Exam 6: Equations and Formulas

Follow the rules for working with measurements. Use the formula $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Given $R _ { 1 } = 39 \Omega$ and $R _ { 2 } = 30 \Omega$ , find R. R = __________Ω

(Short Answer)

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Question 221

Use the formula $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Given $R _ { 1 }$ = 37 ? and $R _ { 2 }$ = 24 ?. Find R.

(Multiple Choice)

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Question 222

Solve the equation and check. $\frac { y } { 3 } - 3 = \frac { y } { 6 }$

(Multiple Choice)

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Question 223

Solve the equation and check. $7 x - 56 = 14$

(Multiple Choice)

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Question 224

Distribute $399 among Peter, Betsy and Emma so that Betsy receives five times as much as Peter, and Emma receives three times as much as Betsy.

(Multiple Choice)

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Question 225

Follow the rules for working with measurements. Use the formula $\frac { 1 } { C } = \frac { 1 } { C _ { 1 } } + \frac { 1 } { C _ { 2 } } + \frac { 1 } { C _ { 3 } }$ . Given $C = 4.85 \times 10 ^ { - 9 } \mathrm {~F}$ , $C _ { 1 } = 6.58 \times 10 ^ { - 7 } F$ and $C _ { 3 } = 7.89 \times 10 ^ { - 9 } F$ , find $C _ { 2 }$ . $C _ { 2 } =$ ×10 $F$

(Short Answer)

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Question 226

Use the formula $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Given R = 3 ? and $R _ { 1 }$ = 4 ?. Find $R _ { 2 }$ .

(Multiple Choice)

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Question 227

Solve the formula for the given letter. $V = \frac { 1 } { 3 } \pi r ^ { 2 } h \text { for } r$

(Multiple Choice)

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Question 228

Solve the equation and check. $1 \frac { 1 } { 4 } x = 21 \frac { 1 } { 4 }$

(Multiple Choice)

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Question 229

Solve the equation and check. $14 + 14 ( 3 - 2 x ) + 12 = 4 - x + 5 ( 2 - 3 x )$

(Multiple Choice)

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Question 230

Solve the equation and check. $2 x - 64 = 0$

(Multiple Choice)

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Question 231

Given the formula: $v _ { f } ^ { 2 } = v _ { i } ^ { 2 } + 2 g h , \quad v _ { f } = 263 , \quad v _ { i } = 0 , \quad g = 16$ Find h.

(Multiple Choice)

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Question 232

Solve the equation and check. $3 x + 13 = 2 x - 14$

(Multiple Choice)

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Question 233

Follow the rules for working with measurements. Use the formula $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } } + \frac { 1 } { R _ { 3 } }$ . Given $R _ { 1 } = 78 \Omega$ , $R _ { 2 } = 60 \Omega$ and $R _ { 3 } = 78 \Omega$ , find R. Give the answer to one decimal place. R = __________Ω

(Short Answer)

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Question 234

Solve the equation and check. $- 8 x + 10 ( x - 6 ) = 28$ x = __________

(Short Answer)

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Question 235

Solve the equation and check. $\frac { 8 } { y } - 7 = 1$ y = __________

(Short Answer)

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Question 236

Given the formula: y = mx + b, $x = 4 , y = 5 , b = 4$ Find m.

(Multiple Choice)

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Question 237

Solve the equation and check. $2 ( 4 y + 1 ) + 13 = 3 + 4 ( y - 5 )$ y = __________

(Short Answer)

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Question 238

Solve the equation. $24 - 12 c = - 6$

(Multiple Choice)

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Question 239

Solve the equation. $x + 9 = 4$

(Multiple Choice)

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(36)

Question 240

Follow the rules for working with measurements. Use the formula $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Given $R _ { 1 } = 39 \Omega$ and $R _ { 2 } = 30 \Omega$ , find R. R = __________Ω

Use the formula $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Given $R _ { 1 }$ = 37 ? and $R _ { 2 }$ = 24 ?. Find R.

Solve the equation and check. $\frac { y } { 3 } - 3 = \frac { y } { 6 }$

Solve the equation and check. $7 x - 56 = 14$

Distribute $399 among Peter, Betsy and Emma so that Betsy receives five times as much as Peter, and Emma receives three times as much as Betsy.

Use the formula $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Given R = 3 ? and $R _ { 1 }$ = 4 ?. Find $R _ { 2 }$ .

Solve the formula for the given letter. $V = \frac { 1 } { 3 } \pi r ^ { 2 } h \text { for } r$

Solve the equation and check. $1 \frac { 1 } { 4 } x = 21 \frac { 1 } { 4 }$

Solve the equation and check. $14 + 14 ( 3 - 2 x ) + 12 = 4 - x + 5 ( 2 - 3 x )$

Solve the equation and check. $2 x - 64 = 0$

Given the formula: $v _ { f } ^ { 2 } = v _ { i } ^ { 2 } + 2 g h , \quad v _ { f } = 263 , \quad v _ { i } = 0 , \quad g = 16$ Find h.

Solve the equation and check. $3 x + 13 = 2 x - 14$

Solve the equation and check. $- 8 x + 10 ( x - 6 ) = 28$ x = __________

Solve the equation and check. $\frac { 8 } { y } - 7 = 1$ y = __________

Given the formula: y = mx + b, $x = 4 , y = 5 , b = 4$ Find m.

