Browse Math problems in the Studdy Learning Bank!

Problem 101

Simplify the expression: $(6+2y)\cdot 3$ and $(2x-3)\cdot 4$

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Problem 102

Find the equation of an absolute value function with vertex at $(-3, -1)$ , opening upwards, and passing through $(0, 2)$ .

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Problem 103

Write the elevation of a telescope, about 2500 meters above sea level, in scientific notation. $2500 = 2.5 \times 10^3$

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Problem 104

Find the roots of the quadratic equation $2x^2 - x - 28 = 0$ by factoring.

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Problem 105

Find $x$ such that $x m = \frac{n}{p}$ .

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Problem 106

Solve for the unknown variable $m$ in the equation $4+m=12$ .

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Problem 107

Pick a random card, then pick a second without replacing the first. What is the probability of getting an 8 then an even number? Express as a simplified fraction.

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Problem 108

Solve for $x$ in the equation $4x + 6 = 2 \frac{1}{2}x + 12$ using inverse operations.

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Problem 109

Match $x$ values to corresponding $y$ values based on their arrangement.

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Problem 110

Multiply binomials $(8p + 4q)(p - 3q)$ and collect like terms.

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Problem 111

Solve for $x$ in the equation $169^{-x}=\frac{1}{\sqrt{13}}$ .

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Problem 112

Find the min/max value and axis of symmetry for $f(x)=-3 x^{2}+12 x-8$ . The $y$ -value of the extremum is the solution.

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Problem 113

Convert -39.825 to a mixed number.

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Problem 114

Identify constant and variable terms: $-9 x^{2}$ (constant), $-3 x y$ (variable), $-\vee-3$ (constant), $-\frac{1}{2}$ (constant), 8.1 (constant), $17 x$ (variable), $-14 a$ (variable).

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Problem 115

Find the exact value of $\tan(2\pi/3)$ .

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Problem 116

Complete the table for the linear equation $4x-3y=12$ and graph the equation.

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Problem 117

Evaluate the rational expression $\frac{x-4}{9x+2}$ for $x=-1$ , and express the answer as a simplified fraction.

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Problem 118

Find the value of $q$ given that the product of $q$ and -4.7 is equal to 9.4.

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Problem 119

Find the possible number of hours the chemistry club can rent a meeting room with a $15 reservation fee and$ 6 per hour fee, given a maximum budget of $63.
Let $t$ be the number of hours. The inequality is: $15 + 6t \leq 63$ .

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Problem 120

Given $a_1=5$ and $r=2$ , which equation represents the $n$ th term of the sequence: $a_n=5(2)^{n-1}$ ?

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Problem 121

Solve for $y$ in the equation $26=-\frac{8}{5}y$ .

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Problem 122

Solve for $n$ in the equation $0.75n=36$ .

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Problem 123

Find the probability that a coin lands showing heads.

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Problem 124

Solve the equation $3^{n}=81$ using the like bases property to find the value of $n$ .

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Problem 125

Simplify $100^{3/2}$ and verify the result using a calculator.

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Problem 126

Complete the table using equivalent ratios. Find the number of cabins for 2.1 hectares and 3 hectares of land.
$10.5 \quad 5$ $2.1 \quad ?$ $3 \quad 7$

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Problem 127

Does $(-2,5)$ satisfy $y=-5x$ ?

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Problem 128

Find two ways to represent 27 using only the digit 3.

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Problem 129

Rewrite the equation $9 p^{2}+26 p-3=0$ by substituting $p=3^{x}$ , then solve the resulting equation $3 \times 9^{x}+3^{x+2}=1+3^{x-1}$ .

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Problem 130

Solve a system of linear equations to find the cost per pound of walnuts and chocolate chips. For 3 lbs walnuts and 5 lbs chocolate chips, total cost is $19. For 9 lbs walnuts and 7 lbs chocolate chips, total cost is$ 35. Find the cost per pound of walnuts: $and per pound of chocolate chips:$

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Problem 131

Find the distance between points $P(9,-17)$ and $Q(16,-14)$ , and the coordinates of the midpoint $M$ of the segment $PQ$ . Simplify the distance.

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Problem 132

Solve for the value of $l$ given the equation $\frac{l}{5}+2=-8$ .

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Problem 133

Simplify the expression $-9(y+8)+9$ .

