Solve

Problem 1

Calculate $31 - 8$ .

See Solution

Problem 2

Solve for $x$ in the equation: $3(x+3)-5=16$ .

See Solution

Problem 3

Find the $z$ -score for $x=7$ given a random variable $X$ with mean 4 and standard deviation 2.

See Solution

Problem 4

Find when balls A and B, rotating at different speeds, meet at the starting point again. A: 2 rotations in 26 min, B: 5 in 35 min.

See Solution

Problem 5

Evaluate $\frac{n p}{n+p}$ for $n=9$ and $p=15$ .

See Solution

Problem 6

Calculate $8 \div 2(2+2)$ .

See Solution

Problem 7

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

See Solution

Problem 8

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

See Solution

Problem 9

Evaluate the integral $\int \frac{9 x+2}{x^{2}+x-6} d x$ .

See Solution

Problem 10

Решите у в уравнении: $4y + 3 = 6y - 7$ .

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Problem 11

Calculate the integral $\int_{2}^{3} 3 x^{2} d t$ .

See Solution

Problem 12

Evaluate the integral $\int_{-2}^{2} \frac{1+x^{2}}{1+2^{x}} d x$ .

See Solution

Problem 13

Find $x$ in the equation $\frac{2}{3}=\frac{5}{x}$ . Options: A $\frac{2}{15}$ , B 6, C $\frac{15}{2}$ , D 8.

See Solution

Problem 14

A boat travels 222 km on 74 liters. How much gas is needed for 39 km?

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Problem 15

Calculate the integral $\int \tan^{3} x \sec x \, dx$ .

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Problem 16

A boat travels 129 km on 43 liters. How far can it go on 57 liters?

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Problem 17

Find $y$ if $\log _{y} \frac{1}{9}=3$ .

See Solution

Problem 18

Solve for $y$ in the equation $y^{2}+7 y-60=0$ .

See Solution

Problem 19

פתרו את המשוואה $3 x + 5 = 14$ ומצאו את ערך $x$ . תשובה: $x =$

See Solution

Problem 20

Find the $z$ -score for $x=7$ given that the mean is 4 and the standard deviation is 2.

See Solution

Problem 21

פתרו את המשוואה $3 x + 5 = 14$ ומצאו את $x =$

See Solution

Problem 22

Find the line equation through the origin with the same slope as the line between points $A(1,5)$ and $B(2,-3)$ .

See Solution

Problem 23

The probability of an athlete not winning 3 races is $\frac{1}{4}$ . Find the probability of winning: (i) only the 2nd race, (ii) all 3 races, (iii) exactly 2 races.

See Solution

Problem 24

Evaluate $-3 \Delta -1$ for the operation $a \Delta b = \frac{a+b}{\sqrt{ab}}$ where $a, b \neq 0$ .

See Solution

Problem 25

Calculate $31 - 8$ .

See Solution

Problem 26

A boat travels 222 km on 74 liters. How much gas for 39 km? Use the ratio: $\frac{74}{222} = \frac{x}{39}$ .

See Solution

Problem 27

A car travels 234 km on 39 liters. How many liters are needed for 414 km?

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Problem 28

Calculate $-32 \div 4$ .

See Solution

Problem 29

Find the integral of $-\frac{1}{5} \sin u \, du$ .

See Solution

Problem 30

Solve the system of equations: $6x - 7y = -8$ and $-x - 4y = -9$ .

See Solution

Problem 31

Solve the equation $\frac{7x - 8}{5} = \frac{2x + 5}{4}$ .

See Solution

Problem 32

Solve the equation: $\frac{5(x+11)}{3}=\frac{3(1+x)}{2}$ for $x$ .

See Solution

Problem 33

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

See Solution

Problem 34

Find $k$ for the planes $x-2y+4z=10$ and $18x+17y+kz=50$ to be perpendicular. Options: (a) -4 (b) 4 (c) 2 (d) -2

See Solution

Problem 35

Solve the system of equations: $10x - 14y = -4$ and $-10x - 20y = -30$ .

See Solution

Problem 36

Find the time when balls A and B return to the starting point, given A rotates 2 times in 26 min and B 5 times in 35 min.

