A sofa was sold at a price of $270 with a 25% profit. What is the cost of the sofa?

                              Question # 1 (Top Left)

Step-by-step Explanation:

To determine:

We have to determine the missing side x.

Given:

The missing side x can be calculated by the formula:

sinФ = opposite ÷ hypotenuse

sin(29°) = x ÷ 3

0.4848 = x ÷ 3

x ÷ 3 = 0.4848

x = 0.4848 × 3

x = 1.45 cm

Hence, x = 1.45 cm is the length of missing side.

                                 Question # 2 (Top Center)

Step-by-step Explanation:

To determine:

We have to determine the missing side x.

Given:

The missing side x can be calculated by the formula:

tanФ = opposite ÷ adjacent

tan(21°) = x ÷ 4

0.3838 = x ÷ 4

x ÷ 4 = 0.3838

x = 0.3838 × 3

x = 1.15 cm

Hence, x = 1.15 cm is the length of missing side.

                             Question # 3 (Top Right)

Step-by-step Explanation:

To determine:

We have to determine the missing side x.

Given:

The missing side x can be calculated by the formula:

cosФ = adjacent ÷ hypotenuse

cos(66°) = x ÷ 8

0.4067 = x ÷ 8

x ÷ 8 = 0.4067

x = 0.4067 × 8

x = 3.25 cm

Hence, x = 3.25 cm is the length of missing side.

                           Question # 4 (Bottom Right)

Step-by-step Explanation:

To determine:

We have to determine the missing side x.

Given:

The missing side x can be calculated by the formula:

cosФ = adjacent ÷ hypotenuse

cos(29°) = 3.7 ÷ x

0.8746 = 3.7 ÷ x

x = 3.7 ÷ 0.8746

x = 4.23 cm

Hence, x = 4.23 cm is the length of missing side.

                                      Question # 5 (Bottom Center)

Step-by-step Explanation:

To determine:

We have to determine the missing side x.

Given:

The missing side x can be calculated by the formula:

sinФ = opposite ÷ hypotenuse

sin(37°) = 5.1 ÷ x

0.6018 = 5.1 ÷ x

x  = 5.1 ÷ 0.6018

x = 8.47 cm

Hence, x = 8.47 cm is the length of missing side.

                              Question # 6 (Bottom Right)

Step-by-step Explanation:

To determine:

We have to determine the missing side x.

Given:

The missing side x can be calculated by the formula:

tanФ = opposite ÷ adjacent

tan(54°) = x ÷ 5.9

1.3763 = x ÷ 5.9

x ÷ 5.9 = 1.3763

x = 1.3763 × 5.9

x = 8.12 cm

Hence, x = 8.12 cm is the length of missing side.

Keywords: missing angle, tanФ, cosФ, sinФ, hypotenuse

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Answer:

[tex]\large\boxed{y=\dfrac{3}{4}x-1}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept (0, b)

We have two points (4, 2) and (0, -1) → b = -1.

Calculate the slope:

[tex]m=\dfrac{-1-2}{0-4}=\dfrac{-3}{-4}=\dfrac{3}{4}[/tex]

Finally:

[tex]y=\dfrac{3}{4}x-1[/tex]

The equation of the line that passes through the points (4, 2) and (0, -1) is y = 0.75x + 1.

The subject of this question is Mathematics, and it involves finding the equation of a line given two points. To find the equation of the line that contains the points (4, 2) and (0, -1), we first find the slope (m) using the formula m = (y2 - y1) / (x2 - x1).

Substituting the given points into the formula, we get m = (-1 - 2) / (0 - 4) = -3 / -4 = 0.75.

We then use the point-slope form of a linear equation, y - y1 = m(x - x1), and substituting m = 0.75, x1 = 4, and y1 = 2, we get the equation of our line as: y - 2 = 0.75(x - 4), which simplifies to y = 0.75x + 1.