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Problem 134

Find $(f-g)(x)$ if $f(x)=-6 x^{\wedge} 2+x+6$ and $g(x)=-x^{\wedge} 2+x+2$ .

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Problem 135

Solve for $x$ and round to nearest hundredth where $7^{x}=245$ .

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Problem 136

Find the $x$ -intercepts and zeros of $f(x)=(x+2)^{2}(x-4)^{3}(x-3)$ . Express the intercepts and zeros as ordered pairs.

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Problem 137

Compute the mean, median, and mode of concrete strengths (in psi) from 9 randomly selected casts: 3950, 4100, 3200, 3000, 2940, 3830, 4100, 4050, 3680. The mean is $\square$ psi, the median is $\square$ psi, and the mode is $\square$ psi.

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Problem 138

Find the value of $x$ in the equation $11 = -5x - 2$ .

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Problem 139

Find the difference between 701 and 627.

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Problem 140

Find the value of resistance $R$ given the current $I$ and voltage $E$ using the formula $I=\frac{E}{R}$ .

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Problem 141

Prove $2 \cot 2x + \tan x \equiv \cot x$ for $x \neq n\pi/2, n \in \mathbb{Z}$ . Then solve $6 \cot 2x + 3 \tan x = \csc^2 x - 2$ for $-\pi \leq x < \pi$ , giving answers to 3 decimal places. (No graphical/numerical solutions).

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Problem 142

Bo spent $\$6.60$ on text messages. How many messages did he send if each message costs $\$0.15$ ?

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Problem 143

Find the value of $x$ that satisfies the equation $4x + 5y = 13$ when the ordered pair $(x, 1)$ is a solution.

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Problem 144

Find the product of $2x + 7$ and $x - 3$ .

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Problem 145

Find missing y-values for $y = x^{2}$ when $x = 0, 1, 2$ in the given table: Input (x) | Output (y) -2 | 4, -1 | 1, 0 | ?, 1 | ?, 2 | ?

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Problem 146

Solve the equation $\sqrt{\frac{1-x}{9}}=0$ for the value of $x$ .

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Problem 147

Solve for the value of t in the equation $\frac{t}{8} + 10 = 13$ .

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Problem 148

Find the value of $a$ given $ab = 0.42$ and $b = 0.648$ .

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Problem 149

Find the point obtained by dilating (0,6) by a scale factor of 1/3 around the origin.

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Problem 150

Find the value of $\frac{x^2 + 15}{x + 3}$ when $x = 5$ .

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Problem 151

Find the opposite of the integer $-28$ .

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Problem 152

Test if $3\%$ of patients treated with a drug develop nausea as an adverse reaction, using a $0.10$ significance level. Identify the null and alternative hypotheses.

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Problem 153

Is the discriminant of the function $\bar{y}=\bar{x} \overline{2}+\overline{4} \bar{x}+\overline{4}$ positive, negative, or zero?

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Problem 154

Find the number that is $\frac{4}{5}$ of 60.

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Problem 155

Solve the compound inequality $4x-2>18$ or $3x+6>9$ . Write the solution in interval notation. If no solution, enter $\boldsymbol{O}$ .

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Problem 156

Solve for $f$ in the equation $5^{f} = 125$ .

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Problem 157

Find the value of $g(x)=2x-5$ evaluated at $x=-2.4$ .

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Problem 158

Find the number that, when multiplied by 3, equals 18.

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Problem 159

Finde eine Gerade $k$ , die die Gerade $y=3x+4$ im Punkt $R(-16,-44)$ rechtwinklig schneidet.

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Problem 160

Find the value of $t$ that satisfies the equation $V(t)=4t^3-27t^2$ .

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Problem 161

Find the exact value of $\sin 67.5^{\circ}$ using trigonometric identities.

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Problem 162

Find the $r$ value for the equation $y=4.95 e^{0.0542 t}$ and explain the type of change it represents.

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Problem 163

Solve the linear rational equation $\frac{8 x+7}{16 x+30}=0$ for the value of $x$ .

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Problem 164

Find the value of $H(-1)-4$ given that $H(x)=8x+4$ .

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Problem 165

Solve for $b$ in the equation $\frac{b-6}{-7}=-10$ .

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Problem 166

Find the current value of a stock bought for $\$ 145$ that has decreased by $4\%$ since purchase.

