Equation

Problem 101

Find म्ट्रिप्र 0 क्या xx und yy

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Problem 102

poble lell 5. Find the area of the surface generated by revolving 2xx=(y4/4)+1/(8y2),1y2{ }^{2} x^{x}=\left(y^{4} / 4\right)+1 /\left(8 y^{2}\right), 1 \leq y \leq 2, about the xx-axis.

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Problem 103

1. Which of the following measures of three angles can be those of a triangle? 1) 40,60,8040^{\circ}, 60^{\circ}, 80^{\circ} 2) 90,60,2090^{\circ}, 60^{\circ}, 20^{\circ} 3) 100,80,50100^{\circ}, 80^{\circ}, 50^{\circ} 4) 40,80,9040^{\circ}, 80^{\circ}, 90^{\circ}
2. The measures of the four angles of a quadrilateral are in the ratio of 12.3:4. What is the measure of the greatest angle of quadrilateral? 1) 144144^{\circ} 2) 135135^{\circ} 3) 125125^{\circ} 4) 150150^{\circ}
3. Difference between two complementary angles is 1010^{\circ}. Calculate the vatues of both angles. 1) 45,4545^{\circ}, 45^{\circ} 2) 40,5040^{\circ}, 50^{\circ} 3) 50,6050^{\circ}, 60^{\circ}
4. What is the next row of numbers? 4) 100,10100^{\circ}, 10^{\circ} \begin{tabular}{|l|l|l|} \hline 48 & 144 & 192 \\ \hline 38 & 114 & 152 \\ \hline 28 & 84 & 112 \\ \hline \end{tabular} 1) 18547218 \quad 54 \quad 72 2) 5818424458 \quad 184 \quad 244 3) 6820427268 \quad 204 \quad 272
5. If 1=135,4=45\angle 1=135^{\circ}, \angle 4=45^{\circ}. Then, find 2\angle 2 and 3\angle 3, respectively 4) 6821429268 \quad 214 \quad 292 1) 145,35145^{\circ}, 35^{\circ} 2) 130,50130^{\circ}, 50 3) 140,40140^{\circ}, 40 4) 45,13545^{\circ}, 135^{\circ}
6. A quadrilateral ABCDA B C D is inscribed in a circle. If ABA B is parallel to CDC D and AC=BDA C=B D, then the quadrilateral must be a 1) parallelogram 2) rhombus 3) trapezium - 4) None of these
7. Which of the following is true if PQ=RS\mathrm{PQ}=\mathrm{RS} ? 1) PQ+QR=RSP Q+Q R=R S 2) PR=QSP R=Q S 3) PQ+QS=RSP Q+Q S=R S 4) PQRS=QRP Q-R S=Q R

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Problem 104

2. Nesta questāo π:2x3yz+5=0,r:(x,y,z)=(2,1,4)+t(2,3,4),tRA(1,2,3)\pi: 2 x-3 y-z+5=0, r:(x, y, z)=(2,1,4)+t(2,-3,4), t \in R \in A(-1,2,3) representam um plano uma reta e um ponto, respectivamente. (a) (Valor: 1,0) Encontre uma equação de um plano perpendicular a rr que passa por AA : (b) (Valor: 1,5) A reta rr e o plano π\pi sâo transversais? Em caso afirmativo, encontre o ponto de interseção entre esses objetos. Em caso negativo, determine a distância entre estes dois objetos.
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Problem 105

8x+8x+8x4x+4x=12\frac{8^{x}+8^{x}+8^{x}}{4^{x}+4^{x}}=12

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Problem 106

4. (Valor: 2,5) Incontre a equaçáo da hipérbole de excentricidade 2 e focos coincidentes com os focos da elipse x225+y29=1\frac{x^{2}}{25}+\frac{y^{2}}{9}=1.
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Voltar Enviar

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Problem 107

4. (Valor: 2,5 ) Encontre a equaçao da hipérbole de excentricidade 2 e focos coincidentes com os focos da ellipse x225+y29=1\frac{x^{2}}{25}+\frac{y^{2}}{9}=1.
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Problem 108

x223x5=0x^{2}-\frac{2}{3} x-5=0

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Problem 109

x4x2=5a0\frac{x-4}{\sqrt{x}-2}=5 a^{0}

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Problem 110

What is the balance after 2 years in a savings account with an initial investment of $800\$ 800 and a 3.5\% annual compound interest rate?

