Browse Math problems in the Studdy Learning Bank!

Problem 4401

Find the value of $2.1 \div 10^{2}$ .

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Problem 4402

Solve the quadratic equation $5 u^{2} = -13 u - 6$ for the value of $u$ .

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Problem 4403

Solve the equation $-4(5x-1)=8-(x+1)$ and choose the correct first step.

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Problem 4404

Find the coordinates of point A given that its x-coordinate is 4 and its y-coordinate satisfies the equation $y=x-5$ .

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Problem 4405

Solve for the value of $u$ that satisfies the quadratic equation $4u^2 + 20u = -25$ .

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Problem 4406

Find the value of $2m + 3p$ when $m=5$ and $p=6$ .

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Problem 4407

Find the equation of a line with y-intercept 50 and slope 7.5.

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Problem 4408

Find the difference between -12 and -27.

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Problem 4409

Question 5: Find the modulus of the complex number $-4+3i$ .
Question 6: Simplify the complex fraction $(2-4i)/(1+3i)$ and find the values of $a$ and $b$ where $a+bi$ is the result.

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Problem 4410

Construct a function to model the rain collected in a vial, given the initial volume of 12 cc, a volume of 27 cc at one point, and a final volume of 37 cc after 2 hours.

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Problem 4411

Solve for Theresa's math quiz score $w$ given Julia's score of 97 was 29 points higher.
$97 = w + 29$ $w = 68$

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Problem 4412

Find an equivalent expression for the distance $6d-6$ that Karina swims, where $d$ is the distance per lap.
A. $6d-6 = -6+6d$ B. $6d-6 = 6-6d$ C. $6d-6 = -6(d+6)$ D. $6d-6 = 6(d-6)$

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Problem 4413

Solve for $x$ in the equation $(x-9)^2 = 49$ .

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Problem 4414

Find the product of the complex numbers $(9+i)$ and $(9-i)$ and express the result in standard form $a+bi$ .

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Problem 4415

The median ticket price for musicals is $95 and for non-musical plays is$ 80. Calculate the difference in median ticket costs between musicals and non-musical plays.

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Problem 4416

Find the class with the highest average and least score variability from $\{A, B, C, D\}$ where each class has a range of $\{56, 55, 48, 57\}$ and mean scores $\{107, 114, 108, 105\}$ .

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Problem 4417

Solve the quadratic inequality $x^2 + 10x + 16 < 0$ using the graphical method.

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Problem 4418

Find the regions of increasing and decreasing for the function $y=\frac{2x+7}{2x}$ where $x \neq 0$ .

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Problem 4419

Solve for y in the equation $\frac{6}{5}=\frac{18}{y}$ .

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Problem 4420

Solve the equation $7 e^{3 x}-4=14$ using natural logarithms. Round the solution to the nearest thousandth.

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Problem 4421

Find the range of values for $h$ that satisfy the inequality $|h-4| < 14$ .

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Problem 4422

Find the quadratic equation of a rocket's trajectory given its maximum height of $1280$ feet and landing point at $(16,0)$ in $8$ seconds.

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Problem 4423

Solve the trigonometric equation $\sec^2 \theta + 2 \sec \theta = 0$ for $\theta$ .

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Problem 4424

Find the ordered pair $(x,y)$ that satisfies the constraints: $x + y \geq 4$ and $2x + y \leq 7$ , where $x$ represents hot dogs at $\$2$ each and $y$ represents peanuts at $\$1$ each, given Cody has $\$7$ .

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Problem 4425

Find the set of real numbers $x$ such that $x + 6 > 0$ .

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Problem 4426

Find the value of $\mathrm{c}$ in the standard form of a quadratic function $y = ax^2 + bx + c$ given the table of values.

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Problem 4427

Find the range of values for $x$ that satisfy the inequality $86 > x - 18$ .

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Problem 4428

Solve the simple arithmetic equation $7+9=$ .