See Solution

Problem 37

Calculate $\frac{6}{2}(1+2)$ .

See Solution

Problem 38

Find $y$ if $\log_{y} \frac{1}{9} = 3$ .

See Solution

Problem 39

Find the $z$ -score for $x = 7$ given that the mean $\mu = 4$ and standard deviation $\sigma = 2$ .

See Solution

Problem 40

Find the $z$ -score for $x = 7$ given $\mu = 4$ and $\sigma = 2$ using $z = \frac{x - \mu}{\sigma}$ .

See Solution

Problem 41

Find $m \angle 12$ if $m \angle 3=2x+14$ and $m \angle 16=4x-16$ , with angles 3 and 12 as alternate exterior angles.

See Solution

Problem 42

Find $m \angle 16$ if $m \angle 1=5x+8$ and $m \angle 16=7x-20$ .

See Solution

Problem 43

Find $m \angle 13$ given $m \angle 7 = 4x + 6$ and $m \angle 15 = 13x - 6$ for parallel lines.

See Solution

Problem 44

Find $m \angle 14$ given $m \angle 1 = 67^{\circ}$ and $m \angle 18 = 42^{\circ}$ with parallel lines $l$ and $m$ . Options: $113^{\circ}$ , $96^{\circ}$ , $105^{\circ}$ , $109^{\circ}$ .

See Solution

Problem 45

Differentiate $x^{e^{x}}$ with respect to $x$ .

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Problem 46

What is the value of $6 \div 2(1+2)$ ?

See Solution

Problem 47

Solve $60 \div 2(3+7)$ .

See Solution

Problem 48

Find the sum of two alternate exterior angles: $6a - 33$ and $2x + 10$ .

See Solution

Problem 49

Find the sum of two alternate exterior angles: $6x - 33$ and $2x + 10$ . What is the sum in degrees?

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Problem 50

Solve the system of equations: $5x - 14y = -23$ and $-6x + 7y = 8$ .

See Solution

Problem 51

A passenger train travels at $29.2 \mathrm{~km/h}$ and a cattle train at $36.5 \mathrm{~km/h}$ . How long until the cattle train catches up?

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Problem 52

Find the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n(n+2)}$ .

See Solution

Problem 53

Find the limit of the sequence $a_{n}=\sqrt{n^{2}+3 n}-n$ . Options: A) 3 B) 2 C) $1 / 2$ D) $3 / 2$ E) 0 F) 1 G) $\infty$ H) does not exist.

See Solution

Problem 54

Solve the equation $-3 h^{2} / 2 - 24 h - 45 / 2 = 0$ .

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Problem 55

If $\overline{F B} \| \overline{E C}$ and $m \angle E F B=103^{\circ}$ , find $m \angle C E F$ .

See Solution

Problem 56

Find the sum of the angle measures of two alternate exterior angles: $5x - 26$ and $2x + 10$ .

See Solution

Problem 57

絲带的长度是繩子长度的幾分之幾？繩子 70 厘米，絲带 21 厘米。

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Problem 58

甲、乙兩地相距 $7 \frac{1}{2}$ 公里，爸爸駕車走了 $1 \frac{1}{2}$ 公里，求他走了全程的幾分之幾？

See Solution

Problem 59

一盒雞蛋有 $\frac{3}{4}$ 打，每隻雞蛋值 $1 \frac{4}{5}$ 元，求兩盒的總價。

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Problem 60

把一條麻繩分成 5 段，每段長 $3 \frac{1}{5}$ 米，剩下 $2 \frac{3}{8}$ 米，求原長多少米？

See Solution

Problem 61

A ball's position is given by $x(t)=0.000015 t^5 - 0.004 t^3 + 0.4 t$ . Find its velocity at $t=10.0$ s.

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Problem 62

Find the sum of two alternate exterior angles: $6x - 33$ and $3x + 13$ . What is their total measure in degrees?

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Problem 63

A ball's position is given by $x(t)=0.000015 t^5 - 0.004 t^3 + 0.4 t$ . Find its velocity at $t=10.0$ s.

See Solution

Problem 64

Find the integral of $x^{2}$ with respect to $x$ .