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Problem 167

Find the product of $\sqrt{121}$ and $\sqrt{36}$ .

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Problem 168

Find all real values of $x$ such that $x \leq \frac{22}{11}$ .

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Problem 169

Find the prime factorization of 25 and 42.

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Problem 170

Solve the linear-quadratic system algebraically: $y=2x^2+13x$ and $y+6x=-9$ . Express the solution in fraction form.

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Problem 171

Solve the equation $16^{3x-2} = 32^{x+4}$ for the value of $x$ .

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Problem 172

Find the value of $k$ in the equation $\frac{60-92}{45-92}=e^{-k(43)}$ .

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Problem 173

Find the value of $b$ given the expression $b=(27+23) 11$ .

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Problem 174

Solve the absolute value equation $2|4x+5| = 0$ and choose the correct solution.

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Problem 175

Solve the linear equation $6a - 11 = 13$ for the variable $a$ .

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Problem 176

Find the value of $\sin \left(2 \tan ^{-1} x\right)$ .

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Problem 177

Solve the system of linear equations $2x + 4y = 26$ and $3x + 3y = 6$ using elimination.

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Problem 178

Select the correct equation for $b=10$ . A. $2(10+4)=16$ B. $2(10+2)=40$ C. $3(10-2)=24$ D. $2(8+10)=42$ E. $3(10-4)=20$

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Problem 179

Determine the property illustrated by the equation $x+7.5=7.5+x$ .

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Problem 180

The math club's membership grows by $3\%$ weekly. Find the function $S(x)$ representing the number of members after $x$ weeks, starting with 10 members.

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Problem 181

Evaluate $1.4^{3}$ and enter the decimal result.

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Problem 182

Simplify the expression $e^{2 \ln x - 5}$ .

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Problem 183

Find the value of $x$ if a number divided by 20 equals 5. A) $x=100$ B) $x=4$ C) $x=50$ D) $x=2$

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Problem 184

Divide $\frac{5 \sqrt{90 a x^{3}}}{25 \sqrt{5 a x}}$ to simplify the expression.

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Problem 185

Solve for $d$ and graph the solution. $d-1>11$ or $\frac{d-11}{3}<-3$ . Plot the endpoints, change a closed endpoint to open, delete a segment.

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Problem 186

Solve for $y$ and graph the solution. Solve the system of linear inequalities: $-13y+6<-15y-6$ or $2y+3\geq8-3y$ . Plot the endpoints and modify the graph.

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Problem 187

Convert between percents and decimals in a table.
Complete the table: $39\% =$ , $6.5\% =$ , $\%\% = 0.34$ , $\%\% = 0.135$ , $\%\%$ .

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Problem 188

Find the solutions to the quadratic equation $x^2 + 7x + 12 = 0$ .

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Problem 189

Write the equation $y = -3x + 9$ in function notation as $f(x)$ .

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Problem 190

Find $f$ when it varies inversely with $g$ and $f=22$ when $g=3$ .

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Problem 191

Find the score in the 70th percentile of a dataset with mean $\mu=79.22$ and standard deviation $\sigma=7.97$ using the Z-score formula $Z = \frac{X - \mu}{\sigma}$ .

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Problem 192

Evaluate the division expression $8 \div (-8)$ .

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Problem 193

Find the value of the expression $\left(7 x y\right)^{2}$ .

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Problem 194

Solve for $c$ where $\frac{c}{3} + 5.48 = 7.29$ .

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Problem 195

Evaluate the expression $4 \cdot 5 - 10 - 2(1 - 2) + 5$ .

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Problem 196

Simplify $\left(5 \times 10^{8}\right)^{4}$ and express the result in scientific notation.

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Problem 197

Find the value of $x$ if the mean of 4, 8, and $x$ is 7.

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Problem 198

Estimate $\sqrt{15}$ to the nearest tenth, then locate it on a number line.

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Problem 199

Solve for the variable $g$ in the equation $2g - 1 = 1$ .

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Problem 200

Find the number line that shows the solution to the equation $6x - 8 = 28$ .

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Math

Problem 101

Simplify the expression: (6+2y)⋅3(6+2y)\cdot 3(6+2y)⋅3 and (2x−3)⋅4(2x-3)\cdot 4(2x−3)⋅4

Problem 102

Find the equation of an absolute value function with vertex at (−3,−1)(-3, -1)(−3,−1), opening upwards, and passing through (0,2)(0, 2)(0,2).