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Problem 111

x32=125x^{\frac{3}{2}}=125

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Problem 112

Suppose a charity recievet a danation of 22. it villion. If this represents 278 d of the charitys doarted funds, what is totol amom Rits denated funds?

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Problem 113

The amount of water in the cooler ww dropped by 37 cups during the day at a work site, ending at 15 cups. Write an equation to represent this situation. Then, solve the equation for ww to determine the amount of water in the cooler at the beginning of the day.

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Problem 114

How much interest is earned on a CD with a 2 year fixed maturity, if the initial investment is $810\$ 810 and the annual interest rate is 2.3%2.3 \% ?

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Problem 115

If you borrow $700\$ 700 for 4 years at an annual interest rate of 8%8 \%, how much will you pay altogether?

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Problem 116

If you borrow $300\$ 300 for 14 years at an annual interest rate of 4%4 \%, how much will you pay altogether?

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Problem 117

If you borrow $900\$ 900 for 4 years at an annual interest rate of 5%5 \%, how much will you pay altogether?

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Problem 118

If you borrow $400\$ 400 for 3 years at an annual interest rate of 4%4 \%, how much will you pay altogether?

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Problem 119

3b+4=83 b+4=-8

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Problem 120

If you borrow $500\$ 500 for 6 years at an annual interest rate of 7%7 \%, how much will you pay altogether? \$[?]

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Problem 121

10. At what point on the parabola y=3x2+2xy=3 x^{2}+2 x is the tangent line parallel to the line y=10x2y=10 x-2 ? [ 6 mark

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Problem 122

2. Traveling at 65 miles/hour, how many minutes will it take to drive 125 miles to San Diego?
Convert 50 years into seconds. Express your answer in scientific notation.
Traveling at 65 miles/hour, how many feet can you travel in 22 minutes? ( 1 mile =5280=5280 feet)

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Problem 123

b235b+300=0b^{2}-35 b+300=0

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Problem 124

Without using a calculator, solve each problem in the set of REAL numbers. Show work. Write your Calculus 1 answer as a set of solutions (for equations) or as interval notation (for inequalities). Keep the numbers in their exact simplified form. (Example: x=20=25x=\sqrt{20}=2 \sqrt{5} ). If solving by factoring is easy, utilize factoring.
1. a) x2=8=±22x^{2}=8= \pm 2 \sqrt{2} b) x2<8x^{2}<8 x28=0(x8)(x+8)2)x+8=0;x=8=4×2=22x8=0x=8=4×2=22\begin{array}{l} x^{2}-8=0 \\ (x-\sqrt{8})(x+\sqrt{8}) \end{array} \left\lvert\, \begin{array}{l} 2) x+\sqrt{8}=0 ; x=-\sqrt{8} \\ =-\sqrt{4 \times 2}=-2 \sqrt{2} \\ x-\sqrt{8}=0 \Rightarrow x=\sqrt{8}=\sqrt{4 \times 2}=2 \sqrt{2} \end{array}\right.
2. a) x2=32x^{2}=-32 b) x2>32x^{2}>32
3. a) x2=3x+18x^{2}=3 x+18 b) x23x+18x^{2} \leq 3 x+18
4. a) 5+16x3x2=0-5+16 x-3 x^{2}=0 b) 5+16x3x2>0-5+16 x-3 x^{2}>0

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Problem 125

[îA, 7 m measured a house and made a scale drawing. In real life, the hall closet is 6 feet lang. It is 10 inches long in the drawing. What is the scale of the drawing? 5 inches: \square feet

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Problem 126

a 12x13=13(x2)\frac{1}{2} x-\frac{1}{3}=\frac{1}{3}(x-2)

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Problem 127

subture the problitems. in the barnits.