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Problem 65

Find $x$ such that $1+x^{2} \geq-\frac{7 x-x^{2}}{3}$ and determine the minimum of $y=1+x^{2}+\frac{7 x-x^{2}}{3}$ .

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Problem 66

Find the length of line segment $AB$ where $A$ and $B$ are intersections of $2x + 3y = 6$ and $x^2 - 2y^2 - xy = 0$ .

See Solution

Problem 67

Find all solutions for the function $f(x)=2 x^{3}-6 x^{2}+9 x-27$ .

See Solution

Problem 68

Find the integral $\int \sin (3 x) d x$ . Choose from: (a) $3 \cos (3 x)+C$ , (b) $\frac{1}{3} \cos (3 x)+C$ , (c) $-3 \cos (3 x)+C$ , (d) $-\frac{1}{3} \cos (3 x)+C$ .

See Solution

Problem 69

Initially, there are 84 white and 57 black pebbles. After adding equal pebbles, the ratio is $11:8$ . Find the final white pebbles.

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Problem 70

Calculate the integral $\int_{1}^{5} \frac{x-1}{x} dx$ and choose the correct answer: (a) $5-\ln 5$ , (b) $4-\ln 5$ , (c) $2-\ln 5$ , (d) $1-\ln 5$ .

See Solution

Problem 71

Find the limit: $\lim _{x \rightarrow 1} \frac{2 \cdot \ln (x)}{\mathrm{e}^{x}-1}$ . Options: (a) $\frac{2}{e}$ (b) 1 (c) 0 (d) nonexistent.

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Problem 72

Find $f(1)$ given $f^{\prime}(x)=3 x^{2}$ and $f(2)=3$ . Choices: (a) -7 (b) -4 (c) 7 (d) 10

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Problem 73

17) Find the area of the region between $y=2x$ and $y=x^2$ . 18) If a cube's side length $S=2$ in decreases at 5 in³/min, find the rate of change of $S$ in in/min.

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Problem 74

8) Find the limit: $\lim _{h \rightarrow 0} \frac{\cos \left((x+h)^{2}\right)-\cos \left(x^{2}\right)}{h}$ .
9) Determine $x$ for the maximum of $y=\frac{4}{3} x^{3}-8 x^{2}+15 x$ on $[0,4]$ .

See Solution

Problem 75

22) Given $\int_{4}^{6} f(x) dx=5$ and $\int_{10}^{4} f(x) dx=8$ , find $\int_{6}^{10}(4 f(x)+10) dx$ .
23) Find the tangent line equation to $y=e^{2x}$ at $x=1$ .

See Solution

Problem 76

Find the limit: $\lim _{x \rightarrow \infty} \frac{4 \cdot \ln (x)+4}{3 x}$ . Choose (a) 2, (b) -2, (c) 0, or (d) nonexistent.

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Problem 77

Find $f'(x)$ if $f(x)=\frac{x^{2}+1}{3 x}$ and evaluate $\int(2 x+3)(x^{2}+3 x)^{4} dx$ .

See Solution

Problem 78

26) Find the integral for the volume of a solid with base $R$ and height 5 times the base: (a) $25 \int_{a}^{b}(g(x)-f(x))^{2} dx$ (b) $5 \int_{a}^{b}(g(x)-f(x)) dx$ (c) $5 \int_{a}^{b}(f(x)-g(x)) dx$ (d) $5 \int_{a}^{b}(f(x)-g(x))^{2} dx$
27) Solve $\frac{dy}{dx}=\frac{x}{y}$ with $y=4$ at $x=2$ : (a) $\sqrt{\frac{1}{2} x^{2}+14}$ (b) $\sqrt{2 x^{2}+8}$ (c) $\sqrt{x^{2}+6}$ (d) $\sqrt{x^{2}+12}$

See Solution

Problem 79

Find the side lengths of $\triangle ABC$ with ratio $2:3:4$ and perimeter 108.

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Problem 80

Find the integral of $f(x) = \sin 2x$ . Choose from: $(-1/2) \cos 2x + C$ or others.