Problem 103

Write the elevation of a telescope, about 2500 meters above sea level, in scientific notation. 2500=2.5×1032500 = 2.5 \times 10^32500=2.5×103

Problem 104

Find the roots of the quadratic equation 2x2−x−28=02x^2 - x - 28 = 02x2−x−28=0 by factoring.

Problem 105

Find xxx such that xm=npx m = \frac{n}{p}xm=pn​.

Problem 106

Solve for the unknown variable mmm in the equation 4+m=124+m=124+m=12.

Problem 107

Pick a random card, then pick a second without replacing the first. What is the probability of getting an 8 then an even number? Express as a simplified fraction.

Problem 108

Solve for xxx in the equation 4x+6=212x+124x + 6 = 2 \frac{1}{2}x + 124x+6=221​x+12 using inverse operations.

Problem 109

Match xxx values to corresponding yyy values based on their arrangement.

Problem 110

Multiply binomials (8p+4q)(p−3q)(8p + 4q)(p - 3q)(8p+4q)(p−3q) and collect like terms.

Problem 111

Solve for xxx in the equation 169−x=113169^{-x}=\frac{1}{\sqrt{13}}169−x=13​1​.

Problem 112

Find the min/max value and axis of symmetry for f(x)=−3x2+12x−8f(x)=-3 x^{2}+12 x-8f(x)=−3x2+12x−8. The yyy-value of the extremum is the solution.

Problem 113

Convert -39.825 to a mixed number.

Problem 114

Identify constant and variable terms: −9x2-9 x^{2}−9x2 (constant), −3xy-3 x y−3xy (variable), −∨−3-\vee-3−∨−3 (constant), −12-\frac{1}{2}−21​ (constant), 8.1 (constant), 17x17 x17x (variable), −14a-14 a−14a (variable).

Problem 115

Find the exact value of tan⁡(2π/3)\tan(2\pi/3)tan(2π/3).

Problem 116

Complete the table for the linear equation 4x−3y=124x-3y=124x−3y=12 and graph the equation.

Problem 117

Evaluate the rational expression x−49x+2\frac{x-4}{9x+2}9x+2x−4​ for x=−1x=-1x=−1, and express the answer as a simplified fraction.

Problem 118

Find the value of qqq given that the product of qqq and -4.7 is equal to 9.4.

Problem 119

Find the possible number of hours the chemistry club can rent a meeting room with a 15reservationfeeand15 reservation fee and 15reservationfeeand6 per hour fee, given a maximum budget of $63.Let ttt be the number of hours. The inequality is: 15+6t≤6315 + 6t \leq 6315+6t≤63.

Problem 120

Given a1=5a_1=5a1​=5 and r=2r=2r=2, which equation represents the nnnth term of the sequence: an=5(2)n−1a_n=5(2)^{n-1}an​=5(2)n−1?

Problem 121

Solve for yyy in the equation 26=−85y26=-\frac{8}{5}y26=−58​y.

Problem 122

Solve for nnn in the equation 0.75n=360.75n=360.75n=36.

Problem 123

Find the probability that a coin lands showing heads.

Problem 124

Solve the equation 3n=813^{n}=813n=81 using the like bases property to find the value of nnn.

Problem 125

Simplify 1003/2100^{3/2}1003/2 and verify the result using a calculator.

Problem 126

Complete the table using equivalent ratios. Find the number of cabins for 2.1 hectares and 3 hectares of land.10.5510.5 \quad 510.55 2.1?2.1 \quad ?2.1? 373 \quad 737

Problem 127

Does (−2,5)(-2,5)(−2,5) satisfy y=−5xy=-5xy=−5x?

Problem 128

Find two ways to represent 27 using only the digit 3.

Problem 129

Rewrite the equation 9p2+26p−3=09 p^{2}+26 p-3=09p2+26p−3=0 by substituting p=3xp=3^{x}p=3x, then solve the resulting equation 3×9x+3x+2=1+3x−13 \times 9^{x}+3^{x+2}=1+3^{x-1}3×9x+3x+2=1+3x−1.

Problem 130

Problem 131

Find the distance between points P(9,−17)P(9,-17)P(9,−17) and Q(16,−14)Q(16,-14)Q(16,−14), and the coordinates of the midpoint MMM of the segment PQPQPQ. Simplify the distance.

