Numbers & Operations

Problem 2101

Find the least common denominator (LCD) of the rational expressions $\frac{x}{x^{2}-4}, \frac{3}{x}, \frac{9}{8-4x}$ . The LCD is $\frac{(x^{2}-4)x(8-4x)}{x(8-4x)}$ .

See Solution

Problem 2102

Solve for y, where 6 is greater than or equal to (y/8) - 4.

See Solution

Problem 2103

Solve the system of linear equations $4x - y = 11$ and $x + y = 4$ using the elimination method. The system has no solution.

See Solution

Problem 2104

Find the solutions to the equation $4x+21=-\left(\frac{1}{3}\right)^{x+4}+6$ .

See Solution

Problem 2105

Find the cost of 4 potted plants and 5 bags of compost given the costs of 7 plants + 2 compost and 3 plants + 4 compost.
Cost of 7 potted plants and 2 bags of compost: $£ 41$ Cost of 3 potted plants and 4 bags of compost: $£ 27$

See Solution

Problem 2106

Compare the doubling times using approximate and exact formulas. Find the population after 30 years if a nation of 100 million grows at $9\%$ per year.
The approximate doubling time is $\frac{\ln(2)}{\ln(1.09)} \approx \square$ years and the exact doubling time is $\frac{\ln(2)}{\ln(1.09)} \approx \square$ years.

See Solution

Problem 2107

Solve for the value of $f$ that satisfies the inequality $-21 > 13 - 17f$ .

See Solution

Problem 2108

Simplify the expression $25 a^{2} - 4 b^{2}$ to find the preferred form.

See Solution

Problem 2109

Verify identity $\frac{1-\cos \theta}{\sin \theta}+\frac{\sin \theta}{1-\cos \theta}=2 \csc \theta$ . Simplify numerator $1+\sin^2 \theta$ .

See Solution

Problem 2110

Solve the equation $2x=26$ . Which operation should be performed to isolate $x$ ?

See Solution

Problem 2111

Find the quadratic function equation from the given table of $(x, y)$ values: $y = a(x - b)^2 + c$

See Solution

Problem 2112

Solve the system of linear equations: $50x - 5y = -75$ , $y = 2$ , $y = 2x$ .

See Solution

Problem 2113

Subtract the two polynomials: $\left(3 x^{5}-2 x^{4}-5\right)-\left(2 x^{4}+x^{2}-10\right)$ .

See Solution

Problem 2114

Find the division equation representing $6,720 \div 21=?$ . Also find the corresponding multiplication equations.

See Solution

Problem 2115

Find the value of $m$ and evaluate $x+14$ when $x=8$ .

See Solution

Problem 2116

Camelle needs to order 4 practice jerseys for each of $y$ players. How many total practice jerseys does she need to order?

See Solution

Problem 2117

Find the value of y when $\frac{\sin 30}{23}=\frac{\sin y}{42}$ .

See Solution

Problem 2118

Find the value of $(-2)^{4}(-2)^{-1}$ .

See Solution

Problem 2119

Solve for $w$ in the equation $\frac{w}{3}-14=26$ .

See Solution

Problem 2120

Find an equation with zeros at -3 and 13, passing through (4,21). Express in factored form $y=a(x-(-3))(x-13)$ and general form $y=a x^{2}+b x+c$ .

See Solution

Problem 2121

Solve for $x$ and express your answers as exact roots: (a) $(x-3)^2 = 4$ , (b) $(x+2)^2 = 9$ .

See Solution

Problem 2122

Find the quadratic function with zeros at $x=0$ and $x=4$ that passes through the point $(-1,-10)$ .

See Solution

Problem 2123

Solve for $v$ in the equation $63=5v-17$ .

See Solution

Problem 2124

Identify the graph of $f(x)=x^{2}-25$ . Label the vertex, axis of symmetry, and x-intercepts. Find the domain (all real numbers) and range.

See Solution

Problem 2125

What does $k$ represent in $\mathbf{y}=\mathbf{k x}$ ? Constant of proportionality.

See Solution

Problem 2126

Simplify $x^{5}y^{3}(-9y^{3})$

See Solution

Problem 2127

Find the exact value of $\tan 165^\circ$ using a half-angle identity.

See Solution

Problem 2128

Solve the system of linear equations $x-2y=6, 2x+5y=3$ and classify it. Solve the system $y=2x-6, 4x-2y=12$ and classify it.

