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3 years ago

For the function g(x)=2x-9 , determine x when g(x)=-15.

Mathematics

1 answer:

____ [38]3 years ago

6 0

Answer:

-3

Step-by-step explanation:

Input -3 for x.

2*-3 - 9

then simplify.

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Match the numerical expressions to their simplified forms

eduard

Answer:

$1.\ \ p^2q = (\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}}$

$2.\ \ pq^{\frac{3}{2}}} = (\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}$

$3.\ \ pq^2 = \frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}$

$4.\ \ p^2q^{\frac{1}{2}} = (p^6q^{\frac{3}{2}})^{\frac{1}{3}}$

Step-by-step explanation:

Required

Match each expression to their simplified form

$(\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}}$

Simplify the expression in bracket by using the following law of indices;

$\frac{a^m}{a^n} = a^{m-n}$

The expression becomes

$(\frac{p^{5-(-3)}}{q^{-4}})^{\frac{1}{4}}$

$(\frac{p^{5+3}}{q^{-4}})^{\frac{1}{4}}$

$(\frac{p^8}{q^{-4}})^{\frac{1}{4}}$

Split the fraction in the bracket

$(p^8*\frac{1}{q^{-4}})^{\frac{1}{4}}$

Simplify the fraction by using the following law of indices;

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

The expression becomes

$(p^8*q^4)^{\frac{1}{4}}$

Further simplify the expression in bracket by using the following law of indices;

$(ab)^m = a^m * b^m$

The expression becomes

$(p^{8*\frac{1}{4}}\ *\ q^4*^{\frac{1}{4}})$

$(p^{\frac{8}{4}}\ *\ q^{\frac{4}{4}})$

$p^2q$

Hence,

$(\frac{p^5}{p^{-3}q^{-4}})^{\frac{1}{4}} = p^2q$

$(\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}$

Simplify the expression in bracket by using the following law of indices;

$\frac{a^m}{a^n} = a^{m-n}$

The expression becomes

$({p^2q^{7-4}}})^{\frac{1}{2}}$

$({p^2q^3}})^{\frac{1}{2}}$

Further simplify the expression in bracket by using the following law of indices;

$(ab)^m = a^m * b^m$

The expression becomes

${p^{2*\frac{1}{2}}q^{3*\frac{1}{2}}}}$

$pq^{\frac{3}{2}}}$

Hence,

$pq^{\frac{3}{2}}} = (\frac{p^2q^7}{q^{4}})^{\frac{1}{2}}$

$\frac{(pq^3)^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}$

Simplify the numerator as thus:

$\frac{p^{\frac{1}{2}} * q^3*^{\frac{1}{2}}}{(pq)^{\frac{-1}{2}}}$

$\frac{p^{\frac{1}{2}} * q^{\frac{3}{2}}}{(pq)^{\frac{-1}{2}}}$

Simplify the denominator as thus:

$\frac{p^{\frac{1}{2}} * q^{\frac{3}{2}}}{p^{\frac{-1}{2}}q^{\frac{-1}{2}}}$

Simplify the expression in bracket by using the following law of indices;

$\frac{a^m}{a^n} = a^{m-n}$

The expression becomes

$p^{\frac{1}{2} - (\frac{-1}{2} )} * q^{\frac{3}{2} - (\frac{-1}{2}) }$

$p^{\frac{1}{2} +\frac{1}{2} } * q^{\frac{3}{2} + \frac{1}{2} }$

$p^{\frac{1+1}{2}} * q^{\frac{3+1}{2}}$

$p^{\frac{2}{2}} * q^{\frac{4}{2}}$

$pq^2$

Hence,

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

$(p^6q^{\frac{3}{2}})^{\frac{1}{3}}$

Simplify the expression in bracket by using the following law of indices;

$(ab)^m = a^m * b^m$

The expression becomes

$p^6*^{\frac{1}{3}}\ *\ q^{\frac{3}{2}}*^{\frac{1}{3}}$

$p^{\frac{6}{3}}\ *\ q^{\frac{3*1}{2*3}}$

$p^2 *\ q^{\frac{3}{6}}$

$p^2 *\ q^{\frac{1}{2}$

$p^2q^{\frac{1}{2}$

Hence

$p^2q^{\frac{1}{2}} = (p^6q^{\frac{3}{2}})^{\frac{1}{3}}$

6 0

3 years ago

Covert 1.64 pounds to grams and milligrams

koban [17]

Answer:

743.8915 grams; 743891.5 milligrams

3 0

3 years ago

Please help me with this its due in 15 minutes plus ill need help with more

Anestetic [448]

Answer:

171 Square Feet

Step-by-step explanation:

We first cut the figure up into smaller parts...

we then use the formula (L x W = A) to find the area

L = Lenth

W = Width

the first rectangle (1)...

15 x 5 = 75

the second figure (2)...

8 x 9 = 72

the third figure (3)...

6 x 4 = 24

now we have to add up all the values to find the area of the entire figure...

75 + 72 + 24 = 171

Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Also remember to rate answers to help other students, While leaving thanks to answers that help you. Have a great day!

3 0

2 years ago

Name and briefly describe the four categories of risk explained in the article.

emmainna [20.7K]

Based on the information provided in the article, the four (4) categories of risk explained include the following:

Market risk: this is a risk that limits the ability of an investment to increase in value, thereby, leading to loss of money in the long-run.
Financial or business risk: it describes the risk that is associated with investing an amount of money in a private business, so as to gain a lot of profit in the long run.
Inflation risk: it describes the risk that is associated with a lower rate of return due to a higher rate of inflation, when an amount of money is invested.
Fraud risk: it describes the risk that is associated with investing an amount of money in a product, stock, company, etc., without doing a background check or due diligence.

<h3>What is risk management?</h3>

Risk management can be defined as a strategic process which involves the identification, evaluation, analysis and control of potential threats (risks) that are present in a business, project, or system, as an obstacle to its capital, revenues, success, and profits.

Based on the information provided in the article, the four (4) categories of risk explained include the following:

Market risk: this is a risk that limits the ability of an investment to increase in value, thereby, leading to loss of money in the long-run.

Financial or business risk: it describes the risk that is associated with investing an amount of money in a private business, so as to gain a lot of profit in the long run.

Inflation risk: it describes the risk that is associated with a lower rate of return due to a higher rate of inflation, when an amount of money is invested.

Fraud risk: it describes the risk that is associated with investing an amount of money in a product, stock, company, etc., without doing a background check or due diligence.

Read more on risk here: brainly.com/question/16352505

#SPJ1

5 0

1 year ago

Using the results from the table, predict the number of times a 3 would be rolled in 400 trials.

sasho [114]

First you should add all the number of rolls.
The number of rolls is 80.
Subtract 80 from 400.
The answer is 320.
Add 320 to the number of rolls of 3.
The answer to the question is 322.
I am sorry if I am wrong.

5 0

3 years ago

Read 2 more answers