Clinton’s garden is 12.25 m long and 14 m
wide. Find the perimeter of Clinton’s garden.

Answer:

(3,2)

Step-by-step explanation:

The system is

x + y = 5

x -y = 1

Add the equations to eliminate y

2x = 6----->x=3

Substitute this value in any equation

3+y = 5----->y=2

The solution is (3,2)

Answer:

269

Step-by-step explanation:

1) Substitute in the given values for each variable:

6(3)+23+(7)(33)-3

2) Simplify:

18+23+231-3

3) Simplify again:

269

Answer:

$3

Step-by-step explanation:

By investing $2,000 Bobby will earn $60 interest

∴By investing $1 Bobby will earn =$(60/2000) interest

so,

By investing $100,

He will earn =$ {(60/2000 ) .100}  

                     =$3

If Bobby invests his money for one year at the same interest rate as his brother, then he will earn $3 amount.

Thus, option A $3 is correct.

Interest that Bobby will earn at same interest rate as his brother after 1 year of investment of $100.

If someone invests P amount for T years with simple interest rate R% per year, then the simple interest that that person will earn is given by:

[tex]SI = \dfrac{P \times R \times T}{100}[/tex]

Putting values of P, R and T of Bobby's brother's investment, we have:

[tex]60 = \dfrac{2000 \times 1 \times R}{100}\\\\6000 = 2000R\\\\R = \dfrac{6000}{2000} = 3\%[/tex]

At that rate, the SI for Bobby's $100 investment for 1 year is:

[tex]SI = \dfrac{100 \times 3 \times 1}{100} = \$3[/tex]

Thus, Bobby will get $3 as interest.

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Answer:

15*10∧-5

Multiple 15 x 0,000001 = 0,000015.

Answer:

see explanation

Step-by-step explanation:

Given the range of f(x), find the domain by equating f(x) to each of the values in the range, that is

5x + 4 = 5 ( subtract 4 from both sides )

5x = 1 ( divide both sides by 5 )

x = [tex]\frac{1}{5}[/tex]

5x + 4 = 6 ( subtract 4 from both sides )

5x = 2 ( divide both sides by 5 )

x = [tex]\frac{2}{5}[/tex]

5x + 4 = 7 ( subtract 4 from both sides )

5x = 3 ( divide both sides by 5 )

x = [tex]\frac{3}{5}[/tex]

5x + 4 = 8 ( subtract 4 from both sides )

5x = 4 ( divide both sides by 5 )

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

Thus

domain = { [tex]\frac{1}{5}[/tex], [tex]\frac{2}{5}[/tex], [tex]\frac{3}{5}[/tex], [tex]\frac{4}{5}[/tex] }

The angles of 115 degrees and (52+x) are the same, because they are alternate interior angles.

Answer:

62º + x = 115º

because AB and CD are parallel, which means 115º and 62+x are "alternate angles"

ALTERNATE ANGLES

Step-by-step explanation:

Final answer:

The sum of -2.5 and (-3.5) is -6.0, which is found by adding the absolute values of the numbers and giving the result a negative sign. The correct number line representation for this sum would show a leftward movement from -2.5 by 3.5 units to end at -6.0.

Explanation:

When calculating the sum of -2.5 and (-3.5), we follow the rule that when two negative numbers are added, the answer has a negative sign. Both numbers in the sum are negative, therefore, we add their absolute values and then give the result a negative sign. The calculation is as follows:

-2.5 + (-3.5) = -(2.5 + 3.5) = -6.0

The number line that shows this sum would start at -2.5 and move left (which indicates adding a negative number) 3.5 units, landing on -6.0.

