All categories

2 years ago

Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers.

1 answer:

6 0

I'll give you a head start so the first thing you wanna do is make a number line of positive and negative numbers I know you can do it

You might be interested in

If a=2b^3 and b= -1/2c ^-2,express a in terms of c.

ElenaW [278]

Answer:

Part 1) $a=-\frac{1}{4c^6}$

Part 2) $a=-\frac{1}{4c^{-6}}$

Step-by-step explanation:

Part 1) we have

$a=2b^{3}$ ----> equation A

$b=-\frac{1}{2}c^{-2}$ ----> equation B

substitute equation B in equation A

$a=2(-\frac{1}{2}c^{-2})^{3}$

Applying property of exponents

$(x^{m})^{n}=x^{m*n}$

$x^{-m} =\frac{1}{x^{m}}$

$a=2(-\frac{1}{2}c^{-2})^{3}=2(-\frac{1}{2})^3(c^{-2})^{3}=2(-\frac{1}{8})(c^{-6})=-\frac{1}{4c^6}$

therefore

$a=-\frac{1}{4c^6}$

Part 2) we have

$a=2b^{3}$ ----> equation A

$b=-\frac{1}{2c^{-2}}=-\frac{c^{2}}{2}$ ----> equation B

substitute equation B in equation A

$a=2(-\frac{c^{2}}{2})^{3}$

Applying property of exponents

$(x^{m})^{n}=x^{m*n}$

$x^{-m} =\frac{1}{x^{m}}$

$a=2(-\frac{c^{2}}{2})^{3}=2(-\frac{c^{6}}{8})$

simplify

$a=-\frac{c^{6}}{4}$

therefore

$a=-\frac{1}{4c^{-6}}$

6 0

3 years ago

a collection of dimes and quarters is worth $19.85. There are 128 coins in all. How many of each type of coin are in the collect

PolarNik [594]

Number of dimes were 81 and number of quarters were 47

Solution:

Let "d" be the number of dimes

Let "q" be the number of quarters

We know that,

value of 1 dime = $ 0.10

value of 1 quarter = $ 0.25

Given that There are 128 coins in all

number of dimes + number of quarters = 128

d + q = 128 ------ eqn 1

Also given that collection of dimes and quarters is worth $19.85

number of dimes x value of 1 dime + number of quarters x value of 1 quarter = 19.85

$d \times 0.10 + q \times 0.25 = 19.85$

0.1d + 0.25q = 19.85 -------- eqn 2

Let us solve eqn 1 and eqn 2

From eqn 1,

d = 128 - q -------- eqn 3

Substitute eqn 3 in eqn 2

0.1(128 - q) + 0.25q = 19.85

12.8 - 0.1q + 0.25q = 19.85

12.8 + 0.15q = 19.85

0.15q = 7.05

Therefore from eqn 3,

d = 128 - q

d = 128 - 47

Thus number of dimes were 81 and number of quarters were 47

4 0

3 years ago

Add using a number line. -2 + 4 5__ 5

pogonyaev

Answer: i.. do.... not... know..

Step-by-step explanation:

6 0

1 year ago

Fill in the box to make the equation true. 5x + something - 3x=4x

Sveta_85 [38]

Answer: 2x

Step-by-step explanation: because 5+2-3=4

5 0

2 years ago

Read 2 more answers

Would someone please help on 1 or 2 questions.

Lera25 [3.4K]

What are your questions? If so what type of mathematic class: Algebra, Algebra 2, Geometery, Trigeometery, Pre-calculus, Calculus..

7 0

3 years ago