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Problem 4429

Katherine buys a random cake. The probability it has figs is $\frac{4}{7}$ , fondant is $\frac{3}{10}$ , and both is $\frac{1}{8}$ . Given figs, find the probability it also has fondant.

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Problem 4430

Solve the linear equation $3 z + 8 = 12 + 3 x - z$ for $z$ and $x$ .

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Problem 4431

Find the equation that models the growth of a population of 100 bacteria that doubles every hour over 3 hours.
$N(t) = 100 \cdot 2^t$ , where $N(t)$ is the number of bacteria and $t$ is the time in hours.

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Problem 4432

Subtract two integers: $-43 - 19 = ?$

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Problem 4433

Find the quadrant of the angle $177^{\circ}$ .

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Problem 4434

Solve the system of linear equations using Gaussian elimination: $2x + y - z = 2, x + 3y + 2z = 1, x + y + z = 2$ .

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Problem 4435

Find the speed of the tip of a woman's shadow when she is $15 \mathrm{~m}$ from a $3 \mathrm{~m}$ tall pole, running at $1.8 \mathrm{~m} / \mathrm{s}$ and is $1.5 \mathrm{~m}$ tall.

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Problem 4436

Solve for $m$ in the equation $11m + 4m + 2m = -17$ .

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Problem 4437

Find the derivative of the functions $f(x)=2x^2$ , $f(x)=2x$ , $f(x)=5$ , $f(x)=-x^2$ , $f(x)=2x+3$ , and $f(x)=ax^2$ .

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Problem 4438

Solve the linear equation $\frac{1}{2} x - 2 = 9 - 5 x$ by graphing to find the value of $x$ .

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Problem 4439

Which linear transformation from $\mathbb{R}^{3}$ to $\mathbb{R}^{2}$ is defined by $T\left(\left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right]\right)=\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right]$ ?

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Problem 4440

Simplify the rational expression $\frac{2 x^{3}+11 x^{2}-21 x}{x^{2}+3 x}$ for $x \neq-3, 0$ .

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Problem 4441

Solve the equation $3x=24$ to find the value of $x$ .

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Problem 4442

Solve for $y$ given the equation $4y = 3y + 6\log 1128$

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Problem 4443

Solve for the acute angle $\theta$ where $3 \cos \theta = \frac{1}{9}$ .

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Problem 4444

Find the value of the expression $|-6|-|6|-(-6)$ .

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Problem 4445

Simplify the expression $\frac{2^{5}}{(-4+8)} \times 2$ .

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Problem 4446

Divide $1 \frac{4}{9}$ by $-\frac{2}{9}$ and write the quotient in simplest form.

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Problem 4447

Transform the polar equation $\theta=\frac{4 \pi}{3}$ to rectangular coordinates and graph the equation.

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Problem 4448

Find the discriminant of $3 x^{2}-7 x-12=0$ and describe the number and type of roots.

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Problem 4449

Simplify the expression $12x(4x+y)$ .

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Problem 4450

Find the value(s) of $x$ that satisfy $x^2 = 25$ .

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Problem 4451

Find a method to evaluate the expression $8+9$ .

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Problem 4452

A college admissions officer takes a random sample of 100 entering freshmen and finds their mean mathematics SAT score is 436. Assuming the population standard deviation is $\sigma=115$ , construct a $99\%$ confidence interval for the mean mathematics SAT score of the entering freshman class, rounded to the nearest whole number.
A $99\%$ confidence interval for the mean mathematics SAT score is $\boxed{395}<\mu<\boxed{477}$ .

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Problem 4453

Find the equation that best describes the direct relationship between the total cost of gas (y) in dollars and the amount of gas purchased (x) in gallons, given that $5 \frac{1}{4}$ gallons of gas cost $\$ 12.60$ .

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Problem 4454

Is the difference between Dani's and Raj's ages always constant? Explain using the data: $Dani's Age = 5, 10, 15, 20$ and $Raj's Age = 10, 15, 20, 25$ .

