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If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1,  then the x=8 and AC=15 units.

Given,

That A is between B and C.

AB= x+2

BC= 4x-7

AC= 2x-1

Then,

BC = AB+AC

4x-7= x+2+2x-1

4x-7= 3x+1

4x-3x=1+7

x=8

Then the length of the line AC is

AC= 2x-1

AC= 2×8-1 =15 units

Hence, If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1,  then the x= 8 and AC= 15 units

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Answer:

-1/4 ,-(-1/-4) and 1/-4 are the answers please

when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).

Take the power set. It has 2^(2n+1) members.

Replace any member which has n+1 or more elements with its complements.

Now the power set has members, which have n or fewer elements, and each such member appears twice.

Therefore, when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).

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The cost of 15 carnival tickets is 37.5 dollars.

The equation y = 2.50x determines the total cost, y, of buying x carnival tickets.

where

Therefore, according to the equation, the cost of 15 carnival ticket can be calculated as follows:

y = 2.50x

where

x = 15

Hence,

y = 2.50 × 15

y = 37.5 dollars

Therefore, the cost of 15 carnival tickets is 37.5 dollars.

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Answer:3 5/7

Step-by-step explanation:

Answer:   A ----------------3 5/7

Answer:-4

Step-by-step explanation:

The solution of the of the expression is as follows:

Three less than the quotient of a number and two has a result of thirteen.

Therefore,

let

the number = x

The quotient of the number and two  = x / 2

Therefore,

x  / 2 - 3 = 13

add 3 to both sides

x  / 2 - 3 = 13

x  / 2 - 3 + 3 = 13 + 3

x / 2 = 16

cross multiply

x = 2 × 16

x = 32

Therefore, the solution of the of the expression is as follows:

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Answer:

k = 2.25 or  9/4

Step-by-step explanation:

2x^2 - 6x + k = 0

2(x^2 - 3x + 2.25) = 0

x                 -1.5

x                 -1.5

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

(x - 1.5) (x - 1.5) = 0

x = 1.5 or 15/10 = 3/2

one solution

[tex] \frac{f(x)}{g(x)} = \frac{x + 5}{ \sqrt{3x + 1} } [/tex]

[tex]x ∈ \: \: ] \frac{ - 1}{3} ,∞[[/tex]

[tex]f(x) - g(x) = x + 5 - \sqrt{3x + 1} [/tex]

[tex]x ∈ \: \: [ \frac{ - 1}{3} ,∞[[/tex]

The 8th term of the geometric sequence is 13122x^22

The explicit form of a geometric sequence is expressed according to the equation;

Tn = ar^n-1

where

r is the common ratio

a is the first term

n is the number of terms

Given the sequence below;

6x,18x^4,54x^7

r = 18x^4/6x

r = 3x^3

a = 6x

n = 8

Substitute to have:

T8 = 6x(3x^3)^8-1

T8 = 6x (3x^3)^7

T8 = 13122x^22

Hence the 8th term of the geometric sequence is 13122x^22

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Answer:

128°

Step-by-step explanation:

The three INTERIOR angles of the triangle are 90  38 and 52°  ( they sum to 180 °)    

   52 °  and 'x'  form a straight line = 180 °    so x = 128°

Answer:

128

Step-by-step explanation:

Add the two farthest angles, 90 and 38, so that's 128

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The data is qualitative one.

Qualitative Data:

Qualitative data consists of Labels, Attributes, Descriptions

This type of data is observed not measured

Examples: Colors, categories, appearances, dogs, etc.

Basically it considers the qualities of the data.

Quantitative Data:

Quantitative data Consists of numbers or counts in the data.

This type is mainly focused on the measurement. Which means it only consider the quantities.

Examples: Length, height, area, speeds, dollar amounts, ages, etc.

Given,

The colors of automobiles on a used car lot.

Here we need to determine the given data is qualitative or quantitative.

Based on the definition of the qualitative or quantitative,

We conclude that the given data is qualitative.

Because it describe the quality of the car.

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Answer:

Let's call the number of Twix bars "x".

Since there are three times as many Twix bars as Milky Ways, the number of Milky Ways is x / 3.

And, since there are 5 fewer Snickers bars than there are Twix bars, the number of Snickers bars is x - 5.

