PLEASE HELP I WILL GIVE OUT BRAINLIST!!!!!

PLEASE HELP I WILL GIVE OUT BRAINLIST!!!!!

Answers

Answer 1

We list the operations done between two functions below:

g(x) / h(x) = (4 · x² + 2 · x - 1) / (2 · x - 3) h(x) - g(x) = - 4 · x² - 2 h(f (x)) = 6 · x² + 1 f(x) + g(x) = 7 · x² + 2 · x + 1 h(f(2)) = 25 f(h(3)) = 29 g(2) + h(2) = 2 2 · f(0) - g(2) = - 15

How to make operations between two functions

In this problem we find three functions, two of them defined by quadratic equations (f(x), g(x)) and the other defined by a linear equation (h(x)). There are five operations that can be used b two functions:

Addition: (f + g) (x) = f(x) + g(x)Subtraction: (f - g) (x) = f(x) - g(x)Multiplication: (f · g) (x) = f(x) · g(x)Division: (f / g) (x) = f(x) / g(x)Composition: (f ° g) (x) = f (g (x))

Now we proceed to determine the result of each operation:

Case 1:

g(x) / h(x) = (4 · x² + 2 · x - 1) / (2 · x - 3)

Case 2:

h(x) - g(x) = (2 · x - 3) - (4 · x² + 2 · x - 1)

h(x) - g(x) = - 4 · x² - 2

Case 3:

h(f (x)) = 2 · (3 · x² + 2) - 3

h(f (x)) = 6 · x² + 1

Case 4:

f(x) + g(x) = (3 · x² + 2) + (4 · x² + 2 · x - 1)

f(x) + g(x) = 7 · x² + 2 · x + 1

Case 5:

h(f(x)) = 6 · x² + 1

h(f(2)) = 6 · 2² + 1

h(f(2)) = 25

Case 6:

f(h(x)) = 3 · (2 · x - 3)² + 2

f(h(x)) = 3 · (4 · x² - 12 · x + 9) + 2

f(h(x)) = 12 · x² - 36 · x + 29

f(h(3)) = 12 · 3² - 36 · 3 + 29

f(h(3)) = 29

Case 7:

g(x) + h(x) = (4 · x² - 12 · x + 9) + (2 · x - 3)

g(x) + h(x) = 4 · x² - 10 · x + 6

g(2) + h(2) = 4 · 2² - 10 · 2 + 6

g(2) + h(2) = 2

Case 8:

2 · f(x) - g(x) = 2 · (3 · x² + 2) - (4 · x² + 2 · x - 1)

2 · f(0) - g(2) = 2 · (3 · 0² + 2) - (4 · 2² + 2 · 2 - 1)

2 · f(0) - g(2) = 4 - 19

2 · f(0) - g(2) = - 15

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Related Questions

Simplify 5(2x-3)-2(3x-8)

Answers

Answer: 4x+1

Step-by-step explanation:

1.  5(2x-3)-2(3x-8)

2. 10x-15-2(3x-8)

3. 10x-15-6x+16

4. 10x+1-6x

5. 4x+1

Answer:

4x+1

Step-by-step explanation:

First you have to expand it like 10x-15-2(3x-8) Basically multiplying 5 with 2x and -3.

Then take -2 multiply with 3x and -8  which will make it  10x-15-6x+16

Now Put together the like terms 10x-6x -15+16

Which makes it 4x+1

Hope it helped! I am a student too.

Brainly wont be there to help you in life its better to study.

Stefan sells Jin a bicycle for ​$147 and a helmet for ​$18. The total cost for Jin is 150​% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend​ originally?

Answers

Originally, Stefan how much spent in the bicycle and helmet is $247.5

How to find the amount Stefan spent

information from the problem

Stefan sells Jin a bicycle for ​$147 and a helmet for ​$18

The total cost for Jin is 150​% of what Stefan spent originally to buy the bike and helmet

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

150%

= 150 / 100

= 1.5

Total amount Jin spent

= 147 + 18

= 165

Original amount spent by Stefan

The factor 1.5 of what Jin spent is calculated

= 1.5 * 165

= 247.5

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Find the equation of the straight line passing through each of the following pairs of points.
(-2 , 6) and ( 10, 0)

Answers

The equation of the straight line passing through two points (-2,-6) and (10,0) is y = x/2-11/2.