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Problem 4455

Find the exact value of $x$ that satisfies the equation $3^{2x-5}=81$ .

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Problem 4456

Solve the equation by expressing each side as a power of the same base and equating exponents: $4^{x+2}=8^{x-6}$ . Choose the correct exponent value.

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Problem 4457

Is $-\sqrt{0/4}$ a rational number?

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Problem 4458

Solve the quadratic equation $11 w^{2} - 22 w + 121 = 81$ for the variable $w$ .

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Problem 4459

Find the value of $x$ where $\frac{7}{8}=\frac{x}{44}$ .

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Problem 4460

Find the cotangent of 14 degrees.

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Problem 4461

Determine which equations can be solved using the zero product property. Options: $-(x-1)(x+9)=0$ , $3 x^{2}-6 x=0$ .

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Problem 4462

Find a number whose quotient when divided by 4 is -7.

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Problem 4463

Simplify the expression $64^{-\frac{3}{2}}$ .

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Problem 4464

Solve for $x$ when $3x - 19 = 0$ , given $x = 10$ .

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Problem 4465

There are 240 students in the 7th grade. $5\%$ are in the Environmental Club. How many students are in the club?

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Problem 4466

Graph the cosine function with period $2\pi$ .

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Problem 4467

Find $y$ when $x=3$ given that $y$ and $x$ have a proportional relationship and $y=9$ when $x=2$ . $y = 13.5$

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Problem 4468

Find the absolute extreme values of $f(x) = \frac{12x^3}{3} + 16x^2 - 12x$ on the interval $[-4, 1]$ . Select the correct choice: A. The absolute maximum is $\square$ at $x = \square$ . B. There is no absolute maximum on the given interval.

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Problem 4469

Compare linear functions $A(x) = mx + b$ and $B(x) = m'x + b'$ where $A$ has $x$ -intercept $-2$ and $y$ -intercept $8$ , and $B$ includes points $(1,-4)$ and $(2,0)$ . The slope of $A$ is the slope of $B$ . The $x$ -intercept of $A$ is the $x$ -intercept of $B$ .

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Problem 4470

Solve the equation $2(x-3)+3=6x-5$ using the Distributive Property. Find the value of $x$ .

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Problem 4471

Solve $7=3x-2$ for $x$ . What operations isolate $x$ ? (a) Divide by 7, then subtract 2 (b) Subtract 2, then divide by 7 (c) Multiply by 3, then add 2 (d) Add 2, then divide by 3

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Problem 4472

Find the range of the values in the table, where $X = \{-1, 3, 3, 4\}$ and $Y = \{-2, 0, -2, 5\}$ .

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Problem 4473

Find $y$ using the equation $y = m x - b$ if $m = 11$ , $x = 2$ , and $b = 5$ .

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Problem 4474

Find the total meal cost after an 18% tip on a $58 meal.
a) Let $m =$ meal cost. The equation is: $\text{Total Meal Cost} = m + 0.18m$
b) The total cost of the meal is = $\$68.44$

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Problem 4475

Find the total number of markers the art teacher has, given that each of the 24 boxes contains 12 markers.

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Problem 4476

Solve the equation $\frac{x}{x-7}+\frac{x+1}{x+7}=\frac{x-1}{x-7}$ and find the values of $x$ .

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Problem 4477

Ming incorrectly says the product is $\frac{4}{63}$ . Find the correct product and the error Ming could have made.

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Problem 4478

Sarah is creating a photo album with 12 pages and a total of 72 photos. Find the number of photos $p$ she puts on each page.

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Problem 4479

Which ordered pairs satisfy an inverse variation relationship? $\{(4,-2), (-5,10)\}, \{(2,3), (4,5)\}, \{(6,3), (8,4)\}, \{(2,6), (-3,-4)\}$

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Problem 4480

Find the equation of the asymptote for the exponential function $f(x) = \left(\frac{1}{2}\right)^{x} - 6$ .

