Cynthia Besch wants to buy a rug for a room that is 18 ft wide and 32 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 176 square feet of carpeting. What dimensions should the rug​ have?

Answer:

104m

Step-by-step explanation:

23+23+29+29=104m

Answer:

Step-by-step explanation:

1/4 of all of it

Based on the amount deposited by Berno and the annual interest on the account, the amount in the account after fifteen years is $49,012.91.

The interest is said to compound quarterly which means that the periodic interest rate is:

= 3.25% / 4

= 0.8125%

The number of periods is:
= 15 x 4

= 60 quarters

The amount in the account after 15 years is:

= 30,000 x (1 + rate) ^ number of periods

= 30,000 x (1 + 0.8215%)⁶⁰

= $49,012.91

In conclusion, the amount in the account after 15 years would be $49,012.91.

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The values of the indicated lengths.

We are given a number line with points A, B, C, D and E on it.

We need to find the lengths of:

DE

AB

AC

BD

CE

BE

Now, we are also given that:

AD = 18 units

AE = 27 units

DE = 27 - 18 = 9 units

AB = 18 / 3 = 6 units ( As AB = BC = CD)

AC = 12 units ( as AB + BC)

BD = 12 units

CE = 6 + 9 = 15 units

BE = 15 + 6 = 21 units.

Therefore, we get the values of the indicated lengths.

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We get that, the amount that Karen can withdraw after 7 years will be $ 17376.98 compounded semi annually with interest rate of 3.32 %.

We are given that:

Principal amount = $ 11,000

Interest rate = 3.32 % compounded semi annually.

Time period = 7 years

t = 7 × 2 = 14 times

Amount = 11,000 ( 1 + 3.32 / 100 )¹⁴

Amount = 11,000 (1.0332)¹⁴

Amount = 11,000 ( 1.57973)

Amount = 17376.98

The amount will become = $ 17376.98 that Karen will withdrew for the down payment on a new house.

Therefore, we get that, the amount that Karen can withdraw after 7 years will be $ 17376.98 compounded semi annually with interest rate of 3.32 %.

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Answer:

283

Step-by-step explanation:

Answer:

3x² + 24x + 36 = 0

Step-by-step explanation:

A quadratic equation has the standard form ax² + bx + c = 0.
a, b and c are constants.

The roots of a quadratic equation represent the two solutions to the quadratic equation

Given that the roots are -2 and -6 we have

x = -2 and x = -6 as the solutions

Add 2 to both sides of x = -2 ==> x + 2 = 0
Add 6 to both sides of x = -6 ==> x + 6= 0

So (x+2)(x+6) = 0 is the factored representation of this equation. We have to multiply by a leading coefficient of 3

So the quadratic equation is
3(x+2)(x+6) = 0

Using the FOIL method
(x + 2)(x + 6) = x² + 6x + 2x + 12 = x² + 8x + 12

The leading coefficient is the coefficient of x² and is given as 3

So the quadratic equation in standard form is
3(x² + 8x + 12) = 0

==>  3x² + 24x + 36 = 0

If you solve this equation on a quadratic equation calculator you will get the solutions x = -2 and x=-6

Answer:

-0.25641025641

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Slope formula: y2 - y1/ x2 - x1 (this means the second y minus the first 1 divided by the second x minus the first x)

36 - 20 = 16

4 - 0 = 4

16/4 = 4

The slope of the line is 4

Answer:

It is an acute angle

Step-by-step explanation:

You can tell by looking at it that it is less than 90 degrees, making it an acute angle.

The solution for given inequality is s ≥ -1/3 or s ≤ -4

In mathematics, an inequality can be taken as a relation which makes a  comparison which is non-equal between two specific numbers or the variables or other mathematical symbols and expressions. It is used mostly when we have to compare two numbers by their size on the number line.

The are various operators which are used while showing the inequality such as the signs of greater than (>) , less than (<), greater than or equals to (≥) , and less than or equals to (≤).

In the given question the inequality is:

-3s+7 ≤ 8 or -2s+4 ≥ 12

solving the equations

=> -3s ≤ 8-7 or -2s ≥ 12-4

=> -3s≤ 1  or -2s ≥ 8

=> -s ≤ 1/3 or -s ≥ 4

=> s ≥ -1/3 or s ≤ -4.