Solve the equation and check. $2 ( 4 y + 1 ) + 13 = 3 + 4 ( y - 5 )$ y = __________

Solve the equation. $24 - 12 c = - 6$

Solve the equation. $x + 9 = 4$

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Polynomials: an Introduction to Algebra

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Quadratic Equations

Geometry

Right Triangle Trigonometry

Trigonometry With Any Angle

Basic Statistics

Binary and Hexadecimal Numbers

Filters

Exam 6: Equations and Formulas

Follow the rules for working with measurements. Use the formula 1R=1R1+1R2\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }R1​=R1​1​+R2​1​ . Given R1=39ΩR _ { 1 } = 39 \OmegaR1​=39Ω and R2=30ΩR _ { 2 } = 30 \OmegaR2​=30Ω , find R. R = __________Ω

Use the formula 1R=1R1+1R2\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }R1​=R1​1​+R2​1​ . Given R1R _ { 1 }R1​ = 37 ? and R2R _ { 2 }R2​ = 24 ?. Find R.

Solve the equation and check. y3−3=y6\frac { y } { 3 } - 3 = \frac { y } { 6 }3y​−3=6y​

Solve the equation and check. 7x−56=147 x - 56 = 147x−56=14

Distribute $399 among Peter, Betsy and Emma so that Betsy receives five times as much as Peter, and Emma receives three times as much as Betsy.

Use the formula 1R=1R1+1R2\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }R1​=R1​1​+R2​1​ . Given R = 3 ? and R1R _ { 1 }R1​ = 4 ?. Find R2R _ { 2 }R2​ .

Solve the formula for the given letter. V=13πr2h for rV = \frac { 1 } { 3 } \pi r ^ { 2 } h \text { for } rV=31​πr2h for r

Solve the equation and check. 114x=21141 \frac { 1 } { 4 } x = 21 \frac { 1 } { 4 }141​x=2141​

Solve the equation and check. 14+14(3−2x)+12=4−x+5(2−3x)14 + 14 ( 3 - 2 x ) + 12 = 4 - x + 5 ( 2 - 3 x )14+14(3−2x)+12=4−x+5(2−3x)

Solve the equation and check. 2x−64=02 x - 64 = 02x−64=0

Given the formula: vf2=vi2+2gh,vf=263,vi=0,g=16v _ { f } ^ { 2 } = v _ { i } ^ { 2 } + 2 g h , \quad v _ { f } = 263 , \quad v _ { i } = 0 , \quad g = 16vf2​=vi2​+2gh,vf​=263,vi​=0,g=16 Find h.

Solve the equation and check. 3x+13=2x−143 x + 13 = 2 x - 143x+13=2x−14

Solve the equation and check. −8x+10(x−6)=28- 8 x + 10 ( x - 6 ) = 28−8x+10(x−6)=28 x = __________

Solve the equation and check. 8y−7=1\frac { 8 } { y } - 7 = 1y8​−7=1 y = __________

Given the formula: y = mx + b, x=4,y=5,b=4x = 4 , y = 5 , b = 4x=4,y=5,b=4 Find m.

Solve the equation and check. 2(4y+1)+13=3+4(y−5)2 ( 4 y + 1 ) + 13 = 3 + 4 ( y - 5 )2(4y+1)+13=3+4(y−5) y = __________

Solve the equation. 24−12c=−624 - 12 c = - 624−12c=−6

Solve the equation. x+9=4x + 9 = 4x+9=4

Basic Concepts

Signed Numbers and Powers of 10

The Metric System

Measurement

Polynomials: an Introduction to Algebra

Ratio and Proportion

Graphing Linear Equations

Systems of Linear Equations

Factoring Algebraic Expressions

Quadratic Equations

Geometry

Right Triangle Trigonometry

Trigonometry With Any Angle

Basic Statistics

Binary and Hexadecimal Numbers

Filters

Follow the rules for working with measurements. Use the formula $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Given $R _ { 1 } = 39 \Omega$ and $R _ { 2 } = 30 \Omega$ , find R. R = __________Ω

Use the formula $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Given $R _ { 1 }$ = 37 ? and $R _ { 2 }$ = 24 ?. Find R.

Solve the equation and check. $\frac { y } { 3 } - 3 = \frac { y } { 6 }$

Solve the equation and check. $7 x - 56 = 14$

Use the formula $\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$ . Given R = 3 ? and $R _ { 1 }$ = 4 ?. Find $R _ { 2 }$ .

Solve the formula for the given letter. $V = \frac { 1 } { 3 } \pi r ^ { 2 } h \text { for } r$

Solve the equation and check. $1 \frac { 1 } { 4 } x = 21 \frac { 1 } { 4 }$

Solve the equation and check. $14 + 14 ( 3 - 2 x ) + 12 = 4 - x + 5 ( 2 - 3 x )$

Solve the equation and check. $2 x - 64 = 0$

Given the formula: $v _ { f } ^ { 2 } = v _ { i } ^ { 2 } + 2 g h , \quad v _ { f } = 263 , \quad v _ { i } = 0 , \quad g = 16$ Find h.

Solve the equation and check. $3 x + 13 = 2 x - 14$

Solve the equation and check. $- 8 x + 10 ( x - 6 ) = 28$ x = __________

Solve the equation and check. $\frac { 8 } { y } - 7 = 1$ y = __________

Given the formula: y = mx + b, $x = 4 , y = 5 , b = 4$ Find m.

Solve the equation and check. $2 ( 4 y + 1 ) + 13 = 3 + 4 ( y - 5 )$ y = __________

Solve the equation. $24 - 12 c = - 6$

Solve the equation. $x + 9 = 4$