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Problem 4481

Find the derivative of the inverse function $f^{-1}(x)$ where $f(x)=\frac{1}{(1-x)^{2}}$ and $x>1$ , evaluated at $x=\frac{1}{4}$ .

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Problem 4482

Find the value of $x$ for which $\frac{x-4}{(x+5)(x-1)}=0$ .

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Problem 4483

Calculate the specified partial derivatives for the following functions: (a) $f(x, y)=x y^{3} e^{y}, \quad f_{y^{2}}^{\prime \prime}=\frac{\partial^{2} f}{\partial y^{2}}$ (b) $f(p, q)=3 p^{3} q^{2}, \quad f_{p^{2}}^{\prime \prime}=\frac{\partial^{2} f}{\partial p^{2}}$ (c) $f(k, l)=5 \sqrt{k} l^{3}, \quad f_{kl}^{\prime \prime}=\frac{\partial^{2} f}{\partial k \partial l}$

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Problem 4484

Determine if the point $(2,-3)$ lies on, inside, or outside the circle defined by the equation $x^{2}+y^{2}=9$ .

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Problem 4485

Gina takes classes at two colleges. Westside fees are $\$ 98$ per credit, Pinewood fees are $\$ 115$ per credit. Gina takes 13 total credits. Express the total amount she paid.

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Problem 4486

Determine the probability a person aged 46+ prefers cash payment from the given data.
$P(\text{Cash} | \text{Age } 46+) = \frac{35}{35 + 25}$

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Problem 4487

The number of parking spaces $y$ varies directly with the number of theaters $x$ in a movie theater complex. Find the direct variation equation and the number of theaters the developer should build given 210 parking spaces.
$y = 30x$

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Problem 4488

Solve the inequality $12+4y < 32$ to find the possible values of $y$ .

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Problem 4489

Test claim that sample from population with mean < 1000 hic (head injury condition units) using 0.01 significance level. Hypotheses: $H_0: \mu = 1000$ hic, $H_1: \mu < 1000$ hic. Test statistic $t = \square$ (rounded to 3 decimal places). $P$ -value = $\square$ (rounded to 4 decimal places). Conclude $H_0$ is rejected, evidence supports claim that sample is from population with mean < 1000 hic. Results suggest most booster seats meet requirement, but one may exceed 1000 hic.

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Problem 4490

Find the velocity of money given that an economy produces 80 cars, each selling for $£ 10,000$ , with a money supply of $£ 16,000$ according to the Equation of Exchange.

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Problem 4491

Expand $(x-4)(x+7)$ and express the result as a polynomial in standard form.

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Problem 4492

Draw a histogram for the lengths of stay (in days) of 19 patients discharged from a hospital, with class boundaries from 1.5 to 13.5 and 6 equal-width classes.

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Problem 4493

Expand the binomial expression $(x-3)(x+7)$ .

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Problem 4494

Find the $x$ -intercepts, axis of symmetry, vertex, and $y$ -intercept of $y =$ $x^{2} - 2x - 8$ $, then sketch the graph.

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Problem 4495

Identify the set of 3 numbers that could represent the sides of a triangle. Options: $\{4,16,21\}$ , $\{9,14,20\}$ , $\{11,14,27\}$ , $\{6,14,20\}$ .

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Problem 4496

Find two integers whose product is $32$ and one is twice the other.

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Problem 4497

Finde die Funktionsgleichung einer kubischen Funktion, die punktsymmetrisch zum Ursprung ist und $\mathrm{g}(\mathrm{x})=\frac{1}{2}\left(4 \mathrm{x}^{3}+\mathrm{x}\right)$ im Ursprung und bei $\mathrm{x}=1$ schneidet.

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Problem 4498

Find the value of $x$ that satisfies the equation $\left(\frac{1}{3}\right)^{x}=27$ . The solution is $\{3\}$ .