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Problem 128

Determine whether the number is a solution 4x4=6x+64 x-4=6 x+6 a. x=6x=6 b. x=5x=-5

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Problem 129

Baker's Financial Planners purchased nine new computers for $950\$ 950 each. It received a 10%10 \% discount because it purchased more than seven and an additional 8%8 \% discount because it took immediate delivery. Terms of payment were 5/10,n/305 / 10, n / 30. Baker's pays the bill within the cash discount period. How much should the check be?

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Problem 130

Verizon offers to sell cellular phones listing for $100.49\$ 100.49 with a chain discount of 15/10/5. Cellular Company offers to sell its cellular phones that list at $103.99\$ 103.99 with a chain discount of 25/525 / 5. If Irene is to buy six phones, how much could she save if she buys from the lower-priced company?

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Problem 131

DJI manufactures the Mavic Air 2 quadcopter and offered a 5/3/25 / 3 / 2 chain discount to primary customers. Drone Nerds is a primary customer and ordered 20 Mavic Air 2's for a total $26,000\$ 26,000 list price.
Required: a. What was the net price of the quadcopters?
Note: Do not round intermediate calculations. Round your final answer to the nearest cent.
Net price b. What was the trade discount amount?
Note: Do not round intermediate calculations. Round your final answer to the nearest cent.
Trade discount

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Problem 132

A local Barnes and Noble paid a $80.35\$ 80.35 net price for each hardbound atlas. The publisher offered a 15%15 \% trade discount. What was the publisher's list price?
Note: Round your answer to the nearest cent.

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Problem 133

15 shares of stock were purchased for $40\$ 40 per share with a $6\$ 6 commission. What is the total cost of this investment?
Total Cost =$[?]=\$[?]

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Problem 134

Which ingution can be used to solve for xx ? 30x5=077x+28=6730x+5=677x+18=6730 x-5=07 \quad 7 x+28=67 \quad 30 x+5=67 \quad 7 x+18=67
Solve for xx. x=x=

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Problem 135

is Look at the diagram.
Which equation can be used to solve for xx ? 2x49=832x+33=832x+49=832x33=83\begin{array}{l|l|l|l} 2 x-49=83 & 2 x+33=83 & 2 x+49=83 & 2 x-33=83 \end{array}
Solve for xx x=x=\square

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Problem 136

अi, look at the diagram.
Which equation can be used to solve for xx ? 30x5=6730 x-5=67 7x+28=677 x+28=67 30x+5=6730 x+5=67 7x+18=677 x+18=67
Solve for xx x=x=\square

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Problem 137

10 shares of stock were purchased for \$25 per share with a \$6 commission. What is the total cost of this investment?
Total Cost =$[?]=\$[?]

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Problem 138

(b) Show that the HCF and LCM of x(a+4)x(a+4) and a3+64a^{3}+64 is a+4a+4 and x(a+4)(a24a+16)x(a+4)\left(a^{2}-4 a+16\right) respectively.

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Problem 139

Título de la tarea: Punto de equilibrio Resultados de aprendizaje: Calcula los costos de producción Analiza los costos Descripción de la tarea: Desarrollar la tarea en un archivo en Excel formulado.
Taller: Punto de Equilibrio
La cadena de establecimientos de restaurantes del Norte S.A. desea un análisis de costo volumen utilidad para el único producto super estrella que maneja. - El precio de venta es de $200,00c/u\$ 200,00 \mathrm{c} / \mathrm{u} - Los costos variables son de $100,00c/u\$ 100,00 \mathrm{c} / \mathrm{u} - Los costos fijos son de $100.000,00\$ 100.000,00
Con estos datos determine:
1. Punto de equilibrio en unidades por el método de ecuación
2. Punto de equilibrio en dólares por el método de ecuación
3. El porcentaje del margen de contribución
4. Suponga que el precio de venta aumenta en 25%25 \%. ¿Cuál será el nuevo punto de equilibrio en unidades y en dólares?