According to the question,

We have the following information:

We have two points: (-2,-6) and (10,0)

Now, first we will find slope of this equation:

(Slope is denoted by m.)

m = (y2-y1)/(x2-x1)

In this case, we have x1 = -2, y1 = -6, x2 = 10 and y2 = 0.

m = {0-(-6)}/{10-(-2)}

m = (0+6)/(10+2)

m = 6/12

m = 1/2

Now, the following formula will be used to find the equation of the straight line:

(y-y1) = m(x-x1)

y-(-6) = 1/2{x-(-1)}

y+6 = 1/2(x+1)

y+6 = x/2+1/2

y = x/2+1/2-6

y = x/2-11/2

Hence, the equation of the straight line passing through two points (-2,-6) and (10,0) is y = x/2-11/2.

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For a concert event there are 30 reserved seat tickets and 20 general admission tickets. There are 1,900 reserved seats available, and fire regulations limit the number of paid ticket holders to 2,800. The promoter must take in at least 63,000 in ticket sales?

Answers

The system of inequalities is as follows:

30x + 20y ≥ 63,000

x ≤ 1900

x + y ≤ 2800

What is inequality?

A relationship between two expressions or values that are not equal to each other is called 'inequality'.

Given that, for a concert event, there are 30 reserved seat tickets and 20 general admission tickets. There are 1,900 reserved seats available, and fire regulations limit the number of paid ticket holders to 2,800.

The system of inequalities can be explained as follows:

30x + 20y ≥ 63,000 → Indicating a take in of at least $63,000 in ticket sales.

x ≤ 1900  → Indicating that 500 reserved seats are available.

x + y ≤ 2800 → Indicating limits of the paid ticket holders to 2800.

x ≥ 0  → Indicating ticket x must be equal or greater than 0.

y ≥ 0  → Indicating ticket y must be equal or greater than 0.

Hence, The system of inequalities is as follows:

30x + 20y ≥ 63,000

x ≤ 1900

x + y ≤ 2800

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An electronics store is having an 18% off sale on everything in the store. To the nearest cent,
which of the following could represent regular prices and sale prices of items in the store during
the sale. Select all that apply.
A regular price: $29.99, sale price: $24.59
B regular price: $55.43, sale price: $45.45
regular price: $215.33, sale price: $172.26
D regular price: $652.30, sale price: $534.89
E regular price: $849.50, sale price: $679.60

Answers

The equations represents regular prices and sale prices of items in the store during the sale are

A) regular price: $29.99, sale price: $24.59

B) regular price: $55.43, sale price: $45.45

D) regular price: $652.30, sale price: $534.89

E) regular price: $849.50, sale price: $679.60

What means percent off?

A product's price is decreased by the percentage indicated by a product's percentage off.

We have,

A regular price: $29.99, sale price: $24.59

B regular price: $55.43, sale price: $45.45

C regular price: $215.33, sale price: $172.26

D regular price: $652.30, sale price: $534.89

E regular price: $849.50, sale price: $679.60

Hence, by calculating discount & subtracting it from original prince we get sale price.

Discount = Original Price x Discount %/100

Final Price = Original Price - Discount

A)

Discount = 29.99 × 18/100

Discount = 29.99 x 0.18 = $5.40

Final Price = 29.99 - 5.3982 = $24.59

B)

Discount = 55.43 × 18/100

Discount = 55.43 x 0.18 = $9.98

Final Price = 55.43 - 9.9774 = $45.45

C)

Discount = 215.33 × 18/100

Discount = 215.33 x 0.18 = $38.76

Final Price = 215.33 - 38.7594 = $176.57

D)

Discount = 652.3 × 18/100

Discount = 652.3 x 0.18 = $117.41

Final Price = 652.3 - 117.414 = $534.89

E)

Discount = 849.5 × 18/100

Discount = 849.5 x 0.18 = $152.91

Final Price = 849.5 - 152.91 = $696.59

Hence by comparing the original price with the final price we can identify the equation represents regular prices and sale prices of items in the store during the sale are

A) regular price: $29.99, sale price: $24.59

B) regular price: $55.43, sale price: $45.45

D) regular price: $652.30, sale price: $534.89

E) regular price: $849.50, sale price: $679.60

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here are six number cards -5,-2,-3,2,0,-1 arrange the cards into three pairs with the same total

Answers

Arrangement of the cards with six number -5,-2, -3 , 2, 0, -1 into three pairs such that they have same total are given by :

( -5 ,2) , (-2, -1) , (-3, 0)

As given in the question,

Given cards with six numbers are as follow:

-5,-2, -3 , 2, 0, -1

Arrangement of six cards in such a way that they have a same total is given by:

-5 + 2 = -3

-3 + 0 = -3

-2 + (-1) = -3

These pairs have the same total which is equal to -3.