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The complete question is:

Solve the given inequality.

-3s+7 ≤ 8 or -2s+4 ≥ 12

Answer:

Step-by-step explanation:

3rd one

For the given right triangle, the tangent of theta is equal to 4/3 so the correct option is D.

Here we have a right triangle, and we want to find the tangent of one shown angle.

Remember that the trigonometric relation for a tangent is:

tan(a) =(opposite cathetus)/(adjacent cathetus).

On the image, we can see that the adjacent cathetus to the given angle has a measure of 6 units, while the opposite cathetus has a measure of 8 units, then we can replace that in the general relation to write:

tan(θ) = 8/6

Now we just can simplify that fraction if we divide both numerator and denominator by 2, we will get:

tan(θ) = 8/6 = 4/3

Then we conclude that the correct option is D.

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Answer:

see image

Step-by-step explanation:

Use distributive property to multiply.

Multiply the numbers together. To multiply variables, add the exponents (for same variables, x's and x's, also y's and y's)

Keep the minus sign and the plus sign in place. See image.

Step-by-step explanation:

remember : to convert a fraction of one denominator into a fraction of another denominator, we need to multiply both (numerator and denominator) by the same factor, so that the denominator changes to the desired number, and the overall value of the fraction remains unchanged.

4 1/3 - 8

first I convert the mixed number into a full fraction :

4 1/3 = (4×3 + 1)/3 = 13/3

then, to be able to subtract 8, I need to convert 8 into a fraction with the same denominator as 13/3 :

8 = (8×3)/3 = 24/3

so, now I can do the subtraction :

13/3 - 24/3 = -11/3

-11/3 = -3 remainder 2 = -(3×3 + 2)/3 = -3 2/3

5 2/5 - (-2 4/15)

again, we convert all mixed numbers into full fractions :

5 2/5 = (5×5 + 2)/5 = 27/5

2 4/15 = (2×15 + 4)/15 = 34/15

now we need to bring both to the same denominator, and because 5 is a factor or 15, we can bring both to fractions of 1/15, for which we only need to transform the first fraction :

27/5 = 27/5 × 3/3 = 81/15

so, the subtraction is actually

81/15 - (-34/15) = 81/15 + 34/15 = 115/15 = 23/3

23/3 = 7 remainder 2 = (7×3 +2)/3 = 7 2/3

Step-by-step explanation:

we have 3 gears meshed with the following teeth . A-20 , B -50 , C -30 . another set of gears have the following teeth . X -20 , y- 25 , Z -30 . Assuming gears A and X are Running at the same rpm . which statement is correct ?

Well, you start out by recognizing that 4/5ths of an ounce equals 1/5 of the apples weight. Therefore, you must multiply 4/5 by 5 to get the whole of the Apple. (1/5*5).

So, this is the lines,

4/5*5= 20/5, or 4 ounce

Another way, is with decimals, so

0.8*5=4.0

If Ian wants to get an expected quiz score of 83, then he needs to spend 3.33 hours in homework that week.

We know that the situation is modeled by the linear equation:

y = 60+ 6.9x

Where y represents the expected quiz score and x the hours spend on homework that week.

If we define y = 83, the value of x will be the number of hours that the students need to do homework such tath the expected quiz score is 83.

Solving the linear equation:

83 = 60 + 6.9*x

(83 - 60)/6.9 = x

23/6.9 = x

3.33 = x

So to get an expected quiz score of 83, they need to spend 3.33 hours in homework that week.

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Answer: The number of hours a student should spend on their homework to expect a score of 83 on the quiz.

Step-by-step explanation: just did it!

The line in standard notation is 2y - 7x = 7 and in slope-intercept form it is:

y = (7/2)*x + 7/2

We want our line to be perpendicular to 2x + 7y = 1

Rewriting that line, we get:

y = (1 - 2x)/7 = 1/7 - (2/7)*x

So the slope is (-2/7), then the slope of a perpendicular line is 7/2.

