John bought a house. He decided to reduce his square backyard by 40 inches along its width. The area of the new backyard is given by the function below, where z represents the length in inches.

A(z)=z^2-40z

Which statement best describes the term 40z?

* The area of the playground after expansion
* The width of the backyard
* The area of the backyard before reduction
* The area reduced from the backyard

The graph of g(x) is the graph of f(x) shifted 8 units to the right.

Option D is correct.

A shift is a rigid translation in that it does not change the shape or size of the graph of the function. All that a shift will do is change the location of the graph. A vertical shift adds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.

According to the question

g(x) = f(x – 8)

If the function is shifted to the left it is going to plus(+).

If the function is shifted to the right it is going to minus(-).

Hence, The graph of g(x) is the graph of f(x) shifted 8 units to the right.

Option D is correct.

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Answer:

8 1/6

Step-by-step explanation:

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The number of quarters in 7 is 28 and the number of quarters in 3/4 is 3. Then the total number of quarters is 33.

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

The quarter is written as one-fourth.

[tex]\rm quarter = \dfrac{1}{4}[/tex]

We have 7 + 3/4

We know that one has 4 quarters then 7 has

→ 7 × 4 = 28

And 3/4 has three quarters.

Then the total quarter will be

[tex]\rm Number\ of \ quarter = 7 \dfrac{3}{4} \times 4 = \dfrac{33}{4} \times 4 = 33[/tex]

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There are 31 quarter inches in 7 3/4 inches. This is determined by converting the mixed number into an improper fraction and then dividing by ¼, which gives us 31/4 or 31 quarter inches.

The question asks how many quarter inches there are in 7 3/4 inches. To find this, we can convert the mixed number into an improper fraction and then divide by the fraction representing a quarter inch (¼ inch).

First, convert 7 ¾ to an improper fraction by multiplying the whole number 7 by the denominator 4 and then adding the numerator 3. This gives us 28 + 3 = 31, so 7 ¾ inches is equivalent to ⅔31/4 or 31 quarter inches. Therefore, 7 3/4 inches is 31 quarter inches long.

Answer:

20cm

Step-by-step explanation:

The two integers are 12 and 18.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, one positive integer is 6 less than twice another.

Let positive integer be x and the other positive integer is 2x-6

x²+(2x-6)²=468

x²+4x²-24x+36=468

5x²-24x+36-468=0

5x²-60x+36x-432=0

5x(x-12)+36(x-12)=0

(x-12)(5x+36)=0

(x-12)=0

x=12

So, 2x-6=18

Therefore, the two integers are 12 and 18.

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Answer:

[tex]y=9000(1.048)^x[/tex]

Step-by-step explanation:

This will be an exponential growth problem.  This is because the amount of burgers is expected to change at the same rate every month.

These equations are of the form

[tex]y=a(1+r)^x[/tex],

where a is the original amount, r is the growth rate and x is the amount of time.

In this problem, the original amount, a, is 9000.

The rate of growth is 4.8%; 4.8% = 4.8/1000 = 0.048

This gives us

[tex]y=9000(1+0.048)^x\\\\y=9000(1.048)^x[/tex]

Answer:

The answer is 9000(1.048)^t  {limit from n = 1 to n = 12}.

Step-by-step explanation:

Answer:

  70.7 ft

Step-by-step explanation:

The triangle formed by home plate, first base, and second base is an isosceles right triangle with hypotenuse 100 ft. Then the side length (base-line distance between bases) is (100 ft)/√2 ≈ 70.7 ft.

___

For an isosceles right triangle with side lengths 1, the hypotenuse can be found from the Pythagorean theorem to be ...

  hypotenuse = √(side² + side²) = √(1²+1²) = √2

Then the diamond distances satisfy the proportion ...

  hypotenuse/side = 100 ft/(base distance) = √2/1

or ...

  base distance = (100 ft)/√2 ≈ 70.71068 ft

 Desiree made 100 cookies this week.  She baked 4 more than three times the total she made last week.  How many cookies did she bake last week.

