Math

Problem 66101

Simplify: a. $5x - 2 - 3x$ ; b. $5x - (2 - 3x)$ . What are the simplified forms?

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Problem 66102

Simplify the expression: -5(2 x-4) + 11 x - 10 = ?

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Problem 66103

Find the equations of the line perpendicular and parallel to $y=-\frac{9}{8} x+1$ through the point $(8,-3)$ .

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Problem 66104

Determine if the lines $8 x+6 y=8$ , $4 y=-3 x+5$ , and $y=-\frac{3}{4} x+7$ are parallel, perpendicular, or neither.

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Problem 66105

The integral that represents the area of the region enclosed by $f(x)=x^{3}-x$ and the $x$ -axis is $\int_{0}^{1}\left(x^{3}-x\right) d x$ $\int_{-1}^{1}\left(x-x^{3}\right) d x$ $\int_{-1}^{1}\left(x^{3}-x\right) d x$ $2 \int_{0}^{1}\left(x-x^{3}\right) d x$

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Problem 66106

3. Multiply: (a) $3.2 \times 6$ (b) $2.85 \times 8$ (c) $7.49 \times 23$ (e) $0.426 \times 23$ (e) $5.82 \times 2.5$ (g) $1.026 \times 1000$ (4) $0.008 \times 1000$ (1) $1.832 \times 17.35$ (k) $0.057 \times 0.06$ (h) $16.92 \times 105.4$ (a) If a bag of paddy weighs 75.25 kg , what is the weight of 150 bags? (b) 1.25 m of cloth is required to make 1 shirt. What is the length of cloth requir make 8 shirts?

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Problem 66107

9. ${ }^{7}$ (a) If the two angles of a triangle are $50^{\circ}$ and $75^{\circ}$ , find the third ang. b) If $2 x^{\circ}, 4 x^{\circ}$ and $6 x^{\circ}$ are the three angles of a triangle, find the valuer is find the angles. (c) If the three angles of a triangle are $x^{\circ},(x+20)^{\circ}$ and $(x-50)^{\circ}$ , find x . Also, find the angles. (d) If the two opposite interior angles of a triangle are $30^{\circ}$ and $55^{\circ}$ exterior angle of a triangle.
10. त(3) In a right angled triangle, one acute angle is $40^{\circ}$ . Find the other atexes that triangle. (b) In an equilateral triangle, one angle is $60^{\circ}$ . Find the remaining anglo (c) In an isosceles triangle, one base angle is $45^{\circ}$ . Find the another bases
स'(d) If one angle of an isosceles triangle is equal to the sum of remaining angles, find the size of each angle.
11. (a) In a $\triangle A B C, \angle A=\angle B=65^{\circ}$ , find $\angle C$ .

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Problem 66108

Attempt All Questions
1. Dichromate ion $\left(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\right)$ in acidic solution is a good oxidizing agent. Which of the following oxidations can be accomplished with dichromate ion in acidic solution? Explain a. $\mathrm{Sn}^{2+}(\mathrm{aq})$ to $\mathrm{Sn}^{4+}(\mathrm{aq})$ b. $\mathrm{Ag}(\mathrm{s})$ to $\mathrm{Ag}^{+}(\mathrm{aq})$
2. For each of the following cell diagrams a. $\operatorname{Pt}(\mathrm{s})\left|\mathrm{Fe}^{2+}(\mathrm{aq}), \mathrm{Fe}^{3+}(\mathrm{aq}) \|\left|\mathrm{Ag}^{+}(\mathrm{aq})\right| \mathrm{Ag}(\mathrm{s})\right.$ b. $\mathrm{Pt}(\mathrm{s})\left|\mathrm{Mn}^{2+}(\mathrm{aq}), \mathrm{MnO}_{4}^{-}(\mathrm{aq})\right|\left|\mathrm{Cu}^{2+}(\mathrm{aq})\right| \mathrm{Cu}(\mathrm{s})$ i. calculate the $E_{\text {cell }}^{o}$ ii. what is the change in Gibbs free energy? iii. is the cell reaction spontaneous or nonspontaneous? Explain.
3. Will the following reaction $\mathrm{Cr}_{2} \mathrm{O}_{7}^{2 \cdot}(\mathrm{aq})+14 \mathrm{H}^{+}+6 \mathrm{Ag}(\mathrm{~s}) \longrightarrow 2 \mathrm{Cr}^{3+}(\mathrm{aq})+6 \mathrm{Ag}^{+}(\mathrm{aq})+7 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) E_{\text {cell }}=-0.023 \mathrm{~V}$ be spontaneous if $\left[\mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}\right]=[\mathrm{Ag}+]=0.675 \mathrm{M},\left[\mathrm{Cr}^{3+}\right]=0.6 \mathrm{M}$ and $\mathrm{pH}=2$ ? Explain.
4. Define the following terms a) Oxidation b) Oxidizing agent c) Salt bridge d) Liquid junction e) Standard electrode potential