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Problem 140

12. The volume of a sphere, VV, is given by the formula V=43πr3V=\frac{4}{3} \pi r^{3}, where rr is the radius of the sphere. (a) Make rr the subject of this formula (b) What is the radius of a sphere with volume 200 cm3200 \mathrm{~cm}^{3}. ( 3 marks)
13. Solve the equation: 2x1+2x+1=3202^{x-1}+2^{x+1}=320. (4 marks)
14. Simplify the expression. (4 marks) a3bc(2b2c)(3c2)+(a2b2c2)(2a)(3bc2)a^{3} b c\left(-2 b^{2} c\right)\left(3 c^{2}\right)+\left(-a^{2} b^{2} c^{2}\right)(2 a)\left(-3 b c^{2}\right)
15. Make " r " the subject of P=11+11+rP=\frac{1}{1+\frac{1}{1+r}}. (4 marks)
16. Find the area of the shaded region. (4 marks)
17. Factorize: 3m(2m4n)6(4n2m)9(6n+3m)3 m(2 m-4 n)-6(4 n-2 m)-9(6 n+3 m). (4 marks)

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Problem 141

Título de la tarea:
Punto de equilibrio Resultados de aprendizaje:
Calcula los costos de producción Analiza los costos
Descripción de la tarea: Desarrollar la tarea en un archivo en Excel formulado.
Taller: Punto de Equilibrio
La cadena de establecimientos de restaurantes del Norte S.A. desea un análisis de costo volumen utilidad para el único producto super estrella que maneja. - El precio de venta es de $200,00c/u\$ 200,00 \mathrm{c} / \mathrm{u} - Los costos variables son de $100,00c/u\$ 100,00 \mathrm{c} / \mathrm{u} - Los costos fijos son de $100.000,00\$ 100.000,00
Con estos datos determine:
1. Punto de equilibrio en unidades por el método de ecuación
2. Punto de equilibrio en dólares por el método de ecuación
3. El porcentaje del margen de contribución
4. Suponga que el precio de venta aumenta en 25%25 \% ¿Cuál será el nuevo punto de equilibrio en unidades y en dólares?

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Problem 142

Find the distance between the points ( -9 , 7) and (9,20)(9,20). 493\sqrt{493} 493 155\sqrt{155} 155

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Problem 143

(x+5)(x4)=0(x+5)(x-4)=0

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Problem 144

1) On trangle rectangie a pourpérinêue som c. sot aire vaut 30 m230 \mathrm{~m}^{2}. Déterminer ses dimensions.

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Problem 145

x+5)(x4)=0x+5)(x-4)=0

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Problem 146

(Vocabulary and Concepts) Fill in the blanks to make each statement true.
1. If a,ba, b, and cc are real numbers, and a0a \neq 0, then the general quadratic equation is \qquad
2. The formula x=b±b24ac2ax=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} is called the \qquad formula.
3. The expression b±b24ac2a\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} can be read as "The \qquad of bb, plus \qquad the \qquad root of bb \qquad minus 4 \qquad aa times cc, all \qquad 2a."
4. To use the quadratic formula, we begin by writing the equation in . \qquad
5. Although the quadratic formula can be used to solve x23x=0x^{2}-3 x=0, the \qquad method is easier.

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Problem 147

25 shares of stock were purchased for \$25 per share with a \$6 commission. What is the total cost of this investment?

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Problem 148

12t(t5)=012 t(t-5)=0

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Problem 149

What is the dividend yield on Stock AA that sells at $30\$ 30 /share, when Company A pays a quarterly dividend of $0.10\$ 0.10 per share?  Dividend Yield =[?]% Dividend Yield = Annual Dividend  Share Price \begin{array}{c} \text { Dividend Yield }=[?] \% \\ \text { Dividend Yield }=\frac{\text { Annual Dividend }}{\text { Share Price }} \end{array}

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Problem 150

An investor purchased 70 shares of stock in a company for $4.760\$ 4.760, with an $8\$ 8 commission. Later, all of the stock was sold at $71\$ 71 per share. What was the gain or loss on this investment?
Gain or Loss =$[?]=\$[?]
Enter a gain as positive and a loss as negative.

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Problem 151

4) What percentage of 126 is 504 ?

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Problem 152

One work was done by team 1 in 10 days and team 2 in 15 days. If we cooperate, how many days will the work be done?

