Mathematics College

Simplify the expression:
a^-2

Answers

Answer 1

1/[tex]a^{2}[/tex] is the answer.

How to simplify the expression?

Given,

a^-2

Solution:

a^-2

Expand it

a^-2 = 1/a^2

= 1/[tex]a^{2}[/tex]

Therefore,

a^-2 = 1/[tex]a^{2}[/tex]

1/[tex]a^{2}[/tex] is the answer.

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Related Questions

Write an expression for the amount of money (in nickels) in n dollars.

PLEASE HELP ITS DUE IN AN HOUR

Answers

An expression for the amount of money (in nickels) in n dollars is 20n nickels.

How many nickels are in a dollar?

A nickel is a five-cent coin produced by the United States Mint that is made of a copper-nickel alloy rather than silver. Because 100 cents equal one dollar and one nickel equals five cents, we conclude that 20 nickels are equivalent to one dollar.

To write an expression for the amount of money (in nickels) in n dollars,

Convert the n dollars to nickels.

1 dollar = 20 nickels

So, n dollars = 20n nickels

The required expression for the amount of money (in nickels) in n dollars is 20n nickels.

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8. If APTS - APOR, find the value of x.5x + 13TP36306.r - 2R

Answers

The triangles PTS and POR are similar, so we can take the ratios of the side to order

[tex]\frac{PT}{ST}=\frac{PQ}{SQ}[/tex]

[tex]\frac{36}{30}\text{ =}\frac{5x\text{ + 13}}{6x\text{ - 2}}[/tex]

[tex]\begin{gathered} \text{cross multiplying} \\ \\ 30\text{ (6x - 2) = 30 (5x + 13)} \\ \\ \text{Expanding the parenthesis} \\ \\ 30\text{ x 6x - 30 x 2 = 30 x 5x + 30 x 13} \\ \\ 180x\text{ -60 = 150x + 390} \end{gathered}[/tex]

We can then solve for x by collecting like terms

180x - 150x = 390 + 60

30x = 450

Divide both sides by 30

x = 450/ 30

x = 15

Write an equation of a the line passing through the point (2,-9) that is perpendicular to the line y=x+6
An equation of the line is…..

Answers

The linear function passing through the point (2,-9) that is perpendicular to the line y=x+6 is:

y = -x -7.

How to write the equation of perpendicular linear functions?

A linear function is modeled according to the following rule:

y = mx + b.

The coefficients of the linear function are as follows:

m is the slope, which is the rate of change of the function.b is the y-intercept, which is the numeric value of the function when x = 0.

When two lines are perpendicular, the multiplication of their slopes is of -1.

For this problem, the line is perpendicular to line y = x + 6, which has slope 1, hence:

m = -1.

Then:

y = -x + b.

When x = 2, y = -9, hence we use this to find the intercept b as follows:

-9 = -2 + b

b = -7.

Hence the rule is:

y = -x -7.

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Answer:

Step-by-step explanation:

Melissa wants to pour 30.78 grams of salt into a container. So far, she has poured 19.1 grams. How much more salt should Melissa pour?

Answers

Answer:

She should pour 11.68 more grams

Step-by-step explanation:

If Melissa wanted to pour 30.78 grams of salt into a container and already has poured 19.1 grams she should pour 11.68 grams more

Suppose you buy a phone for $750 and sign up for a one-year service contract that costs $110 per month. What is the total cost you will pay over the length of the contract?

Answers

Answer:

$2070

Step-by-step explanation:

→ Find the total cost of 12 months

750 + ( 12 × 110 ) = 2070

ANSWER:
$1,320

EXPLANATION:
If the contract is only one year and it is $110 per month in that year, we know that there are 12 months in a year, so our work should look like, 110 x 12 = 1,320

Have an AWESOME day! :)

Find each value.Show calculations for each problem

Answers

In the given expression :

[tex]a_n=-8n[/tex]

we need to find the value of n at which, an = -24

[tex]\begin{gathered} \text{Substitute the value of a}_n=-24\text{ in teh express}ionofa_n \\ a_n=-8n \\ -24=-8n \\ or \\ -8n=-24 \\ \text{Dividing both side by (-8)} \\ \frac{-8n}{-8}=\frac{-24}{-8} \\ n=3 \end{gathered}[/tex]

Thus, at n=3, the an = -24

Which of the following shows a correct way of simplifying 6+(3-5x)

Answers

Answer: 9 - 5x

Step-by-step explanation:

6 + (3 - 5x) = 6 + 3 - 5x = 9 - 5x

The line y=kx+4 goes through the point (2,-2)
K=-3
Sketch the graph of the line (need ASAP!!)