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Problem 66109

1. What is hydrodynamic voltammetry? State two (2) applications of voltammetry.
2. What is the potential of a cell consisting of a silver electrode dipped in silver nitrate solution with $[\mathrm{Ag}+]=0.01 \mathrm{M}$ and a standard calomel reference electrode $\left(\mathrm{E}_{\mathrm{ref}}=+0.242\right.$ V). Neglect liquid-junction potential.
3. Briefly describe a simple electrochemical cell used in potentiometric analysis. Write a cell diagram for this cell.
4. Calculate the ionic strengths of the following solutions A) 0.20 M NaCl and $0.30 \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}$ B) $0.1 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$

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Problem 66110

5. Calculate the activity coefficients of sodium and chloride ions for a 0.04 M NaCl solution
6. What is an electrode of the first kind? Write a general Nernst equation for this indicator electrode.
7. A solution of $0.25 \mathrm{M} \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}$ and $0.35 \mathrm{M} \mathrm{Cr}^{3+}$ has a pH of 2.0 . What is the $\mathrm{E}_{\text {cell }}$ of this half-cell?
8. In an acidic solution, $\mathrm{O}_{2}(\mathrm{~g})$ oxidizes $\mathrm{Cr}^{2+}(\mathrm{aq})$ to $\mathrm{Cr}^{3+}(\mathrm{aq})$ . The $\mathrm{O}_{2}(\mathrm{~g})$ is reduced to $\mathrm{H}_{2} \mathrm{O}(\mathrm{l})$ . $E_{\text {cell }}^{o}$ for this reaction is +1.653 V . What is the electrode potential for the $\mathrm{Cr}^{3+} / \mathrm{Cr}^{2+}$ half-cell?

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Problem 66111

5. Calculate the activity coefficients of sodium and chloride ions for a 0.04 M NaCl solution
6. What is an electrode of the first kind? Write a general Nernst equation for this indicator electrode.
7. A solution of $0.25 \mathrm{M} \mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}$ and $0.35 \mathrm{M} \mathrm{Cr}^{3+}$ has a pH of 2.0 . What is the $\mathrm{E}_{\text {cell }}$ of this half-cell?

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Problem 66112

6. What is an electrode of the first kind? Write a general Nernst equation for this indicator electrode.
7. A solution of $0.25 \mathrm{M} \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}$ and $0.35 \mathrm{M} \mathrm{Cr}^{3+}$ has a pH of 2.0 . What is the $\mathrm{E}_{\text {cell }}$ of this halfcell?

