms of $b$ and $x$?

$a = \dfrac{x}{8} - (b + 9)$

$a = \dfrac{x}{8(b + 9)}$

$a = \dfrac{8(b + 9)}{x}$

$a = 8x(b + 9)$

1

$x^2 - 5x - 24 = 0$
What is the sum of the solutions to the given equation?

1

$y = 76$
$y = x^2 - 5$
The graphs of the given equations in the $xy$-plane intersect at the point $(x, y)$. What is a possible value of $x$?

$-\dfrac{76}{5}$

$-9$

$5$

$76$

1

What is the positive solution to the given equation?
$-4x^2 - 7x = -36$

$\dfrac{7}{4}$

$\dfrac{9}{4}$

$4$

$7$

1

$y = x + 1$
$y = x^2 + x$
If $(x, y)$ is a solution to the system of equations above, which of the following could be the value of $x$?

$-1$

$0$

$2$

$3$

1

$5\lvert x\rvert = 45$
What is the positive solution to the given equation?

1

$y = x^2 + 1.7$
$y = 1.7 - x$
Which graph represents the given system of equations?

A. null

B. null

C. null

D. null

1

$(x + 2)(x - 5)(x + 9) = 0$
What is a positive solution to the given equation?

3

4

5

18

1

$b = 42cf$
The given equation relates the positive numbers $b$, $c$, and $f$. Which equation correctly expresses $c$ in terms of $b$ and $f$?

$c = \dfrac{b}{42f}$

$c = \dfrac{b - 42}{f}$

$c = 42bf$

$c = 42 - b - f$

1

$y = x + 9$
$y = x^2 + 16x + 63$
A solution to the given system of equations is $(x, y)$. What is the greatest possible value of $x$?

$-6$

$7$

$9$

$63$

1

$y + k = x + 26$
$y - k = x^2 - 5x$
In the given system of equations, $k$ is a constant. The system has exactly one distinct real solution. What is the value of $k$?

1

$x(x + 1) - 56 = 4x(x - 7)$
What is the sum of the solutions to the given equation?

1

$k^2 - 53 = 91$
What is the positive solution to the given equation?

144

72

38

12

1

Which ordered pair is a solution to the system of equations above?

(1 + square root of 3, square root of 3)

(square root of 3, − square root of 3)

(1 + square root of 5, square root of 5)

(square root of 5, −1 + square root of 5)

1

$|x - 9| + 45 = 63$
What is the sum of the solutions to the given equation?

1

How many solutions are there to the system of equations above?

There are exactly 4 solutions.

There are exactly 2 solutions.

There is exactly 1 solution.

There are no solutions.

1

The graph of the function $f$, defined by $f(x) = -\frac{1}{2}(x - 4)^2 + 10$, is shown in the $xy$-plane above. If the function $g$ (not shown) is defined by $g(x) = -x + 10$, what is one possible value of $a$ such that $f(a) = g(a)$?

1

$x^2 + y + 7 = 7$
$20x + 100 - y = 0$
The solution to the given system of equations is $(x, y)$. What is the value of $x$?

1

Blood volume, $V_B$, in a human can be determined using the equation $V_B = \dfrac{V_P}{1 - H}$, where $V_P$ is the plasma volume and $H$ is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and the plasma volume?

$H = 1 - \dfrac{V_P}{V_B}$

$H = \dfrac{V_B}{V_P}$

$H = 1 + \dfrac{V_B}{V_P}$

$H = V_B - V_P$

1

$-2x^2 + 20x + c = 0$
In the given equation, $c$ is a constant. The equation has exactly one solution. What is the value of $c$?

$-68$

$-50$

$-32$

$0$

PSAT: Advanced Math - Nonlinear equations in one variable and systems of equations in two variables

PSAT: Advanced Math - Nonlinear equations in one variable and systems of equations in two variables

$|p| + 61 = 65$Which value is a solution to the given equation?

$p = 20 + \dfrac{16}{n}$The given equation relates the numbers $p$ and $n$, where $n$ is not equal to $0$ and $p > 20$. Which equation correctly expresses $n$ in terms of $p$?

The graph of a system of a linear equation and a nonlinear equation is shown. What is the solution $(x, y)$ to this system?

$57x^2 + (57b + a)x + ab = 0$In the given equation, $a$ and $b$ are positive constants. The product of the solutions to the given equation is $kab$, where $k$ is a constant. What is the value of $k$?

The solutions to $x^2 + 6x + 7 = 0$ are $r$ and $s$, where $r < s$. The solutions to $x^2 + 8x + 8 = 0$ are $t$ and $u$, where $t < u$. The solutions to $x^2 + 14x + c = 0$, where $c$ is a constant, are $r + t$ and $s + u$. What is the value of $c$?

If $u - 3 = \dfrac{6}{t - 2}$, what is $t$ in terms of $u$?

$w^2 + 12w - 40 = 0$Which of the following is a solution to the given equation?

$|x - 2| = 9$What is one possible solution to the given equation?

$3x(x-4)(x+5)=0$What is one of the solutions to the given equation?

$x^2 = (22)(22)$What is the positive solution to the given equation?

The equation $12t + b = c$ relates the variables $t$, $b$, and $c$. Which of the following correctly expresses the value of $c - b$ in terms of $t$?

$\dfrac{4x^2}{x^2-9}-\dfrac{2x}{x+3}=\dfrac{1}{x-3}$What value of $x$ satisfies the equation above?

The total revenue from sales of a product can be calculated using the formula $T = PQ$, where $T$ is the total revenue, $P$ is the price of the product, and $Q$ is the quantity of the product sold. Which of the following equations gives the quantity of product sold in terms of $P$ and $T$?

$6r = 7s + t$The given equation relates the variables $r$, $s$, and $t$. Which equation correctly expresses $s$ in terms of $r$ and $t$?

What are the solutions to the given equation?

In the $xy$-plane, the graph of $y = x^2 - 9$ intersects line $p$ at $(1,a)$ and $(5,b)$, where $a$ and $b$ are constants. What is the slope of line $p$?

$P = \dfrac{W}{t}$The power $P$ produced by a machine is represented by the equation above, where $W$ is the work performed during an amount of time $t$. Which of the following correctly expresses $W$ in terms of $P$ and $t$?

$y = x^2$$2y + 6 = 2(x + 3)$If $(x, y)$ is a solution of the system of equations above and $x > 0$, what is the value of $xy$?

$\dfrac{14x}{7y} = 2\sqrt{w + 19}$The given equation relates the distinct positive real numbers $w$, $x$, and $y$. Which equation correctly expresses $w$ in terms of $x$ and $y$?

In the given equation, $c$ is a positive constant. Which of the following is one of the solutions to the given equation?$\dfrac{x^{2}}{\sqrt{x^{2}+c^{2}}} = \dfrac{c^{2}}{\sqrt{x^{2}-c^{2}}} + 39$

$|-5x + 13| = 73$What is the sum of the solutions to the given equation?

$14j + 5k = m$The given equation relates the numbers $j$, $k$, and $m$. Which equation correctly expresses $k$ in terms of $j$ and $m$?

$5(x + 7) = 15(x - 17)(x + 7)$What is the sum of the solutions to the given equation?

$-x^{2} + bx - 676 = 0$In the given equation, $b$ is a positive integer. The equation has no real solution. What is the greatest possible value of $b$?

$8j = k + 15m$The given equation relates the distinct positive numbers $j$, $k$, and $m$. Which equation correctly expresses $j$ in terms of $k$ and $m$?

$2x^2 - 8x - 7 = 0$One solution to the given equation can be written as $\frac{8 - \sqrt{k}}{4}$, where $k$ is a constant. What is the value of $k$?

$y = 5x + 4$$y = 5x^2 + 4$Which ordered pair $(x, y)$ is a solution to the given system of equations?

$7m = 2(n + p)$The given equation relates the positive numbers $m$, $n$, and $p$. Which equation correctly gives $m$ in terms of $n$ and $p$?

$x = 49$$y = \sqrt{x} + 9$The graphs of the given equations intersect at the point $(x, y)$ in the $xy$-plane. What is the value of $y$?

$x = 8a(b + 9)$The given equation relates the positive numbers $a$, $b$, and $x$. Which equation correctly expresses $a$ in terms of $b$ and $x$?

$x^2 - 5x - 24 = 0$What is the sum of the solutions to the given equation?

