2
3(9x - 6) = 4x + 10
What is the value of X In the equation

Answer:

a₁₅ = 240

Step-by-step explanation:

to find the 15 th term substitute n = 15 into the general term

a₁₅ = 15(15 + 1) = 15(16) = 15 × 16 = 240

Using linear function concepts, it is found that:

i) The equation of BC is given by: [tex]y = -\frac{2}{3}x + \frac{20}{3}[/tex].

ii) The coordinates of C are C(0,10) and the coordinate of D are D(14,6).

The diagram is missing, and is shown in the graph at the end of the answer.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the coordinates are given as follows:

A(2, 14), B(-2,8) and C(x,0).

From the diagram, AB and BC are perpendicular, meaning that the multiplication of their slopes is of -1.

Given two points, the slope is given by change in y divided by change in x. Hence the slope of AB is given as follows:

mAB = (8 - 14)/(-2 - 2) = 3/2.

The slope of BC is given as follows:

mBC = (0 - 8)/(x - (-2))

mBC = -8/(x + 2).

The multiplication of the slopes is of -1, hence:

mAB x mBC = -1

-12/(x + 2) = -1

- x - 2 = -12

x = 10.

Hence, the slope of BC is:

mBC = -8/(x + 2) = -8/12 = -2/3.

Then:

y = -2/3x + b.

When x = 10, y = 0, hence we can find b as follows:

0 = -2/3(10) + b

b = 20/3.

Hence:

The equation of BC is given by: [tex]y = -\frac{2}{3}x + \frac{20}{3}[/tex].

From the diagram, we also have that AB and CD are parallel, meaning that they have the same slope, hence, considering D(x,y), we have that:

mCD = mAB

y/(x - 10) = 3/2

y = 1.5(x - 10)

y = 1.5x - 15.

AD and BC are also parallel, hence:

mAD = mBC

(y - 14)/(x - 2) = -2/3

Since y = 1.5x - 15, we have that:

(1.5x - 15 - 14)/(x - 2) = -2/3

(1.5x - 29)/(x - 2) = -2/3

3(1.5x - 29) = -2(x - 2)

4.5x - 87 = -2x + 4.

6.5x = 91

x = 91/6.5

x = 14.

y = 1.5x - 15 = 1.5(14) - 15 = 21 - 15 = 6.

Hence:

The coordinates of C are C(0,10) and the coordinate of D are D(14,6).

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Answer: 3.5 cups

To solve, we'll need to multiply because we know the SIZE of the groups and the amount of groups but we don't know the total amount.

The unit rate in minutes per meter is 25/2

We are given the time taken to fill an empty aquarium = 15/2 minutes

Also, the depth of aquarium = 3/5 meters

To find the unit rate in minutes per meter, we will simply keep the values in formula. We do not need to change the units, as they are already in required ones, which are minutes and meters.

Unit rate = minutes ÷ meter

Unit rate = 15/2 ÷ 3/5

Rewriting the fraction

Unit rate = 15×5 ÷ 3×2

Performing multiplication in both numerator and denominator

Unit rate = 75 ÷ 6

Performing division of both numerator and denominator by 3

Unit rate = 25/2

So, the unit rate in minutes per meter is 25/2.

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Answer:

The value is not a solution of the inequality.

Step-by-step explanation:

5 - x < 8

1. Substitute the variable, x, with -3: 5 - - 3 < 8

2. Use the KCC (keep,change,change) method to turn subtraction into addition: 5 + + 3 < 8

3. Add the numbers on left side of the inequality to get the answer: 8 < 8 - False statement - 8 is not less than 8.

Answer:

75 * (625 percent) = 468.75

Step-by-step explanation:

If earth is approximately 5×[tex]10^{9}[/tex] years old, the the approximate age of earth is option C 4,953,000,000 years

Given,

The age of Earth =  5×[tex]10^{9}[/tex] years old

We know,

5×[tex]10^{9}[/tex]= 5000000000 years old

From the given option the closest number to 5×[tex]10^{9}[/tex] is 4,953,000,000 years old

Hence, if earth is approximately 5×[tex]10^{9}[/tex] years old, the the approximate age of earth is option C 4,953,000,000 years

Complete question is:

Earth is approximately 5x109 years old. For which of these ages could this be an approximation? Select all that apply.

A. 4.37 x 100 years

B. 4.679999999 x 10º years

C. 4,953,000,000 years

D. 4,625,800,000 years

E. 50,000,000,000 years​

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Answer:

your question is did you mean why 2n is 2n 2 serve that this queston with not involved

The numbers are 20 and 36.

As per the information in question, let the smaller number x. So, according to question, large number will be (x + 16).

Now, writing the equation that will form -

x + x + 16 = 56

Performing addition of variables on Left Hand Side

2x + 16 = 56

Shifting the number from Left Hand Side to Right Hand Side

2x = 56 - 16

Performing subtraction on Right Hand Side

2x = 40

Shifting 2 to denominator on Right Hand Side

x = 40÷2

Performing division to find the value of x

x = 20

So, smaller number is 20.

