You plant a spruce tree that is

is 8 inches tall that grows 6 inches a year.

ches a year and a hemlock tree that

a.write a system of linear equations that represent this situation.

b. Solve the system using any method.

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:

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:

20*2 is 40

add 4?

its 44

Answer:

44

Step-by-step explanation:

20 * 2 = 40

40 + 4 = 44

Hope this helps :)

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.

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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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:

[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:

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.

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:

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

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]

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:

                              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:

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:

$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:

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:

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:

c) supply

Step-by-step explanation:

Answer:

supply

Step-by-step explanation:

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: 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:

[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:

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: 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:

[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:

3. 113.04

4. 137.1

5. $9.24

Answer:

3. 113.04

4. 137.1

5. $9.24

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

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:

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.