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Problem 4499

Find the prime factorization of 124.

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Problem 4500

Identify the non-quadratic function from $y=3x^2-5x+8$ , $y=2x^3+8x-7$ , $f(x)=-4(x-1)^2+3$ , $y=1-16x+0.5x^2$ .

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Math

Problem 4401

Find the value of 2.1÷1022.1 \div 10^{2}2.1÷102.

Problem 4402

Solve the quadratic equation 5u2=−13u−65 u^{2} = -13 u - 65u2=−13u−6 for the value of uuu.

Problem 4403

Solve the equation −4(5x−1)=8−(x+1)-4(5x-1)=8-(x+1)−4(5x−1)=8−(x+1) and choose the correct first step.

Problem 4404

Find the coordinates of point A given that its x-coordinate is 4 and its y-coordinate satisfies the equation y=x−5y=x-5y=x−5.

Problem 4405

Solve for the value of uuu that satisfies the quadratic equation 4u2+20u=−254u^2 + 20u = -254u2+20u=−25.

Problem 4406

Find the value of 2m+3p2m + 3p2m+3p when m=5m=5m=5 and p=6p=6p=6.

Problem 4407

Find the equation of a line with y-intercept 50 and slope 7.5.

Problem 4408

Find the difference between -12 and -27.

Problem 4409

Question 5: Find the modulus of the complex number −4+3i-4+3i−4+3i.Question 6: Simplify the complex fraction (2−4i)/(1+3i)(2-4i)/(1+3i)(2−4i)/(1+3i) and find the values of aaa and bbb where a+bia+bia+bi is the result.

Problem 4410

Construct a function to model the rain collected in a vial, given the initial volume of 12 cc, a volume of 27 cc at one point, and a final volume of 37 cc after 2 hours.

Problem 4411

Solve for Theresa's math quiz score www given Julia's score of 97 was 29 points higher.97=w+2997 = w + 2997=w+29 w=68w = 68w=68

Problem 4412

Find an equivalent expression for the distance 6d−66d-66d−6 that Karina swims, where ddd is the distance per lap.A. 6d−6=−6+6d6d-6 = -6+6d6d−6=−6+6d B. 6d−6=6−6d6d-6 = 6-6d6d−6=6−6d C. 6d−6=−6(d+6)6d-6 = -6(d+6)6d−6=−6(d+6) D. 6d−6=6(d−6)6d-6 = 6(d-6)6d−6=6(d−6)

Problem 4413

Solve for xxx in the equation (x−9)2=49(x-9)^2 = 49(x−9)2=49.

Problem 4414

Find the product of the complex numbers (9+i)(9+i)(9+i) and (9−i)(9-i)(9−i) and express the result in standard form a+bia+bia+bi.

Problem 4415

The median ticket price for musicals is 95andfornon−musicalplaysis95 and for non-musical plays is 95andfornon−musicalplaysis80. Calculate the difference in median ticket costs between musicals and non-musical plays.

Problem 4416

Find the class with the highest average and least score variability from {A,B,C,D}\{A, B, C, D\}{A,B,C,D} where each class has a range of {56,55,48,57}\{56, 55, 48, 57\}{56,55,48,57} and mean scores {107,114,108,105}\{107, 114, 108, 105\}{107,114,108,105}.

Problem 4417

Solve the quadratic inequality x2+10x+16<0x^2 + 10x + 16 < 0x2+10x+16<0 using the graphical method.

Problem 4418

Find the regions of increasing and decreasing for the function y=2x+72xy=\frac{2x+7}{2x}y=2x2x+7​ where x≠0x \neq 0x=0.

Problem 4419

Solve for y in the equation 65=18y\frac{6}{5}=\frac{18}{y}56​=y18​.

Problem 4420

Solve the equation 7e3x−4=147 e^{3 x}-4=147e3x−4=14 using natural logarithms. Round the solution to the nearest thousandth.

