All categories

4 years ago

PLEASE HELP ASAP Simplify:

Mathematics

1 answer:

Minchanka [31]4 years ago

5 0

Answer:

Step-by-step explanation:

x^0 y^-3

-----------------

x^2 y^-1

When dividing powers with the same base, we subtract

x^(0-2) y^(-3--1)

x^-2 y^(-3+1)

x^-2 y^-2

When they have a negative power a^-b = 1/a^b

-------------

x^2 y^2

You might be interested in

The product of 5 and y added to 3

bazaltina [42]

Write equation:-

The product of 5 and y added to 3

5 × y + 3

6 0

3 years ago

Solve each equation. Show your work please. Part 1

Free_Kalibri [48]

Answer:

x = -10 1/6
x = 24 3/5
x = -7 1/4

Step-by-step explanation:

The relevant rules of logarithms are ...

log(a)+log(b) = log(ab)

log(a)-log(b) = log(a/b)

The base of the logarithm doesn't matter, as long as all bases are the same.

In each case, we can simplify the left side to a single log, then take the antilog and finish solving the linear equation.

1. log(3-x) +log(6) = log(79)

log(6(3-x)) = log(79)

6(3 -x) = 79

3 -x = 79/6

x = 3 -79/6

x = -10 1/6

2. log(5x +3) -log(2) = log(63)

log((5x+3)/2) = log(63)

(5x +3)/2 = 63

5x +3 = 126

5x = 123

x = 24.6

3. log(-4x -7) +log(2) = log(44)

log(2(-4x-7)) = log(44)

2(-4x -7) = 44

4x +7 = -22

4x = -29

x = -7 1/4

5 0

3 years ago

Which statement about sqrt x-5 minus sqrt x=5 true?

Allushta [10]

Answer:

9 is an extraneous solution.

Step-by-step explanation:

Extraneous solution is a solution that when plugged into the equation do not hold true.

Here we are given an algebraic equation in terms of single variable x as:

$\sqrt{x-5}-\sqrt{x}=5-----(1)$

Now, we will solve this equation to obtain the solution as:

on squaring both side of the equation we obtain:

$(\sqrt{x-5}-\sqrt{x})^2=5^2$

$x-5+x-2\sqrt{x-5}\sqrt{x}=25\\\\2x-5-2\sqrt{x-5}\sqrt{x}=25\\\\2x-30=2\sqrt{x-5}\sqrt{x}\\\\on\ dividing\ both\ side\ by\ 2\ we\ obtain:\\\\x-15=\sqrt{x-5}\sqrt{x}$

Again on squaring both side of the equation we obtain:

$x^2+225-30x=(x-5)x\\\\\x^2+225-30x=x^2-5x\\\\225=-5x+30x\\\\225=25x\\\\x=9$

Now when we plug x=9 back to the original equation i.e. equation (1) we get:

$\sqrt{9-5}-\sqrt{9}=5\\\\\sqrt{4}-\sqrt{9}=5\\\\2-3=5\\\\-1=5$

Hence, the equation does not hold true.

Hence, 9 is a extraneous solution

5 0

3 years ago

Need helpp fastt plss will give brainliest to who is correct plss helpp

Citrus2011 [14]

Answer:

333 inches = 27.75 feet = 9.25 yards

6 0

3 years ago

Thomas Malthus, a political economist, showed that the human population would outstrip available resources unless kept in check

vredina [299]

Answer:

C. Darwin realized this also applied to plant and animal populations, and this struggle for existence resulted in an opportunity for natural selection to act on differences within populations.

Step-by-step explanation:

Thomas Malthus in his Malthusian theory of population concluded that since population increases geometrically and resources only increase arithmetically, there will reach a point in time when the resources will be not be able to sufficiently cater for the population.

The Charles Darwin theory of Evolution is based on five key observations and conclusions drawn from them. These observations and inferences are summarized as:

Species are more fertile. They birth more offspring than can grow to adulthood.
Populations remain fairly stable with miniscule fluctuations.
Food resources are limited, but are relatively constant most of the time.

Based off these observations, it is seen that there will be a struggle amongst the members of the specie for the limited resources.

In sexually reproducing species, generally no two individuals are identical. Variation is rampant.
Much of this variation is heritable.

From the last two observations, the species that survive then pass on their traits to their offspring and the cycle repeats itself with each subsequent generation being better evolved than the previous ones.

Thus, Darwin discovered that the Malthusian theory of population also applies to plant and animal populations where scarcity of resources gives room for natural selection to take place due to the variation within populations.

4 0

4 years ago