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2 years ago

How to simplify fractions with negative exponents in the denominator and numerator?

Mathematics

1 answer:

zzz [600]2 years ago

8 0

Answer:

$\displaystyle\frac{x^{-a}}{x^{-b}} = x^{b-a}$

Step-by-step explanation:

We have to write the rule to simplify fractions with negative exponents in the denominator and numerator.

If we have positive exponents, the simplification takes place as following:

$\displaystyle\frac{x^a}{x^b} = x^{a-b}$

The powers of the same base of numerator and denominator are subtracted.

In case of negative exponents, the simplification takes place in the following manner:

$\displaystyle\frac{x^{-a}}{x^{-b}} = x^{-a-(-b)} = x^{-a+b} = x^{b-a}$

The powers of the same base of denominator and numerator are subtracted.

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A water delivery truck is filling the water tank at Morgan's house. The truck arrived with 2400 L of water. The number of liters

Luda [366]

Answer:

11.81 minutes

Step-by-step explanation:

Here is a simple step-by-step explaination of how to solve this word problem:

Since the truck has 2,400L in it to begin with, the first part of our equation will be 2,400L

$L = 2400L

$

Next we know that the water in the truck decreases at a rate of 110L/min, or Liters per minute.

So we will put that in the equation:

$L = -110L + 2400L$

Now that we have our equation set up, its time to solve.

To figure out how much water it needs to lose in total to end up with 1100 L left, we subtract 1,100 from 2,400.

$2,400 - 1,100= 1,300

$

Now we can take that number and divide it by how many liters per minute were lost.

$1,300/110=11.81$

So the total amount of time it took for the truck to have 1,100 L left is 11.81 minutes. Your answer would be

B. $L=-110t + 2400, t=11.8$ min

Hope this helps! : )

3 0

2 years ago

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Solve this equation. Enter your answer in the box. 13(y+7)=3(y−1).

Fofino [41]

★To Solve :

$\rm\blue{13(y+7) = 3(y-1)}$

⠀⠀⠀⠀⠀

★SOLUTION :

$\rm\red\leadsto{13(y+7) = 3(y-1)}$

$\rm\red\leadsto{13\times{y}+13\times7= 3\times{y}-3\times1}$

$\rm\red\leadsto{13y+91=3y-3}$

$\rm\red\leadsto{13y-3y=-3-91}$

$\rm\red\leadsto{10y=-94}$

$\rm\red\leadsto{} y =\dfrac{ { \cancel{-94}}^{ \:-45 } }{ { \cancel{10}}^{ \: 5} }$

$\rm\red\leadsto{y=}\dfrac{-47}{5}$

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3 years ago

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Divide.Enter the quotient in the simplest form. 7/10 divided by 4/5 Please hurry

slamgirl [31]

I think it’s .22 I’m not sure hope this helps :)

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2 years ago

The negative sign can be read as "the opposite of."

Luda [366]

If this is a True or False question, that is true.

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3 years ago

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At a garden shop, a customer buys 5 geraniums and 4 lilies for $48. Another customer pays $58 for 4 geraniums and 6 lilies. Writ

masha68 [24]

Answer:

A lily costs $7 and a geranium $4.

Step-by-step explanation:

From the question, we can write two equations. let the number of lilies be l and the number of geraniums be g, then:

5 g + 4 l = 48

4 g + 6 l = 58

Multiply the first equation by 4 and the second by 5, the number of lilies in the other gives:

20 g + 16 l = 192

20 g + 30 l = 290

Subtract the first equation from the second gives:

14 l = 98 which dividing by 14 gives l = 7

Substituting the value l = 7 in the first equation gives:

5 g + 28 = 48

Subtract 20 from both sides gives:

5 g = 20 divide by 5 gives g = 4

So, a lily costs $7 and a geranium costs $4.

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2 years ago