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The learner will translate sentences into algebraic formulas.

Translating Sentences into Algebraic Formulas

Translate the following sentence into an algebraic formula.

The length of one leg of a right triangle is equal to the square root of the difference between the squares of the lengths of the hypotenuse and the other leg.

$a=\sqrt{c^{2}-b^{2}}$
$a=\sqrt{c^{2}-b}$
$a=\sqrt{c-b}$
$a=\left ( \sqrt{c}-\sqrt{b} \right )^{2}$

Question 1 of 10

Translating Sentences into Algebraic Formulas

Translate the following sentence into an algebraic formula.

The width of a rectangular piece of sheet metal is 10.5 inches less than its length.

$W=L-10.5$
$W=\frac{L}{10.5}$
$W=10.5-L$
$L=W-10.5$

Question 1 of 10

Translating Sentences into Algebraic Formulas

Translate the following sentence into an algebraic formula.

Trisha is 5 inches less than 3 times as tall as Maggie.

$T=(M+3)-5$
$T=3M-5$
$T=(5-3)M$
$T=5-3M$

Question 1 of 10

Translating Sentences into Algebraic Formulas

Translate the following sentence into an algebraic formula.

The height of a right circular cylinder is equal to its volume divided by the product of π and the square of its radius.

$h=\frac{V}{\pi r^{2}}$
$h=\frac{V}{\pi \sqrt{r}}$
$h=\frac{V}{\pi +r^{2}}$
$h=\frac{V}{\pi }r^{2}$

Question 1 of 10

Translating Sentences into Algebraic Formulas

Translate the following sentence into an algebraic formula.

The weight of Mary's car is 500 pounds more than one-half of the weight of Joe's car.

$J=500+\frac{1}{2}M$
$M=500+2J$
$M=500+\left (J-\frac{1}{2} \right )$
$M=\frac{1}{2}J+500$

Question 1 of 10

Translating Sentences into Algebraic Formulas

Translate the following sentence into an algebraic formula.

The area of a trapezoid is equal to one-half the sum of its bases multiplied by its height.

$A=\left (\frac{1}{2}B+b \right )h$
$A=\left ( \frac{Bb}{2} \right )h$
$A=\frac{1}{2}(B-b)h$
$A=\left ( \frac{B+b}{2} \right )h$

Question 1 of 10

Translating Sentences into Algebraic Formulas

Translate the following sentence into an algebraic formula.

The cutting time of a drill is equal to the quotient of the length of the cut and the product of the tool feed and the revolution rate of the drill.

$T=L-Fv$
$T=\frac{L}{F+v}$
$T=\frac{L}{Fv}$
$T=\frac{LF}{v}$

Question 1 of 10

Translating Sentences into Algebraic Formulas

Translate the following sentence into an algebraic formula.

The cutting speed of a lathe is one-twelfth of π times the product of the diameter of the workpiece and the speed of the workpiece.

$C=\frac{\pi dv}{12}$
$C=\frac{1}{12}\pi +dv$
$C=\frac{1}{12}\pi d+v$
$C=\frac{\pi }{12}(d+v)$

Question 1 of 10

Translating Sentences into Algebraic Formulas

Translate the following sentence into an algebraic formula.

The number of teeth on a spur gear is equal to the product of π and the quotient of the pitch diameter and the circular pitch.

$N=\frac{D}{\pi P_{c}}$
$N=\pi +\frac{D}{P_{c}}$
$N=\pi (D-P_{c})$
$N=\frac{\pi D}{P_{c}}$

Question 1 of 10

Translating Sentences into Algebraic Formulas

Translate the following sentence into an algebraic formula.

The outside diameter of a spur gear is equal to the product of the circular pitch and the quotient of 2 more than the number of teeth on the gear and π.

$D_{o}=P_{c}+\frac{N+2}{\pi }$
$D_{o}=P_{c}\left ( \frac{2N}{\pi } \right )$
$D_{o}=P_{c}\left (\frac{N+2}{\pi } \right )$
$D_{o}=P_{c}(2N+\pi )$

Question 1 of 10

Author

Wade Wells

Published: 6/18/2014

Last Updated: 6/18/2014

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Translating Sentences into Algebraic Formulas by Fox Valley Technical College is licensed under a Creative Commons Attribution 3.0 Unported License.

Translating Sentences into Algebraic Formulas

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Translating Sentences into Algebraic Formulas

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Translating Sentences into Algebraic Formulas

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Translating Sentences into Algebraic Formulas

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Question 1 of 10

Translating Sentences into Algebraic Formulas

Question 1 of 10

Translating Sentences into Algebraic Formulas

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Translating Sentences into Algebraic Formulas

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Translating Sentences into Algebraic Formulas

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Translating Sentences into Algebraic Formulas

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Translating Sentences into Algebraic Formulas

Question 1 of 10

Translating Sentences into Algebraic Formulas