Browse Math problems in the Studdy Learning Bank!

Problem 7901

Solve for the unknown variable $v$ in the equation $5 v = 12.5$ .

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Problem 7902

Solve the quadratic equation $39.4=9k^2$ for the value of $k$ .

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Problem 7903

Write the equation of a parabola in vertex form and intercept form, then show they are equivalent. Identify the axis of symmetry from each equation form. Parabola vertex: $(2, -9)$ , opens upwards.
Vertex form: $y = a(x - 2)^2 - 9$ Intercept form: $y = a(x - p)(x - q)$ Show equivalence by converting to general form: $y = ax^2 + bx + c$
The axis of symmetry is given by $x = h$ in vertex form and the average of the x-intercepts in intercept form.

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Problem 7904

Simplify the expression $\frac{3 x}{4-3}-8 \times(-1)+4$ .

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Problem 7905

Find the equation of a curve with $\frac{dy}{dx} = 42yx^{13}$ and $y$ -intercept at 2.

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Problem 7906

Redefine homework problems for better discoverability:
1. If $y$ varies directly with $x$ , and $y$ doubles, then $x$ \_\_\_\_\_\_\_\_.
2. Determine if the given table represents direct, indirect, or neither variation.
3. If $s$ varies inversely with $t$ and $s=12$ when $t=8$ , find the function rule and $s$ when $t=3$ .
4. Find the vertex of $f(x)=|x-3|+2$ .
5. Describe the translation from $f(x)=|x|$ to $f(x)=|x-3|+2$ .
6. Plot at least 3 points and graph $f(x)=|x-3|+2$ .

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Problem 7907

Show that for positive real numbers $u$ and $v$ , and a positive real number $a \neq 1$ , $\log_{a}\left(\frac{u}{v}\right) = \log_{a}u - \log_{a}v$ .

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Problem 7908

Find the number of solutions for $x$ in the equation $16=-16 \times 2+16 x+12$ .

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Problem 7909

Solve for $x$ where $615=5x^{3}$ . Express the answer to the hundredths place.

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Problem 7910

Find the logarithm of 1.6.

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Problem 7911

Rotate a point on the unit circle to the angle $5\pi/4$ and find the exact value of $\tan(5\pi/4)$ .

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Problem 7912

Convert 8 yards of fishing line to inches using the provided conversion table.
$1 \mathrm{yd} = 3 \mathrm{ft}$ and $1 \mathrm{ft} = 12 \mathrm{in}$ , so 8 yards is $8 \times 3 \times 12 = 288$ inches.

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Problem 7913

Find the interval where $x + \sqrt[3]{x} = 1$ has a solution, per the Intermediate Value Theorem.

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Problem 7914

State the opposite of $-7$ , which is $7$ .

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Problem 7915

Find the radius of the circle with equation $2x^2 + 2y^2 = 50$ .

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Problem 7916

Find the focus of the ellipse with equation $\frac{(x+4)^{2}}{16}+\frac{(y-3)^{2}}{20}=1$ .

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Problem 7917

Find the time it takes for Aaron and Anna to paint a door together, given that Aaron can paint it in 6 hours and Anna in 3 hours.

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Problem 7918

Determine if each ordered pair $\{(3,0), (4,-1), (5,-4)\}$ is a solution to the system of linear inequalities: $x-3y < 7, 2x+y > 1$ .

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Problem 7919

Use the Distributive Property to solve $2(m+3)=22$ . Describe distributing the 2 to each term inside the parentheses. The solution is $m=7$ .

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Problem 7920

Find the square of the complex number $(5+4i)$ and express the result in standard form.

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Problem 7921

Find the value of $\frac{26}{5}$ .

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Problem 7922

Find the derivative of $f(x) = (x^{3} + x^{2})^{\tan x}$ using logarithmic differentiation.

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Problem 7923

Find the value of $a-b$ where the lines with slopes $2$ and passing through $(1,10)$ , and passing through $(2,4)$ and $(6,8)$ , intersect at $(a,b)$ .

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Problem 7924

Find the distance between the line $y = x + 3$ and the point $W(1, -3)$ . Round the answer to the nearest tenth.

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Problem 7925

Determine validity of argument using Euler diagram: "All mockingbirds have wings. All wings have feathers. All mockingbirds have feathers." Is this argument valid or invalid?