See Solution

Problem 2129

Determine the total number of subjects, the number who did not use marijuana, and the probability a random subject did not use marijuana given drug test results.
Total subjects: $\square$ Subjects who did not use marijuana: $\square$ Probability a random subject did not use marijuana: $\square$

See Solution

Problem 2130

If $f^{-1}$ is the inverse of $f$ , then $f$ and $f^{-1}$ graphs are symmetric about $y=x$ .

See Solution

Problem 2131

Simplify the expression $7(3x + 3) - 5$ .

See Solution

Problem 2132

Find the solution to $-4|-2 x+6|=-24$ . The possible solutions are $x=0$ or $x=-6$ .

See Solution

Problem 2133

Find values of $x$ satisfying $2|x+5.3|=4.2$ . $x$ can be -3.2 or 7.4.

See Solution

Problem 2134

Convert 244 centiliters to milliliters.

See Solution

Problem 2135

Find the amounts of two Italian dressings (6% and 12% vinegar) to make 330 mL of 11% vinegar dressing.

See Solution

Problem 2136

Find the 25th and 90th percentiles of serum cholesterol levels (mg/dL) for 15 individuals: $198, 259, 196, 249, 186, 240, 208, 222, 218, 191, 244, 257, 254, 211, 189$ . (a) 25th percentile: $[\frac{\mathrm{mg}}{\mathrm{dL}}]$ . (b) 90th percentile: $\square \frac{\mathrm{mg}}{\mathrm{dL}}$ .

See Solution

Problem 2137

Solve for the value of $x$ that satisfies the equation $2(4x + 7) = 62$ .

See Solution

Problem 2138

Graph the exponential function $g(x) = \frac{1}{4}(5)^{x}$ . Plot 5 points on the graph and use the graph-a-function tool.

See Solution

Problem 2139

Determine which choice, if any, uses deductive reasoning to show that the sum of 3 even integers is even.
$2x + 2y + 2z = 2(x + y + z)$

See Solution

Problem 2140

Solve radical equations using isolation, squaring, and checking for extraneous solutions. Practice: $\sqrt{6 x+9}+2=11$ , $\sqrt{x-3}+3=x$ .

See Solution

Problem 2141

Solve the two-step equation $-0.45 x+0.33=-0.66$ . What is the solution?

See Solution

Problem 2142

Add numbers on a number line. (a) $5+9$ (b) $3+2$

See Solution

Problem 2143

Find the real roots of each quadratic equation. If no real roots, use a graph to explain. a) $0=x^{2}-4x+3$ b) $0=2x^{2}-7x-15$ c) $0=-x^{2}-2x+3$

See Solution

Problem 2144

Find the missing trigonometric function values for a 30° angle without using a calculator.

See Solution

Problem 2145

Find the equation with the correct sign on the product of the numbers.
A. $17 \cdot 3=-51$ B. $(-11) 9=99$ C. $25(-5)=125$ D. $(-12)(-12)=144$

See Solution

Problem 2146

Simplify the expression $(x-3y)-(3x+3y)$ .

See Solution

Problem 2147

Convert the equation from vertex form to standard form: $y = (x + 4)^{2} - 12$

See Solution

Problem 2148

Solve for $x$ in the equation $x - (-6) = 15$ .

See Solution

Problem 2149

Find the degree 4 Maclaurin polynomial for $(1+x)^{1/3}$ and use it to approximate $\sqrt[3]{1.1}$ .

See Solution

Problem 2150

Solve the expression $2^{3}-8 \div 4 \times 2+7$ using the order of operations.

See Solution

Problem 2151

Find the equation that matches "38 minus a number is 19".
A. $38-n=19$ B. $\frac{38}{n}=19$ C. $\frac{n}{19}=38$ D. $n-38=19$

See Solution

Problem 2152

Find a situation that can be represented by the equation $x+14=25$ .

See Solution

Problem 2153

Find the formula for the binomial probability mass function $p(x)$ with $n=7$ and $p=0.8$ . $p(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x}$ for $x=0,1,2,\ldots,7$ .

See Solution

Problem 2154

Find the roots of the cubic equation $x^3 - 5x^2 + 2x + 8 = 0$ given that $-1$ is a root.

See Solution

Problem 2155

Find the sum of $343$ and $636$ .

See Solution

Problem 2156

Solve for $x$ in the equation $10^{x}=50$ .