Required pairs can be written as follow:

( -5 , 2) , ( -3 , 0) , ( -2 , -1)

Therefore , arrangement of the cards with six number -5,-2, -3 , 2, 0, -1 into three pairs such that they have same total are given by :

( -5 ,2) , (-2, -1) , (-3, 0)

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Line 1: 4x + 2y = 12

Line 2: 3x - 6y =18

State the slope of each line, then determine if the lines are parallel, perpendicular, or neither.

slope of line 1 =

slope of line 2 =

Are the lines parallel, perpendicular, or neither?

Answers

Answer:

lines are perpendicular

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

line 1

4x + 2y = 12 ( subtract 4x from both sides )

2y = - 4x + 12 ( divide through by 2 )

y = - 2x + 6 ← in slope- intercept form

slope of line 1 = - 2

line 2

3x - 6y = 18 ( subtract 3x from both sides )

- 6y = - 3x + 18 ( divide through by - 6 )

y = [tex]\frac{1}{2}[/tex] x - 3 ← in slope- intercept form

slope of line 2 = [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes

Clearly the lines are not parallel

• the product of the slopes of perpendicular lines = - 1

- 2 × [tex]\frac{1}{2}[/tex] = - 1

then Line 1 and Line 2 are perpendicular to each other

Slope of line one is -2 while the slope of line 2 is 1/2 (a half). And the lines are perpendicular I believe

!!!!!PLEASE ANSWER I REALLY NEED IT!!!!

Answers

Answer:

1. TPR

2.NM

3. 6

Step-by-step explanation:

1. The triangle NKM matches up with TPR. We also already knew KMN= PRT. So, it was just a matter of aligning the order.

2.  If you flip PRT then TR will match with NM

3. 4x-3=21

4x-3+3=21+3

Simplify: 4x=24

4x/4=24/4

x=6

Answer:

TPR

NM

6

The triangle NKM matcheswith TPR. We also already knew KMN= PRT. Now it was just a matter of aligning the order. 

 If you would like just basically flip the following: PRT then TR would match with NM which is what we need.

Finding: 4x - 3= 214x - 3 + 3 = 21 + 3

Simplify: 4x= 244x/ 4= 24/ 4x = 6

Answering: x = 6

Princess bought 7 items from a
candy shop. She purchased
chocolate bars for $1.50 each and
bags of gummy bears for $3 each.
If she spent a total of $13.50, how
many chocolate bars did she buy?

Answers

Answer:

She bought 5 chocolate bars.

Step-by-step explanation:

let x = number of chocolate bars

let y = number of gummy bears

[tex]\begin{cases}x + y = 7\\1.5x + 3y = 13.5\end{cases}\\\\\\\to - \begin{cases}3x + 3y = 21\\1.5x + 3y = 13.5\end{cases}\\\\\\\to 1.5x = 7.5\\\to x = 5\\\\[/tex]

Answer:

she purchased 3 chocolate bars

Step-by-step explanation:

hope this helps :)

what i did to find this problem is that i multiplied 3 x 3, which is 9, and then multiplied 1.50 x 3, which was 4.50. i added 9 + 4.50 and i got the answer!

Divide. If there is a remainder, include it as a simplified fraction.
(-24a³ + 16a²) ÷ 4a

Answers

Answer: -6a^2+4a

Step-by-step explanation: simplify

Carmen worked for 13 hours each day for 5 days. Then the next day she worked 6 hours. How many hours did Carmen work in
all?