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Problem 7926

Find the sum of $9.727\ \text{mL}$ and $16.50\ \text{mL}$ .

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Problem 7927

Find the values of $x$ and $y$ in an equilateral triangle with side length 2 units and an altitude drawn.

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Problem 7928

Solve the quadratic equation $4x^2 = 25$ for real values of $x$ .

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Problem 7929

List all values on $[-\frac{5\pi}{2}, \frac{5\pi}{2}]$ that satisfy $\left(x, -\frac{\sqrt{3}}{2}\right)$ on the graph of $y=\sin x$ .

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Problem 7930

(a) Find the largest $\delta$ such that $|x-1|<\delta$ implies $|4x-4|<0.5$ . (b) Find the largest $\delta$ such that $|x-1|<\delta$ implies $|4x-4|<0.05$ .

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Problem 7931

Solve the linear equation $-11(x+3.9)=-39.3$ for the value of $x$ .

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Problem 7932

Multiply $0.5128 \cdot 10$ and choose the correct result from the options.

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Problem 7933

Solve for $t$ in the equation $10t=90$ .

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Problem 7934

Find the value of the expression $1-(+3)-(-5)$ .

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Problem 7935

Quantity with initial value of 8900 grows exponentially at $65\%$ per hour. Find the value after 411 minutes, rounded to nearest hundredth.

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Problem 7936

Determine the sign of $-4/(-13)$ .

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Problem 7937

Berechne die Summe aus $-3,8$ und $5 \frac{1}{6}$ und addiere das Produkt aus 0,1 und $\frac{4}{3}$ .

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Problem 7938

Convert parametric equations $x=-\frac{t^{2}}{3}, y=t$ to rectangular form.

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Problem 7939

Solve: $\left(3 \times 10^{9}\right)\left(4 \times 10^{5}\right) /\left(6 \times 10^{-3}\right)$ , $2 \times 10^{-15}$ , $2 \times 10^{17}$ , $2 \times 10^{11}$ , undefined.

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Problem 7940

Find the sign that makes the statement $-8 ? |-8|$ true, where the valid signs are $>, <, \text{or } =$ .

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Problem 7941

Solve the linear equation $\frac{4}{5} x=-8$ for the unknown variable $x$ .

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Problem 7942

Denise has 4 more pens than 2 times the number of pens in a box. Write an expression for the number of pens Denise has, where $\mathrm{p}$ is the number of pens in a box.

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Problem 7943

Determine if the function $m(x) = -5x^5 + 3x^3 + x$ is even, odd, or neither.

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Problem 7944

Solve the equation $4(2k + 3) = 44$ for the value of $k$ .

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Problem 7945

Determine if the function where $y$ decreases by $x^2$ as $x$ increases by 1 is linear or nonlinear. Explain your reasoning.

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Problem 7946

Solve the inequality $y-4 \leq 4x+8$ for real values of $x$ and $y$ .

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Problem 7947

Skylar has a bag with pineapple, apple, and peach chews. She randomly selects a chew 23 times, recording the results. Repeat the experiment 2000 times - how many times would you expect Skylar to select a peach chew? Round to the nearest whole number.
$\text{Peach chews selected} = \frac{6}{23} \cdot 2000 \approx 522$

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Problem 7948

Find the largest zero of the function $y = 6x^2 + 19x - 24$ to the nearest hundredth.

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Problem 7949

Increase 1200 by $6\%$

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Problem 7950

Show that the sum of $0.2\overline{5}$ and $0.4\overline{4}$ equals $\frac{7}{10}$ .

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Problem 7951

Solve for the positive value of $x$ in the equation $x^{4/3} = 16$ . Express the answer as a simplified integer or improper fraction.

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Problem 7952

Determine the best trigonometric substitution to simplify integrals: $\int \frac{3}{\sqrt{3+x^{2}}} dx$ and $\int \frac{11}{\left(9-81 x^{2}\right)^{3 / 2}} dx$ .

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Problem 7953

Find the total number of registered doctors if $33.6\%$ were female and there were 48,200 female registered doctors.

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Problem 7954

Solve the quadratic equation $x^2 + 13x + 40 = 0$ and find the values of $x$ .

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Problem 7955

Subtract $7x^2 + 4x - 9$ from $5x^2 + 10x - 5$ . Express the result as a trinomial in descending degree order.