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Problem 153

The following table shows the balance on a credit card over the period of 1 month, that charges a 18%18 \% APR (interest rate). \begin{tabular}{|c|c|c|} \hline Days & Balance & Description \\ \hline 151-5 & $200\$ 200 & Initial Balance \\ \hline 6206-20 & $350\$ 350 & $150\$ 150 purchase \\ \hline 213021-30 & $150\$ 150 & $200\$ 200 payment \\ \hline \end{tabular}
What is the finance charge, on the average daily balance, for this card over this 1 month period?
Finance Charge =$[?]=\$[?]

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Problem 154

The balance on a credit card, that charges a 28.5\% APR interest rate, over a 1 month period has a daily balance of $145\$ 145. What is the finance charge, on the average daily balance, for this 1 month period? 28.5%=0.28528.5 \%=0.285
Hint: Divide the decimal by 12 to get the monthly interest rate. De not round that answer. Take that answer and multiply it to the average daily balance.
Finance charge = \? ? ]$

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Problem 155

What is the monthly interest payment for an account with a balance of $100.00\$ 100.00 and an A.P.R. of 12%12 \% ?

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Problem 156

What is the interest earned after 1 year in a savings account with an initial investment of \$826 and a 3.5\% simple interest rate?

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Problem 157

What is the total payment required to pay off a promissory note issued for $400.00\$ 400.00 at 6%6 \% ordinary interest and a 90-day term?

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Problem 158

What is the balance after 3 years in a savings account with an initial investment of $700\$ 700 and a 4.6%4.6 \% annual compound interest rate?

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Problem 159

What is the interest earned after 1 year in a savings account with an initial investment of $1,550\$ 1,550 and a 4.2%4.2 \% simple interest rate?

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Problem 160

\begin{tabular}{|l|r|} \hline \multicolumn{2}{|c|}{ Instailment } \\ \hline Principal & $2.550\$ 2.550 \\ \hline Term Length & 3%3 \% years \\ \hline Interest Rate & 9%9 \% \\ \hline Monthly Payment & $71\$ 71 \\ \hline \end{tabular}
How much of the 40 th payment will go to interest if there is an outstanding principal of \210?Intereston210? Interest on 40^{\text {th }}Payment Payment =\[?][?]

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Problem 161

What is the monthly interest payment for an account with a balance of $400.00\$ 400.00 and an A.P.R. of 27%27 \% ?

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Problem 162

What is the monthly interest payment for an account with a balance of $100.00\$ 100.00 and an A.P.R. of 18%18 \% ? $[?]\$[?]

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Problem 163

How much money will a borrower using Loan 1 pay in interest over the life of the loan? \begin{tabular}{|l|r|r|} \hline & \multicolumn{1}{|c|}{ Loan 1 } & \multicolumn{1}{c|}{ Loan 2 } \\ \hline Principal & $5000.00\$ 5000.00 & $5000.00\$ 5000.00 \\ \hline Monthly Payment & $148.00\$ 148.00 & $113.00\$ 113.00 \\ \hline Duration & 36 months & 48 months \\ \hline \end{tabular} $[?]\$[?]

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Problem 164

b) Given that et2dt=π\int_{-\infty}^{\infty} e^{-t^{2}} d t=\sqrt{\pi}, calculate the improper integral: xe(x+3)2dx\int_{-\infty}^{\infty} x e^{-(x+3)^{2}} d x

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Problem 165

Cell Phones. A cellular phone company currently has three towers: one in Tampa, one in Orlando, and one in Gainesville to serve the central Florida region. The company then has decided to add additional towers "halfway" between each city. If Orlando is 80 mifes east of Tampa and Gainesville is 100 miles north of Tampa, how many miles from Tampa is each "halfway" tower?
Round your answers to the nearest integer.
Distance from Tampa to the halfway tower between Tampa and Orlando is \square 40 miles
Distance from Tampa to the halfway tower between Tampa and Gainesville is \square 50 miles
Distance from Tampa to the halfway tower between Gainsville and Orlando is \square 64 miles

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Problem 166

9) Хэвлыийн чехийн ажиттан минутанд 1151 \frac{1}{5} хуудас уддэг байв. Тэгвэл 60 хуудастай номын хэдэн минутанд үлдэх вэ?