Answers

We can see that the value of k is -3, then the line is:

y = -3*x + 4

By finding two points of the line, we can graph the line like in the image you can see below.

How to sketch a graph of the line?

Here we have the following linear equation:

y = k*x + 4

We know that this line goes through the point (2, -2), then we can replace these values in the above equation so we get the value of k.

-2 = k*2 + 4

Solving this, we can find the value of k.

-2 - 4 = k*2

-6 = k*2

-6/2 = k = -3

So the value of k, the slope of the line, is k = -3.

Then the line is:

y = -3*x + 4

If we evaluate in x = 1, we get:

y = -3*1 + 4 = 1

So, at this point we know that the line passes through points (1, 1) and (2, -2).

Now we can draw these two points on a coordinate axis, and then connect them with a line. That will be the graph of the linear equation.

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Reduce 36/60 to simplest terms

Answers

Answer:

3/5

Step-by-step explanation:

You can first start small, seeing that both numbers are positive we can divide them by 2, and you will then get 18/30. They are still both positive so you can reduce it by 2, you will then get 9/15. Now that they are both odd you can tell they are both a multiple of 3, when you divide them by 3 you get 3/5. When you finish dividing your numbers to smaller numbers, when you notice they can not reduce to any other number, you have your simplest term.

Answer:

3/5

Step-by-step explanation:

Use inductive reasoning to find a pattern for the answer then use the pattern to guess the result of the final calculation and perform the operations to see if your answer is correct

Answers

Given:

1 = 1²

1 + 3 = 2²

1 + 3 + 5 = 3²

1 + 3 + 5 + 7 = 4²

1 + 3 + 5 + 7 + 9 = 5²

1 + 3 + 5 + 7 + 9 + 11 = ___

Let's find the answer and determine the pattern.

Here, we have:

1 + 3 = 4

Now, write the sum as a perfect square:

4 = 2²

For the third equation:

1 + 3 + 5 = 9

Now, write the sum as a perfect square:

9 = 3²

This means the result will be the sum written as a perfect square.

Thus, we have:

1 + 3 + 5 + 7 + 9 + 11 = 36

Now, let's write the sum (36) as a perfect square:

36 = 6²

Therefore, we have:

1 + 3 + 5 + 7 + 9 + 11 = 6²

• ANSWER:

6²

How can we guarantee that a polynomial is not a perfect square, considering just the constant term? For instance, in 4, the constant term is -121, in 2, the constant term is 36. Which of them cannot be a perfect square and why, based only on the constant term?

Answers

Regarding perfect squares, it is found that:

A negative constant guarantees that the polynomial is not a perfect square.The polynomial with a constant term of -121 is not a perfect square.

Perfect squares

Perfect square expressions are formed with the notable products of the square of the sum or the square of the subtraction, as follows:

(a + b)² = a² + 2ab + b² -> square of the sum.(a - b)² = a² - 2ab + b² -> square of the subtraction.

The constant term of perfect squares, in both cases, is given by:

b².

Since the number is squared, it will always be a positive value, meaning that a negative constant term guarantees that the polynomial is not a perfect square.

The polynomial with a negative constant in this problem has a constant of -121, hence it is not a perfect square.

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1677/203 as a reduced fraction

Answers

This is an improper fraction since the absolute value of the numerator (1677) is greater than the absolute value of the denominator (203). We can say that this fraction cannot be reduced.

Identify the sample space of the probability experiment: answering a multiple choice question with A, B, C, and D as the possible answers.

Answers

By definition, a sample space is a collection or a set of possible outcomes of a random experiment. In our problem, we have four different outcomes. A, B, C and D. This is our sample space

[tex]S=\lbrace A,B,C,D\rbrace[/tex]

What is the congruence, if any , that will prove the given triangles congruent?

Answers

Given:

The triangle FTP and triangle JTA is given.

In the given triangles,

[tex]\begin{gathered} \angle P\cong\angle A \\ \angle F\cong\angle J \\ \angle T\cong\angle T \end{gathered}[/tex]

As only three angles of both triangles are similar we can not say that the given traingles are congruent.

So, Option A is correct.

PLS ANSWER THIS MATH PROBLEM!!

Answers

For the linear function y = 2/3x + 1 given in this problem, we have that:

a) The slope is of 2/3 and the intercept is of 1.

b) The y-intercept is marked at y = 1 on the y-axis.

c) Using the slope and the intercept, point (3,3) is the second point used to graph the function.

d) The graph of the linear function y = 2/3x + 1 is given at the end of the answer.