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Answer:

20*2 is 40

add 4?

its 44

Answer:

44

Step-by-step explanation:

20 * 2 = 40

40 + 4 = 44

Hope this helps :)

Answer:

[tex]\large\boxed{\int\bigg(x(x-6)^3\bigg)dx=\dfrac{1}{5}(x-6)^5+\dfrac{3}{2}(x-6)^4+C}[/tex]

Step-by-step explanation:

[tex]\int\bigg(x(x-6)^3\bigg)dx\Rightarrow\left[\begin{array}{ccc}x-6=u\\x=u+6\\dx=du\end{array}\right]\Rightarrow\int\bigg((u+6)u^3\bigg)du\\\\=\int(u^4+6u^3)du=\dfrac{1}{5}u^5+\dfrac{6}{4}u^4+C=\dfrac{1}{5}(x-6)^5+\dfrac{3}{2}(x-6)^4+C[/tex]

Answer: The answer is A my friend.

Step-by-step explanation:

All possible outcomes:

Yellow shirt, white trouser

Yellow shirt, black trouser

Green shirt, white trouser

Green shirt, black trouser

Hope this helps. Please hit the thanks button if it is right. I would appreciate it. :)

Answer:

There are 4 chairs in one row.

Step-by-step explanation:

Let [tex]$ x $[/tex] be the number of chairs in one row.

That is the length of one row.

Now, from the given data, three rows of length 3x can be formed with one chair left.

Or, if 15 extra chairs given, we can form 7 rows of the same length.

This means that there are [tex]$ 3x + 1 $[/tex] chairs in the first case. And since with 15 extra chairs we can form 7 rows, the equation would be

[tex]$ (3x + 1) + 15 = 7x $[/tex]

Solving this for '[tex]$ x $[/tex]', we get:

[tex]$ 3x + 16 = 7x $[/tex]

[tex]$ \implies 4x = 16 $[/tex]

[tex]$ \implies x = 4 $[/tex]

Therefore, the length of each row is four.

That is, there are four chairs in one row.

Answer:

0,-9,-5

Step-by-step explanation:

Answer:

Multiplying 8 by 3 will give the same quotient.

Step-by-step explanation:

We have to find the quotient of 8 divided by [tex]\frac{1}{3}[/tex], so, we have to follow the following steps.

[tex]8 \div \frac{1}{3} = \frac{8}{\frac{1}{3}} = 8 \times 3 = 24[/tex]

So, it is clear from the above steps that dividing 8 by [tex]\frac{1}{3}[/tex] is equivalent to multiplying 8 by 3.

Therefore, multiplying 8 by 3 will give the same quotient. (Answer)

Answer:

3/4 divied by 8 im sorry if it wrong im not to smart cuz my mom or dad doesnt help me :( and im homeschooled

Step-by-step explanation:

Age of Jen is 13.6 years old

Solution:

Let "x" be the age of Jack and "y" be the age of Jen

Given that This Christmas, your brother Jack will be 2 years from being twice as old as your sister Jen

The above sentence can be written mathematically as:

Jack age + 2 = twice of age of Jen

[tex]x + 2 = 2y\\\\x = 2y - 2---- eqn 1[/tex]

The sum of Jacks age and three times Jen's age is 66

Jack age + three times Jen age = 66

x + 3y = 66 ---- eqn 2

Substitute eqn 1 in eqn 2

2y - 2 + 3y = 66

5y - 2 = 66

5y = 68

Thus age of Jen is 13.6 years old

Step-by-step explanation:

Compare the ratios of their heights, widths, and lengths.  If they're the same, then the solids are similar.

10/5 = 2

6/3 = 2

6/3 = 2

The ratios are the same, so the solids are similar.

Answer: 147

Step-by-step explanation:

Supplementary: Angles that equal 180

180-33=147

147+33=180

The measure of supplement angle X is 147°.

Given that, angle X and angle Y are supplementary angles.

Supplementary angles refer to the pair of angles that always sum up to 180°. These two angles are called supplements of each other.

Here,

∠X+∠Y=180°

⇒ ∠X+33°=180°

⇒ ∠X=180°-33°

⇒ ∠X=147°

Hence, the measure of supplement angle X is 147°.

