Each pair of values is from a direct variation. Find the missing value. (3,7),(8, y)

Answer:

12−3x

Step-by-step explanation:

12+3.4x−5.4x−x

Combine 3.4x and −5.4x to get −2x.

12−2x−x

Combine −2x and −x to get −3x.

12−3x

After simplification of given expression. We get, the value of x is 4.

To simplify this 12 + 3.4x - 5.4x - x,

12 + 3.4x - 5.4x - x = 0

3.4x - 5.4x = - 2x

12  - 2x - x

-2x - x = -3x

-3x + 12 = 0

-3x = -12,

x = 4

Therefore, the value of x is 4.

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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:

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.

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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Max rides his scooter toward Kim and then passes her at a constant speed. His distance in feet, d, from Kim t seconds after he started riding his scooter is given by d = |150 – 9t|. Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.

Two expressions with equal sign is called as equation.

Max rides his scooter toward Kim and then passes her at a constant speed. His distance in feet, d, from Kim t seconds after he started riding his scooter is given by d = |150 – 9t|.

Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.

Therefore Then 150 in the equation represents the initial distance between Max and Kim. 150 is how far Max is from Kim before he starts and 9 in the equation represents the rate at which Max is closing in on Kim. 9 feet per second is Max's rate.

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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:

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 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:

11.1111 for 40 km

279.4 for 11 in

Step-by-step explanation:

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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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 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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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 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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We have expression ln 9+ln 2 as a single natural logarithm ln 18

A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x. When adding parentheses for clarity, the values ln(x), loge(x), or log (x). In order to avoid ambiguity, this is notably done when the argument to the logarithm is not a single symbol.

The power to which e would need to be raised in order to equal x is the natural logarithm of x.

For instance, e2.0149... = 7.5, thus ln 7.5 equals 2.0149.

Since e1 = e, the natural logarithm of e itself, or ln e, is equal to 1, while the natural logarithm of 1 is 0, since e0 = 1.

We have been asked to express ln 9+ln 2 as a single natural logarithm.

⇒ ln 9 + ln 2

⇒ ln (9) = ln (2)

Use the quotient property of logarithms

⇒ ln (9 × 2)

⇒ ln 18

Finally, we have expressed ln 9+ln 2 as a single natural logarithm ln 18

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Answer: 51357

901×57=51357

Answer:D

Step-by-step explanation:Hope that helped

Answer:

So There will be 2 congruent angle

We must invest $6294.256 if we want exactly $ 8000 after four years.

The formula for calculating the amount (A) on a principal (P) invested at the rate of r%, compounded continuously, after t years is-

[tex]A = Pe^{rt}[/tex]

Here, we are given that rate of interest = 6% and we need exactly $8000 after four years.

Thus r = 6/100 = 0.06 and t = 4

Putting the values in the compound interest formula we get,

8000 = P[tex]e^{(0.06*4)}[/tex]

8000 = P[tex]e^{(0.24)}[/tex]

P[tex]e^{(0.24)}[/tex] = 8000

[tex]e^{(0.24)}[/tex] = 1.271

⇒  1.271P = 8000P

= 8000/ 1.271P

= 6294.256

Thus, we must invest $6294.256 if we want exactly $ 8000 after four years.

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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:

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

Answer:1.  

Step-by-step explanation: 1.  because ,  and Step-by-step explanation:We have been given two triangles  and . We are asked to find the relationship between these triangles.By angle sum property let us find measure of angle C of triangle ADC.Let us find measure of angle T of triangle RTS.We can see that ,  and . Therefore,  and 1st option is the correct choice.

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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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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The domain of the function is [-2, 2] and the range of the function is [-1, 2].

If there is a function y = x + a, then the domain is the set of all values that x can take and the range is the set of all the values that y can take for the function to exist.

Here, we are given a function as shown in the graph.

As we can see the function is defined only for the given points, that is, it has 2 endpoints.

Just by looking at the graph we can see that x can take values from -2 to 2. Thus, the domain of the function is [-2, 2].

We use closed brackets as x can be -2 and 2 as well. Similarly, we can see that y can take values from -1 to 2.

Thus, the range of the function is [-1, 2].

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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.