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Problem 66113

$y=x^{2}+4 x+4$

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Problem 66114

$\begin{array}{l} \text { : (2) (2) } \\ x-\ln x>0 \end{array}$ $\begin{array}{l} \ln \ln \left(g_{c}\right): f(x)=\frac{\ln x}{x-\ln x}: x>0 \\ \text { 3-3h11 } f(0)=-1 \end{array}$ $\begin{array}{l} \lim _{x \rightarrow+\infty} f(x) \text { با. } \end{array}$ $\begin{array}{l} f^{\prime}(x)=\frac{1-\ln x}{(x-\ln x)^{2}} \end{array}$ $\begin{array}{l} \text { المحدادل } \end{array}$

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Problem 66115

Fill in the information about the parabolas below. (a) For each parabola, choose whether it opens upward or downward. $y=-x^{2}: \text { (Choose one) } v y=-\frac{1}{3} x^{2}: \text { (Choose one) } v \quad y=\frac{1}{2} x^{2}: \text { (Choose one) } v \text { (Choose one) } v$ (b) Choose the parabola with the narrowest graph. $y=-x^{2}$ $y=-\frac{1}{3} x^{2}$ $y=\frac{1}{2} x^{2}$ $y=-3 x^{2}$ (c) Choose the parabola with the widest graph. $y=-x^{2}$ $y=-\frac{1}{3} x^{2}$ $y=\frac{1}{2} x^{2}$ $y=-3 x^{2}$

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Problem 66116

How many proportional relationships are shown in the coordinate plane below?
Choose 1 answer:
A 0 (B) 1 (C) 2 (D) 3

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Problem 66117

Whante $\int_{D} 2 d A$ , where $D=\{(x, y): 0 \leq x \leq 1, x \leq y \leq 1+x)$ . $A .0$ B. 3 0.4
3. Folluate $\iint_{D} 10 d A$ , where $D=\{(x, y): 0 \leq y \leq 2,0 \leq x \leq y\}$ . A. 1 B. 5 C. 10 D. 20
14. If $f(x, y)=4$ , evaluate $\iint_{R} f(x, y) d A$ , where $R=\{(r, \theta): 1 \leq r \leq 2,0 \leq \theta \leq \pi\}$ . A. $\pi$ B. $3 \pi$ C. $6 \pi$ D. $10 \pi$
15. Express $\int_{-a}^{a} \int_{0}^{\sqrt{a^{2}-x^{2}}}\left(x^{2}+y^{2}\right)^{3 / 2} d y d x$ in polar coordinates. A. $\int_{0}^{\pi / 2} \int_{0}^{a} r^{5} d r d \theta$ B. $\int_{0}^{\pi} \int_{0}^{a} r^{4} d r d \theta$ C. $\int_{0}^{\pi} \int_{0}^{a} r^{3} d r d \theta$ D. $\int_{0}^{\pi} \int_{0}^{2 \cos \theta} r^{2} d r d \theta$
16. Express $\iiint_{E} x z^{3} d V$ , where $E=\left\{(x, y, z): 0 \leq x \leq 1,0 \leq y \leq x, 0 \leq z \leq x^{2} y^{2}\right\}$ in a form that can be evaluated. A. $\int_{0}^{x^{2} y^{2}} \int_{0}^{x} \int_{0}^{1} x z^{3} d x d y d z$ B. $\int_{0}^{x} \int_{0}^{1} \int_{0}^{x^{2} y^{2}} x z^{2} d z d x d y$ C. $\int_{0}^{1} \int_{0}^{x^{2} y^{2}} \int_{0}^{x} x z^{2} d y d z d x$ D). $\int_{0}^{1} \int_{0}^{x} \int_{0}^{x^{2} y^{2}} x z^{2} d z d y d x$
17. | et $E=\left\{(r, 0, z): 0 \leq 0 \leq \pi, 0 \leq r \leq 2,1 \leq z \leq r^{2}\right\}$ and $f(x, y, z)=2$ . lixpress $\iiint_{E} f(x, y, z) d V$ in cylindrical condinates. ค. $\int_{0}^{\pi} \int_{0}^{2} \int_{1}^{r^{2}} z r d \% d r d 0$
13. $\int_{0}^{11} \int_{0}^{2} \int_{1}^{r^{2}} \% d \% d r d()$ (i. $\int_{0}^{3 x} \int_{0}^{2} \int_{1}^{r^{2}} z r^{2} d z d r d 0$ 1) $\int_{1}^{11} \int_{11}^{2} \int_{1}^{r^{2}} z r d \% d 0 d r$
Pape 3 ald