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A customer will pay $10.59, including sales tax, for a pair of sunglasses.

Step-by-step explanation:

Given,

Purchase price of sunglasses = $5.50

Mark up = 80%

Amount of mark up = 80% of purchase price

Amount of mark up = [tex]\frac{80}{100}*5.50=0.80*5.50[/tex]

Amount of mark up = $4.40

Retail price = Purchase price+mark up

Retail price = 5.50+4.40 = $9.90

Sales tax = 7% of retail price

Sales tax = [tex]\frac{7}{100}*9.90=0.07*9.90[/tex]

Sales tax = $0.69

Total paid by customer = retail price + sales tax

Total paid by customer = 9.90 + 0.69 = $10.59

A customer will pay $10.59, including sales tax, for a pair of sunglasses.

Keywords: addition, percentage

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Answer:

Exact form : x = 16/15

Decimal form : x=1.06666666666...

Mixed Number form : x=1 1/15

Step-by-step explanation: Move all term that don't contain x to rightside and solve.

Hope this helps you out.

Answer:

A classroom of 24 students will go on a field trip to a museum. Each student pays $8 to go. So far, 15 of the students have paid to go. How much money, x, will be collected from all 24 students?

Answer:

Farrah purchased the car in 2016 at the price of $22,440.

Step-by-step explanation:

Given:

Cost of the car in 2017 = $20,140

Depreciation in the cost after 2016 was = $2300

To find cost of the car in 2016.

Solution:

Let cost of the car in dollars in 2016 be = [tex]x[/tex]

Depreciation in value after a year was by = $2300

Thus, cost of car in dollars in 2017 will be = [tex]Original\ cost-Depreciation\ =x-2300[/tex]

Given cost of car in 2017 = $20,140

So, we have:

[tex]x-2300=20140[/tex]

Solving for [tex]x[/tex]

Adding 2300 both sides.

[tex]x-2300+2300=20140+2300[/tex]

∴ [tex]x=22440[/tex]

Thus, cost of the car in 2016 was = $22,440

Answer:

[tex]12-c[/tex]  Cookies

Step-by-step explanation:

The question is to find how many cookies did Cindy receive (write as an expression)?

Total cookies baked = 96

If evenly divided among 8 grandchildren, each would get:

[tex]\frac{96}{8}=12[/tex]

Each grandchildren would have gotten 12 cookies

Now, Cindy received "c" fewer than this (12), so Cindy received:

12 - c  Cookies

Cindy Received = 12 - c  Cookies

Answer:

96/8 - c.

Step-by-step explanation:

She is divideing among the grandkids so it would be 98/8-c

Answer:

47

Step-by-step explanation:

Let a, b, and c be those three numbers.

When two of the three numbers are added at a time, the possible sums are 32, 39, 23. Let

[tex]a+b=32\\ \\a+c=39\\ \\b+c=23[/tex]

Add these three equations:

[tex]a+b+a+c+b+c=32+39+23\\ \\2a+2b+2c=94[/tex]

Divide this equation by 2:

[tex]a+b+c=47[/tex]

The sum of all three numbers is 47.

Answer:

Therefore

[tex]75\div 5 - [(9-7)\times 3 ]\times 2 = 3[/tex]

Step-by-step explanation:

To Find:

Value of expression

75 ÷ 5 - [( 9 - 7 ) × 3 ] × 2

Solution:

PEDMAS rule

It explains the order of operations to solve an expression.

According to Pedmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.),

then division, multiplication, addition and subtraction from left to right.

P - parenthesis

E- exponent

D/M - Div or Multiply which ever comes first

A/S - Add or Sub which ever comes first.