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Problem 81

已知向量 $\vec{a}, \vec{b}$ 满足 $|\vec{a}|=1,|\vec{b}|=\sqrt{3},|\vec{a}-2 \vec{b}|=3$ ，求 $\vec{a} \cdot \vec{b}$ 。

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Problem 82

Find the area of a circular tray with a diameter of 28 cm. Use $\pi=\frac{22}{7}$ .

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Problem 83

Find the dimensions of a rectangle with area $21 \mathrm{yd}^{2}$ and length $1 \mathrm{yd}$ less than twice the width.

See Solution

Problem 84

Find the area between the curves $y=3 x^{2}$ , $y=0$ , and $x=3$ . Choose integration with respect to $x$ or $y$ .

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Problem 85

Tom has 4 different marbles and 3 identical yellow ones. How many unique pairs of marbles can he select?

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Problem 86

Tom has 4 unique marbles and 3 identical yellow ones. How many ways can he choose 2 marbles?

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Problem 87

A box has 24 fruits: 7 cherries, 8 oranges, 9 lemons. How many lemons must be sold for cherry pick probability to be 50%? A. 0 B. 1 C. 2 D. 3

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Problem 88

If $\sum_{n=0}^{\infty} \cos ^{2 n} \theta=5$ , find $\cos 2 \theta$ .

See Solution

Problem 89

Solve for $x$ in the equation $2 x + 9 = 16$ .

See Solution

Problem 90

Solve for $x$ in the equation: $1 + 2 = x$ .

See Solution

Problem 91

Evaluate the integral: $\int \frac{3 a x}{b^{2}+c^{2} x^{2}} \, dx$

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Problem 92

Find the apparent distance from the top of a 4.20 cm benzene layer to the bottom of a 6.20 cm water layer at normal incidence.

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Problem 93

Find the slope of the line given by $y-8=-\frac{1}{2}(x-2)$ . Answer as an integer or fraction.

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Problem 94

Three forces $F_{1}, F_{2}, F_{3}$ at point $O$ are in equilibrium. Given $F_{1} = 10.0 \mathrm{~N}$ , $F_{2} = 5.0 \mathrm{~N}$ , angle = 60°. Find $F_{3}$ .

See Solution

Problem 95

An object creates a focused image $30.9 \mathrm{~cm}$ right of a converging lens. A diverging lens $14.2 \mathrm{m}$ away shifts the screen $18.5 \mathrm{~cm}$ right. Find the diverging lens' focal length in cm.

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Problem 96

A mud house has a cone roof over a cylinder. Given dimensions, find $A B$ , volume, surface area, and house choice.

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Problem 97

A lens creates a real image $249 \mathrm{~cm}$ from the object and $1 \frac{2}{3}$ times its size. Find the focal length.

See Solution

Problem 98

Find the focal length of a lens given an object height of 3.25 cm, distance to image 6 cm, and distance to lens 16 cm.

See Solution

Problem 99

Calculate the sum: $500 + 300 + 200$ .

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Problem 100

Lulu had twice as many red buttons as green. After giving away $\frac{1}{3}$ red and $\frac{4}{5}$ green, she had 368 left. How many did she start with?

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Solve

Problem 1

Calculate 31−8 31 - 8 31−8.

Problem 2

Solve for x x x in the equation: 3(x+3)−5=16 3(x+3)-5=16 3(x+3)−5=16.

Problem 3

Find the z z z-score for x=7 x=7 x=7 given a random variable X X X with mean 4 and standard deviation 2.

Problem 4

Find when balls A and B, rotating at different speeds, meet at the starting point again. A: 2 rotations in 26 min, B: 5 in 35 min.

Problem 5

Evaluate npn+p \frac{n p}{n+p} n+pnp​ for n=9 n=9 n=9 and p=15 p=15 p=15.

Problem 6

Calculate 8÷2(2+2) 8 \div 2(2+2) 8÷2(2+2).

Problem 7

Solve 3x−5=16 3x - 5 = 16 3x−5=16 for x x x and express your answer in set notation.

Problem 8

Solve 3x−5=16 3x - 5 = 16 3x−5=16 for x x x and express your answer in set notation.