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Problem 66118

16. Express $\iiint_{E} x z^{3} d V$ , where $E=\left\{(x, y, z): 0 \leq x \leq 1,0 \leq y \leq x, 0 \leq z \leq x^{2} y^{2}\right\}$ in a form that can be evaluated. A. $\int_{0}^{x^{2} y^{2}} \int_{0}^{x} \int_{0}^{1} x z^{3} d x d y d z$ B. $\int_{0}^{x} \int_{0}^{1} \int_{0}^{x^{2} y^{2}} x z^{2} d z d x d y$ C. $\int_{0}^{1} \int_{0}^{x^{2} y^{2}} \int_{0}^{x} x z^{2} d y d z d x$ D. $\int_{0}^{1} \int_{0}^{x} \int_{0}^{x^{2} y^{2}} x z^{2} d z d y d x$

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Problem 66119

${ }_{1}^{8} 3$

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Problem 66120

ate $\iint_{D} 2 d A$ , where $D=((x, y): 0 \leq x \leq 1, x \leq y \leq 1+x)$ .

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Problem 66121

Here is a regular hexagon and a regular pentagon.
Work out the size of the angle marked $x$ . You must show all your working.

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Problem 66122

The table shows some information about the profit made each day at a cricket club on 100 days. (a) Complete the cumulative frequency table. \begin{tabular}{|c|c|} \hline Pront (£x) & \begin{tabular}{c} Crmulative \\ frequency \end{tabular} \\ \hline $0 \leq x<50$ & \\ \hline $0 \leq x<100$ & \\ \hline $0 \leq x<150$ & \\ \hline $0 \leq x<200$ & \\ \hline $0 \leq x<250$ & \\ \hline $0 \leq x<300$ & \\ \hline \end{tabular} (b) On the grid, draw a cumulative frequency graph for this information. \begin{tabular}{|c|c|} \hline Proft ( $£ x)$ & Frequency \\ \hline $0 \leq x<50$ & 10 \\ \hline $50 \leq x<100$ & 15 \\ \hline $100 \leq x<150$ & 25 \\ \hline $150 \leq x<200$ & 30 \\ \hline $200 \leq x<250$ & 5 \\ \hline $250 \leq x<300$ & 15 \\ \hline \end{tabular} (1) (2) (c) Use your graph to find an estimate for the number of days on which the profit was less than $£ 125$ days $\qquad$ (d) Use your graph to find an estimate for the interquartile range.

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Problem 66123

$f(x)=-3 x^{2}+2 x+3$
Round to the nearest hundredth if necessary. If there is more than one $x$ -intercept, separate them If applicable, click on "None". \begin{tabular}{|ll|} \hline vertex: & (II, $\square$ \\ $x$ -intercept(s): & $\square$ \\ \hline \end{tabular}

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Problem 66124

Evaluate $3 x^{2}+2 x y-y^{3}$ for $x=2$ and $y=-1$ . What is the result?

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Problem 66125

Evaluate $\frac{2 x-31}{y-5}$ for $x=-7$ and $y=-4$ . Is it a number or undefined?

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Problem 66126

Find where the function $f(x)=|6-x|$ is not differentiable and explain the reason.

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Problem 66127

Determine the relationship (parallel, perpendicular, or neither) for the lines: $y=4x+5$ , $4x-16y=32$ , $y=-\frac{1}{4}x-2$ .

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Problem 66128

Fill in the table for $x$ and $2x + 7$ with $x = 0, 1, -1$ . Simplify your answers.

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Problem 66129

A plane flew 180 miles against a $30-\mathrm{mph}$ wind and returned with a $15-\mathrm{mph}$ tailwind. Total time was 180 min. Find the plane's speed in still air.