3x + 4 = 100                                      x = 32 cookies               

Answer:

1) 45%

2) [tex]\frac{16}{5}[/tex]

3) 2.335

   237.5%

4) 0.0001

   [tex]\frac{1}{1000}[/tex]

5) 120%

 [tex]\frac{6}{5}[/tex]

6) 533.3%

    5.333        

Step-by-step explanation:

1) Divide the numerator by the denominator and multiply by 100, then:

[tex]\frac{9}{20}=0.45*100=45\%[/tex]

2) Write 320 has the numerator and 100 has the denominator, then reduce the fraction:

[tex]\frac{320}{100}=\frac{32}{10}=\frac{16}{5}[/tex]

3) As a decimal:

Divide the numerator by the denominator and add it to the integer part:

[tex]2+0.375=2.375[/tex]

As a percent:

Multiply the decimal number obtained above by 100:

[tex]2.375*100=237.5\%[/tex]

4) As a decimal:

Divide it by 100:

[tex]\frac{0.1}{100}=0.0001[/tex]

As a fraction:

As you can see, the decimal point were moved three spaces to the left. Therefore, the integer 1 is divided by 1000. Write 1 as the numerator and 1000 has the denominator:

[tex]\frac{1}{1000}[/tex]

5) As a percent:

Multiply 1.2 by 100, then:

[tex]1.2*100=120\%[/tex]

As a fraction:

To make 1.2 an integer you must multiply by 10, therefore, 12 will be the numerator and 10 the denominator:

[tex]\frac{12}{10}[/tex]

Reduce it:

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

6) As a decimal:

Divide the numerator by the denominator and add it to the integer part:

[tex]5+0.33=5.333[/tex]

Multiply the decimal number obtained above by 100:

[tex]5.33*100=533.3\%[/tex]

Answer:

9/20 as a percent- 45%

320% as a fraction- 16/5

2 3/8 as a decimal- 2.38

2 3/8 as a percent- 237.5%

.1% as a decimal- 0.001

.1% as a fraction- 1/100

1.2 as a percent- 120%

1.2 as a fraction- 6/5

5 1/3 as a percent- 533.3%

5 1/3 as a decimal- 5.33

Final answer:

To find an acute angle using a protractor, choose the angle less than 90°. The acute angle could be 75°.

Explanation:

To determine an acute angle using a protractor, we look for an angle that is less than 90 degrees, as acute angles are those that measure less than 90 degrees.

75° could be the measure of the angle as it falls within the range of acute angles.

Hence, in this case, the angle that could be the measure of the acute angle is 75°.

Answer:

C/ 0.45m + 6

Step-by-step explanation:

i did the quiz

The inequality statement |−2|<|−5| shows that 2 is less than 5.

In mathematics, an inequality compares two expressions or values, indicating their relative size. Symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to) represent inequalities.

The inequality statement |−2|<|−5| compares the magnitude of two numbers, -2 and -5. To find the absolute value of a number, we remove the negative sign. So, |−2| is equal to 2 and |−5| is equal to 5. Therefore, the inequality statement |−2|<|−5| means that 2 is less than 5.

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Solution:

Present Value of car= $ 23,495

Down Payment = $ 500

Total Amount paid monthly for 3 years that is 36 months, if you pay $ 429.95 per month=$ 15478.20

Total amount paid for the car as an agreement which includes Down payment of $ 500 as well as monthly Payment of $ 429.95 for 36 months= $ 15478.20+$ 500=$ 15978.20

As, given Interest is  30% of the payment.

So, total interest = 30% of $ 15978

[tex]=\frac{30}{100}\times 15978.20[/tex]

= $ 4793.40

But if you will calculate interest on payment of $ 429.95 at the rate of 30%, it gives

[tex]=\frac{30}{100}\times 429.95[/tex]

= $128.985

So, total interest for 3 years= $128.985 ×36=$ 4643.46

Also, if you will calculate interest on payment of ($500+$429.95=$929.95) at the rate of 30%

[tex]=\frac{30}{100}\times 929.95[/tex]

=$278.985

Total interest for 3 years= $278.985 ×36=$10,043.46