So first we will solve the Parenthesis we get

Step 1. Parenthesis  operation

75 ÷ 5 - [( 2 ) × 3 ] × 2

Step 2. Parenthesis operation

[tex]75\div 5 - [(2)\times 3 ]\times 2[/tex]

Step 3. Division

[tex]15 - [6]\times 2[/tex]

Step 4. Multiplication

[tex]15 - 12[/tex]

Step 5. Subtraction

3

Therefore

[tex]75\div 5 - [(9-7)\times 3 ]\times 2 = 3[/tex]

58.....2wt.r3y2teyt3y2.te.32ty.32tye.t32y.tey32t..enkuuhuh

Answer:

$0.38

Step-by-step explanation:

Since there are two cups in a pint so you divide 0.76 by 2

Answer:

.38 cents

Step-by-step explanation:

Since there are 2 cups in one pint, you have to divided .76 (cents) by 2 and you get .38 (cents)

Answer:

they will have the same y-coordinate from the point it was reflected because it is reflected over the y-axis.

but you didn't provide the following statements, so i do not know.

The values of the coordinates will be same for y ordinate but will be negated for x abscissa , which means (x,y) will become (-x, y)

When the graph is reflected over y axis, then all the x coordinates of all points become negation of themselves. It is because those x coordinates who were on the positive sides now are on the negative sides and those who were on the negative side are now on the positive side.

Thus:

(x,y) turns to  (-x,y)

Thus, the values of the coordinates will be same for y ordinate but will be negated for x abscissa , which means (x,y) will become (-x, y)

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Answer:

(1) 9.106 cm

(2)  49.612 inches

Step-by-step explanation:

Answer:

1. C =9.106 cm              2.C =49.612 inches

Step-by-step explanation:

To solve these problems, we will follow the steps below;

First write down the formula for calculating the circumference of the circle

C= 2πr

where c is the circumference of the circle    and r is the radius of the circle

1) From the question diameter = 2.9 cm, but radius is half of the diameter, this implies that radius = [tex]\frac{d}{2}[/tex]= [tex]\frac{2.9}{2}[/tex]=1.45 cm  

We can now proceed to insert the values into the formula;

C= 2πr

   = 2×3.14×1.45

   =9.106 cm

C =9.106 cm

2) From the question, radius = 7.9 inches and π=3.14

We can now go ahead to insert the values into the formula  C= 2πr

C = 2×3.14× 7.9

    =49.612 inches

C =49.612 inches

For this case we assume that the initial amount of money is $20.

So:

[tex]\frac {1} {5} (20) = 4[/tex]

[tex]\frac {3} {8} (20) = 7.5[/tex]

[tex]\frac {2} {7} (20) = 5.71[/tex]

Adding we have:

[tex]4 + 7.5 + 5.71 = 17.21[/tex]

Ken has:

[tex]20-17.21 = 2.79[/tex]

Answer:

Ken can spend what he planned and he has $2.79 left.

Answer:

c) supply

Step-by-step explanation:

Answer:

supply

Step-by-step explanation:

Answer:

3. 113.04

4. 137.1

5. $9.24

Answer:

3. 113.04

4. 137.1

5. $9.24

Answer:

$318.79

Step-by-step explanation:

To do this problem, to find the real end amount paid, you must add up all the prices and add the sales tax. To do this, you add them to 296.55, and multiply it by the decimal form of the sales tax added to 1, so 1.075 which is 318.791 rounded to 318.79

Answer:

15a)  True 15b) False 15c) True

16)[tex]\frac{4*2}{5*2}=\frac{8}{25}=\frac{4*3}{5*3}=\frac{12}{15}[/tex]

[tex]\frac{5*2}{6*2}=\frac{10}{12}=\frac{5*3}{6*3}=\frac{15}{18}[/tex]

Step-by-step explanation:

*Rewriting the question with Retrieved missing information:

15. Mr. Clements painted his barn for hours in the morning. He painted  his barn [tex]3\frac{3}{5}[/tex] hours in the morning. He painted the barn for [tex]5\frac{3}{4}[/tex] hours in the afternoon.Select True or False for each statement.

15a. A common denominator of the mixed numbers is 20.

15b. The amount of time spent painting in the morning can be rewritten as [tex]3\frac{15}{20}[/tex]

15c. Mr. Clements spent [tex]2\frac{3}{20}[/tex]

hours longer painting in the afternoon than the morning.