Problem 132

Solve for the value of lll given the equation l5+2=−8\frac{l}{5}+2=-85l​+2=−8.

Problem 133

Simplify the expression −9(y+8)+9-9(y+8)+9−9(y+8)+9.

Problem 134

Find (f−g)(x)(f-g)(x)(f−g)(x) if f(x)=−6x∧2+x+6f(x)=-6 x^{\wedge} 2+x+6f(x)=−6x∧2+x+6 and g(x)=−x∧2+x+2g(x)=-x^{\wedge} 2+x+2g(x)=−x∧2+x+2.

Problem 135

Solve for xxx and round to nearest hundredth where 7x=2457^{x}=2457x=245.

Problem 136

Find the xxx-intercepts and zeros of f(x)=(x+2)2(x−4)3(x−3)f(x)=(x+2)^{2}(x-4)^{3}(x-3)f(x)=(x+2)2(x−4)3(x−3). Express the intercepts and zeros as ordered pairs.

Problem 137

Compute the mean, median, and mode of concrete strengths (in psi) from 9 randomly selected casts: 3950, 4100, 3200, 3000, 2940, 3830, 4100, 4050, 3680. The mean is □\square□ psi, the median is □\square□ psi, and the mode is □\square□ psi.

Problem 138

Find the value of xxx in the equation 11=−5x−211 = -5x - 211=−5x−2.

Problem 139

Find the difference between 701 and 627.

Problem 140

Find the value of resistance RRR given the current III and voltage EEE using the formula I=ERI=\frac{E}{R}I=RE​.

Simplify the expression: $(6+2y)\cdot 3$ and $(2x-3)\cdot 4$

Find the equation of an absolute value function with vertex at $(-3, -1)$ , opening upwards, and passing through $(0, 2)$ .

Write the elevation of a telescope, about 2500 meters above sea level, in scientific notation. $2500 = 2.5 \times 10^3$

Find the roots of the quadratic equation $2x^2 - x - 28 = 0$ by factoring.

Find $x$ such that $x m = \frac{n}{p}$ .

Solve for the unknown variable $m$ in the equation $4+m=12$ .

Solve for $x$ in the equation $4x + 6 = 2 \frac{1}{2}x + 12$ using inverse operations.

Match $x$ values to corresponding $y$ values based on their arrangement.

Multiply binomials $(8p + 4q)(p - 3q)$ and collect like terms.

Solve for $x$ in the equation $169^{-x}=\frac{1}{\sqrt{13}}$ .

Find the min/max value and axis of symmetry for $f(x)=-3 x^{2}+12 x-8$ . The $y$ -value of the extremum is the solution.

Identify constant and variable terms: $-9 x^{2}$ (constant), $-3 x y$ (variable), $-\vee-3$ (constant), $-\frac{1}{2}$ (constant), 8.1 (constant), $17 x$ (variable), $-14 a$ (variable).

Find the exact value of $\tan(2\pi/3)$ .

Complete the table for the linear equation $4x-3y=12$ and graph the equation.

Evaluate the rational expression $\frac{x-4}{9x+2}$ for $x=-1$ , and express the answer as a simplified fraction.

Find the value of $q$ given that the product of $q$ and -4.7 is equal to 9.4.

Find the possible number of hours the chemistry club can rent a meeting room with a $15 reservation fee and$ 6 per hour fee, given a maximum budget of $63.
Let $t$ be the number of hours. The inequality is: $15 + 6t \leq 63$ .

Given $a_1=5$ and $r=2$ , which equation represents the $n$ th term of the sequence: $a_n=5(2)^{n-1}$ ?

Solve for $y$ in the equation $26=-\frac{8}{5}y$ .

Solve for $n$ in the equation $0.75n=36$ .

Solve the equation $3^{n}=81$ using the like bases property to find the value of $n$ .

Simplify $100^{3/2}$ and verify the result using a calculator.

Complete the table using equivalent ratios. Find the number of cabins for 2.1 hectares and 3 hectares of land.
$10.5 \quad 5$ $2.1 \quad ?$ $3 \quad 7$

Does $(-2,5)$ satisfy $y=-5x$ ?