So, the total number of candy bars can be found by adding the number of each type of candy bar:

x + x / 3 + x - 5 = total number of candy bars

Combining like terms, we get:

5x / 3 - 5 = total number of candy bars

To find the value of x, we can solve this equation for x.

5x / 3 = total number of candy bars + 5

5x / 3 = total number of candy bars + 5

5x = 3(total number of candy bars + 5)

5x = 3(total number of candy bars) + 15

5x = 3(total number of candy bars) + 15

5x - 15 = 3(total number of candy bars)

5x - 15 = 3(total number of candy bars)

(5x - 15) / 3 = total number of candy bars

So, the total number of candy bars can be found by dividing (5x - 15) by 3. The value of x represents the number of Twix bars, and the rest of the candy bars can be found using the relationships described in the problem.

The required answer would be 3.7×10¹⁰ which is written in the form of scientific notation.

Scientific Notation is a way of writing down in the easy form of very large or very small numbers.

We have been given that expression as:

⇒ (7×10⁹)(5.3×10²)

⇒ 7×5.3 ×10⁹×10²

We have to add exponents of tens and apply the multiplication operation between 7 and 5.3,

⇒ 37 ×10⁹⁺²

⇒ 3.7×10⁻¹ ×10¹¹

⇒ 3.7×10¹⁰

Hence, the required answer is 3.7×10¹⁰ which is expressed in scientific notation.

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Given the midpoint, the value of PT will be 10 2/7.

Q is the midpoint of PT,

so PQ = QT.

R is the midpoint of QT,

so QR=RT.

S is the midpoint off RT,

so RS=ST.

Let us say RS = ST = x .

Then, RT= RS + ST= x + x = 2x ,

so RT = QR = 2x

Then, QT = QR+RT = 2x+2x = 4x ,

and PQ = QT = 4x .

Then, PS= PQ+QR+RS=4x+2x+x=7x ,

and PT=PQ+QT=4x+4x=8x

The problem says that PS = 9

Therefore, 7x = 9 and x = 9/

PT = 8x = 8 × 9/7 = 10 2/7.

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P, Q, R, S, and T are on line k such that Q is the midpoint of segment PT, R is the midpoint of segment QT, and S is the midpoint of segment RT. If segment PS = 9, then what is PT?

Answer:

160

Step-by-step explanation:

180 (a straight angle's degrees) /9 = 20

20 * 8 = 160

Check:

160 + 20 = 180

The populations of both towns would be​ equal in nine months.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let's assume that both town's populations will be equal in x months.

After x months, the population of the first town is given by

200x - 75x + 57,900  

The population of the second town after x months is  given by

60,600 - 175x

In order for the population of both towns to be equal, we have

200x - 75x + 57,900 = 60,600 - 175x

This is the required equation that represents the given situation.

200x - 75x + 57,900 = 60,600 - 175x

Rearrange the likewise terms and apply arithmetic operation

200x - 75x + 175x = 60,600 - 57,900

300x = 2700

x = 2700/300

x = 9

Therefore, the populations of both towns would be​ equal in nine months.

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The 65-th percentile is  approximately 83.8 ounces.

A number at or below which a particular percentage falls in its frequency distribution, or a score below which a given percentage falls, is known as the k-th percentile in statistics. The 50th percentile, for instance, is the score at or below which 50% of the distribution's scores can be found.

The percentile can be calculated by using the formula

Percentile Value = μ + zσ  where

z is the z-score , μ is the mean and σ is the standard deviation.

Here the percentile that is to be calculated is 65.

So we take the value that is closest to 0.65 from the z-table.

We get the value of the data to be 0.39

Now putting the values in the equation we get:

Percentile Value = μ + zσ  

or, Percentile Value = 83 + (0.39 × 2)

or, Percentile Value = 83.78

or, Percentile Value ≈ 83.8

Hence the 65th percentile value of the function is given by 83.8  .

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The linear equation for the remaining Federal Helium Reserves, r(t) = 20 -1.9t

There is 20 billion cubic feet of Helium in 2010. Helium is depleted by about 1.9 billion cubic feet each year.

Let 'r' denotes the remaining Federal Helium Reserves in billions of cubic feet.

Let 't' denotes the number of years since 2010.

We have to find a linear equation to represent the depletion of Helium through years since 2010. A linear equation will have two variables, one dependent and one independent variable. Here, let 'r' be the dependent variable and 't' be the independent variable.