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Problem 167

How much money is needed to make a 6.5%6.5 \% down payment on a $500,000\$ 500,000 asset?

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Problem 168

Use integration tables to evaluate the integral 0π227xcosxdx\int_{0}^{\frac{\pi}{2}} 27 x \cos x d x.

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Problem 169

Distanța București-Arad este de 560 km . Distanța pe hartă este de 5,6 cm5,6 \mathrm{~cm}. a) Determinați scara hărții. S= distanța din desen  distanța din teren =S=\frac{\text { distanța din desen }}{\text { distanța din teren }}=

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Problem 170

State ohm's law and write the formula down, showing the relation between V (voltage). and RR (resistance).

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Problem 171

Given AA is a non-singular matrix such that A22AI=0A^{2}-2 A-I=0. II and 0 are the identity matrix and null matrix respectively. Find A1A^{-1}. A+2IA+2 I I A2IA-2 I AA

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Problem 172

epression of a point 100 mts from the foot of the tree is 6060^{\circ}. Find the height of the tree.

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Problem 173

Aiden took out a car loan for 4 years. The maturity value of the loan was \$24,666, and Aiden hac paid \$1,894 in interest. What was the principal amount of the loan?
Hint: Use the formula P=MVIP=M V-I, where PP is the principal, MV is the maturity value, and / is the interest paid. \26,56026,560 \30,750 30,750 $22,772\$ 22,772 \$32,558

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Problem 174

Percentage Increase: ( New Value - Original Value ) Original value ×100%\frac{(\text { New Value - Original Value })}{\text { Original value }} \times 100 \% Percentage Decrease:  (amount of decrease)  original value ×100%\frac{\text { (amount of decrease) }}{\text { original value }} \times 100 \% Complete the table:

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Problem 175

3sin(3xπ)cos(3xπ)=1\sqrt{3} \sin (3 x-\pi)-\cos (3 x-\pi)=1

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Problem 176

QUESTION THREE a) With the aid of a diagram, describe the 4 -sector model of the circular flow of income (10 MARKS) ii. Compute the gross national product (GNP). Gre Go GP + sols sin(men\sin (\mathrm{men} ( MARks)
Given the following nominal data in the figure above: i. Compute GDP using the expenditure approach. (4 MARKS b) What impact would each of the following have on real GDP? i. On average, people in a country decide to increase the number of hours they work by 5 (2 MAR ii. The price level and nominal GDP increase by 10%,dcr2as210 \%, \rightarrow d_{\infty} \mathrm{cr}^{2} a s^{2} (2 MAF

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Problem 177

Question 4 5 Points (CE Board May 2017) The angle of intersection of a circular curve is 453045^{\circ} 30^{\prime} and its radius is 198.17 m . If the PC is at STA 0+7000+700, compute the right angle offset from P at STA 0+736.580+736.58 on the curve to the tangent through PC. (A) 3.37 m (B) 2.98 m (C) 3.09 m (D) 3.87 m

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Problem 178

2. Find the values of the unknowns xx and yy in the following-diagrams: (i) (ii) (iii)

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Problem 179

(y2)=25(x+3)(y-2)=\frac{2}{5}(x+3)

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Problem 180

Ester and George want to make trail mix. In order to get the right balance of ingredients for their tastes they bought 4 pounds of raisins at $4.71\$ 4.71 per pound, 3 pounds peanuts for $3.45\$ 3.45 per pound, and 2 pounds of chocolate chips for $2.16\$ 2.16 per pound. Determine the cost per pound of the trail mix.
The cost per pound of the trail mix is $\$ \square (Round to the nearest cent as needed.)

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Problem 181

The scores and their percents of the final grade for a statistics student are given. An error occurred grading the final exam. Instead of getting 87 , the student scored 98. What is the student's new weighted mean? \begin{tabular}{lccc} & Score & \begin{tabular}{c} Percent of \\ Final Grade \end{tabular} & \begin{tabular}{c} Weighted \\ Score \end{tabular} \\ Homework & 87 & 10 & 8.7 \\ Quiz & 78 & 25 & 19.5 \\ Project & 97 & 20 & 19.4 \\ Speech & 90 & 15 & 13.5 \\ Final Exam & 87 & 30 & 26.1 \\ & & Weighted Mean & 87.2 \end{tabular}
The student's new weighted mean score is \square (Do not round.)