Larger number = x + 16

Larger number = 20 + 16

Larger number = 36

Hence, the numbers are 20 and 36.

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Answer:21/2

Step-by-step explanation:

Answer:

-7/6

Step-by-step explanation:

If the temperature changes by -7/18 degrees, that shows us that it will continue to decrease, so we can assume the answer will be negative, which means we can get rid of the answers 21/6 and 7/6. If you add and multiply -7 by 3, you'll get -21, which would be -21/18. Then you would simply the answer, giving you -7/6.

Hope this helps!!! :)

Answer: π=v/(hr^2)

Step-by-step explanation:

v=pi r^2 h solve for pi

v=πhr^2 solve for π

v/h=πhr^2/h

v/h=πr^2

1/r^2 * v/h = πr^2 * 1/r^2

v*1/(h*r^2) = πr^2/r^2

π=v/(hr^2)

When p = 0.125 the equation -3p + ( 1/8 ) = ( - 1/4 ) is true.

The given equation is:

-3p + ( 1/8 ) = ( - 1/4 )

On the left-hand side of the equation, the denominator of the two terms is not the same.

So, the LCM of 1 and 8 is 8.

Therefore,

- 3p × ( 8 / 8 ) + ( 1 / 8 ) × ( 1 / 1 ) = ( - 1 /4 )

- 24p / 8 + 1 / 8 = - 1 / 4

( - 24p + 1 ) / 8 = - 1 / 4

Now multiplying each side of the equation by 8.

We get,

[ ( - 24p + 1 ) / 8 ] × 8 = ( - 1 / 4 ) × 8

- 24p + 1 = - 8 / 4

- 24p + 1 = - 2

Subtracting 1 from each side of the equation,

- 24p + 1 - 1 = - 2 - 1

-24p = - 3

Now, divide each side of the equation by 24.

- 24p / 24 = - 3 / 24

- p = ( - 1 / 8 )

Multiplying by - 1 on each side of the equation,

( - p ) × ( - 1 ) = ( - 1 / 8 ) × ( - 1 )

p = 1 / 8

p = 0.125

The value of p = 0.125 will make the equation true.

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By using horizontal and vertical translations, we find that the expression for g(x) is g(x) = [tex]\sqrt[5]{x - 2}[/tex] + 1. (Correct choice: C)

The picture presents us the graphs of two functions. The blue function represents the parent function f(x), whose form is [tex]f(x) = \sqrt[5]{x}[/tex], whereas the black function is the transformed function g(x), which is the result of applying two transformations:

Then, we must apply the following definition involving the concepts of horizontal and vertical translations:

g(x) = f(x - 2) + 1     (1)

If we know that [tex]f(x) = \sqrt[5]{x}[/tex], then the complete expression of the function is:

g(x) = [tex]\sqrt[5]{x-2}[/tex] + 1

Hence, by using horizontal and vertical translations, we find that the resulting expression for g(x) is g(x) = [tex]\sqrt[5]{x - 2}[/tex] + 1. (Correct choice: C)

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Answer:

Step-by-step explanation:

I hope this answer help you

Answer:

h = 16.0 cm

Step-by-step explanation:

Note: I am assuming that the surface area of 258 is the total surface area which includes the Lateral Area (L) and Base Area(B)

Total Surface Area of a right cone

= Lateral Area(L) + Base Area(B)

All numbers in intermediate calculations are rounded to tenth of centimeter i.e. 1 decimal point

Base Area is the area of the circle with radius 4 = [tex]\displaystyle \pi \cdot16 = 50.3[/tex] cm²
Total Area = 258 cm²

So Lateral Area = 258 - 50.3 = 207.7 cm²

Lateral Area is given by the formula
[tex]\displaystyle L = \pi r s \textrm{ where s is the slant height }[/tex]

So we get

[tex]\displaystyle \rm pi \cdot 4 \cdot s = 207.7\\\\\textrm {This gives } s = \dfrac{207.7}{4\pi} = 16.5\\\\[/tex] cm

Slant height is given by the formula:
[tex]s = \sqrt{r^2 + h^2} \textrm{ where r is the radius and h the height}[/tex]
Plugging in values we get
[tex]16.5 = \sqrt{4^2 + h^2} = \sqrt{16 + h^2}[/tex]

Square both sides
[tex]16.5^2 = 16 + h^2[/tex]

==> [tex]h^2 = 16.5^2 - 16 = 256.25\\\\h = \sqrt{256.25} = 16.003 = 16.0[/tex]  rounded to 1 decimal place

So final answers is h = 16 cm

Answer:

-1/6

Step-by-step explanation:

Step-by-step explanation:

the ratio is 4:8:5 for Richard, Allan and Fliss.

the sequence is important.

the money pool between them has 4+8+5 = 17 equal units.