How to we graph the linear function?

In slope-intercept format, a linear function is defined as follows:

y = mx + b.

For this problem, the function is:

y = 2/3x + b.

Hence:

The slope is of m = 2/3, meaning that when the input x increases by 3, the output y increases by 2.The intercept is of b = 1, meaning that the graph of the function crosses the y-axis(vertical axis), at y = 1.

From the intercept, we know that point (0,1), which has x = 0 and y = 1, is part of the graph of the function.

Considering the concept of the slope, of change in y divided by change in x, we have that:

y + 2 = 1 + 2 = 3.x + 3 = 0 + 3 = 3.

Hence point (3,3) also belongs to the graph of the given function. Given two points, we can graph a line passing through them, hence the graph is given at the end of the answer, and represents the function y = 2/3x + 1.

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Solve the inequality & graph the answer.
3)>2
14
A) v> 280:
10
B) v<--:
7
C) v> -34:
D) v<-34:
11110
276 278 280 282 284 286
7
O
0 2
++++++ +0
-40 -38 -36 -34 -32 -30
-40 -38 -36 -34 -32-30

Answers

Answer:

Solve the inequality & graph the answer. 3)>2 14 A) v> 280: 10 B) v<--: 7 C) v> -34: D) v<-34: 11110 276 278 280 282 284 286 7 O 0 2 ++++++ +0 -40 -38 -36 -34 -32 -30 -40 -38 -36 -34 -32-30

Step-by-step explanation:

A farmer with 1700 m of fancy ones to enclose a rectangular plot the borders on a river if no fence is required along the river what is the largest area that can be enclosed?

Answers

Answer

Largest Area that can be enclosed = 361250 m²

Explanation

Let the length of the fencing along the river be L

Let the width of the fencing be W

A sketch of the problem will make it clearer

Perimeter = L + 2W

Perimeter is giving as the total length of the fencing to be 1700 m

L + 2W = 1700

L = 1700 - 2W

The area of the structure is given as

Area = LW

The area is what we want to maximize

Recall, L = 1700 - 2W

Area = LW = (1700 - 2W) × W = 1700W - 2W²

A = 1700W - 2W²

At maximum point, the derivative of any function is zero

Hence,

(dA/dW) = 1700 - 4W

At maximum point,

(dA/dW) = 0

1700 - 4W = 0

4W = 1700

Divide both sides by 4

(4W/4) = (1700/4)

W = 425 m

Recall, L = 1700 - 2W

L == 1700 - 2(425)

L = 1700 - 850

L = 850 m

Maximum Area

= (Length at maximum area) × (Width at maximum area)

= 850 × 425

= 361250 m²

Hope this Helps!!!

Match each word with the phrase that best defines it.
insurance
liability
compensate
premium
deductible
to pay the value of something that has been
lost or stolen
the amount of money a consumer must pay
an insurance company
a responsibility to pay for or to fix a problem
a financial service that protects a consumer
in exchange for payments
the money a consumer must pay for a claim
before the policy takes over

Answers

Insurance - A financial service that protects a consumer

Liability - A responsibility to pay for or to fix a problem

Compensate - To pay the value of something that has been lost or stolen

Premium - The amount of money a consumer must pay an insurance company

Deductible - The money of a consumer must pay for a claim before the policy takes over

Insurance is a legal agreement, evidenced by a policy, under which a policyholder receives financial security or compensation from an insurance provider against losses.

Liability is a general phrase that refers to many types of coverages to assist in defending you or your company in the event that a claim or lawsuit is made against you or your organization.

The amount that the insurance provider has agreed to pay for insured losses that are mentioned in your policy is referred to as "compensation."

You pay a premium when you purchase an insurance policy. Your recurring payments for many popular insurance products, such as life, car, business, homeowners, and renters, are known as premiums.

The sum of money you must contribute to an insured loss is known as a deductible.

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Which is a function?
{(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}
{(6, 3), (5, 2), (4, 1), (3, 0), (4, –1), (5 ,–2), (6 ,–3)}
{(1000, 10), (1000, 12), (1000, 16), (100, 5), (100, 7), (78, 3), (90, 5)}
{(7, 2), (100, 10), (13, –7), (7, 9), (10, 100), (4, –2), (5, 5)}

Answers

Answer: {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}

Step-by-step explanation:

Each value of x corresponds to only one value of y, making the relation a function.

Mellisa is buying party favors to make gift bags

Answers

what’s the question??