$y = 76$$y = x^2 - 5$The graphs of the given equations in the $xy$-plane intersect at the point $(x, y)$. What is a possible value of $x$?

What is the positive solution to the given equation?$-4x^2 - 7x = -36$

$y = x + 1$$y = x^2 + x$If $(x, y)$ is a solution to the system of equations above, which of the following could be the value of $x$?

$5\lvert x\rvert = 45$What is the positive solution to the given equation?

$y = x^2 + 1.7$$y = 1.7 - x$Which graph represents the given system of equations?

$(x + 2)(x - 5)(x + 9) = 0$What is a positive solution to the given equation?

$b = 42cf$The given equation relates the positive numbers $b$, $c$, and $f$. Which equation correctly expresses $c$ in terms of $b$ and $f$?

$y = x + 9$$y = x^2 + 16x + 63$A solution to the given system of equations is $(x, y)$. What is the greatest possible value of $x$?

$y + k = x + 26$$y - k = x^2 - 5x$In the given system of equations, $k$ is a constant. The system has exactly one distinct real solution. What is the value of $k$?

$x(x + 1) - 56 = 4x(x - 7)$What is the sum of the solutions to the given equation?

$k^2 - 53 = 91$What is the positive solution to the given equation?

Which ordered pair is a solution to the system of equations above?

$|x - 9| + 45 = 63$What is the sum of the solutions to the given equation?

How many solutions are there to the system of equations above?

The graph of the function $f$, defined by $f(x) = -\frac{1}{2}(x - 4)^2 + 10$, is shown in the $xy$-plane above. If the function $g$ (not shown) is defined by $g(x) = -x + 10$, what is one possible value of $a$ such that $f(a) = g(a)$?

$x^2 + y + 7 = 7$$20x + 100 - y = 0$The solution to the given system of equations is $(x, y)$. What is the value of $x$?

$-2x^2 + 20x + c = 0$In the given equation, $c$ is a constant. The equation has exactly one solution. What is the value of $c$?

$|p| + 61 = 65$Which value is a solution to the given equation?

$p = 20 + \dfrac{16}{n}$The given equation relates the numbers $p$ and $n$, where $n$ is not equal to $0$ and $p > 20$. Which equation correctly expresses $n$ in terms of $p$?

The graph of a system of a linear equation and a nonlinear equation is shown. What is the solution $(x, y)$ to this system?

$57x^2 + (57b + a)x + ab = 0$In the given equation, $a$ and $b$ are positive constants. The product of the solutions to the given equation is $kab$, where $k$ is a constant. What is the value of $k$?

The solutions to $x^2 + 6x + 7 = 0$ are $r$ and $s$, where $r < s$. The solutions to $x^2 + 8x + 8 = 0$ are $t$ and $u$, where $t < u$. The solutions to $x^2 + 14x + c = 0$, where $c$ is a constant, are $r + t$ and $s + u$. What is the value of $c$?

If $u - 3 = \dfrac{6}{t - 2}$, what is $t$ in terms of $u$?

$w^2 + 12w - 40 = 0$Which of the following is a solution to the given equation?

$|x - 2| = 9$What is one possible solution to the given equation?

$3x(x-4)(x+5)=0$What is one of the solutions to the given equation?

$x^2 = (22)(22)$What is the positive solution to the given equation?

The equation $12t + b = c$ relates the variables $t$, $b$, and $c$. Which of the following correctly expresses the value of $c - b$ in terms of $t$?

$\dfrac{4x^2}{x^2-9}-\dfrac{2x}{x+3}=\dfrac{1}{x-3}$What value of $x$ satisfies the equation above?

The total revenue from sales of a product can be calculated using the formula $T = PQ$, where $T$ is the total revenue, $P$ is the price of the product, and $Q$ is the quantity of the product sold. Which of the following equations gives the quantity of product sold in terms of $P$ and $T$?

$6r = 7s + t$The given equation relates the variables $r$, $s$, and $t$. Which equation correctly expresses $s$ in terms of $r$ and $t$?

What are the solutions to the given equation?

In the $xy$-plane, the graph of $y = x^2 - 9$ intersects line $p$ at $(1,a)$ and $(5,b)$, where $a$ and $b$ are constants. What is the slope of line $p$?

$P = \dfrac{W}{t}$The power $P$ produced by a machine is represented by the equation above, where $W$ is the work performed during an amount of time $t$. Which of the following correctly expresses $W$ in terms of $P$ and $t$?

$y = x^2$$2y + 6 = 2(x + 3)$If $(x, y)$ is a solution of the system of equations above and $x > 0$, what is the value of $xy$?

$\dfrac{14x}{7y} = 2\sqrt{w + 19}$The given equation relates the distinct positive real numbers $w$, $x$, and $y$. Which equation correctly expresses $w$ in terms of $x$ and $y$?

In the given equation, $c$ is a positive constant. Which of the following is one of the solutions to the given equation?$\dfrac{x^{2}}{\sqrt{x^{2}+c^{2}}} = \dfrac{c^{2}}{\sqrt{x^{2}-c^{2}}} + 39$

$|-5x + 13| = 73$What is the sum of the solutions to the given equation?

$14j + 5k = m$The given equation relates the numbers $j$, $k$, and $m$. Which equation correctly expresses $k$ in terms of $j$ and $m$?

$5(x + 7) = 15(x - 17)(x + 7)$What is the sum of the solutions to the given equation?

$-x^{2} + bx - 676 = 0$In the given equation, $b$ is a positive integer. The equation has no real solution. What is the greatest possible value of $b$?

$8j = k + 15m$The given equation relates the distinct positive numbers $j$, $k$, and $m$. Which equation correctly expresses $j$ in terms of $k$ and $m$?

$2x^2 - 8x - 7 = 0$One solution to the given equation can be written as $\frac{8 - \sqrt{k}}{4}$, where $k$ is a constant. What is the value of $k$?

$y = 5x + 4$$y = 5x^2 + 4$Which ordered pair $(x, y)$ is a solution to the given system of equations?

$7m = 2(n + p)$The given equation relates the positive numbers $m$, $n$, and $p$. Which equation correctly gives $m$ in terms of $n$ and $p$?

$x = 49$$y = \sqrt{x} + 9$The graphs of the given equations intersect at the point $(x, y)$ in the $xy$-plane. What is the value of $y$?

$x = 8a(b + 9)$The given equation relates the positive numbers $a$, $b$, and $x$. Which equation correctly expresses $a$ in terms of $b$ and $x$?

$|p| + 61 = 65$
Which value is a solution to the given equation?

$p = 20 + \dfrac{16}{n}$
The given equation relates the numbers $p$ and $n$, where $n$ is not equal to $0$ and $p > 20$. Which equation correctly expresses $n$ in terms of $p$?

$57x^2 + (57b + a)x + ab = 0$
In the given equation, $a$ and $b$ are positive constants. The product of the solutions to the given equation is $kab$, where $k$ is a constant. What is the value of $k$?

$w^2 + 12w - 40 = 0$
Which of the following is a solution to the given equation?

$|x - 2| = 9$
What is one possible solution to the given equation?

$3x(x-4)(x+5)=0$
What is one of the solutions to the given equation?

$x^2 = (22)(22)$
What is the positive solution to the given equation?

$\dfrac{4x^2}{x^2-9}-\dfrac{2x}{x+3}=\dfrac{1}{x-3}$
What value of $x$ satisfies the equation above?

$6r = 7s + t$
The given equation relates the variables $r$, $s$, and $t$. Which equation correctly expresses $s$ in terms of $r$ and $t$?

$P = \dfrac{W}{t}$
The power $P$ produced by a machine is represented by the equation above, where $W$ is the work performed during an amount of time $t$. Which of the following correctly expresses $W$ in terms of $P$ and $t$?

$y = x^2$
$2y + 6 = 2(x + 3)$
If $(x, y)$ is a solution of the system of equations above and $x > 0$, what is the value of $xy$?

$\dfrac{14x}{7y} = 2\sqrt{w + 19}$
The given equation relates the distinct positive real numbers $w$, $x$, and $y$. Which equation correctly expresses $w$ in terms of $x$ and $y$?

In the given equation, $c$ is a positive constant. Which of the following is one of the solutions to the given equation?
$\dfrac{x^{2}}{\sqrt{x^{2}+c^{2}}} = \dfrac{c^{2}}{\sqrt{x^{2}-c^{2}}} + 39$

$|-5x + 13| = 73$
What is the sum of the solutions to the given equation?

$14j + 5k = m$
The given equation relates the numbers $j$, $k$, and $m$. Which equation correctly expresses $k$ in terms of $j$ and $m$?

$5(x + 7) = 15(x - 17)(x + 7)$
What is the sum of the solutions to the given equation?

$-x^{2} + bx - 676 = 0$
In the given equation, $b$ is a positive integer. The equation has no real solution. What is the greatest possible value of $b$?

$8j = k + 15m$
The given equation relates the distinct positive numbers $j$, $k$, and $m$. Which equation correctly expresses $j$ in terms of $k$ and $m$?

$2x^2 - 8x - 7 = 0$
One solution to the given equation can be written as $\frac{8 - \sqrt{k}}{4}$, where $k$ is a constant. What is the value of $k$?

$y = 5x + 4$
$y = 5x^2 + 4$
Which ordered pair $(x, y)$ is a solution to the given system of equations?

$7m = 2(n + p)$
The given equation relates the positive numbers $m$, $n$, and $p$. Which equation correctly gives $m$ in terms of $n$ and $p$?

$x = 49$
$y = \sqrt{x} + 9$
The graphs of the given equations intersect at the point $(x, y)$ in the $xy$-plane. What is the value of $y$?

$x = 8a(b + 9)$
The given equation relates the positive numbers $a$, $b$, and $x$. Which equation correctly expresses $a$ in terms of $b$ and $x$?

$x^2 - 5x - 24 = 0$
What is the sum of the solutions to the given equation?

$y = 76$
$y = x^2 - 5$
The graphs of the given equations in the $xy$-plane intersect at the point $(x, y)$. What is a possible value of $x$?

What is the positive solution to the given equation?
$-4x^2 - 7x = -36$

$y = x + 1$
$y = x^2 + x$
If $(x, y)$ is a solution to the system of equations above, which of the following could be the value of $x$?

$5\lvert x\rvert = 45$
What is the positive solution to the given equation?

$y = x^2 + 1.7$
$y = 1.7 - x$
Which graph represents the given system of equations?

$(x + 2)(x - 5)(x + 9) = 0$
What is a positive solution to the given equation?

$b = 42cf$
The given equation relates the positive numbers $b$, $c$, and $f$. Which equation correctly expresses $c$ in terms of $b$ and $f$?

$y = x + 9$
$y = x^2 + 16x + 63$
A solution to the given system of equations is $(x, y)$. What is the greatest possible value of $x$?

$y + k = x + 26$
$y - k = x^2 - 5x$
In the given system of equations, $k$ is a constant. The system has exactly one distinct real solution. What is the value of $k$?

$x(x + 1) - 56 = 4x(x - 7)$
What is the sum of the solutions to the given equation?

$k^2 - 53 = 91$
What is the positive solution to the given equation?

$|x - 9| + 45 = 63$
What is the sum of the solutions to the given equation?

$x^2 + y + 7 = 7$
$20x + 100 - y = 0$
The solution to the given system of equations is $(x, y)$. What is the value of $x$?

$-2x^2 + 20x + c = 0$
In the given equation, $c$ is a constant. The equation has exactly one solution. What is the value of $c$?

$|p| + 61 = 65$
Which value is a solution to the given equation?

$p = 20 + \dfrac{16}{n}$
The given equation relates the numbers $p$ and $n$, where $n$ is not equal to $0$ and $p > 20$. Which equation correctly expresses $n$ in terms of $p$?

$57x^2 + (57b + a)x + ab = 0$
In the given equation, $a$ and $b$ are positive constants. The product of the solutions to the given equation is $kab$, where $k$ is a constant. What is the value of $k$?

$w^2 + 12w - 40 = 0$
Which of the following is a solution to the given equation?

$|x - 2| = 9$
What is one possible solution to the given equation?

$3x(x-4)(x+5)=0$
What is one of the solutions to the given equation?

$x^2 = (22)(22)$
What is the positive solution to the given equation?

$\dfrac{4x^2}{x^2-9}-\dfrac{2x}{x+3}=\dfrac{1}{x-3}$
What value of $x$ satisfies the equation above?

$6r = 7s + t$
The given equation relates the variables $r$, $s$, and $t$. Which equation correctly expresses $s$ in terms of $r$ and $t$?

$P = \dfrac{W}{t}$
The power $P$ produced by a machine is represented by the equation above, where $W$ is the work performed during an amount of time $t$. Which of the following correctly expresses $W$ in terms of $P$ and $t$?

$y = x^2$
$2y + 6 = 2(x + 3)$
If $(x, y)$ is a solution of the system of equations above and $x > 0$, what is the value of $xy$?

$\dfrac{14x}{7y} = 2\sqrt{w + 19}$
The given equation relates the distinct positive real numbers $w$, $x$, and $y$. Which equation correctly expresses $w$ in terms of $x$ and $y$?

In the given equation, $c$ is a positive constant. Which of the following is one of the solutions to the given equation?
$\dfrac{x^{2}}{\sqrt{x^{2}+c^{2}}} = \dfrac{c^{2}}{\sqrt{x^{2}-c^{2}}} + 39$

$|-5x + 13| = 73$
What is the sum of the solutions to the given equation?

$14j + 5k = m$
The given equation relates the numbers $j$, $k$, and $m$. Which equation correctly expresses $k$ in terms of $j$ and $m$?

$5(x + 7) = 15(x - 17)(x + 7)$
What is the sum of the solutions to the given equation?

$-x^{2} + bx - 676 = 0$
In the given equation, $b$ is a positive integer. The equation has no real solution. What is the greatest possible value of $b$?

$8j = k + 15m$
The given equation relates the distinct positive numbers $j$, $k$, and $m$. Which equation correctly expresses $j$ in terms of $k$ and $m$?

$2x^2 - 8x - 7 = 0$
One solution to the given equation can be written as $\frac{8 - \sqrt{k}}{4}$, where $k$ is a constant. What is the value of $k$?

$y = 5x + 4$
$y = 5x^2 + 4$
Which ordered pair $(x, y)$ is a solution to the given system of equations?

$7m = 2(n + p)$
The given equation relates the positive numbers $m$, $n$, and $p$. Which equation correctly gives $m$ in terms of $n$ and $p$?

$x = 49$
$y = \sqrt{x} + 9$
The graphs of the given equations intersect at the point $(x, y)$ in the $xy$-plane. What is the value of $y$?

$x = 8a(b + 9)$
The given equation relates the positive numbers $a$, $b$, and $x$. Which equation correctly expresses $a$ in terms of $b$ and $x$?

$x^2 - 5x - 24 = 0$
What is the sum of the solutions to the given equation?

$y = 76$
$y = x^2 - 5$
The graphs of the given equations in the $xy$-plane intersect at the point $(x, y)$. What is a possible value of $x$?

What is the positive solution to the given equation?
$-4x^2 - 7x = -36$

$y = x + 1$
$y = x^2 + x$
If $(x, y)$ is a solution to the system of equations above, which of the following could be the value of $x$?

$5\lvert x\rvert = 45$
What is the positive solution to the given equation?

$y = x^2 + 1.7$
$y = 1.7 - x$
Which graph represents the given system of equations?

$(x + 2)(x - 5)(x + 9) = 0$
What is a positive solution to the given equation?

$b = 42cf$
The given equation relates the positive numbers $b$, $c$, and $f$. Which equation correctly expresses $c$ in terms of $b$ and $f$?

$y = x + 9$
$y = x^2 + 16x + 63$
A solution to the given system of equations is $(x, y)$. What is the greatest possible value of $x$?

$y + k = x + 26$
$y - k = x^2 - 5x$
In the given system of equations, $k$ is a constant. The system has exactly one distinct real solution. What is the value of $k$?

$x(x + 1) - 56 = 4x(x - 7)$
What is the sum of the solutions to the given equation?

$k^2 - 53 = 91$
What is the positive solution to the given equation?

$|x - 9| + 45 = 63$
What is the sum of the solutions to the given equation?

$x^2 + y + 7 = 7$
$20x + 100 - y = 0$
The solution to the given system of equations is $(x, y)$. What is the value of $x$?

$-2x^2 + 20x + c = 0$
In the given equation, $c$ is a constant. The equation has exactly one solution. What is the value of $c$?