Problem 9

Evaluate the integral ∫9x+2x2+x−6dx \int \frac{9 x+2}{x^{2}+x-6} d x ∫x2+x−69x+2​dx.

Problem 10

Решите у в уравнении: 4y+3=6y−74y + 3 = 6y - 74y+3=6y−7.

Problem 11

Calculate the integral ∫233x2dt \int_{2}^{3} 3 x^{2} d t ∫23​3x2dt.

Problem 12

Evaluate the integral ∫−221+x21+2xdx \int_{-2}^{2} \frac{1+x^{2}}{1+2^{x}} d x ∫−22​1+2x1+x2​dx.

Problem 13

Find x x x in the equation 23=5x \frac{2}{3}=\frac{5}{x} 32​=x5​. Options: A 215 \frac{2}{15} 152​, B 6, C 152 \frac{15}{2} 215​, D 8.

Problem 14

A boat travels 222 km on 74 liters. How much gas is needed for 39 km?

Problem 15

Calculate the integral ∫tan⁡3xsec⁡x dx \int \tan^{3} x \sec x \, dx ∫tan3xsecxdx.

Problem 16

A boat travels 129 km on 43 liters. How far can it go on 57 liters?

Problem 17

Find y y y if log⁡y19=3 \log _{y} \frac{1}{9}=3 logy​91​=3.

Problem 18

Solve for y y y in the equation y2+7y−60=0 y^{2}+7 y-60=0 y2+7y−60=0.

Problem 19

פתרו את המשוואה 3x+5=14 3 x + 5 = 14 3x+5=14 ומצאו את ערך x x x. תשובה: x= x = x=

Problem 20

Find the z z z-score for x=7 x=7 x=7 given that the mean is 4 and the standard deviation is 2.

Problem 21

פתרו את המשוואה 3x+5=14 3 x + 5 = 14 3x+5=14 ומצאו את x= x = x=

Problem 22

Find the line equation through the origin with the same slope as the line between points A(1,5) A(1,5) A(1,5) and B(2,−3) B(2,-3) B(2,−3).

Problem 23

The probability of an athlete not winning 3 races is 14 \frac{1}{4} 41​. Find the probability of winning: (i) only the 2nd race, (ii) all 3 races, (iii) exactly 2 races.

Problem 24

Evaluate −3Δ−1 -3 \Delta -1 −3Δ−1 for the operation aΔb=a+bab a \Delta b = \frac{a+b}{\sqrt{ab}} aΔb=ab​a+b​ where a,b≠0 a, b \neq 0 a,b=0.

Problem 25

Calculate 31−8 31 - 8 31−8.

Problem 26

A boat travels 222 km on 74 liters. How much gas for 39 km? Use the ratio: 74222=x39 \frac{74}{222} = \frac{x}{39} 22274​=39x​.

Problem 27

A car travels 234 km on 39 liters. How many liters are needed for 414 km?

Problem 28

Calculate −32÷4-32 \div 4−32÷4.

Problem 29

Find the integral of −15sin⁡u du-\frac{1}{5} \sin u \, du−51​sinudu.

Problem 30

Solve the system of equations: 6x−7y=−86x - 7y = -86x−7y=−8 and −x−4y=−9-x - 4y = -9−x−4y=−9.

Problem 31

Solve the equation 7x−85=2x+54 \frac{7x - 8}{5} = \frac{2x + 5}{4} 57x−8​=42x+5​.

Problem 32

Solve the equation: 5(x+11)3=3(1+x)2 \frac{5(x+11)}{3}=\frac{3(1+x)}{2} 35(x+11)​=23(1+x)​ for x x x.

Problem 33

Solve 3x−5=16 3x - 5 = 16 3x−5=16 for x x x and express your answer in set notation.

Problem 34

Find k k k for the planes x−2y+4z=10 x-2y+4z=10 x−2y+4z=10 and 18x+17y+kz=50 18x+17y+kz=50 18x+17y+kz=50 to be perpendicular. Options: (a) -4 (b) 4 (c) 2 (d) -2

Problem 35

Solve the system of equations: 10x−14y=−410x - 14y = -410x−14y=−4 and −10x−20y=−30-10x - 20y = -30−10x−20y=−30.