Problem 4421

Find the range of values for hhh that satisfy the inequality ∣h−4∣<14|h-4| < 14∣h−4∣<14.

Problem 4422

Find the quadratic equation of a rocket's trajectory given its maximum height of 128012801280 feet and landing point at (16,0)(16,0)(16,0) in 888 seconds.

Problem 4423

Solve the trigonometric equation sec⁡2θ+2sec⁡θ=0\sec^2 \theta + 2 \sec \theta = 0sec2θ+2secθ=0 for θ\thetaθ.

Problem 4424

Find the ordered pair (x,y)(x,y)(x,y) that satisfies the constraints: x+y≥4x + y \geq 4x+y≥4 and 2x+y≤72x + y \leq 72x+y≤7, where xxx represents hot dogs at $2\$2$2 each and yyy represents peanuts at $1\$1$1 each, given Cody has $7\$7$7.

Problem 4425

Find the set of real numbers xxx such that x+6>0x + 6 > 0x+6>0.

Problem 4426

Find the value of c\mathrm{c}c in the standard form of a quadratic function y=ax2+bx+cy = ax^2 + bx + cy=ax2+bx+c given the table of values.

Problem 4427

Find the range of values for xxx that satisfy the inequality 86>x−1886 > x - 1886>x−18.

Problem 4428

Solve the simple arithmetic equation 7+9=7+9=7+9=.

Problem 4429

Katherine buys a random cake. The probability it has figs is 47\frac{4}{7}74​, fondant is 310\frac{3}{10}103​, and both is 18\frac{1}{8}81​. Given figs, find the probability it also has fondant.

Problem 4430

Solve the linear equation 3z+8=12+3x−z3 z + 8 = 12 + 3 x - z3z+8=12+3x−z for zzz and xxx.

Problem 4431

Find the equation that models the growth of a population of 100 bacteria that doubles every hour over 3 hours.N(t)=100⋅2tN(t) = 100 \cdot 2^tN(t)=100⋅2t, where N(t)N(t)N(t) is the number of bacteria and ttt is the time in hours.

Problem 4432

Subtract two integers: −43−19=?-43 - 19 = ?−43−19=?

Problem 4433

Find the quadrant of the angle 177∘177^{\circ}177∘.

Problem 4434

Solve the system of linear equations using Gaussian elimination: 2x+y−z=2,x+3y+2z=1,x+y+z=22x + y - z = 2, x + 3y + 2z = 1, x + y + z = 22x+y−z=2,x+3y+2z=1,x+y+z=2.

Problem 4435

Find the speed of the tip of a woman's shadow when she is 15 m15 \mathrm{~m}15 m from a 3 m3 \mathrm{~m}3 m tall pole, running at 1.8 m/s1.8 \mathrm{~m} / \mathrm{s}1.8 m/s and is 1.5 m1.5 \mathrm{~m}1.5 m tall.

Problem 4436

Solve for mmm in the equation 11m+4m+2m=−1711m + 4m + 2m = -1711m+4m+2m=−17.

Problem 4437

Find the derivative of the functions f(x)=2x2f(x)=2x^2f(x)=2x2, f(x)=2xf(x)=2xf(x)=2x, f(x)=5f(x)=5f(x)=5, f(x)=−x2f(x)=-x^2f(x)=−x2, f(x)=2x+3f(x)=2x+3f(x)=2x+3, and f(x)=ax2f(x)=ax^2f(x)=ax2.

Problem 4438

Solve the linear equation 12x−2=9−5x\frac{1}{2} x - 2 = 9 - 5 x21​x−2=9−5x by graphing to find the value of xxx.

Problem 4439

Problem 4440

Simplify the rational expression 2x3+11x2−21xx2+3x\frac{2 x^{3}+11 x^{2}-21 x}{x^{2}+3 x}x2+3x2x3+11x2−21x​ for x≠−3,0x \neq-3, 0x=−3,0.

