Question

exercises 10-1
write each statement as an equation.

1. some number divided by 6 is 7.
2. two times the sum of a number and 9 is 20.
3. a number divided by 7 is -35.
4. the square root of some number is equal to 20 plus 5.
5. twelve decreased by some number is 8.
6. three times the sum of 8 and a number is 30.
7. to find the area, \\(a\\), of a circle, multiply the square of the radius, \\(r\\), by \\(\pi\\).
8. one third the sum of 45 and a number is 16.
9. if you multiply a number by 6 and then add 1, the result is 55.
10. three more than the square of a number is 52.
11. eight less than some number is -2.
12. one less than the quotient of 25 and a number is 4.
13. the square root of the difference between a certain voltage, \\(v\\), and 9 is 4.
14. seven more than one half of the square of resistance, \\(r\\), is 15.
15. a current of a 15.3 a is the square root of the fraction formed by the power, \\(p\\), divided by a resistance of 12.25 \\(\omega\\).

Explanation:

Translate statements 1 to 5 into algebraic equations

Let \(n\) represent the unknown number in each statement unless specified otherwise.

1. "Some number divided by 6 is 7":

$$\frac{n}{6} = 7$$

1. "Two times the sum of a number and 9 is 20":

$$2(n + 9) = 20$$

1. "A number divided by 7 is -35":

$$\frac{n}{7} = -35$$

1. "The square root of some number is equal to 20 plus 5":

$$\sqrt{n} = 20 + 5$$

1. "Twelve decreased by some number is 8":

$$12 - n = 8$$

Translate statements 6 to 10 into algebraic equations

1. "Three times the sum of 8 and a number is 30":

$$3(8 + n) = 30$$

1. "To find the area, \(A\), of a circle, multiply the square of the radius, \(r\), by \(\pi\)":

$$A = \pi r^2$$

1. "One third the sum of 45 and a number is 16":

$$\frac{1}{3}(45 + n) = 16$$

1. "If you multiply a number by 6 and then add 1, the result is 55":

$$6n + 1 = 55$$

1. "Three more than the square of a number is 52":

$$n^2 + 3 = 52$$

Translate statements 11 to 15 into algebraic equations

1. "Eight less than some number is -2":

$$n - 8 = -2$$

1. "One less than the quotient of 25 and a number is 4":

$$\frac{25}{n} - 1 = 4$$

1. "The square root of the difference between a certain voltage, \(V\), and 9 is 4":

$$\sqrt{V - 9} = 4$$

1. "Seven more than one half of the square of resistance, \(R\), is 15":

$$\frac{1}{2}R^2 + 7 = 15$$

1. "A current of 15.3 A is the square root of the fraction formed by the power, \(P\), divided by a resistance of 12.25 \(\Omega\)":

$$15.3 = \sqrt{\frac{P}{12.25}}$$

Answer:

No.	Answer
2	\(2(n + 9) = 20\)
3	\(\frac{n}{7} = -35\)
4	\(\sqrt{n} = 20 + 5\)
5	\(12 - n = 8\)
6	\(3(8 + n) = 30\)
7	\(A = \pi r^2\)
8	\(\frac{1}{3}(45 + n) = 16\)
9	\(6n + 1 = 55\)
10	\(n^2 + 3 = 52\)
11	\(n - 8 = -2\)
12	\(\frac{25}{n} - 1 = 4\)
13	\(\sqrt{V - 9} = 4\)
14	\(\frac{1}{2}R^2 + 7 = 15\)
15	\(15.3 = \sqrt{\frac{P}{12.25}}\)