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Problem 66130

Evaluate $\frac{x^{2}+y}{3 y}$ for $x=-3$ and $y=-2$ . Choose A or B: A. $\frac{x^{2}+y}{3 y}=\square$ or B. Undefined.

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Problem 66131

A tank fills in 9h, 12h with pipes and drains in 15h. How long to fill it with all pipes working? Give answer in h and min.

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Problem 66132

Determine if the lines $y=\frac{4}{3} x-5$ , $8 x-6 y=6$ , and $3 y=4 x+7$ are parallel, perpendicular, or neither.

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Problem 66133

1. Find the derivative $\frac{d y}{d t}$ for $y=5 t^{3}+t^{2}+4 t-1$ .
2. Find the second derivative $\frac{d^{2} y}{d u^{2}}$ for $y=2 u^{4}+4 u^{3}+4$ .
3. Find the fifth derivative $\frac{d^{5} y}{d \theta^{5}}$ for $y=2 \sin (\theta)+5 \cos (\theta)$ .

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Problem 66134

Find $f(64)$ for the function $f(x)=x+\sqrt{x}+4$ .

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Problem 66135

Find $\delta$ for $\varepsilon=0.01$ in the limit $\lim _{x \rightarrow 4} 8 x=32$ .

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Problem 66136

Solve $6 \leq 12x - 4 < 16$ and find time to fill a tank with pipes filling in 9h, 12h, and draining in 15h.

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Problem 66137

Fill in the table for $x$ and $-\frac{1}{5} x$ at $x = 0, 5, -5$ . Simplify your answers.

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Problem 66138

Determine if the following lines are parallel, perpendicular, or neither: Line 1: $4x - 10y = 8$ Line 2: $y = -\frac{5}{2}x - 4$ Line 3: $2y = -5x + 3$

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Problem 66139

Find $\delta$ so that if $|x-2|<\delta$ , then $|4x-8|<0.9$ .

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Problem 66140

Simplify these expressions using positive exponents: a. $2^{-9} \cdot 2^{-6}$ , b. $2^{9} \cdot 2^{6}$ , c. $5^{15} \div 5^{3}$ , d. $5^{15} \div 5^{-3}$ , e. $(-3)^{-2}$ , f. $\frac{b^{2}}{b^{-3}}$ .

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Problem 66141

Find the fixed cost $F$ and variable cost $V$ from the cost function $C(x)$ using points (0, 660), (31, 1343), (95, 2750).
$\begin{array}{l} F= \\ V= \end{array}$

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Problem 66142

SDJ, Inc. has net working capital \$2,630, current liabilities \$5,970, and inventory \$3,860. Find the current and quick ratios.

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1 ...659 660 661 662

Math

Problem 66101

Simplify: a. 5x−2−3x5x - 2 - 3x5x−2−3x; b. 5x−(2−3x)5x - (2 - 3x)5x−(2−3x). What are the simplified forms?

Problem 66102

Simplify the expression: -5(2 x-4) + 11 x - 10 = ?

Problem 66103

Find the equations of the line perpendicular and parallel to y=−98x+1y=-\frac{9}{8} x+1y=−89​x+1 through the point (8,−3)(8,-3)(8,−3).

Problem 66104

Determine if the lines 8x+6y=88 x+6 y=88x+6y=8, 4y=−3x+54 y=-3 x+54y=−3x+5, and y=−34x+7y=-\frac{3}{4} x+7y=−43​x+7 are parallel, perpendicular, or neither.

Problem 66105

Problem 66106

Problem 66107

Problem 66108

Problem 66109

Problem 66110

Problem 66111

Problem 66112

Problem 66113

y=x2+4x+4y=x^{2}+4 x+4y=x2+4x+4

Problem 66114

Problem 66115

Problem 66116

How many proportional relationships are shown in the coordinate plane below?Choose 1 answer:A 0 (B) 1 (C) 2 (D) 3

Problem 66117

Problem 66118

Problem 66119

183{ }_{1}^{8} 318​3

Problem 66120

ate ∬D2dA\iint_{D} 2 d A∬D​2dA, where D=((x,y):0≤x≤1,x≤y≤1+x)D=((x, y): 0 \leq x \leq 1, x \leq y \leq 1+x)D=((x,y):0≤x≤1,x≤y≤1+x).