See Solution

Problem 2157

Find the value of $9m-1$ when $m=2$ .

See Solution

Problem 2158

Find the product of $y^{4}$ and $y^{3}$ .

See Solution

Problem 2159

Simplify the expression: $\left(\frac{4r^{2}}{r^{-4}}\right)^{-2}$ .

See Solution

Problem 2160

Describe the transformation(s) of polynomial $p(x) = -3(x-2)(x-4)(x+1)$ when transformed to $-p(x)$ .

See Solution

Problem 2161

Solve for the variable $v$ given the equation $56=14v$ .

See Solution

Problem 2162

Graph the square root function $f(x) = \sqrt{x + 2}$ over the domain $-2 \leq x \leq 7$ .

See Solution

Problem 2163

Find the vector $2\vec{v}-\vec{u}$ given $\vec{u}=[5,-3,-1]$ and $\vec{v}=[2,-1,4]$ . [2 marks]

See Solution

Problem 2164

Find the inverse function $f^{-1}(x)$ of $f(x)=\sqrt{7x+2}$ where $x \geq -\frac{2}{7}$ .

See Solution

Problem 2165

Find the number $x$ such that $4x + 9 = 2x - 1$ .

See Solution

Problem 2166

Factor the expression $30 x^{2} + 14 y^{4} x^{3}$ using the greatest common factor.

See Solution

Problem 2167

In Alabama, 44% of the population favors the incumbent for governor. Find the probability that at least 72 out of 150 randomly sampled respondents favor the incumbent, using a normal approximation with continuity correction.
$X \sim \text{Binomial}(n=150, p=0.44)$
$P(X \geq 72)$
$Y \sim \text{Normal}(\mu=66, \sigma=5.24)$
$P(Y \geq 71.5)$
Use continuity correction
Probability: 0.8001

See Solution

Problem 2168

Solve the quadratic equation $4x^2 = 1.0 - x$ for x.

See Solution

Problem 2169

Find the statement that represents the equation $\frac{2}{5} x+9=9$ .

See Solution

Problem 2170

Liv and 2 friends each have $\frac{1}{6}$ of the original stack of programs. Show work: Liv has $\frac{1}{2}$ of the stack, which she divides equally among herself and 2 friends, giving each $\frac{1}{6}$ of the original stack.

See Solution

Problem 2171

Luis and Kelly have $32 total dollars. If Luis has$ x $and Kelly has$ y $, then the equation$ x + y = 32$ best models this relationship.

See Solution

Problem 2172

Solve the equation $-11x-7=-3x^2$ to the nearest tenth.

See Solution

Problem 2173

Find the value of $b$ when $x=12$ , given the equation $2b + 3(b + x) - 6 = 70$ .

See Solution

Problem 2174

Solve the equation $x \cdot 12 = -4(-6x - 3)$ for $x$ .

See Solution

Problem 2175

Find the largest value among $\{0.0827, 0.093, 0.4, 0.56\}$ .

See Solution

Problem 2176

Find the value of a piecewise function $w(t)$ when $t=-7$ .

See Solution

Problem 2177

Find the homogeneous solution (no constants) for the difference equation: $x_{n+3} - 9 x_{n+2} + 27 x_{n+1} - 27 x_{n} = 0$ .

See Solution

Problem 2178

Solve for the value of $s$ in the equation $\frac{6}{7} \cdot s = 4$ .

See Solution

Problem 2179

Solve for $p$ in the equation $p-9=25$ . The solution is $p=34$ .

See Solution

Problem 2180

Solve the equation $\frac{16^{1/3}}{4^{x/3}}=1$ to find the value of $x$ .

See Solution

Problem 2181

Find the difference between $(10 m+3)$ and $(4 m-2)$ . Options: A) $14 m-1$ , B) $6 m+5$ , C) $6 m-1$ , D) $14 m+5$ .

See Solution

Problem 2182

Solve for $f$ where $1.9 + 3f = -14$ .

See Solution

Problem 2183

Find the solution to the differential equation $\frac{d y}{d x}=e^{2 x}+2 y$ . Options: A. $y=e^{2 x}$ , B. $y=-e^{2 x}$ , C. $y=x e^{2 x}$ , D. $y=-x e^{2 x}$ .

See Solution

Problem 2184

Finden Sie die Lösungen für das lineare Gleichungssystem $x+y=2$ und $x=1.5y-8$ .