Find the value of $2.1 \div 10^{2}$ .

Solve the quadratic equation $5 u^{2} = -13 u - 6$ for the value of $u$ .

Solve the equation $-4(5x-1)=8-(x+1)$ and choose the correct first step.

Find the coordinates of point A given that its x-coordinate is 4 and its y-coordinate satisfies the equation $y=x-5$ .

Solve for the value of $u$ that satisfies the quadratic equation $4u^2 + 20u = -25$ .

Find the value of $2m + 3p$ when $m=5$ and $p=6$ .

Question 5: Find the modulus of the complex number $-4+3i$ .
Question 6: Simplify the complex fraction $(2-4i)/(1+3i)$ and find the values of $a$ and $b$ where $a+bi$ is the result.

Solve for Theresa's math quiz score $w$ given Julia's score of 97 was 29 points higher.
$97 = w + 29$ $w = 68$

Find an equivalent expression for the distance $6d-6$ that Karina swims, where $d$ is the distance per lap.
A. $6d-6 = -6+6d$ B. $6d-6 = 6-6d$ C. $6d-6 = -6(d+6)$ D. $6d-6 = 6(d-6)$

Solve for $x$ in the equation $(x-9)^2 = 49$ .

Find the product of the complex numbers $(9+i)$ and $(9-i)$ and express the result in standard form $a+bi$ .

The median ticket price for musicals is $95 and for non-musical plays is$ 80. Calculate the difference in median ticket costs between musicals and non-musical plays.

Find the class with the highest average and least score variability from $\{A, B, C, D\}$ where each class has a range of $\{56, 55, 48, 57\}$ and mean scores $\{107, 114, 108, 105\}$ .

Solve the quadratic inequality $x^2 + 10x + 16 < 0$ using the graphical method.

Find the regions of increasing and decreasing for the function $y=\frac{2x+7}{2x}$ where $x \neq 0$ .

Solve for y in the equation $\frac{6}{5}=\frac{18}{y}$ .

Solve the equation $7 e^{3 x}-4=14$ using natural logarithms. Round the solution to the nearest thousandth.

Find the range of values for $h$ that satisfy the inequality $|h-4| < 14$ .

Find the quadratic equation of a rocket's trajectory given its maximum height of $1280$ feet and landing point at $(16,0)$ in $8$ seconds.

Solve the trigonometric equation $\sec^2 \theta + 2 \sec \theta = 0$ for $\theta$ .

Find the ordered pair $(x,y)$ that satisfies the constraints: $x + y \geq 4$ and $2x + y \leq 7$ , where $x$ represents hot dogs at $\$2$ each and $y$ represents peanuts at $\$1$ each, given Cody has $\$7$ .

Find the set of real numbers $x$ such that $x + 6 > 0$ .

Find the value of $\mathrm{c}$ in the standard form of a quadratic function $y = ax^2 + bx + c$ given the table of values.

Find the range of values for $x$ that satisfy the inequality $86 > x - 18$ .

Solve the simple arithmetic equation $7+9=$ .

Katherine buys a random cake. The probability it has figs is $\frac{4}{7}$ , fondant is $\frac{3}{10}$ , and both is $\frac{1}{8}$ . Given figs, find the probability it also has fondant.

Solve the linear equation $3 z + 8 = 12 + 3 x - z$ for $z$ and $x$ .

Find the equation that models the growth of a population of 100 bacteria that doubles every hour over 3 hours.
$N(t) = 100 \cdot 2^t$ , where $N(t)$ is the number of bacteria and $t$ is the time in hours.

Subtract two integers: $-43 - 19 = ?$

Find the quadrant of the angle $177^{\circ}$ .

Solve the system of linear equations using Gaussian elimination: $2x + y - z = 2, x + 3y + 2z = 1, x + y + z = 2$ .