Problem 66121

Here is a regular hexagon and a regular pentagon.Work out the size of the angle marked xxx. You must show all your working.

Problem 66122

Problem 66123

Problem 66124

Evaluate 3x2+2xy−y33 x^{2}+2 x y-y^{3}3x2+2xy−y3 for x=2x=2x=2 and y=−1y=-1y=−1. What is the result?

Problem 66125

Evaluate 2x−31y−5\frac{2 x-31}{y-5}y−52x−31​ for x=−7x=-7x=−7 and y=−4y=-4y=−4. Is it a number or undefined?

Problem 66126

Find where the function f(x)=∣6−x∣f(x)=|6-x|f(x)=∣6−x∣ is not differentiable and explain the reason.

Problem 66127

Determine the relationship (parallel, perpendicular, or neither) for the lines: y=4x+5y=4x+5y=4x+5, 4x−16y=324x-16y=324x−16y=32, y=−14x−2y=-\frac{1}{4}x-2y=−41​x−2.

Problem 66128

Fill in the table for xxx and 2x+72x + 72x+7 with x=0,1,−1x = 0, 1, -1x=0,1,−1. Simplify your answers.

Problem 66129

A plane flew 180 miles against a 30−mph30-\mathrm{mph}30−mph wind and returned with a 15−mph15-\mathrm{mph}15−mph tailwind. Total time was 180 min. Find the plane's speed in still air.

Problem 66130

Evaluate x2+y3y\frac{x^{2}+y}{3 y}3yx2+y​ for x=−3x=-3x=−3 and y=−2y=-2y=−2. Choose A or B: A. x2+y3y=□\frac{x^{2}+y}{3 y}=\square3yx2+y​=□ or B. Undefined.

Problem 66131

A tank fills in 9h, 12h with pipes and drains in 15h. How long to fill it with all pipes working? Give answer in h and min.

Problem 66132

Determine if the lines y=43x−5y=\frac{4}{3} x-5y=34​x−5, 8x−6y=68 x-6 y=68x−6y=6, and 3y=4x+73 y=4 x+73y=4x+7 are parallel, perpendicular, or neither.

Problem 66133

Problem 66134

Find f(64)f(64)f(64) for the function f(x)=x+x+4f(x)=x+\sqrt{x}+4f(x)=x+x​+4.

Problem 66135

Find δ\deltaδ for ε=0.01\varepsilon=0.01ε=0.01 in the limit lim⁡x→48x=32\lim _{x \rightarrow 4} 8 x=32limx→4​8x=32.

Problem 66136

Solve 6≤12x−4<166 \leq 12x - 4 < 166≤12x−4<16 and find time to fill a tank with pipes filling in 9h, 12h, and draining in 15h.

Problem 66137

Fill in the table for xxx and −15x-\frac{1}{5} x−51​x at x=0,5,−5x = 0, 5, -5x=0,5,−5. Simplify your answers.

Problem 66138

Determine if the following lines are parallel, perpendicular, or neither: Line 1: 4x−10y=84x - 10y = 84x−10y=8 Line 2: y=−52x−4y = -\frac{5}{2}x - 4y=−25​x−4 Line 3: 2y=−5x+32y = -5x + 32y=−5x+3

Problem 66139

Find δ\deltaδ so that if ∣x−2∣<δ|x-2|<\delta∣x−2∣<δ, then ∣4x−8∣<0.9|4x-8|<0.9∣4x−8∣<0.9.

Problem 66140

Simplify these expressions using positive exponents: a. 2−9⋅2−62^{-9} \cdot 2^{-6}2−9⋅2−6, b. 29⋅262^{9} \cdot 2^{6}29⋅26, c. 515÷535^{15} \div 5^{3}515÷53, d. 515÷5−35^{15} \div 5^{-3}515÷5−3, e. (−3)−2(-3)^{-2}(−3)−2, f. b2b−3\frac{b^{2}}{b^{-3}}b−3b2​.