Rewrite the equation $9 p^{2}+26 p-3=0$ by substituting $p=3^{x}$ , then solve the resulting equation $3 \times 9^{x}+3^{x+2}=1+3^{x-1}$ .

Find the distance between points $P(9,-17)$ and $Q(16,-14)$ , and the coordinates of the midpoint $M$ of the segment $PQ$ . Simplify the distance.

Solve for the value of $l$ given the equation $\frac{l}{5}+2=-8$ .

Simplify the expression $-9(y+8)+9$ .

Find $(f-g)(x)$ if $f(x)=-6 x^{\wedge} 2+x+6$ and $g(x)=-x^{\wedge} 2+x+2$ .

Solve for $x$ and round to nearest hundredth where $7^{x}=245$ .

Find the $x$ -intercepts and zeros of $f(x)=(x+2)^{2}(x-4)^{3}(x-3)$ . Express the intercepts and zeros as ordered pairs.

Compute the mean, median, and mode of concrete strengths (in psi) from 9 randomly selected casts: 3950, 4100, 3200, 3000, 2940, 3830, 4100, 4050, 3680. The mean is $\square$ psi, the median is $\square$ psi, and the mode is $\square$ psi.

Find the value of $x$ in the equation $11 = -5x - 2$ .

Find the value of resistance $R$ given the current $I$ and voltage $E$ using the formula $I=\frac{E}{R}$ .

Bo spent $\$6.60$ on text messages. How many messages did he send if each message costs $\$0.15$ ?

Find the value of $x$ that satisfies the equation $4x + 5y = 13$ when the ordered pair $(x, 1)$ is a solution.

Find the product of $2x + 7$ and $x - 3$ .

Find missing y-values for $y = x^{2}$ when $x = 0, 1, 2$ in the given table: Input (x) | Output (y) -2 | 4, -1 | 1, 0 | ?, 1 | ?, 2 | ?

Solve the equation $\sqrt{\frac{1-x}{9}}=0$ for the value of $x$ .

Solve for the value of t in the equation $\frac{t}{8} + 10 = 13$ .

Find the value of $a$ given $ab = 0.42$ and $b = 0.648$ .

Find the value of $\frac{x^2 + 15}{x + 3}$ when $x = 5$ .

Find the opposite of the integer $-28$ .

Test if $3\%$ of patients treated with a drug develop nausea as an adverse reaction, using a $0.10$ significance level. Identify the null and alternative hypotheses.

Is the discriminant of the function $\bar{y}=\bar{x} \overline{2}+\overline{4} \bar{x}+\overline{4}$ positive, negative, or zero?

Find the number that is $\frac{4}{5}$ of 60.

Solve the compound inequality $4x-2>18$ or $3x+6>9$ . Write the solution in interval notation. If no solution, enter $\boldsymbol{O}$ .

Solve for $f$ in the equation $5^{f} = 125$ .

Find the value of $g(x)=2x-5$ evaluated at $x=-2.4$ .

Finde eine Gerade $k$ , die die Gerade $y=3x+4$ im Punkt $R(-16,-44)$ rechtwinklig schneidet.

Find the value of $t$ that satisfies the equation $V(t)=4t^3-27t^2$ .

Find the exact value of $\sin 67.5^{\circ}$ using trigonometric identities.

Find the $r$ value for the equation $y=4.95 e^{0.0542 t}$ and explain the type of change it represents.

Solve the linear rational equation $\frac{8 x+7}{16 x+30}=0$ for the value of $x$ .

Find the value of $H(-1)-4$ given that $H(x)=8x+4$ .

Solve for $b$ in the equation $\frac{b-6}{-7}=-10$ .

Find the current value of a stock bought for $\$ 145$ that has decreased by $4\%$ since purchase.

Find the product of $\sqrt{121}$ and $\sqrt{36}$ .

Find all real values of $x$ such that $x \leq \frac{22}{11}$ .

Solve the linear-quadratic system algebraically: $y=2x^2+13x$ and $y+6x=-9$ . Express the solution in fraction form.

Solve the equation $16^{3x-2} = 32^{x+4}$ for the value of $x$ .

Find the value of $k$ in the equation $\frac{60-92}{45-92}=e^{-k(43)}$ .

Find the value of $b$ given the expression $b=(27+23) 11$ .

Solve the absolute value equation $2|4x+5| = 0$ and choose the correct solution.