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Problem 7956

Find the hourly wage given the relationship between hours worked and money earned: $\$ x$ per hour.

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Problem 7957

If $A$ is a $3 \times 5$ matrix, then $\operatorname{rank}(A) < 3$ .

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Problem 7958

Find the angle between the vectors $\langle-7,5,4\rangle$ and $\langle-1,8,7\rangle$ . Round the angle to the nearest degree.

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Problem 7959

Simplify the expression $\frac{2}{3}+3^{3}-\frac{2}{5} \div 1 \frac{3}{5}$ and express the solution as a mixed number or fraction in lowest terms.

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Problem 7960

Find the determinant of $2BA^{-1}$ given $\det(A)=2$ and $\det(B)=4$ .

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Problem 7961

Graph the logarithmic function $f(x) = \log_3 x$ and identify its key characteristics.

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Problem 7962

Find the present value of a firm's 3-year cash flow stream with $5,000,$ 25,000, and $14,000 at 8% discount rate.

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Problem 7963

Solve the equation $\frac{10.4-x}{1.2}=1.6$ for the unknown variable $x$ .

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Problem 7964

Find the frequency of the function $f(x) = -3 \sin(4x) + 9$ .

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Problem 7965

Find the slope of line $b$ perpendicular to line $a$ with equation $y=\frac{-9}{4} x+\frac{1}{7}$ . Express the answer as a fraction.

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Problem 7966

The beach house costs $\$ 800000$ now. Inflation is expected to increase the price by $5\%$ annually over 20 years. How much will the house cost after 20 years? If they invest equal end-of-year payments earning $13\%$ annually, how much must they invest each year to buy the house in 20 years?

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Problem 7967

Find the eigenvalues $\lambda_{1}, \lambda_{2}, \lambda_{3}$ of matrix $A=\left(\begin{array}{ccc}3 & 0 & 0 \\ \frac{1}{2} & 5 & 0 \\ \frac{1}{12} & \frac{1}{6} & 0\end{array}\right)$ and their corresponding eigenvectors.

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Problem 7968

The function $s(m)=5+4(m-1)$ represents Rudy's stamp collection. The value 4 represents the number of stamps Rudy adds to his collection each month. Rudy collected stamps for 4 months and his collection is worth $\$ 4$ .

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Problem 7969

Find the number of ways to answer a 5-question quiz with 4-choice multiple-choice questions, assuming all questions are answered.

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Problem 7970

A lake covers 11 square km, decreasing exponentially by 2% per year: $A(t)=11 \cdot(0.98)^{t}$ . By what factor does the area decrease in 10 years?

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Problem 7971

Evaluate the limit of $f(x)=\sqrt{x}$ as $x$ approaches $6$ . The value of the limit is $\sqrt{6}$ .

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Problem 7972

Solve for $z$ in the equation $3(z-7)=3$ .

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Problem 7973

Find the value of the expression $\left(-\frac{3}{2}\right) \times (-6)$ .

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Problem 7974

Solve for the variable $z$ in the equation $1-y+z=A$ .

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Problem 7975

Solve for $W$ , where $A=9W$ .

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Problem 7976

Simplify the expression: $6-12 \div 4+9^{2} \times 2$

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Problem 7977

Find the equation of the secant line for the natural logarithm function $f(x) = \ln(x)$ on the interval $[1, 7]$ .

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Problem 7978

Find the second polynomial Jim subtracted from the original polynomial $-4 x^{2}-2 x-5$ to get the difference $-9 x^{2}+x-4$ .

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Problem 7979

Solve the equation $468 * 5 =$ ?

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Problem 7980

Describe the power $3^{4}$ . Check all correct descriptions: The power is 3 and 4 multiplied. The power is 3 to the fourth. The power means 3 factors of 4 are multiplied. The power can be expanded as $3 \cdot 3 \cdot 3 \cdot 3$ . The value of this power is 81.

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Problem 7981

Find the value of h when $-6|2h-5|=50$ .

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Problem 7982

Find the function $y(x)$ that satisfies the first-order differential equation $y' = y \sin x$ , where $y = \pi e^{-\cos x}$ is a solution.

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Problem 7983

Find the value of $f(-4)$ for $f(x)=\frac{-14-x^{2}}{9}$ , rounded to the nearest hundredth.

