the age of a mother is three times that of her son. after 5 years sum of their ages will be 50 years. Express it as a linear equation in two variables.​

                              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:

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

The figure is a 4 sided pyramid, so it has 4 triangles and the base is square.

The net would be the lower left one.

Answer:

C

Step-by-step explanation:

The Neolithic Revolution allowed people to live in permanent settlements.

Explanation:

The Neolithic Revolution is the phase of transition in which many of the human cultures in the world shifted their lifestyle to permanent settlement and agriculture from hunting and gathering.

This era is also named as First Agricultural Revolution or Neolithic Demographic Transition. The agricultural practices led the cultures to develop the knowledge of domestication of animals and they began to observe and experiment with the plants (to learn or know how they grow and develop).

Neolithic period is named as revolution because this period changed the way of life of most of the communities. This first occurred in so-called "Fertile Crescent" or Mesopotamia (modern Iraq).

The Neolithic Revolution allowed people to live in permanent settlements.

Answer: Option B

Step-by-step explanation:

Answer:

c) supply

Step-by-step explanation:

Answer:

supply

Step-by-step explanation:

Answer:

In the quotient [tex]x^4+2x^3+x^2+5x+10=0[/tex] , the coefficient of x is 5.

Step-by-step explanation:

Given rational expression is [tex]\frac{-x^5+3x^3-3x^2+20}{x-2}[/tex]

Nicolette used synthetic division to solve the given rational expression.

Nicolette's work is given below:

Given that x-2 is a zero of given rational expression

By using synthetic division for the given rational expression.

2_|        -1     0     3     -3       0       20

             0   -2     -4    -2     -10      -20

 ____________________________

           -1      -2     -1     -5    -10     |  0

Therefore the simplified expression can be written as below

[tex]-x^4-2x^3-x^2-5x-10=0[/tex]

Taking negative sign outside.

[tex]-(x^4+2x^3+x^2+5x+10)=0[/tex]

Multiply negative sign with "0" we get "0"

Therefore [tex]x^4+2x^3+x^2+5x+10=0[/tex]

In the quotient [tex]x^4+2x^3+x^2+5x+10=0[/tex], the coefficient of x is 5.

Answer:

$545

Step-by-step explanation:

Let the total cost per year be y.

He spent a flat amount of $125 per year.

Then he spend an additional $35 per months. There are 12 months in a year so that's a total of 35*12=$420.

Add up the cost

y = 125 + 420 = $545

Answer:

The price of each CD before tax was $15.30.

Step-by-step explanation:

Given:

Miguel bought 6 CDs that were each the same price.

Including sales tax, he paid a total of $99.60.

Each CD had a tax of $1.30.

Now, to find the price of each CD before tax:

So, to get the price of 1 CD including tax by using unitary method:

Total price of 6 CDs including tax = $99.60.

So, the price of 1 CD including the sales tax = $99.60 ÷ 6 = $16.60.

Thus, the price of each CD including tax = $16.60.

Tax  on each CD = $1.30.

Now, by subtracting we get the price of each CD before tax:

[tex]\$16.60-\$1.30[/tex]

[tex]=\$15.30.[/tex]

Therefore, the price of each CD before tax was $15.30.

Answer:

see explanation

Step-by-step explanation:

Note the common ratio r between consecutive terms of the sequence

r = 6 ÷ 3 = 12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 2

The explicit rule for a geometric sequence is

[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 3 and r = 2, thus

[tex]a_{n}[/tex] = 3[tex](2)^{n-1}[/tex] ← explicit rule

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:

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: 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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Answer:

x=-2

Step-by-step explanation:

4x (+ 5-5) = -3-5

4x = -8

4x/4 = -8/4

x=-2

4(-2) + 5= -3

-8 + 5 = -3

-3 = -3

Answer is Correct.

Answer:

[tex] \: \: \: \: \: \: 4x + 5 = - 3 \\ = > 4x = -3 - 5 \\ = > 4x = - 8 \\ = > x = \frac{ - 8}{4} \\ = > x > - 2[/tex]

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:

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:

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:

3. 113.04

4. 137.1

5. $9.24

Answer:

3. 113.04

4. 137.1

5. $9.24

Answer:

you can make 14 muffins

Step-by-step explanation:

To get this answer you first need to know that 1 cup makes 8 muffins. Next know that there's 1 3/4 cups of flour. Because you know that 1 cup makes 8 muffins you need to figure out how many muffins 3/4 a cup of flour can make. To do this you divide 8 by 4. Hence 8 divided by 4 is 2. So know you know that for every 1/4 cup you can make 2 muffins. Now since there's 3/4 cup of flour you then multiply 2 by 3 which is 6. Now you have to add 1 cup ( 8 muffins) to 3/4 cup ( 6 muffins ) of flour which then equals 14. You then get the answer , 1 3/4 cups of flour can make 14 muffins. Hope this helped ;)

Answer:

one number is 90 and the other one 9

Step-by-step explanation:

Let's refer to the larger number as "x", and the smaller as "y", so we can create equations with those unknowns and solve them algebraically.

Now let's write the first phrase we are given in mathematical form:

"One number is 10 times as large as another one"

Remember that our larger number is "x", so the first equation out of this phrase is:

x = 10 * y

Now for the second phrase:

"Their difference is 81"

Here we need to make the difference setting the larger number first (x), minus the smaller number (y), so as to get a positive difference of 81 units:

x - y =81

now we solve this system by substituting "x" in the second equation with "10 * y" according to what our first equation states:

10 y - y = 81

9 y = 81

y = 81/9

y = 9

and therefore now that we know the value of number y (9) we can go back to the first equation to find what number "x" is:

x = 10 * (9)

x = 90

Finally: x = 90, and y = 9

Answer:

The correct answer is D. 69

Step-by-step explanation:

Let's recall that if an exterior angle has its vertex where two rays share an endpoint outside a circle, the measure of that exterior angle is found by dividing the difference between the measures of the intercepted arcs by two.

Therefore, we have:

x = (Measure of arch CD - Measure of arch BD)/2

Replacing with the real values:

x = (210 - 72)/2

x = 138/2 = 69°

The correct answer is D. 69

Answer:

2/13

Step-by-step explanation:

There are 4 kings and 4 queens in a standard deck of 52 cards.  So the probability is:

P = 8/52

P = 2/13

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:

15×2x

Step-by-step explanation:

Answer:

15 more than twice a number if it is a certain number u would multiply 15 times what ever number u chose

Step-by-step explanation:

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

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:

[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]

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:

[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:

20*2 is 40

add 4?

its 44

Answer:

44

Step-by-step explanation:

20 * 2 = 40

40 + 4 = 44

Hope this helps :)

Equation #1: x+y=40

Equation #2: 7x+4y=193

Monica bought 11 red bricks.

Step-by-step explanation:

Given,

Cost of one red brick = $7

Cost of one gray brick = $4

Total spent on bricks = $193

Total bricks bought = 40

Let,

x represents the number of red bricks bought.

y represents the number of gray bricks bought.

What is the system that models this situation?

Equation #1: x+y=40

Equation #2: 7x+4y=193

How many red bricks did Monica purchase?

Multiplying Eqn 1 by 4

[tex]4(x+y=40)\\4x+4y=160\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](7x+4y)-(4x+4y)=193-160\\7x+4y-4x-4y=33\\3x=33[/tex]

Dividing both sides by 3

[tex]\frac{3x}{3}=\frac{33}{3}\\x=11[/tex]

Monica bought 11 red bricks.

Keywords: linear equation, elimination method

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