Solve systems using inverses:
Solve the system:
4x - 5y + z = 9 6X + 8y - Z=27 3x – 2y + 5z = 40
(?, ?, ?)

Answers

Answer:

Step-by-step explanation:

4 x - 5 y + z = 9z = - 27 + 6 x + 8 y3 x

Which Zeros of the polynomial function partially graphed below have even multiplicity?

Answers

The Zeros of the polynomial function partially graphed below have even multiplicity are x = -3 and x = 3.

What are the Zeros of the Polynomial?

The zeros of a Polynomial graph are simply the points where the graph curve crosses the x-axis.

In simply terms, the Zeros of a function are the values of the independent variable that make the function equal to 0. Multiplicity just refers to how many copies of a given zero exist.

From the given graph, the zeros of the Polynomial function are x = 2 and x = 3 and x = -3

An odd multiplicity means the graph of the function crosses the x-axis at that point. An even multiplicity means the curve contacts the x-axis at that point and backs instead of crossing.

Thus, the odd multiplicity is at x = 3

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the linear equation 3x- 4y =7 has:
a, unique solution
b, two solutions
c, infinitely many solutions
d,no solution

Answers

The linear equation is 3x+4y=7. The solution to the equation 3x+4y=7 is unique.

Given that,

The linear equation is 3x+4y=7

Any equation with a maximum degree of 1 is said to be linear. No variable in a linear equation, thus, has an exponent greater than 1.The graph of a linear equation is always a straight line.

There are numerous options if x and y are not positive integers (natural numbers), thus it is best if they are.

The x and y are positive integers so it is a unique solution.

Therefore, The solution to the equation 3x+4y=7 is unique.

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PLEASE HELP ME I MISSED CLASS BECAUSE I WAS SICK AND I DONT I UNDERSTAND

Answers

Answer:

see explanation

Step-by-step explanation:

(a)

the angles shown are alternate interior angles and are congruent

(c)

since they are congruent , then

27x - 5 = 130 ( add 5 to both sides )

27x = 135 ( divide both sides by 27 )

x = 5

(d)

then

27x - 5 = 27(5) - 5 = 135 - 5 = 130

The expression below is scientificnotation for what number?9.9x10^7

Answers

To change the number from scientific notation to normal number multiply 9.9 by 10^7

[tex]9.9\times10,000,000=99,000,000[/tex]

The number is 99,000,000

Find the measure of <1 and <2

Answers

Answer:

150°

Step-by-step explanation:

Both the measure of <1 and <2 are 150°

What is the ratio of blue paint to total paint in the mixture?

Answers

The ratio of blue paint to the total paint in the mixture is 5:8.

How is a ratio calculated?Ratios contrast two figures by ordinarily dividing them. The term "antecedent" refers to the dividend and "consequent" to the divisor. A ratio in mathematics demonstrates how many times one number is present in another.It is a comparison or relationship between two amounts of the same quantity to determine how much larger one number is than the other. Where b is not equal to zero, it is expressed as a/b or a: b.

Given:

In the figure, there are 10 blocks of blue paint and 6 blocks of red paint.

Total paint in the mixture = 10+6 = 16

Ratio of blue paint to total paint = 10/16 = 5/8

Therefore, the required ratio is 5:8.

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1 over 6 divided by 6 divided by 6

Answers

Answer:

1/216

Step-by-step explanation:

[tex] \frac{1}{6} \div 6 \div 6[/tex]

[tex] \frac{1}{6} \div \frac{6}{1} \div \frac{6}{1} [/tex]

[tex] \frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} [/tex]

[tex] \frac{1}{216} [/tex]

Which probability distribution table corresponds with this frequency distribution table?

Answers

The probability distribution table corresponds with the given frequency distribution table is option (D)

Probability is defined as the ratio of number of favorable outcome to the total number of outcomes. The value of the probability varies from 0 to 1.

Probability = Number of favorable outcomes / Total number of outcomes

The total frequency = 3+7+2+3+5

= 20

The probability of each outcomes

Substitute the values in the equation

p(1) = 3/20 = 0.15

p(2) = 7/20 = 0.35

p(3) = 2/20 = 0.1

p(4) = 3/20 = 0.15

p(5) = 5/20 = 0.25

Hence, the probability distribution table corresponds with the given frequency distribution table is option (D)

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2sinxcosx/sin^2x+cos^2x-1=1

Answers

The simplified equation is sin(2x) = 2

How to determine the value of the trigonometry formula?

The trigonometry ratio is given as

2sinxcosx/sin^2x+cos^2x-1= 1

Rewrite the equation of the trigonometry formula properly