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Problem 7984

Find the degree 4 polynomial $P(x)$ with roots at $x=4$ (multiplicity 2), $x=0$ (multiplicity 1), and $x=-2$ (multiplicity 1), passing through $(1,-135)$ .

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Problem 7985

Redefine a linear function $y=6x+13$ , find its inverse, and determine the relationship between the functions.
$f(x) = 6x + 13$ $x = (y-13)/6$ $g(y) = (y-13)/6$ $g$ undoes the process of $f$ , $f=g^{-1}$ , $f$ and $g$ are inverses.

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Problem 7986

Find the antiderivative of $R(x) = \frac{100 e^{x+5}}{(1+e^{x+5})^2}$ , where $x$ is the natural log of a histamine dose in mM. Evaluate the antiderivative at $x=-8.9$ and round to 3 decimal places.

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Problem 7987

Simplify the expression $(30 a - 0.23 g)^2$ .

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Problem 7988

Simplify the expression $(r+f+6)(r+f-6)$ .

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Problem 7989

Rewrite parametric equations $x = t, y = -t^2/3$ in rectangular form.

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Problem 7990

Graph the quadratic inequality $y < -2x^2 - 8x - 12$ . Determine which ordered pairs $(x, y)$ are solutions.

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Problem 7991

Simplify the expression $(v-3f)^2$ and express the result as a single term.

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Problem 7992

Solve the system of linear equations: $x = -4$ and $y + 6.2x = -13$ .

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Problem 7993

Simplify the expression $12 \times 5$ . Show your work.

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Problem 7994

Solve the exponential equation $9^{x+3}=27^{-2x+4}$ for the unknown variable $x$ .

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Problem 7995

Calculate the ratio of input and output power in decibels, given input power is $20 \mathrm{~W}$ and output power is $40 \mathrm{~W}$ .

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Problem 7996

Find the equation of a circle with center at $(-3, 6)$ given that the line $3x - y - 5 = 0$ is tangent to the circle.

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Problem 7997

Find the solution set of the equation $|x-6| + 4 = 10$ .

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Problem 7998

Find the child's age using the dosage formula: $A = \frac{100 \times D}{4 \times N} - 5$ . Rearrange the formula to recover the child's age $A$ .

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Problem 7999

Find the value of $x$ given the equation of a line $y-y_1 = m(x-x_1)$

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Problem 8000

Find the distance represented by a 6-inch line segment on a scale drawing where 4 inches represents 25 miles.

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Math

Problem 7901

Solve for the unknown variable vvv in the equation 5v=12.55 v = 12.55v=12.5.

Problem 7902

Solve the quadratic equation 39.4=9k239.4=9k^239.4=9k2 for the value of kkk.

Problem 7903

Problem 7904

Simplify the expression 3x4−3−8×(−1)+4\frac{3 x}{4-3}-8 \times(-1)+44−33x​−8×(−1)+4.

Problem 7905

Find the equation of a curve with dydx=42yx13\frac{dy}{dx} = 42yx^{13}dxdy​=42yx13 and yyy-intercept at 2.

Problem 7906

Problem 7907

Show that for positive real numbers uuu and vvv, and a positive real number a≠1a \neq 1a=1, log⁡a(uv)=log⁡au−log⁡av\log_{a}\left(\frac{u}{v}\right) = \log_{a}u - \log_{a}vloga​(vu​)=loga​u−loga​v.

Problem 7908

Find the number of solutions for xxx in the equation 16=−16×2+16x+1216=-16 \times 2+16 x+1216=−16×2+16x+12.

Problem 7909

Solve for xxx where 615=5x3615=5x^{3}615=5x3. Express the answer to the hundredths place.

Problem 7910

Find the logarithm of 1.6.

Problem 7911

Rotate a point on the unit circle to the angle 5π/45\pi/45π/4 and find the exact value of tan⁡(5π/4)\tan(5\pi/4)tan(5π/4).

Problem 7912

Convert 8 yards of fishing line to inches using the provided conversion table.1yd=3ft1 \mathrm{yd} = 3 \mathrm{ft}1yd=3ft and 1ft=12in1 \mathrm{ft} = 12 \mathrm{in}1ft=12in, so 8 yards is 8×3×12=2888 \times 3 \times 12 = 2888×3×12=288 inches.