Problem 66141

Find the fixed cost FFF and variable cost VVV from the cost function C(x)C(x)C(x) using points (0, 660), (31, 1343), (95, 2750). F=V= \begin{array}{l} F= \\ V= \end{array} F=V=​

Problem 66142

SDJ, Inc. has net working capital \$2,630, current liabilities \$5,970, and inventory \$3,860. Find the current and quick ratios.

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Simplify: a. $5x - 2 - 3x$ ; b. $5x - (2 - 3x)$ . What are the simplified forms?

Find the equations of the line perpendicular and parallel to $y=-\frac{9}{8} x+1$ through the point $(8,-3)$ .

Determine if the lines $8 x+6 y=8$ , $4 y=-3 x+5$ , and $y=-\frac{3}{4} x+7$ are parallel, perpendicular, or neither.

$y=x^{2}+4 x+4$

How many proportional relationships are shown in the coordinate plane below?
Choose 1 answer:
A 0 (B) 1 (C) 2 (D) 3

${ }_{1}^{8} 3$

ate $\iint_{D} 2 d A$ , where $D=((x, y): 0 \leq x \leq 1, x \leq y \leq 1+x)$ .

Here is a regular hexagon and a regular pentagon.
Work out the size of the angle marked $x$ . You must show all your working.

Evaluate $3 x^{2}+2 x y-y^{3}$ for $x=2$ and $y=-1$ . What is the result?

Evaluate $\frac{2 x-31}{y-5}$ for $x=-7$ and $y=-4$ . Is it a number or undefined?

Find where the function $f(x)=|6-x|$ is not differentiable and explain the reason.

Determine the relationship (parallel, perpendicular, or neither) for the lines: $y=4x+5$ , $4x-16y=32$ , $y=-\frac{1}{4}x-2$ .

Fill in the table for $x$ and $2x + 7$ with $x = 0, 1, -1$ . Simplify your answers.

A plane flew 180 miles against a $30-\mathrm{mph}$ wind and returned with a $15-\mathrm{mph}$ tailwind. Total time was 180 min. Find the plane's speed in still air.

Evaluate $\frac{x^{2}+y}{3 y}$ for $x=-3$ and $y=-2$ . Choose A or B: A. $\frac{x^{2}+y}{3 y}=\square$ or B. Undefined.

Determine if the lines $y=\frac{4}{3} x-5$ , $8 x-6 y=6$ , and $3 y=4 x+7$ are parallel, perpendicular, or neither.

Find $f(64)$ for the function $f(x)=x+\sqrt{x}+4$ .

Find $\delta$ for $\varepsilon=0.01$ in the limit $\lim _{x \rightarrow 4} 8 x=32$ .

Solve $6 \leq 12x - 4 < 16$ and find time to fill a tank with pipes filling in 9h, 12h, and draining in 15h.

Fill in the table for $x$ and $-\frac{1}{5} x$ at $x = 0, 5, -5$ . Simplify your answers.

Determine if the following lines are parallel, perpendicular, or neither: Line 1: $4x - 10y = 8$ Line 2: $y = -\frac{5}{2}x - 4$ Line 3: $2y = -5x + 3$

Find $\delta$ so that if $|x-2|<\delta$ , then $|4x-8|<0.9$ .

Simplify these expressions using positive exponents: a. $2^{-9} \cdot 2^{-6}$ , b. $2^{9} \cdot 2^{6}$ , c. $5^{15} \div 5^{3}$ , d. $5^{15} \div 5^{-3}$ , e. $(-3)^{-2}$ , f. $\frac{b^{2}}{b^{-3}}$ .

Find the fixed cost $F$ and variable cost $V$ from the cost function $C(x)$ using points (0, 660), (31, 1343), (95, 2750).
$\begin{array}{l} F= \\ V= \end{array}$