Answer:

The number of turbines is 74

Step-by-step explanation:

* Lets explain how to solve the problem

- Four 3 megawatt wind turbines can supply enough electricity

 to power 3000 homes

∴ The number of turbines is 4

∵ Each turbine give 3 megawatt

∴ The four turbines give ⇒ 4 × 3 = 12 megawatt

- This quantity give enough electricity to power 3000 homes

∴ The number of homes for the 12 megawatt is 3000

- We need to find how many turbines can cover enough electricity

  to power 55,000 homes, so we must to know the quantity of

  electricity that be enough to power 55,000 homes

* Lets use the cross multiplication to solve the problem

∵         megawatt    :     number of homes

                  12          :              3,000

                  ?            :            55,000

- By using cross multiplication

∴ [tex]?=\frac{(55,000)(12)}{3,000}=\frac{660,000}{3000}=220[/tex]

∴ The enough electricity to power 3000 homes = 220 megawatt

∵ Each turbine gives 3 megawatt

- Find the number of turbines divides the total megawatt by the the

  megawatt of one turbine

∴ The number of turbines = 220 ÷ 3 = 73.3

- If we take 73 only the electricity will not be enough to cover all

 homes, so we must to take 74 turbines

∴ The number of turbines is 74

To power 55,000 homes, approximately 74 wind turbines are required. Each turbine can power 750 homes, derived from the initial data where 4 turbines power 3,000 homes.

To determine how many 3 megawatt wind turbines are required to power 55,000 homes, we can use a simple proportion based on the given data.

We know that:

Now, we need to find out how many turbines are needed to power 55,000 homes:

Since we can't have a fraction of a turbine in practical terms, we would need 74 turbines to ensure all 55,000 homes are powered.

Answer: The numbers are 7 and 17

Step-by-step explanation: twice of 7 is 14 and 3 + 14 = 17

Answer:

[tex]200[/tex]

Step-by-step explanation:

This book has 500 pages in total.

We should split up the place values.

1 - 9

One only appears once.

1

10 - 19

One appears 11 times.

1 + 11

20 - 99

One only appears 8 times.

1 + 11 + 8

Add:

1 + 11 + 8

=> 20

Since the same is for  200-299, and so on. Let us add twenty four times.

20 * 4

=> 80

Looking back to 100-199, there are 120 ones.

Add:

120 + 80

=> 200

The total number of times that the digit 1 appears in the page numbers is: 200

In the first 99 pages there are:

1 one in the first 9 pages,

11 ones in pages 10-19 (one each for 10 and 12-19, and two for 11)

8 ones in pages 20-99 (21, 31, 41, 51, 61, 71, 81, and 91)

So we have 20 ones in the first 99 pages.

Likewise we have 20 ones in pages 200-299, 20 ones in pages 300-399, and 20 ones in pages 400-499. There are 0 ones on page 500.

For pages 100-199, there are 100 ones for the hundreds digits in addition to the 20 ones found in the tens and ones digits.

So we have a total of 20 + 120 + 20 + 20 + 20 = 200 ones on the page numbers.

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Answer:

-7.

Step-by-step explanation:

2- + (2+7)

First work out the parentheses   ( by order of operations PEMDAS)

= 2 - + 9  

= 2 - 9    (as - + = -)

= -7.

Answer:

a. $500

b. $250

Step-by-step explanation:

a. For zero items produced, cost will be-

[tex]C(0) = 10(0) + 500 = 0 + 500 = 500[/tex]

b. For zero items produced, cost will be-

[tex]C(25) = 10(25) + 500 = 250 + 500 = 750[/tex]

c. If [tex]C(x)_{max} = 1500[/tex]

[tex]10x + 500 = 1500\\10x = 1000\\x = 100[/tex]

∴ domain for cost function will be [tex][0,100][/tex] and range will be 100

Answer: A) fixed cost is $500

B) Cost of making 25 items is $750

C) Domain: [0,100]

Range :[500,1500]

I got 100% on test with these answers

Answer:

The strategy to evaluate these expressions is called PEMDAS.

Step-by-step explanation:

[tex]15-[(3^2+6)\div5][/tex]

We're going to be following the rule of PEMDAS:

Keep in mind that multiplication/division and addition/subtraction are done from left to right.

In the first expression (written above), we'll first evaluate everything inside the brackets first (brackets are used when there are parentheses inside of it - but they serve the same function). There are parentheses in these brackets, so that will be the absolute first step in evaluating.

Solve for [tex]3^2+6[/tex] then rewrite the expression.