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Problem 182

What value of xx makes this equation true? 90=100+x-90=-100+x 10-10 10 190-190 190

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Problem 183

A certain state uses the progressive tax rate below for calculating individual income tax. Calculate the state income tax owed on an \60,000 per year salary. \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Income \\ Range (\$) \end{tabular} & \begin{tabular}{c} Progressive \\ Tax Rate \end{tabular} \\ \hline 0-24,000 & 4 \% \\ \hline 24,001-52,000 & 6 \% \\ \hline 52,001+ & 8 \%$ \\ \hline \end{tabular}

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Problem 184

Calculate the commission that a sales person would earn if they received 5%5 \% commission on a $3,000\$ 3,000 painting that they sold.

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Problem 185

Hans is putting money into a savings account. He starts with $750\$ 750 in the savings account, and each week he adds $30\$ 30. Let SS represent the total amount of money in the savings account (In dollars), and let WW represent the number of weeks Hans has been adding money. Write an equation relating SS to WW. Then use this equation to find the total amount of money in the savings account after 18 weeks.
Equation: \square \square Total amount of money after 18 weeks: $\$ \square

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Problem 186

A construction crew is lengthening a road. The road started with a length of 53 miles, and the crew is adding 4 miles to the road each day. Let LL represent the total length of the road (in miles), and let DD represent the number of days the crew has worked. Write an equation relating LL to DD. Then use this equation to find the total length of the road after the crew has worked 33 days.
Equation: \square
Total length of the road after 33 days: \square miles

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Problem 187

6) Solve the equation. 19.24.4n=619.2-4.4 n=6 n=3n=-3 n=8n=8 n=3n=3 n=8n=-8

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Problem 188

10) Solve the equation. n+238n=3n1n+23-8 n=-3 n-1 n=6n=6 n=5.5n=5.5 n=2.2n=-2.2 n=4n=-4

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Problem 189

Without sketching the graph, find the xx-intercepts and yy-intercepts of the graph of the equation. 6x+3y=726 x+3 y=72
What is/are the x-intercept(s)? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The x-intercept(s) is/are \square . (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no xx-intercepts.

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Problem 190

If the federal government used the progressive tax rate below for individual income tax, calculate the federal income tax owed on a $74,300\$ 74,300 salary. \begin{tabular}{|c|c|} \hline Standard Deduction & $12,200\$ 12,200 \\ \hline Income Range (\) & \begin{tabular}{l} Progressive \\ Tax Rate \end{tabular} \\ \hline 0 - \quad 9,700 & 10 \% \\ \hline 9,701 - 39,475 & 12 \% \\ \hline 39,476-84,200 & 22 \% \\ \hline 84,201-160,275 & 249 \% \\ \hline 160,276+ & 32 \%$ \\ \hline \end{tabular}

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Problem 191

52=2y52=2 y

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Problem 192

What is the balance after 2 years in a savings account with an initial investment of $1,250\$ 1,250 and a 5\% annual compound interest rate?

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Problem 193

A certain state uses the progressive tax rate below for calculating individual income tax. Calculate the state income tax owed on an $80,000\$ 80,000 per year salary. \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Income \\ Range (\) \end{tabular} & \begin{tabular}{c} Progressive \\ Tax Rate \end{tabular} \\ \hline 0-4,000 & 2 \% \\ \hline 4,001-22,000 & 4 \% \\ \hline 22,001+ & 5 \%$ \\ \hline \end{tabular}

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Problem 194

Health insurance coverage for an employee is $2,470\$ 2,470 per year. Their employer pays 80%80 \% of that cost. How much is taken from the employee's biweekly paycheck?

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Problem 195

How much interest is earned on a CD with a 2 year fixed maturity, if the initial investment is $790\$ 790 and the annual interest rate is 2.4%2.4 \% ?  Interest = $[?]\text { Interest = } \$[?]