Problem 7913

Find the interval where x+x3=1x + \sqrt[3]{x} = 1x+3x​=1 has a solution, per the Intermediate Value Theorem.

Problem 7914

State the opposite of −7-7−7, which is 777.

Problem 7915

Find the radius of the circle with equation 2x2+2y2=502x^2 + 2y^2 = 502x2+2y2=50.

Problem 7916

Find the focus of the ellipse with equation (x+4)216+(y−3)220=1\frac{(x+4)^{2}}{16}+\frac{(y-3)^{2}}{20}=116(x+4)2​+20(y−3)2​=1.

Problem 7917

Find the time it takes for Aaron and Anna to paint a door together, given that Aaron can paint it in 6 hours and Anna in 3 hours.

Problem 7918

Determine if each ordered pair {(3,0),(4,−1),(5,−4)}\{(3,0), (4,-1), (5,-4)\}{(3,0),(4,−1),(5,−4)} is a solution to the system of linear inequalities: x−3y<7,2x+y>1x-3y < 7, 2x+y > 1x−3y<7,2x+y>1.

Problem 7919

Use the Distributive Property to solve 2(m+3)=222(m+3)=222(m+3)=22. Describe distributing the 2 to each term inside the parentheses. The solution is m=7m=7m=7.

Problem 7920

Find the square of the complex number (5+4i)(5+4i)(5+4i) and express the result in standard form.

Problem 7921

Find the value of 265\frac{26}{5}526​.

Problem 7922

Find the derivative of f(x)=(x3+x2)tan⁡xf(x) = (x^{3} + x^{2})^{\tan x}f(x)=(x3+x2)tanx using logarithmic differentiation.

Problem 7923

Find the value of a−ba-ba−b where the lines with slopes 222 and passing through (1,10)(1,10)(1,10), and passing through (2,4)(2,4)(2,4) and (6,8)(6,8)(6,8), intersect at (a,b)(a,b)(a,b).

Problem 7924

Find the distance between the line y=x+3y = x + 3y=x+3 and the point W(1,−3)W(1, -3)W(1,−3). Round the answer to the nearest tenth.

Problem 7925

Determine validity of argument using Euler diagram: "All mockingbirds have wings. All wings have feathers. All mockingbirds have feathers." Is this argument valid or invalid?

Problem 7926

Find the sum of 9.727 mL9.727\ \text{mL}9.727 mL and 16.50 mL16.50\ \text{mL}16.50 mL.

Problem 7927

Find the values of xxx and yyy in an equilateral triangle with side length 2 units and an altitude drawn.

Problem 7928

Solve the quadratic equation 4x2=254x^2 = 254x2=25 for real values of xxx.

Problem 7929

List all values on [−5π2,5π2][-\frac{5\pi}{2}, \frac{5\pi}{2}][−25π​,25π​] that satisfy (x,−32)\left(x, -\frac{\sqrt{3}}{2}\right)(x,−23​​) on the graph of y=sin⁡xy=\sin xy=sinx.

Problem 7930

(a) Find the largest δ\deltaδ such that ∣x−1∣<δ|x-1|<\delta∣x−1∣<δ implies ∣4x−4∣<0.5|4x-4|<0.5∣4x−4∣<0.5. (b) Find the largest δ\deltaδ such that ∣x−1∣<δ|x-1|<\delta∣x−1∣<δ implies ∣4x−4∣<0.05|4x-4|<0.05∣4x−4∣<0.05.

Problem 7931

Solve the linear equation −11(x+3.9)=−39.3-11(x+3.9)=-39.3−11(x+3.9)=−39.3 for the value of xxx.

Problem 7932

Multiply 0.5128⋅100.5128 \cdot 100.5128⋅10 and choose the correct result from the options.

Problem 7933

Solve for ttt in the equation 10t=9010t=9010t=90.

Problem 7934

Find the value of the expression 1−(+3)−(−5)1-(+3)-(-5)1−(+3)−(−5).

Problem 7935

Quantity with initial value of 8900 grows exponentially at 65%65\%65% per hour. Find the value after 411 minutes, rounded to nearest hundredth.

Problem 7936

Determine the sign of −4/(−13)-4/(-13)−4/(−13).

Problem 7937

Berechne die Summe aus −3,8-3,8−3,8 und 5165 \frac{1}{6}561​ und addiere das Produkt aus 0,1 und 43\frac{4}{3}34​.