Now finish evaluating inside the parentheses by dividing 15 by 5.

The last step to evaluate the expression is to subtract 3 from 15.

[tex]4\times[50-3(1+3)^2][/tex]

Evaluate everything inside the the brackets. Start with the parentheses since that is first according to PEMDAS. Add 1 and 3 together then rewrite the expression.

Exponents are solved next after parentheses in PEMDAS, so evaluate the exponent.

Multiplication is done before subtraction, so multiply 3 and 16 together.

Finish evaluating inside the brackets by subtracting 48 from 50.

The last step in evaluating the second expression is to multiply 4 and 2 together, which gives us 8.

Answer: Second option.

Step-by-step explanation:

Given the function f(x):

[tex]f(x) = x^2 - 2x + 8[/tex]

Find [tex]f(x -2)[/tex]:

[tex]f(x -2)=(x-2)^2 - 2(x-2) + 8[/tex]

Remember that:

[tex](a\±b)^2=a^2\±2ab+b^2[/tex]

Then, simplifying:

[tex]f(x -2)=x^2-2(x)(2)+2^2 - 2x+4+ 8\\\\f(x-2)=x^2-6x+16[/tex]

So the function g(x) is:

[tex]g(x)=x^2-6x+16[/tex]

Use the following formula to find the x-coordinate of the vertex of g(x):

[tex]x=\frac{-b}{2a}[/tex]

In this case:

 [tex]a=1\\b=-6[/tex]

Then:

[tex]x=-\frac{-(-6)}{2(1)}=3[/tex]

Substitute this value into the function g(x) in order to find the y-coordinate of the vertex. Since [tex]g(x)=y[/tex], you get:

[tex]y=3^2-6(3)+16=7[/tex]

Therefore, the vertex of g(x) is:

[tex](3,7)[/tex]

Answer:

Second one

Step-by-step explanation:

Step-by-step explanation:

first 3(-x+5) you distribut

then you would get 15-3x+15=21+6x and u combine like terms which is 3x and 6x which is 9 and u get 15-9x+15=21tthen u sabtract 15x on both side and get 15-9=21 then u subtract 15 ok both side and get x = 0.7

Hey!

--------------------------------

Solution:

3x - 6 = -4

3x + (-6) = -4

3x + (-6) + 6 = -4 + 6 (Add 6 to both sides)

3x = 2 (Simplify)

3x/3 = 2/3 (Divide both sides by 3)

x = 2/3 (Simplify)

--------------------------------

Answer:

x = 2/3

--------------------------------

Hope This Helped! Good Luck!

Final answer:

The two consecutive integers whose sum is 373 are 186 and 187. We derived the equations n + (n + 1) = 373 and solved for n to find the first integer.

Explanation:

To find two consecutive integers whose sum is 373, let's denote the first integer as n. The next consecutive integer will be n + 1. When we add these two integers together, their sum should equal 373, which gives us the equation:

n + (n + 1) = 373

Simplifying this equation, we get:

2n + 1 = 373

To solve for n, we subtract 1 from both sides of the equation:

2n = 372

Divide both sides by 2:

n = 186

So the first integer is 186. The next consecutive integer is:

n + 1 = 186 + 1 = 187

Therefore, the two consecutive integers that sum to 373 are 186 and 187.

Answer:

10 years

Step-by-step explanation:

Answer:

max showed less improvement!

Step-by-step explanation:

Max percentage improvement in the first exam = (6/30 × 100) %

= (600/30) %

= 20 %

Maria percentage improvement in the first exam = (30/60 × 100) %

= (3000/60) %

= 50 %

Hence, 20 % < 50 %

Final answer:

Max improved by 6 marks from his previous score, while Maria improved by 30 marks. Therefore, Max showed less improvement than Maria.

Explanation:

Max scored 6 marks higher than his previous score of 30, making his new score 36. Maria scored 30 marks more than her previous score of 60, taking her new score to 90. To determine who showed less improvement, we compare the amount of increase in their scores.

Max's improvement: 30 + 6 = 36

Maria's improvement: 60 + 30 = 90

Max improved by 6 marks, and Maria improved by 30 marks. Therefore, Max showed less improvement.