Problem 36

Find the time when balls A and B return to the starting point, given A rotates 2 times in 26 min and B 5 times in 35 min.

Problem 37

Calculate 62(1+2) \frac{6}{2}(1+2) 26​(1+2).

Problem 38

Find y y y if log⁡y19=3 \log_{y} \frac{1}{9} = 3 logy​91​=3.

Problem 39

Find the z z z-score for x=7 x = 7 x=7 given that the mean μ=4 \mu = 4 μ=4 and standard deviation σ=2 \sigma = 2 σ=2.

Problem 40

Calculate $31 - 8$ .

Solve for $x$ in the equation: $3(x+3)-5=16$ .

Find the $z$ -score for $x=7$ given a random variable $X$ with mean 4 and standard deviation 2.

Evaluate $\frac{n p}{n+p}$ for $n=9$ and $p=15$ .

Calculate $8 \div 2(2+2)$ .

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

Evaluate the integral $\int \frac{9 x+2}{x^{2}+x-6} d x$ .

Решите у в уравнении: $4y + 3 = 6y - 7$ .

Calculate the integral $\int_{2}^{3} 3 x^{2} d t$ .

Evaluate the integral $\int_{-2}^{2} \frac{1+x^{2}}{1+2^{x}} d x$ .

Find $x$ in the equation $\frac{2}{3}=\frac{5}{x}$ . Options: A $\frac{2}{15}$ , B 6, C $\frac{15}{2}$ , D 8.

Calculate the integral $\int \tan^{3} x \sec x \, dx$ .

Find $y$ if $\log _{y} \frac{1}{9}=3$ .

Solve for $y$ in the equation $y^{2}+7 y-60=0$ .

פתרו את המשוואה $3 x + 5 = 14$ ומצאו את ערך $x$ . תשובה: $x =$

Find the $z$ -score for $x=7$ given that the mean is 4 and the standard deviation is 2.

פתרו את המשוואה $3 x + 5 = 14$ ומצאו את $x =$

Find the line equation through the origin with the same slope as the line between points $A(1,5)$ and $B(2,-3)$ .

The probability of an athlete not winning 3 races is $\frac{1}{4}$ . Find the probability of winning: (i) only the 2nd race, (ii) all 3 races, (iii) exactly 2 races.

Evaluate $-3 \Delta -1$ for the operation $a \Delta b = \frac{a+b}{\sqrt{ab}}$ where $a, b \neq 0$ .

Calculate $31 - 8$ .

A boat travels 222 km on 74 liters. How much gas for 39 km? Use the ratio: $\frac{74}{222} = \frac{x}{39}$ .

Calculate $-32 \div 4$ .

Find the integral of $-\frac{1}{5} \sin u \, du$ .

Solve the system of equations: $6x - 7y = -8$ and $-x - 4y = -9$ .

Solve the equation $\frac{7x - 8}{5} = \frac{2x + 5}{4}$ .

Solve the equation: $\frac{5(x+11)}{3}=\frac{3(1+x)}{2}$ for $x$ .

Solve $3x - 5 = 16$ for $x$ and express your answer in set notation.

Find $k$ for the planes $x-2y+4z=10$ and $18x+17y+kz=50$ to be perpendicular. Options: (a) -4 (b) 4 (c) 2 (d) -2

Solve the system of equations: $10x - 14y = -4$ and $-10x - 20y = -30$ .

Calculate $\frac{6}{2}(1+2)$ .

Find $y$ if $\log_{y} \frac{1}{9} = 3$ .

Find the $z$ -score for $x = 7$ given that the mean $\mu = 4$ and standard deviation $\sigma = 2$ .

Find the $z$ -score for $x = 7$ given $\mu = 4$ and $\sigma = 2$ using $z = \frac{x - \mu}{\sigma}$ .

Find $m \angle 12$ if $m \angle 3=2x+14$ and $m \angle 16=4x-16$ , with angles 3 and 12 as alternate exterior angles.

Find $m \angle 16$ if $m \angle 1=5x+8$ and $m \angle 16=7x-20$ .