Problem 7938

Convert parametric equations x=−t23,y=tx=-\frac{t^{2}}{3}, y=tx=−3t2​,y=t to rectangular form.

Problem 7939

Solve: (3×109)(4×105)/(6×10−3)\left(3 \times 10^{9}\right)\left(4 \times 10^{5}\right) /\left(6 \times 10^{-3}\right)(3×109)(4×105)/(6×10−3), 2×10−152 \times 10^{-15}2×10−15, 2×10172 \times 10^{17}2×1017, 2×10112 \times 10^{11}2×1011, undefined.

Problem 7940

Find the sign that makes the statement −8?∣−8∣-8 ? |-8|−8?∣−8∣ true, where the valid signs are >,<,or =>, <, \text{or } =>,<,or =.

Problem 7941

Solve for the unknown variable $v$ in the equation $5 v = 12.5$ .

Solve the quadratic equation $39.4=9k^2$ for the value of $k$ .

Simplify the expression $\frac{3 x}{4-3}-8 \times(-1)+4$ .

Find the equation of a curve with $\frac{dy}{dx} = 42yx^{13}$ and $y$ -intercept at 2.

Show that for positive real numbers $u$ and $v$ , and a positive real number $a \neq 1$ , $\log_{a}\left(\frac{u}{v}\right) = \log_{a}u - \log_{a}v$ .

Find the number of solutions for $x$ in the equation $16=-16 \times 2+16 x+12$ .

Solve for $x$ where $615=5x^{3}$ . Express the answer to the hundredths place.

Rotate a point on the unit circle to the angle $5\pi/4$ and find the exact value of $\tan(5\pi/4)$ .

Convert 8 yards of fishing line to inches using the provided conversion table.
$1 \mathrm{yd} = 3 \mathrm{ft}$ and $1 \mathrm{ft} = 12 \mathrm{in}$ , so 8 yards is $8 \times 3 \times 12 = 288$ inches.

Find the interval where $x + \sqrt[3]{x} = 1$ has a solution, per the Intermediate Value Theorem.

State the opposite of $-7$ , which is $7$ .

Find the radius of the circle with equation $2x^2 + 2y^2 = 50$ .

Find the focus of the ellipse with equation $\frac{(x+4)^{2}}{16}+\frac{(y-3)^{2}}{20}=1$ .

Determine if each ordered pair $\{(3,0), (4,-1), (5,-4)\}$ is a solution to the system of linear inequalities: $x-3y < 7, 2x+y > 1$ .

Use the Distributive Property to solve $2(m+3)=22$ . Describe distributing the 2 to each term inside the parentheses. The solution is $m=7$ .

Find the square of the complex number $(5+4i)$ and express the result in standard form.

Find the value of $\frac{26}{5}$ .

Find the derivative of $f(x) = (x^{3} + x^{2})^{\tan x}$ using logarithmic differentiation.

Find the value of $a-b$ where the lines with slopes $2$ and passing through $(1,10)$ , and passing through $(2,4)$ and $(6,8)$ , intersect at $(a,b)$ .

Find the distance between the line $y = x + 3$ and the point $W(1, -3)$ . Round the answer to the nearest tenth.

Find the sum of $9.727\ \text{mL}$ and $16.50\ \text{mL}$ .

Find the values of $x$ and $y$ in an equilateral triangle with side length 2 units and an altitude drawn.

Solve the quadratic equation $4x^2 = 25$ for real values of $x$ .

List all values on $[-\frac{5\pi}{2}, \frac{5\pi}{2}]$ that satisfy $\left(x, -\frac{\sqrt{3}}{2}\right)$ on the graph of $y=\sin x$ .

(a) Find the largest $\delta$ such that $|x-1|<\delta$ implies $|4x-4|<0.5$ . (b) Find the largest $\delta$ such that $|x-1|<\delta$ implies $|4x-4|<0.05$ .

Solve the linear equation $-11(x+3.9)=-39.3$ for the value of $x$ .

Multiply $0.5128 \cdot 10$ and choose the correct result from the options.

Solve for $t$ in the equation $10t=90$ .

Find the value of the expression $1-(+3)-(-5)$ .