So our equation is something like:

y = (7/2)*x + b

To find the value of b we replace the values of the point (1, 7), it gives:

7 = (7/2)*1 + b

7 = 7/2 + b

7 - 7/2 = b

7/2 = b

Then the linear equation in slope-intercept is:

y = (7/2)*x + 7/2

And the standard form is:

y - (7/2)*x = 7/2

2y - 7x = 7

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Her total cost after purchasing 12x packs of Vanilla Coke is given by the following linear function:

y = 2 + 7x.

A linear function is modeled according to the following rule:

y = mx + b

In which:

For this problem, we have that:

Hence her total cost after purchasing 12x packs of Vanilla Coke is given by the following linear function:

y = 2 + 7x.

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Based on the karats on the gold necklace, the weight in grams of the pure gold in the necklace is B. 40.5 grams

When something is said to be 18 karats of gold, it means that there is about 75% pure gold and then 25% of other materials.

If the necklace has 75% gold, the pure gold in grams is:

= 75% x 54

= 40.5 grams

In conclusion, the pure gold weighs 40.5 grams.

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Answer:

Important Ideas:    

Led American troops in War

Led Constitutional Convention
Served as first US President

Minor Details:
Had a $25,000 yearly salary

Had problems with teeth
Had a brother named Lawrence

Using proportions, it is found that the inflation rate was of 5.7%.

The inputs to the table will be given as follows:

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

The inflation rate is found by the proportion of the 2016 CPI to the 2014 CPI, hence:

185/175 - 1 = 1.057 - 1 = 0.057.

The inflation rate was of 5.7%.

To find the amounts that complete each table, we have to find the 2014 table, and multiply the amounts by 1.057, hence:

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Answer: [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

[tex]f(x)=\frac{2}{9}x+4[/tex] has a domain of all real numbers since it is a polynomial function.

The solution for the inequality is given by: -1  < m < 2 .

In mathematics, an inequality is a link that compares two numbers or other mathematical expressions unfairly. Size comparisons between two numbers are commonly made on the number line. Various types of inequalities can be represented using various notations, such as:

a is smaller than b, as shown by the symbol a<b.

When the expression a > b is employed, it means that an is larger than b.

In no circumstance is a the same as b. These relationships are referred to as strict inequalities since a is strictly less than or strictly greater than b. Equivalence isn't taken into account.

The given inequality is of the form:

−15+ 6 |2m − 1| < 3

Now let us solve the inequality :

or ,  6 |2m − 1| < 3 + 15

or ,  6 |2m − 1| < 18

or,  |2m − 1| < 3

or, -3 < 2m-1 < 3

or, -3+1 < 2m < 3 + 1

or, -2 < 2m < 4

or, -1 < m < 2

Hence  the solution of the inequality is -1  < m < 2 .

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Using proportions, it is found that:

3. Due to the lower cost per pound, the twelve-pack is the better value.

4. Due to the lower cost per cup, the Pacific Coast Coffee is the better value.

5. Lettuce and Asparagus cost the same per pound.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

For item 3, the cost per pound is the proportion of the cost by the weight, hence:

Due to the lower cost per pound, the twelve-pack is the better value.

For item 4, we follow the same procedure, hence:

Due to the lower cost per cup, the Pacific Coast Coffee is the better value.

In item 5, we have that:

Lettuce and Asparagus cost the same per pound.

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The annual simple interest rate of the loan is 15% on the premise that Jean would $225 extra after 1 year

How is simple interest determined?

The simple interest whose dollar is $225 on the loan is the principal of $1500 multiplied by the interest rate which is unknown, can be assumed to be R, multiplied as well as the period of loan, I mean how long it takes for the loan to be repaid, which is one year as indicated by the below simple interest rate formula:

I=PRT

I=interest amount in dollars=$225

P=loan amount=$1,500

R=interest rate=unknown

T=period of loan=1 year

$225=$1500*R*1

$225=$1500*R

R=$225/$1500

R=15.00%

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Answer:

38 yd

Step-by-step explanation:

Definition:

the perimeter of a polygon is equal to the sum of all sides’ lengths.

Let P be the perimeter.

Then

P = 8 + 9 + 5 + 7 + 9 = 38

Answer:

Step-by-step explanation:

Rewrite

y − 4 − 3 >. y − 4 (−3>)

Answer: I'm assuming you want our favorite so shaggy

Step-by-step explanation: