Which of the following statements is true about the Pythagorean theorem?

Choose the correct statement below.

The interest the friend will have after her college graduation in 4 years is $240 and an exponential model is not reasonable for this situation.

The formula to be used to is given as :

            I = Prt (1)

where, I = simple interest

          P = principal amount or amount initially deposited.

          r = annual interest rate

         t = time

According to the question we have been given that

         P = $1000

         r = 0.06

       t = 4 years

Putting the required values in equation (1) we get

        I = 1000*0.06*4

        I = 240

Thus $240 interest the friend will have after her college graduation in 4 years.

a) the exponential model is not reasonable for this situation as simple interest is not an exponential function.

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Answer:

-0.0238095238

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

First divide 45 by 9.

After you divide you should have 5.

Next you multiply 5 times 12.

Which gives you 60.

Hope this helps! :)

The function g(x)= x^ square root of 1+x is neither an even function nor an odd function

The function is given as

g(x)= x^ square root of 1+x

Rewrite the above function equation properly

So, we have

g(x) = x^(√x+1)

Calculate g(-x)

So, we have

g(-x) = -x^(√-x+1)

Evaluate

g(-x) = -x^(√-x+1)

Calculate -g(x)

So, we have

-g(x) = -x^(√x+1)

In the above computations;

g(x) does not equal g(-x) and -g(x)

Hence, the function g(x)= x^ square root of 1+x is neither an even function nor an odd function

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Answer:

11.1111 for 40 km

279.4 for 11 in

Step-by-step explanation:

Answer:

2/2, 6/2

Step-by-step explanation:

2/2 can be simplified as 1 and 6/2 can be simplified as 3

The simplified form of number is 2

To find the simplified form of the number, we will find the number whose square is equal to 4. As per the known fact, only 2 is the number whose square is 4.

Firstly rewriting the number -

Number = [tex]4^{1/2}[/tex]

Now, rewriting the number with base as 2 and exponent also as 2, as stated in theory above -

Number = [tex]2^{2(1/2)}[/tex]

Cancelling 2 from the exponent as it is present in both numerator and denominator. Rewriting the number with 2 as base and 1 as exponent to find the simplified form of the number.

Number = 2

Hence, the simplified number is 2

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The answer is square root of 3

The given equation contains square root forms hence we must simplify it before proceeding further

we know that 12= 2^2 *3

Thus applying it in the equation, the equation becomes

5[tex]\sqrt{3}[/tex]-2[tex]\sqrt{12}[/tex]

Thus writing 12 as 2^2X3

5[tex]\sqrt{3}[/tex]-2[tex]\sqrt{2^2*3}[/tex]

Now taking out square root of 2^2 which is 2,

the equation becomes

5[tex]\sqrt{3}[/tex]-4[tex]\sqrt{3}[/tex]

=[tex]\sqrt{3}[/tex]

Thus the answer is square root of 3

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Answer:

So There will be 2 congruent angle

Answer:

Step-by-step explanation:

It is not possible for a triangle to have more than one vertex with internal angle greater than or equal to 90°, or it would no longer be a triangle.

Answer:

$310.59

Step-by-step explanation:

68% of what number is 211.20

.68x = 211.20  Divide both sides by .68

x = 310.5882352968  Round to the nearest cent

x = 310.59

The value of x = 16, y = 172 and z = 2.

x - 4z = 12x - y - 6z = 42x + 3y - 2z = 8

let x - 4z = 8 be equation (1), 12x - y - 6z = 8 be equation (2) and 42x + 3y - 2z = 8 be equation (3)

x - 4z = 8

x = 8 + 4z

12x - y - 6z = 8

12(8 + 4z) -y - 6z =8

96 + 48z - y - 6z = 8

42z - y = -88

y = 42z + 88

42x + 3y - 2z = 8

42(8+4z) + 3(42z + 88) - 2z = 8

336 + 168z + 126z + 264 - 2z = 8

168z + 126z + 2z = 336+264 - 8

296z= 592

z = 2

substituting the value of z

x = 8 + 4z

= 8 + 4(2)

8+8 = 16

y = 42z + 88

42(2) + 88

84 + 88= 172

The value of x = 16, y = 172 and z = 2.

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The fraction of the tank that was full of petrol that he had used is 1/4

From the question, we are to determine the fraction of the tank that was full of petrol that he has used

From the given information,

On Monday, Nassim filled up his tank

and

On Tuesday, his tank was 3/4 full

The fraction of the tank when filled is 1/1, that is, 1

Thus,

The fraction of the tank that he had used = 1 - 3/4

The fraction of the tank that he had used = 1/4

Hence, the fraction of the tank that was full of petrol that he had used is 1/4

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Answer:

33

Step-by-step explanation:

Convert the percentage to a decimal.

55 ÷ 100 = 0.55

Multiply 60 by 0.55

60 × 0.55 = 33

Answer:

33

Step-by-step explanation:

55 x 60 divided by 100

= 33

The result to the equation given by rounding this to the nearest ten-thousandth is 4.0000.

Rounding off means simplifying a number by keeping its overall value but moving it closer to the next number. It is used for whole numbers and decimals with tens, hundreds, thousands, and so on.

If the digit in the smallest spot is less than 5, it is left alone. Rounding down occurs when any number of digits then after the number become zero. If the digit inside the smallest place is larger than or equal to 5, it is multiplied by +1.

the equation 3 x=36

3x = 36

x = 36/3

x = 4.0000

the answer to the equation given is =  4.0000

The result to the equation given by rounding this to the nearest ten-thousandth is 4.0000.

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Answer:

Step-by-step explanation:

Answer:D

Step-by-step explanation:Hope that helped

Using greatest common factor (GCF), Mr. Raymond should put 6 students in each group. If that happens, he will have 3 groups of 6th graders and 4 groups of 7th graders.

The greatest common factor (GCF) of a set of numbers is defined as the largest common positive integer that divides each number into equal parts with zero remainder.

If Mr. Raymond has 18 6th graders students and 24 7th grader students he wants to put in equal groups wherein each group will have students of only one grade level, find the GCF of 18 and 24 to find how many students he will put in each group.

18 : 1, 2, 3, 6, 9, 18

24 : 1, 2, 3, 4, 6, 8, 12, 24

GCF = 6

Hence, he should put 6 students in each group.

Dividing each level of students to groups of 6.

6th graders = 18/6

6th graders = 3 groups

7th graders = 24/6

7th graders = 4 groups

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Answer:

Total length of the pipe = 125 inches

Let the shorter piece be x inches

So, the longer piece is 4x.4x + x = 1255x = 125x = 25

Therefore, the lengths of the two pieces are 25 inches and 100 inches

Step-by-step explanation:

Answer: 51357

901×57=51357

Answer:

18-2x=4x is given

18=6x is addition property of equality

3=x is I think division property of equality bc you divided to get x=3

Answer:

what?

Step-by-step explanation:

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An experimental study is used in the given situation.

Observational Study is defined as the type of study where there is no influence on the response of the participant.

Experimental Study is defined as the type of study where the participant is put into a setup and then the participants are observed .

In the given question ,

As the individual are first categorized into to two groups , one on a healthy, moderate diet and the other group not on any diet.

So, we can see that in this a setup has been created , they are put in different conditions  , and then they are observed .

Therefore ,  an experimental study is used in the given situation.

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Answer:

7. 17

8. -7

9. 64/3 or 21 1/3

Step-by-step explanation:

7. 3x-4 and the value of x is 7. Plug 7 into the x values in the expression that is given.

3x-4  --> 3(7) - 4

When simplified, 3(7) - 4 becomes 21-4 which is 17.

8. -5x+8 and the value of x is 3. Same as before, but this time you'll plug 3 into the x values in the given expression.

-5x+8 --> -5(3) + 8

When simplified,  -5(3) + 8 becomes -15+8 which is -7.

9. 10x+18 and the value of x is 1/3. Plug in 1/3 into the x values in the expression.

10x+18 --> 10(1/3)+18

When simplified, 10(1/3)+18 becomes 10/3+18. To solve this, turn 18 in a fraction over 3. 3x18=54 and that gives you the numerator. 10/3+54/3= 64/3. If you wanted it in a mixed fraction, it would be 21 1/3.

Answer:

2.088 x 10^5

Step-by-step explanation:

7.2 x 10 x 2.9 x 10^3 = 20.88 x 10^4

= 2.088 x 10^5

Tax levied is $4.17 if the price of album is $27.80.

Kathy will get $3.03 after buying the album and paying the tax.

A tax is a mandatory financial charge or other sort of levy that is placed on a taxpayer by a governmental entity in order to pay for public services and other expenses.

The total amount is calculated by adding the tax on the cost of product or service.

The pre-tax price of an item must first be multiplied by the sales tax percentage once it has been translated to a decimal form in order to determine the amount of sales tax that will apply to the purchase. To determine the item's Total Amount, the sales tax must be computed and then added to the pre-tax price.

a) Given data: Tax%=0.15 of cost of album

Selling Price=$27.80.

Tax=Tax%×Selling Price

=0.15×27.80

=$4.17

b) Given data: Amount given by Kathy = $35

Tax=$4.17

Total Amount = Selling Price + Tax

=$4.17+$29.80

=$31.97

Amount left can be calculated by subtracting the amount given by Kathy from the Total Amount.

Amount=$35-$31.97

=$31.97

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The area of the computer chip is 2.44 x 10^-15 square units

The area of a shape is the amount of space on the shape

The dimensions of the computer chip are given as

7.18 x 10^-7 and 3.4 x 10^-9

The area of the computer chip is the product of the dimensions of the computer chip

So, we have

Area = Length x Width

This gives

Area = 7.18 x 10^-7 x 3.4 x 10^-9

Rewrite as

Area = 7.18 x 3.4 x 10^-7 x 10^-9

Evaluate the products

Area = 24.412 x 10^-16

Rewrite as

Area = 2.4412 x 10^-15

Approximate

Area = 2.44 x 10^-15

Hence, the area of the computer chip is 2.44 x 10^-15 square units

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The variable w is as follows:

We have to find the variable w in the equation.

-61 = 8 - 1 / 3(12w + 42) - w

subtract 8 from both sides of the equation

-61 = 8 - 1 / 3(12w + 42) - w

-61 - 8 = 8 - 8 - 1 / 3(12w + 42) - w

-69 = - 1 / 3(12w + 42) - w

69 = 1 / 3(12w + 42) + w

Therefore,

[tex]\frac{1}{3(12w+42)}+w[/tex] = 69

[tex]\frac{1+3w(12w+42)}{3(12w+42)}[/tex] = 69

[tex]\frac{1 + 36w^{2} +126w}{3(12w+42)}[/tex] = 69

cross multiply

1 + 36w² + 126w = 2484w + 8694

36w² + 126w - 2484w - 8694 + 1 = 0

36w² - 2358w - 8693 = 0

using,

[tex]\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex] and [tex]\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]

a = 36

b = -2358

c = -8693

Hence,

[tex]\frac{2358+\sqrt{(-2358)^{2}-4(36)(-8693) } }{2(36)}[/tex]  and [tex]\frac{2358-\sqrt{(-2358)^{2}-4(36)(-8693) } }{2(36)}[/tex]

Therefore,

[tex]w = \frac{393+\sqrt{189221} }{12}[/tex] and [tex]w = \frac{393-\sqrt{189221} }{12}[/tex]

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