Find the speed of the tip of a woman's shadow when she is $15 \mathrm{~m}$ from a $3 \mathrm{~m}$ tall pole, running at $1.8 \mathrm{~m} / \mathrm{s}$ and is $1.5 \mathrm{~m}$ tall.

Solve for $m$ in the equation $11m + 4m + 2m = -17$ .

Find the derivative of the functions $f(x)=2x^2$ , $f(x)=2x$ , $f(x)=5$ , $f(x)=-x^2$ , $f(x)=2x+3$ , and $f(x)=ax^2$ .

Solve the linear equation $\frac{1}{2} x - 2 = 9 - 5 x$ by graphing to find the value of $x$ .

Simplify the rational expression $\frac{2 x^{3}+11 x^{2}-21 x}{x^{2}+3 x}$ for $x \neq-3, 0$ .

Solve the equation $3x=24$ to find the value of $x$ .

Solve for $y$ given the equation $4y = 3y + 6\log 1128$

Solve for the acute angle $\theta$ where $3 \cos \theta = \frac{1}{9}$ .

Find the value of the expression $|-6|-|6|-(-6)$ .

Simplify the expression $\frac{2^{5}}{(-4+8)} \times 2$ .

Divide $1 \frac{4}{9}$ by $-\frac{2}{9}$ and write the quotient in simplest form.

Transform the polar equation $\theta=\frac{4 \pi}{3}$ to rectangular coordinates and graph the equation.

Find the discriminant of $3 x^{2}-7 x-12=0$ and describe the number and type of roots.

Simplify the expression $12x(4x+y)$ .

Find the value(s) of $x$ that satisfy $x^2 = 25$ .

Find a method to evaluate the expression $8+9$ .

Find the equation that best describes the direct relationship between the total cost of gas (y) in dollars and the amount of gas purchased (x) in gallons, given that $5 \frac{1}{4}$ gallons of gas cost $\$ 12.60$ .

Is the difference between Dani's and Raj's ages always constant? Explain using the data: $Dani's Age = 5, 10, 15, 20$ and $Raj's Age = 10, 15, 20, 25$ .

Find the exact value of $x$ that satisfies the equation $3^{2x-5}=81$ .

Solve the equation by expressing each side as a power of the same base and equating exponents: $4^{x+2}=8^{x-6}$ . Choose the correct exponent value.

Is $-\sqrt{0/4}$ a rational number?

Solve the quadratic equation $11 w^{2} - 22 w + 121 = 81$ for the variable $w$ .

Find the value of $x$ where $\frac{7}{8}=\frac{x}{44}$ .

Determine which equations can be solved using the zero product property. Options: $-(x-1)(x+9)=0$ , $3 x^{2}-6 x=0$ .

Simplify the expression $64^{-\frac{3}{2}}$ .

Solve for $x$ when $3x - 19 = 0$ , given $x = 10$ .

There are 240 students in the 7th grade. $5\%$ are in the Environmental Club. How many students are in the club?

Graph the cosine function with period $2\pi$ .

Find $y$ when $x=3$ given that $y$ and $x$ have a proportional relationship and $y=9$ when $x=2$ . $y = 13.5$

Solve the equation $2(x-3)+3=6x-5$ using the Distributive Property. Find the value of $x$ .

Solve $7=3x-2$ for $x$ . What operations isolate $x$ ? (a) Divide by 7, then subtract 2 (b) Subtract 2, then divide by 7 (c) Multiply by 3, then add 2 (d) Add 2, then divide by 3

Find the range of the values in the table, where $X = \{-1, 3, 3, 4\}$ and $Y = \{-2, 0, -2, 5\}$ .

Find $y$ using the equation $y = m x - b$ if $m = 11$ , $x = 2$ , and $b = 5$ .

Find the total meal cost after an 18% tip on a $58 meal.
a) Let $m =$ meal cost. The equation is: $\text{Total Meal Cost} = m + 0.18m$
b) The total cost of the meal is = $\$68.44$