Find $m \angle 13$ given $m \angle 7 = 4x + 6$ and $m \angle 15 = 13x - 6$ for parallel lines.

Find $m \angle 14$ given $m \angle 1 = 67^{\circ}$ and $m \angle 18 = 42^{\circ}$ with parallel lines $l$ and $m$ . Options: $113^{\circ}$ , $96^{\circ}$ , $105^{\circ}$ , $109^{\circ}$ .

Differentiate $x^{e^{x}}$ with respect to $x$ .

What is the value of $6 \div 2(1+2)$ ?

Solve $60 \div 2(3+7)$ .

Find the sum of two alternate exterior angles: $6a - 33$ and $2x + 10$ .

Find the sum of two alternate exterior angles: $6x - 33$ and $2x + 10$ . What is the sum in degrees?

Solve the system of equations: $5x - 14y = -23$ and $-6x + 7y = 8$ .

A passenger train travels at $29.2 \mathrm{~km/h}$ and a cattle train at $36.5 \mathrm{~km/h}$ . How long until the cattle train catches up?

Find the sum of the series $\sum_{n=1}^{\infty} \frac{1}{n(n+2)}$ .

Find the limit of the sequence $a_{n}=\sqrt{n^{2}+3 n}-n$ . Options: A) 3 B) 2 C) $1 / 2$ D) $3 / 2$ E) 0 F) 1 G) $\infty$ H) does not exist.

Solve the equation $-3 h^{2} / 2 - 24 h - 45 / 2 = 0$ .

If $\overline{F B} \| \overline{E C}$ and $m \angle E F B=103^{\circ}$ , find $m \angle C E F$ .

Find the sum of the angle measures of two alternate exterior angles: $5x - 26$ and $2x + 10$ .

甲、乙兩地相距 $7 \frac{1}{2}$ 公里，爸爸駕車走了 $1 \frac{1}{2}$ 公里，求他走了全程的幾分之幾？

一盒雞蛋有 $\frac{3}{4}$ 打，每隻雞蛋值 $1 \frac{4}{5}$ 元，求兩盒的總價。

把一條麻繩分成 5 段，每段長 $3 \frac{1}{5}$ 米，剩下 $2 \frac{3}{8}$ 米，求原長多少米？

A ball's position is given by $x(t)=0.000015 t^5 - 0.004 t^3 + 0.4 t$ . Find its velocity at $t=10.0$ s.

Find the sum of two alternate exterior angles: $6x - 33$ and $3x + 13$ . What is their total measure in degrees?

A ball's position is given by $x(t)=0.000015 t^5 - 0.004 t^3 + 0.4 t$ . Find its velocity at $t=10.0$ s.

Find the integral of $x^{2}$ with respect to $x$ .

Find $x$ such that $1+x^{2} \geq-\frac{7 x-x^{2}}{3}$ and determine the minimum of $y=1+x^{2}+\frac{7 x-x^{2}}{3}$ .

Find the length of line segment $AB$ where $A$ and $B$ are intersections of $2x + 3y = 6$ and $x^2 - 2y^2 - xy = 0$ .

Find all solutions for the function $f(x)=2 x^{3}-6 x^{2}+9 x-27$ .

Initially, there are 84 white and 57 black pebbles. After adding equal pebbles, the ratio is $11:8$ . Find the final white pebbles.

Calculate the integral $\int_{1}^{5} \frac{x-1}{x} dx$ and choose the correct answer: (a) $5-\ln 5$ , (b) $4-\ln 5$ , (c) $2-\ln 5$ , (d) $1-\ln 5$ .

Find the limit: $\lim _{x \rightarrow 1} \frac{2 \cdot \ln (x)}{\mathrm{e}^{x}-1}$ . Options: (a) $\frac{2}{e}$ (b) 1 (c) 0 (d) nonexistent.

Find $f(1)$ given $f^{\prime}(x)=3 x^{2}$ and $f(2)=3$ . Choices: (a) -7 (b) -4 (c) 7 (d) 10

17) Find the area of the region between $y=2x$ and $y=x^2$ . 18) If a cube's side length $S=2$ in decreases at 5 in³/min, find the rate of change of $S$ in in/min.