16. Tom exercised:

[tex]\frac{4}{5}[/tex]

hour on Monday and

[tex]\frac{5}{6}[/tex]

hour on Tuesday. Part A. Complete the calculations below to write equivalent fractions with a common denominator.

15a)  True

Turning the Mixed Numbers into Improper ones:

He painted the his barn:

[tex]3\frac{3}{5}=\frac{18}{5}[/tex] Keep the denominator, and for the numerator multiply the denominator 5 by 3 and add 3 = 18. (In the morning).

[tex]5\frac{3}{4}=\frac{23}{4}[/tex] (In the afternoon)

The Prime factorization [tex]\frac{23}{4},\frac{18}{5}[/tex] help us to obtain the common denomination, i.e. 20

15b) False

This is a matter of simplification. In this mixed number, the fraction can be simplified this way:

[tex]3\frac{15}{20}=3\frac{15:5}{20:5}\Rightarrow 3\frac{3}{4}[/tex]

15c) True

Subtracting the working hours, knowing the common denominator by prime factorization is 20.

For Mixed Numbers:

[tex]5\frac{3}{4}-3\frac{3}{5}=5\frac{15}{20}-3\frac{12}{20}=2\frac{3}{20}[/tex]

For the same mixed numbers turned into improper fractions:

[tex]\frac{23}{4}-\frac{18}{5}=\frac{115-72}{20}=\frac{43}{20}[/tex]

Notice that:

[tex]2\frac{3}{20}==\frac{43}{20}=2.15[/tex]

16A

Equivalent fractions are fractions multiplied by a same constant, on the numerator and denominator:

[tex]\frac{4*2}{5*2}=\frac{8}{25}=\frac{4*3}{5*3}=\frac{12}{15}[/tex]

[tex]\frac{5*2}{6*2}=\frac{10}{12}=\frac{5*3}{6*3}=\frac{15}{18}[/tex]

15a is False as a common denominator isn't clear; 15b is False because the time in the morning is undefined; 15c is True assuming the morning was 3 hours. 16 needs further clarification.

So, correct answer is 15a. False   15b. False   15c.True

Answer:

[tex]AB=9\sqrt{3}\ units[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC

The cosine of angle of 30 degrees is equal to divide the adjacent side to angle of 30 degrees by the hypotenuse

so

[tex]cos(30^o)=\frac{AB}{AC}[/tex]

we have

[tex]cos(30^o)=\frac{\sqrt{3}}{2}[/tex]

[tex]AC=18\ units[/tex]

substitute

[tex]\frac{\sqrt{3}}{2}=\frac{AB}{18}[/tex]

solve for AB

[tex]AB=(18)\frac{\sqrt{3}}{2}[/tex]

[tex]AB=9\sqrt{3}\ units[/tex]

Answer:

T

Step-by-step explanation:

Answer:

[tex]\large \boxed{5.0 \, \% }[/tex]

Step-by-step explanation:

1. Calculate the amount of tax

    Total cost = selling price + sales tax

     Sales tax = total cost - selling price

     Total cost = $651

-Selling price = - 620

       Sales tax = $  31

2. Calculate the percent tax

[tex]\text{\% Tax} = \dfrac{\text{\$31}}{\text{\$620}} \times 100 \, \% = \mathbf{5.0 \, \%}\\\\ \text{The sales tax percentage is $\large \boxed{\mathbf{5.0 \, \% }}$}[/tex]

Answer:

20 times

Step-by-step explanation:

1,000 divided by 50 will be 20 try using lone division :)

Answer:

20 times

Step-by-step explanat

Answer:

They won [tex]\£63[/tex] in total

Step-by-step explanation:

Let

x ----> Mark's money

y ----> Henry's money

we know that

[tex]x=27[/tex] ----> equation A

[tex]\frac{x}{y}=\frac{3}{4}[/tex] ----> equation B

substitute equation A in equation B

[tex]\frac{27}{y}=\frac{3}{4}[/tex]

solve for y

[tex]y=27(4)/3\\y=36[/tex]

we have that

[tex]x+y=27+36=\£63[/tex]