See Solution

Problem 2185

Solve the system of linear equations: $-8x = -7x + 10, x = 10$ . Find the values of $x, X$ .

See Solution

Problem 2186

Find linear relation between $x$ and $y$ from given data points. Determine the correct linear equation $y=mx$ .

See Solution

Problem 2187

Explain why the graph of $y=-2 \sqrt[3]{x}$ is continuous but not differentiable at $x=0$ .

See Solution

Problem 2188

Solve for t the absolute value equation: |5t-8|+1=10.

See Solution

Problem 2189

Find the derivative of the function $h(x) = e^{2x^2} - 9x + 3/x$ .

See Solution

Problem 2190

Simplify the expressions using product-to-sum-to-product: $\cos (7 x) \cos (4 x)$ and $\sin (8 x)-\sin (2 x)$ .

See Solution

Problem 2191

Find the best model equation for the pea plant height data over 10 days: $y=0.3x+2.9$ , $y=0.5x+2.4$ , $y=2.8\cdot(1.1^x)$ , or $y=2.5\cdot(1.2^x)$ .

See Solution

Problem 2192

Solve the linear equation $-(2x-8)=-3x+\frac{1}{2}(12x-6)$ for the unknown variable $x$ .

See Solution

Problem 2193

Solve the proportion $\frac{8}{y}=\frac{9}{12}$ to find the value of $y$ .

See Solution

Problem 2194

Find the cost per litre of engine oil if a 11-litre drum costs $336. Calculate the cost per litre.

See Solution

Problem 2195

Use synthetic division to simplify $\frac{x^{5}-2 x^{4}+8 x^{3}-28 x^{2}+15 x-9}{x-2}$ . Write the result as $q(x) + \frac{r}{d(x)}$ , where $q(x)$ is a polynomial, $r$ is an integer, and $d(x)$ is a linear polynomial. Simplify any fractions.

See Solution

Problem 2196

Evaluate $\frac{3 x(4-x)^{2}}{7 x-4}$ : which operation should be done first?

See Solution

Problem 2197

Find 4 paths to (1,-1) to show $\lim_{(x,y)\to(1,-1)} f(x,y)$ doesn't exist for $f(x,y)$ . Provide curve equations and graphs.

See Solution

Problem 2198

Solve the quadratic equation $y^{2} = -8x$ for $y$ .

See Solution

Problem 2199

Differentiate $y=(x+2)(x^{3}+2x+1)$ and choose the correct setup.

See Solution

Problem 2200

Find the closest bond angle around the central atom in $\mathrm{SO}_{4}^{-2}$ ions: $109.5^{\circ}$ , $120^{\circ}$ , or $90^{\circ}$ ?

See Solution

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Numbers & Operations

Problem 2101

Find the least common denominator (LCD) of the rational expressions xx2−4,3x,98−4x\frac{x}{x^{2}-4}, \frac{3}{x}, \frac{9}{8-4x}x2−4x​,x3​,8−4x9​. The LCD is (x2−4)x(8−4x)x(8−4x)\frac{(x^{2}-4)x(8-4x)}{x(8-4x)}x(8−4x)(x2−4)x(8−4x)​.

Problem 2102

Solve for y, where 6 is greater than or equal to (y/8) - 4.

Problem 2103

Solve the system of linear equations 4x−y=114x - y = 114x−y=11 and x+y=4x + y = 4x+y=4 using the elimination method. The system has no solution.

Problem 2104

Find the solutions to the equation 4x+21=−(13)x+4+64x+21=-\left(\frac{1}{3}\right)^{x+4}+64x+21=−(31​)x+4+6.

Problem 2105

Find the cost of 4 potted plants and 5 bags of compost given the costs of 7 plants + 2 compost and 3 plants + 4 compost.Cost of 7 potted plants and 2 bags of compost: £41£ 41£41 Cost of 3 potted plants and 4 bags of compost: £27£ 27£27

Problem 2106

Problem 2107

Solve for the value of fff that satisfies the inequality −21>13−17f-21 > 13 - 17f−21>13−17f.

Problem 2108

Simplify the expression 25a2−4b225 a^{2} - 4 b^{2}25a2−4b2 to find the preferred form.

Problem 2109

Verify identity 1−cos⁡θsin⁡θ+sin⁡θ1−cos⁡θ=2csc⁡θ\frac{1-\cos \theta}{\sin \theta}+\frac{\sin \theta}{1-\cos \theta}=2 \csc \thetasinθ1−cosθ​+1−cosθsinθ​=2cscθ. Simplify numerator 1+sin⁡2θ1+\sin^2 \theta1+sin2θ.

Problem 2110

Solve the equation 2x=262x=262x=26. Which operation should be performed to isolate xxx?

Problem 2111

Find the quadratic function equation from the given table of (x,y)(x, y)(x,y) values: y=a(x−b)2+cy = a(x - b)^2 + cy=a(x−b)2+c

Problem 2112

Solve the system of linear equations: 50x−5y=−7550x - 5y = -7550x−5y=−75, y=2y = 2y=2, y=2xy = 2xy=2x.

Problem 2113

Subtract the two polynomials: (3x5−2x4−5)−(2x4+x2−10)\left(3 x^{5}-2 x^{4}-5\right)-\left(2 x^{4}+x^{2}-10\right)(3x5−2x4−5)−(2x4+x2−10).

Problem 2114

Find the division equation representing 6,720÷21=?6,720 \div 21=?6,720÷21=?. Also find the corresponding multiplication equations.

Problem 2115

Find the value of mmm and evaluate x+14x+14x+14 when x=8x=8x=8.

Problem 2116

Camelle needs to order 4 practice jerseys for each of yyy players. How many total practice jerseys does she need to order?

Problem 2117

Find the value of y when sin⁡3023=sin⁡y42\frac{\sin 30}{23}=\frac{\sin y}{42}23sin30​=42siny​.

Problem 2118

Find the value of (−2)4(−2)−1(-2)^{4}(-2)^{-1}(−2)4(−2)−1.

Problem 2119

Solve for www in the equation w3−14=26\frac{w}{3}-14=263w​−14=26.

Problem 2120

Find an equation with zeros at -3 and 13, passing through (4,21). Express in factored form y=a(x−(−3))(x−13)y=a(x-(-3))(x-13)y=a(x−(−3))(x−13) and general form y=ax2+bx+cy=a x^{2}+b x+cy=ax2+bx+c.

Problem 2121

Solve for xxx and express your answers as exact roots: (a) (x−3)2=4(x-3)^2 = 4(x−3)2=4, (b) (x+2)2=9(x+2)^2 = 9(x+2)2=9.

Problem 2122

Find the quadratic function with zeros at x=0x=0x=0 and x=4x=4x=4 that passes through the point (−1,−10)(-1,-10)(−1,−10).

Problem 2123

Solve for vvv in the equation 63=5v−1763=5v-1763=5v−17.

Problem 2124

Identify the graph of f(x)=x2−25f(x)=x^{2}-25f(x)=x2−25. Label the vertex, axis of symmetry, and x-intercepts. Find the domain (all real numbers) and range.

Problem 2125

What does kkk represent in y=kx\mathbf{y}=\mathbf{k x}y=kx? Constant of proportionality.

Problem 2126

Simplify x5y3(−9y3)x^{5}y^{3}(-9y^{3})x5y3(−9y3)

Problem 2127

Find the exact value of tan⁡165∘\tan 165^\circtan165∘ using a half-angle identity.

Problem 2128

Solve the system of linear equations x−2y=6,2x+5y=3x-2y=6, 2x+5y=3x−2y=6,2x+5y=3 and classify it. Solve the system y=2x−6,4x−2y=12y=2x-6, 4x-2y=12y=2x−6,4x−2y=12 and classify it.

Problem 2129

Problem 2130

If f−1f^{-1}f−1 is the inverse of fff, then fff and f−1f^{-1}f−1 graphs are symmetric about y=xy=xy=x.

Problem 2131

Simplify the expression 7(3x+3)−57(3x + 3) - 57(3x+3)−5.

Problem 2132

Find the solution to −4∣−2x+6∣=−24-4|-2 x+6|=-24−4∣−2x+6∣=−24. The possible solutions are x=0x=0x=0 or x=−6x=-6x=−6.

Problem 2133

Find values of xxx satisfying 2∣x+5.3∣=4.22|x+5.3|=4.22∣x+5.3∣=4.2. xxx can be -3.2 or 7.4.

Problem 2134

Convert 244 centiliters to milliliters.

Problem 2135

Find the amounts of two Italian dressings (6% and 12% vinegar) to make 330 mL of 11% vinegar dressing.

Problem 2136

Problem 2137

Solve for the value of xxx that satisfies the equation 2(4x+7)=622(4x + 7) = 622(4x+7)=62.

Problem 2138

Graph the exponential function g(x)=14(5)xg(x) = \frac{1}{4}(5)^{x}g(x)=41​(5)x. Plot 5 points on the graph and use the graph-a-function tool.

Problem 2139

Determine which choice, if any, uses deductive reasoning to show that the sum of 3 even integers is even.2x+2y+2z=2(x+y+z)2x + 2y + 2z = 2(x + y + z)2x+2y+2z=2(x+y+z)

Problem 2140

Solve radical equations using isolation, squaring, and checking for extraneous solutions. Practice: 6x+9+2=11\sqrt{6 x+9}+2=116x+9​+2=11, x−3+3=x\sqrt{x-3}+3=xx−3​+3=x.

Problem 2141

Solve the two-step equation −0.45x+0.33=−0.66-0.45 x+0.33=-0.66−0.45x+0.33=−0.66. What is the solution?

Find the least common denominator (LCD) of the rational expressions $\frac{x}{x^{2}-4}, \frac{3}{x}, \frac{9}{8-4x}$ . The LCD is $\frac{(x^{2}-4)x(8-4x)}{x(8-4x)}$ .

Solve the system of linear equations $4x - y = 11$ and $x + y = 4$ using the elimination method. The system has no solution.

Find the solutions to the equation $4x+21=-\left(\frac{1}{3}\right)^{x+4}+6$ .

Find the cost of 4 potted plants and 5 bags of compost given the costs of 7 plants + 2 compost and 3 plants + 4 compost.
Cost of 7 potted plants and 2 bags of compost: $£ 41$ Cost of 3 potted plants and 4 bags of compost: $£ 27$

Solve for the value of $f$ that satisfies the inequality $-21 > 13 - 17f$ .

Simplify the expression $25 a^{2} - 4 b^{2}$ to find the preferred form.

Verify identity $\frac{1-\cos \theta}{\sin \theta}+\frac{\sin \theta}{1-\cos \theta}=2 \csc \theta$ . Simplify numerator $1+\sin^2 \theta$ .

Solve the equation $2x=26$ . Which operation should be performed to isolate $x$ ?

Find the quadratic function equation from the given table of $(x, y)$ values: $y = a(x - b)^2 + c$

Solve the system of linear equations: $50x - 5y = -75$ , $y = 2$ , $y = 2x$ .

Subtract the two polynomials: $\left(3 x^{5}-2 x^{4}-5\right)-\left(2 x^{4}+x^{2}-10\right)$ .

Find the division equation representing $6,720 \div 21=?$ . Also find the corresponding multiplication equations.

Find the value of $m$ and evaluate $x+14$ when $x=8$ .

Camelle needs to order 4 practice jerseys for each of $y$ players. How many total practice jerseys does she need to order?

Find the value of y when $\frac{\sin 30}{23}=\frac{\sin y}{42}$ .

Find the value of $(-2)^{4}(-2)^{-1}$ .

Solve for $w$ in the equation $\frac{w}{3}-14=26$ .

Find an equation with zeros at -3 and 13, passing through (4,21). Express in factored form $y=a(x-(-3))(x-13)$ and general form $y=a x^{2}+b x+c$ .

Solve for $x$ and express your answers as exact roots: (a) $(x-3)^2 = 4$ , (b) $(x+2)^2 = 9$ .

Find the quadratic function with zeros at $x=0$ and $x=4$ that passes through the point $(-1,-10)$ .

Solve for $v$ in the equation $63=5v-17$ .

Identify the graph of $f(x)=x^{2}-25$ . Label the vertex, axis of symmetry, and x-intercepts. Find the domain (all real numbers) and range.

What does $k$ represent in $\mathbf{y}=\mathbf{k x}$ ? Constant of proportionality.

Simplify $x^{5}y^{3}(-9y^{3})$

Find the exact value of $\tan 165^\circ$ using a half-angle identity.

Solve the system of linear equations $x-2y=6, 2x+5y=3$ and classify it. Solve the system $y=2x-6, 4x-2y=12$ and classify it.

If $f^{-1}$ is the inverse of $f$ , then $f$ and $f^{-1}$ graphs are symmetric about $y=x$ .

Simplify the expression $7(3x + 3) - 5$ .

Find the solution to $-4|-2 x+6|=-24$ . The possible solutions are $x=0$ or $x=-6$ .

Find values of $x$ satisfying $2|x+5.3|=4.2$ . $x$ can be -3.2 or 7.4.

Solve for the value of $x$ that satisfies the equation $2(4x + 7) = 62$ .

Graph the exponential function $g(x) = \frac{1}{4}(5)^{x}$ . Plot 5 points on the graph and use the graph-a-function tool.

Determine which choice, if any, uses deductive reasoning to show that the sum of 3 even integers is even.
$2x + 2y + 2z = 2(x + y + z)$

Solve radical equations using isolation, squaring, and checking for extraneous solutions. Practice: $\sqrt{6 x+9}+2=11$ , $\sqrt{x-3}+3=x$ .

Solve the two-step equation $-0.45 x+0.33=-0.66$ . What is the solution?

Add numbers on a number line. (a) $5+9$ (b) $3+2$

Find the real roots of each quadratic equation. If no real roots, use a graph to explain. a) $0=x^{2}-4x+3$ b) $0=2x^{2}-7x-15$ c) $0=-x^{2}-2x+3$

Find the equation with the correct sign on the product of the numbers.
A. $17 \cdot 3=-51$ B. $(-11) 9=99$ C. $25(-5)=125$ D. $(-12)(-12)=144$

Simplify the expression $(x-3y)-(3x+3y)$ .

Convert the equation from vertex form to standard form: $y = (x + 4)^{2} - 12$

Solve for $x$ in the equation $x - (-6) = 15$ .

Find the degree 4 Maclaurin polynomial for $(1+x)^{1/3}$ and use it to approximate $\sqrt[3]{1.1}$ .

Solve the expression $2^{3}-8 \div 4 \times 2+7$ using the order of operations.

Find the equation that matches "38 minus a number is 19".
A. $38-n=19$ B. $\frac{38}{n}=19$ C. $\frac{n}{19}=38$ D. $n-38=19$

Find a situation that can be represented by the equation $x+14=25$ .

Find the formula for the binomial probability mass function $p(x)$ with $n=7$ and $p=0.8$ . $p(x) = \binom{7}{x}(0.8)^x(0.2)^{7-x}$ for $x=0,1,2,\ldots,7$ .

Find the roots of the cubic equation $x^3 - 5x^2 + 2x + 8 = 0$ given that $-1$ is a root.

Find the sum of $343$ and $636$ .

Solve for $x$ in the equation $10^{x}=50$ .

Find the value of $9m-1$ when $m=2$ .

Find the product of $y^{4}$ and $y^{3}$ .

Simplify the expression: $\left(\frac{4r^{2}}{r^{-4}}\right)^{-2}$ .

Describe the transformation(s) of polynomial $p(x) = -3(x-2)(x-4)(x+1)$ when transformed to $-p(x)$ .

Solve for the variable $v$ given the equation $56=14v$ .

Graph the square root function $f(x) = \sqrt{x + 2}$ over the domain $-2 \leq x \leq 7$ .

Find the vector $2\vec{v}-\vec{u}$ given $\vec{u}=[5,-3,-1]$ and $\vec{v}=[2,-1,4]$ . [2 marks]

Find the inverse function $f^{-1}(x)$ of $f(x)=\sqrt{7x+2}$ where $x \geq -\frac{2}{7}$ .

Find the number $x$ such that $4x + 9 = 2x - 1$ .

Factor the expression $30 x^{2} + 14 y^{4} x^{3}$ using the greatest common factor.

Solve the quadratic equation $4x^2 = 1.0 - x$ for x.

Find the statement that represents the equation $\frac{2}{5} x+9=9$ .

Liv and 2 friends each have $\frac{1}{6}$ of the original stack of programs. Show work: Liv has $\frac{1}{2}$ of the stack, which she divides equally among herself and 2 friends, giving each $\frac{1}{6}$ of the original stack.

Luis and Kelly have $32 total dollars. If Luis has$ x $and Kelly has$ y $, then the equation$ x + y = 32$ best models this relationship.

Solve the equation $-11x-7=-3x^2$ to the nearest tenth.

Find the value of $b$ when $x=12$ , given the equation $2b + 3(b + x) - 6 = 70$ .

Solve the equation $x \cdot 12 = -4(-6x - 3)$ for $x$ .