When comparing improvement, it's useful to look at the actual increase in marks gained, not necessarily the percentage improvement unless specifically asked. Here, the simple comparison of the additional marks scored determines who improved less. Though both students improved their scores, the difference in their points increased is a clear indicator of whose improvement was less significant.

Answer:

A

Step-by-step explanation:

Note that i² = - 1

Given

(7 - 5i)(2 + 3i) ← expand factors using FOIL

= 14 + 21i - 10i - 15i² ← collect like terms

= 14 + 11i + 15

= 29 + 11i → A

Answer:

A

Step-by-step explanation:

In mathematics, a horizontal line has a slope of 0, and its equation is always 'y = b', where 'b' is the y-coordinate of any point on the line. In this situation, since our line passes through the point (3,7), the equation of the horizontal line is 'y = 7'.

In the context of mathematics, a horizontal line is a line whose equation is in the form y = b where 'b' represents the y-intercept, or the y-coordinate of a certain point on the line. In this question, you are asked to find the point-slope form of a horizontal line passing through the point (3,7).

However, for a horizontal line, the point-slope form y = mx + b becomes y = b because m, the slope of a horizontal line, is 0. And the y-coordinate of any point on a horizontal line is the same.

So, since the line is passing through the point (3,7), the y-coordinate 7 is constant throughout the horizontal line. Therefore, the equation of the horizontal line through (3,7) would be y = 7.

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Answer:

Im pretty sure its 13.137

        I hope this helps!

Answer:

[tex]13.13[/tex]

Step-by-step explanation:

We first we need to look at the equation:

381 ÷ 29

So we first have to look at how many times 29 goes into 38, since 29 is already in the tens place.

It only goes in once. Meaning that right now you have one as your tens place.

1

Now you need to subtract 29 by 38

==> 9

So drop down the one from 381 to get 91, then find out how many times 29 goes into 91

==> 3 times

So now 3 is your tens place

13

Now do 91 - 29

==> 62

62 left?!

That means we need to [tex]annex^{1}[/tex]  :

drop down 0 into 62 to get 620:

Find out how many times 29 goes into 620:

==> 13

13.13

annex = drop down 0 after a decimal

Subtracting a number from x shifts the graph that may places tot he right

Subtracting a number at the end of the equation, shifts the graph that many units down.

The answer would be: Shift the graph of y = x^2 right 2 units and then down 10 units.

Answer:

Shift the graph of y = x^2 right 2 units and then down 10 units.

Step-by-step explanation:

The graph of y= x^2 can be transformed to the graph of the given equation: y = (x - 2)2 - 10. This can be done by shifting the graph of y = x^2 right 2 units and then down 10 units.

Step-by-step explanation:

Area of parallelogram = ( base ) ( height )

area of parallelogram = ( 2.9 ft ) ( 5.5 ft )

( as given )

area of parallelogram =15.95 ft²

Answer:

See explanation

Step-by-step explanation:

A dog owner observes that from birth to age 14 weeks, the puppy’s weight can be modelled by the equation

[tex]w = 365\cdot (1.23)^t \ (0\le t \le  14)[/tex]

In this equation,

When w=4,000, then

[tex]4,000=365\cdot (1.23)^t\\ \\(1.23)^t =\dfrac{4,000}{365}=\dfrac{800}{73}\\ \\t=\log_{1.23}\dfrac{800}{73}\approx 11.5651[/tex]

This means that puppy will weight 4,000 grams nearly at the middle between 11th week and 12th week.

Mistake in the Question:

The number 3 is not a fraction.

Answer:

Suppose if it is 3/8 then do the following:

Multiply

3

__ by an equivalent fraction that equals 1.

8

An equivalent fraction is equal to 1 such as 2 or 3

                                                                       __   __

                                                                        2     3

An equivalent fraction is the same as multiplying by 1 so the ratio does not change.

This fraction would be equal to a        where a is an integer.

                                                   __  = 1

                                                    a

Hence an example would be that

2     3        6

__ . __ =  __

2     8       16

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