Then the amount of Helium depleted in 't' years = 1.9t

So, the remaining Helium in the Federal Helium Reserve since 2010 = 20 - 1.9t.

Thus, r(t) = 20 - 1.9t

This is a linear equation because it depends on only one variable, 't'.

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Considering the definition of an equation and the way to solve it, the number of points Carlos scored in the last game is 19.

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being:

and knowing that in the last game, Fabio had 7 points less than 2 times as many points as Carlos, the equation to determine the number of points Carlos scored in the last game is:

2C - 7= F

Fabio scored 31 points in the game. So you get:

2C - 7= 31

Solving:

2C= 31 + 7

2C= 38

C= 38 ÷ 2

C=19

Finally, the number of points Carlos scored in the last game is 19.

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The remainder when polynomial function is divide by linear function is 773.

Given that the polynomial functon f(x)=3x⁴+5 and the linear function is x+4.

As it is given that we have to find the remainder the polynomial

f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4.

f(x)=3x⁴+5    .......(1)

g(x)=x+4       .......(2)

We know the remainder theorem that when a polynomial f(x) is divided by a linear expression (x−a), the remainder will be f(a).

From equation (2), we have a linear expression.

Now, on simplifying equation (2) to obtain the zero of g(x), we get

g(x)=x+4=0

x+4=0

Now, on comparing (x+4) and (x−a), we get

a=-4      ......(3)

Here, we have to get the value of f(a).

Now, using the remainder theorem, we can say that to get the remainder when the polynomial f(x)=3x⁴+5 is divided by g(x)=x+4, we have to replace x by -4 in the polynomial f(x)=3x⁴+5, we get

f(-4)=3(-4)⁴+5

f(-4)=3(256)+5

f(-4)=768+5

f(-4)=773

Therefore, the remainder when the polynomial f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4 is 773.

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Average of 5 courses is 72

• In simple words, average is the number which is the representative of the list of the numbers.

• Average of numbers is calculated by the sum of the numbers divided by total numbers.

We are given that

Number of courses took by Adrianna = 4

Average of her course grade = 90

Number of course took by Roberto = 5

We also know that , Both students have the same sum of course grades

Let the average of Roberto be x

Average = Sum / Total Subjects

Sum = Average * Total Subjects

So,

90 * 4 = x * 5

x = 360/5

x = 72

Therefore, average of Roberto is 72

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Answer: 4r-8+4y

Step-by-step explanation: Distribution is when you multiply every term inside the parantheses by the outside term. So 4(r-2+y)=4(r)+4(-2)+4(y). This is the same as 4r-8+4y. Since none of these are like terms we have the fewest symbols possible.

Answer:

0.4761

Step-by-step explanation:

It is in the 10ths place making it bigger than 0.04761 and 0.04671

Then in the hundreths place for 0.4761  7 is bigger than the 6 in in the hundreths place of 0.4671, so the answer is

0.4761

Answer:

x= -9/5

Step-by-step explanation:

I hope this helps!

Answer:

number 2. A
number 3. C

number 4. B

Step-by-step explanation:

if the answer's are correct then comment or like

The equation which can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased is 1.8x+2.5y=19.4 and if Stephen purchased 8 pounds of peaches then he also purchased 2 pounds of crumbles.

Given that the cost of peaches is $1.80 per pound and cost of crumbles is $2.50 per pound and the total expenditure done by Stephen is $19.40.

We are required to find the equation that can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased and find the number of crumbles that Stephen purchased if he had 8 pounds of peaches.

Suppose the number of pounds of peaches be x and the number of crumbles be y.

The equation will be as under:

x*1.80+y*2.50=19.40

1.80x+2.50y=19.40---------1

Put the value of x=8 to find the number of crumbles.

1.8 *8+2.50y=19.40

14.4+2.50y=19.40

2.50y=19.4-14.4

2.50y=5

y=5/2.5

y=50/25

y=2

Hence the equation which can be used to determine the number of pounds of peaches and crumbles that Stephen could have purchased is 1.8x+2.5y=19.4 and if Stephen purchased 8 pounds of peaches then he also purchased 2 pounds of crumbles.

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The sum of the first twenty terms of the given AP is 1380.

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