Richard has 4 units of these 17, Allan has 8 units, and Fliss has the remaining 5 units.

we don't know the value of such a unit yet.

this we get from the second hint :

Allan gets £9 more than Fliss.

remember, Allan has 8 units, Fliss 5.

so, Allan has 3 units more than Fliss.

that means these 3 units are worth £9.

and that means each unit is worth 9/3 = £3.

Richard has 4 units, that means he has

4×3 = £12

The daily recommended grams of fat  by the nutritional label is 98 grams.

The nutritional label on a food stated that one serving contained 3 grams of fat which is 3.06% of the daily recommended level.

let

the recommended level = x

Therefore, the product of the percentage and the required daily  recommendation level is equals to the 3 grams.

grams of fat = 3.06% × x

3 =  3.06% × x

3 = 3.06 / 100 × x

3 = 3.06x / 100

cross multiply

3 = 3.06x / 100

300 = 3.06x

300 = 3.06x

divide both sides by 3.06

300 / 3.06 = 3.06x / 3.06

x = 98.0392156863

x = 98 grams

Therefore, the daily recommended grams of fat  by the nutritional label is 98 grams.

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Answer: 1

Step-by-step explanation:

In order to find GCF, take the prime factorization of 3 and 13.

3: 1*3 ==> Prime factorization of 3

13: 1*13 ==> Prime factorization of 3

The common factor is 1.

GCF of 13 and 3 is 1

Answer:

Slope = - 3

Step-by-step explanation:

The function of the line:

y = - 3x + 7

=> Slope = - 3

Answer:

[tex]-\frac{38}{3}[/tex]

Step-by-step explanation:

[tex]-12-\frac{2}{3}\\-12 = \frac{-36}{3} = \left(-36\right) \div 3\\\frac{-36}{3}-\frac{2}{3}\\=\frac{-36-2}{3}\\=\frac{-38}{3}[/tex]

Hope this helps!

The correct option is Quantity a: the number of prime numbers between 0 and 100, inclusive is greater.

A prime number is a natural number greater than 1 that is not the sum of two lesser natural numbers (or a prime). Any natural number greater than one that is not prime is referred to as a composite number. For instance, the product 1 5 and 5 1 are the only two ways to write the number 5, making it a prime. The fact that it is the sum of two smaller integers (2 x 2), 4, however, makes it composite. Primes play a significant role in number theory because of the fundamental theorem of arithmetic, it states that any natural number greater than one is either a prime number itself or may be factored as a unique prime product up to the order of the primes. the prime number (or a prime).

The number of primes reduces almost exponentially as we move up the number line. The prime numbers between 0 and 100 are therefore far more numerous than those between 101 and 200. It is crucial to understand this general number theory point, but it may also be rapidly illustrated by attempting to find some primes in these two groups.

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The value of expression is -61

In the given question is that:

Evaluate the expression when n = 2

and, Equation is = 14n - 61 + 1- 31

Now, According to the question :

Put the value of n= 2 in above equation:

then, 14 x 2 - 61 +1 - 31

= -61

Hence, The value of expression is -61

Composition of Functions:

The composition of function is the process of creating another function by applying a function as an input to another function.

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Answer:

Step-by-step explanation:

The number of new setups the internet service company perform in the neighborhood is 22 setups.

The correct answer is option B

Number of new setups the internet service company perform = Total amount the internet service company earned ÷ Amount the internet service company charge per new setup

= $770 / $35

= 22 setups

Therefore, the number of new setups the internet service company perform in the neighborhood is 22 setups.

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The average number of viewers over the two weeks is  4. 85  x 10^5. Option D

Average is simply a number taken as the representative of a list of numbers.

It is determined by taking the sum of the numbers divided by the number of listed numbers.

Given the number of viewers as;

5.6 x 105 viewers  and 4.1 x 105 viewers

Average = 5. 6 x 10^5 + 4.1 x 10^5 / 2

Average = 9. 7  x 10^5 / 2

Average = 4. 85  x 10^5

The average number of viewers over the two weeks is  4. 85  x 10^5

Thus, the average number of viewers over the two weeks is  4. 85  x 10^5. Option D

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The expression as a number in scientific notation is 4.2 * 10^5

The expression is given as:

quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared

Rewrite properly as:

[7 * 10^3 * 5.4 * 10^4]/[9 * 10^2]

Evaluate the product of 7 and 5.4

So, we have:

[37.8* 10^3 * 10^4]/[9 * 10^2]

Evaluate the product of 10^3 and 10^4

So, we have:

[37.8* 10^7]/[9 * 10^2]

Evaluate the quotient of 37.8 and 9

So, we have:

[4.2 * 10^7]/[10^2]

Evaluate the quotient of 10^7 and 10^2

So, we have:

4.2 * 10^5

Hence, the expression as a number in scientific notation is 4.2 * 10^5

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The retail price of the CD rack is $45.

From the information, the storage rack it's sold to stores at a wholesale price of $18 and the store has a 150% markup.

The retail price will be:

= $18 + (150% ×$18)

= $18 + $27

= $45

Therefore, the retail price of the CD rack is $45.

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