Quantity with initial value of 8900 grows exponentially at $65\%$ per hour. Find the value after 411 minutes, rounded to nearest hundredth.

Determine the sign of $-4/(-13)$ .

Berechne die Summe aus $-3,8$ und $5 \frac{1}{6}$ und addiere das Produkt aus 0,1 und $\frac{4}{3}$ .

Convert parametric equations $x=-\frac{t^{2}}{3}, y=t$ to rectangular form.

Solve: $\left(3 \times 10^{9}\right)\left(4 \times 10^{5}\right) /\left(6 \times 10^{-3}\right)$ , $2 \times 10^{-15}$ , $2 \times 10^{17}$ , $2 \times 10^{11}$ , undefined.

Find the sign that makes the statement $-8 ? |-8|$ true, where the valid signs are $>, <, \text{or } =$ .

Solve the linear equation $\frac{4}{5} x=-8$ for the unknown variable $x$ .

Denise has 4 more pens than 2 times the number of pens in a box. Write an expression for the number of pens Denise has, where $\mathrm{p}$ is the number of pens in a box.

Determine if the function $m(x) = -5x^5 + 3x^3 + x$ is even, odd, or neither.

Solve the equation $4(2k + 3) = 44$ for the value of $k$ .

Determine if the function where $y$ decreases by $x^2$ as $x$ increases by 1 is linear or nonlinear. Explain your reasoning.

Solve the inequality $y-4 \leq 4x+8$ for real values of $x$ and $y$ .

Find the largest zero of the function $y = 6x^2 + 19x - 24$ to the nearest hundredth.

Increase 1200 by $6\%$

Show that the sum of $0.2\overline{5}$ and $0.4\overline{4}$ equals $\frac{7}{10}$ .

Solve for the positive value of $x$ in the equation $x^{4/3} = 16$ . Express the answer as a simplified integer or improper fraction.

Determine the best trigonometric substitution to simplify integrals: $\int \frac{3}{\sqrt{3+x^{2}}} dx$ and $\int \frac{11}{\left(9-81 x^{2}\right)^{3 / 2}} dx$ .

Find the total number of registered doctors if $33.6\%$ were female and there were 48,200 female registered doctors.

Solve the quadratic equation $x^2 + 13x + 40 = 0$ and find the values of $x$ .

Subtract $7x^2 + 4x - 9$ from $5x^2 + 10x - 5$ . Express the result as a trinomial in descending degree order.

Find the hourly wage given the relationship between hours worked and money earned: $\$ x$ per hour.

If $A$ is a $3 \times 5$ matrix, then $\operatorname{rank}(A) < 3$ .

Find the angle between the vectors $\langle-7,5,4\rangle$ and $\langle-1,8,7\rangle$ . Round the angle to the nearest degree.

Simplify the expression $\frac{2}{3}+3^{3}-\frac{2}{5} \div 1 \frac{3}{5}$ and express the solution as a mixed number or fraction in lowest terms.

Find the determinant of $2BA^{-1}$ given $\det(A)=2$ and $\det(B)=4$ .

Graph the logarithmic function $f(x) = \log_3 x$ and identify its key characteristics.

Find the present value of a firm's 3-year cash flow stream with $5,000,$ 25,000, and $14,000 at 8% discount rate.

Solve the equation $\frac{10.4-x}{1.2}=1.6$ for the unknown variable $x$ .

Find the frequency of the function $f(x) = -3 \sin(4x) + 9$ .

Find the slope of line $b$ perpendicular to line $a$ with equation $y=\frac{-9}{4} x+\frac{1}{7}$ . Express the answer as a fraction.

The function $s(m)=5+4(m-1)$ represents Rudy's stamp collection. The value 4 represents the number of stamps Rudy adds to his collection each month. Rudy collected stamps for 4 months and his collection is worth $\$ 4$ .

A lake covers 11 square km, decreasing exponentially by 2% per year: $A(t)=11 \cdot(0.98)^{t}$ . By what factor does the area decrease in 10 years?

Evaluate the limit of $f(x)=\sqrt{x}$ as $x$ approaches $6$ . The value of the limit is $\sqrt{6}$ .

Solve for $z$ in the equation $3(z-7)=3$ .

Find the value of the expression $\left(-\frac{3}{2}\right) \times (-6)$ .

Solve for the variable $z$ in the equation $1-y+z=A$ .