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Problem 196

21.33. An electron is projected with
Figure 21.38 an initial speed v0=1.60×106 m/sv_{0}=1.60 \times 10^{6} \mathrm{~m} / \mathrm{s} into the uniform field between the parallel plates in Fig. 21.38. Assume that the ficld between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the Exercise 21.33. field at a point midway between the plates. (a) If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field. (b) Suppose that in Fig. 21.38 the electron is replaced by a proton with the same initial speed v0v_{0}. Would the proton hit one of the plates? If the proton would not hit one of the plates, what would be the magnitude and direction of its vertical displacement as it exits the region between the plates? (c) Compare the paths traveled by the electron and the proton and explain the differences. (d) Discuss whether it is reasonable to ignore the effects of gravity for each particle.

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Problem 197

In Exercises 32-33, find the exact distance between the two points.
32. G(1,5)G(-1,-5) and H(3,8)GH=H(3,-8) \quad G H= \qquad
33. G(2,5)G(2,5) and H(4,1)GH=H(4,-1) G H= \qquad

Use the information to find the midpoint between points AA and BB. In a three-dimensional coordinate system, the midpoint between A(x1,y1,z1)A\left(x_{1}, y_{1}, z_{1}\right) and B(x2,y2,z2)B\left(x_{2}, y_{2}, z_{2}\right) is (x1+x22,y1+y22,z1+z22)\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}, \frac{z_{1}+z_{2}}{2}\right).
34. A(3,0,4)A(-3,0,4) B(7,2,8)B(7,2,8)

Use the information to find the distance between points AA and BB. Leave answers in simplified radical form. In a threedimensional coordinate system, the distance between the two points A(x1,y1,z1)A\left(x_{1}, y_{1}, z_{1}\right) and B(x2,y2,z2)B\left(x_{2}, y_{2}, z_{2}\right) is AB=(x2x1)2+(y2y1)2+(z2z1)2A B=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}+\left(z_{2}-z_{1}\right)^{2}}
35. A(2,1,2)A(-2,1,2) B(2,3,4)B(2,-3,4)

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Problem 198

The following expression equals -2 : 24÷44(x÷6)+10-2^{4} \div 4-4(x \div 6)+10
Solve for the variable xx.

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Problem 199

48.3÷(7)=-48.3 \div(-7)=

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Problem 200

Worksheet TWO
1. Given: ABC\triangle A B C right angle at CAB=2,AC=3C A B=2, A C=\sqrt{3}, then find the basic trigonometric value for angle β\beta.
2. Given : sin30=12,cos30=32\sin 30^{\circ}=\frac{1}{2}, \cos 30^{\circ}=\frac{\sqrt{3}}{2}, Find the remaining trigonometric values of 3030^{\circ} by using these values. 3.  For i. θ=20\text { For i. } \theta=20^{\circ} ii. θ=30\theta=30^{\circ} Find cos2θ+sin2θ\cos ^{2} \theta+\sin ^{2} \theta
4. Given : δ=60\delta=60^{\circ}, then show that 1+tan2δ=sec2δ1+\tan ^{2} \delta=\sec ^{2} \delta
5. If θ=0.10\theta=0.1^{0}, then show that cos20.10=csc20.101\cos ^{2} 0.1^{0}=\csc ^{2} 0.1^{0}-1
6. If the trigonometric point P(θ)P(\theta) has coordinate (4,3)(4,3), then find the basic trigonometric for θ\theta.
7. Given : cosθ=35\cos \theta=\frac{-3}{5} for θ\theta a 2nd 2^{\text {nd }} quadrant angle, find the remaining basic trigonometri ratios.
8. Express the remaining trigonometric ratios interims of sinθ\sin \theta for a given angle θ\theta. 10. In ABC,m(<A)=120,AB=4,AC=2\triangle A B C, m(<A)=120^{\circ}, A B=4, A C=2 units, then find i. BC ii. cosine of angle B
11. Find the exact values of each of the following using the half angle formula and cCc C the result obtained by using the angle sum formula. a. cos15\cos 15^{\circ} b. sin15\sin 15^{\circ} c. tan15\tan 15^{\circ} d. tan22.5\tan 22.5^{\circ}

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