Answers

71 Hours

13 x 5 = 6565 + 6 = 71

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3(x - 10) = -9
solve for x

Answers

Answer:

7

Step-by-step explanation:

First distribute 3 into (x-10)

this will get you 3x-30=-9

then since 30 is negative, you do the opposite and add 30 to -9

-9+30 is 21 (when you add the 30 you are adding it to both sides, this will remove the original -30 because they are opposites)

You are left with 3x=21

Currently x is being multiplied by 3. Do the opposite and divide 21 by 3

21 divided by 3 is 7.

x=7

Answer:

x = 7

Step-by-step explanation:

1. Distribute

3(x - 10) = -9

3x - 30 = -9

2. Add 30 to both sides

3x - 30 = -9

3x - 30 + 30 = -9 + 30

3. Simplify

Add the numbers:

3x - 30 + 30 = -9 + 30

3x = -9  + 30

Add the numbers:

3x = -9 + 30

3x = 21

4. Divide both sides by the same factor

3x = 21

3x/3 = 21/3

Simplify

3x/3 = x

21/3 = 7

x = 7

May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 10 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

The following equation can be used to determine c, the cost of a taxicab ride of m miles.

c = 3.5m + 3

What will happen to the cost of the taxicab ride if the distance increases by 2 miles?

A. The cost will go up by $2.00
B. The cost will go up by $3.50
C. The cost will go up by $6.50
D. The cost will go up by $7.00

Answers

C. The cost will go up by 6.50

A fruit company needs to mail an order of 8,927 watermelons. If each crate can hold 79 watermelons, how many crates will the company need?

i suck at division.

Answers

Answer:

113 crates

Step-by-step explanation:

hope it helped :)

Please help

1. what is 1+1=
2. 2+_=22
3. 10,999,999 divided by 2 (round it in the nearest whole number)

Answers

Answer:1. 2

2. 20

3. 5499999.5 or5500000

Step-by-step explanation:

Answer:

1. 2

2. 20

3. 5,499,999.5 = 5,500,000

Which of the following is equivalent to the expression below?

ln(e^4)

Answers

The equivalent expression is;

⇒ ln (e⁴) = 4

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ ln (e⁴)

Now,

Since, We know that;

ln (eˣ) = x

So, We can apply the above rule, we get;

⇒ ln (e⁴) = 4

Thus, The equivalent expression is;

⇒ ln (e⁴) = 4

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What is the simplified form of this expression? (x+y)(x³y-3)

Answers

The simplified form of this expression is x^4y-3x+y^2x^3-3y

From the question, we have

(x+y)(x^3 y-3)

= xx^3 y-x⋅3+yx^3 y-y⋅3

=x^4y-3x+y^(1+1) x^3-3y

=x^4y-3x+y^2 x^3-3y

The simplified form of this expression is x^4y-3x+y^2 x^3-3y

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Suppose adam wants to have $750,000 in his ira at the end of 30 years. He decides to invest in an annuity paying 6% interest, compounded annually. What does he have to contribute each year to reach this goal? enter your answer, rounded to the nearest cent. Omit the dollar sign and the comma.

Answers

Each year Adam have to contribute $9486.68  to reach his goal of $750000 .

In the question ,

it is given that ,

Adam wants to have $75000 at the end of 30 years .

So ,the future value (FV) = 75000

the interest rate compounded annually = 6%

So , i = 6% = 0.06

given n = 30 , where n is the number of periods in which payments will be made .

we know , that the formula to calculate the Future value of the Annuity is

[tex]FV=PMT\times(\frac{(1+i)^{n}-1) }{i} )[/tex]

where ,

FV = Future Value

PMT = Periodic Payment

i = interest rate

n [tex]=[/tex] number of periods in which payments will be made .

Substituting the values in the formula ,

we get ,

75000 = PMT×((1+0.06)³⁰-1)/0.06)

75000×0.06 = PMT×(1+0.06)³⁰-1)

PMT = 45000/(1+0.06)³⁰-1)

PMT = 9486.6836

PMT ≈ 9486.68

Therefore , Each year Adam have to contribute $9486.68  to reach his goal of $750000 .

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According to the fundamental theorem of algebra, how many zeros does the function f(x) = 3x4 + x + 2 have? (2 points) 1 2 3 4.

Answers

ANSWER

The Fundamental Theorem of Algebra states that when we work.There are 1 zero in f(x) = 3x4 + x + 2 .

According to the fundamental theorem of algebra, the equation [tex]f(x) = 3x^4+x+2[/tex] has 4 solutions.

Given equation;

[tex]f(x) = 3x^4+x+2[/tex]

Fundamental theorem of algebra:

The following is another way to phrase the theorem: Every non-zero, single-variable, degree n polynomial with complex coefficients has precisely 'n' complex roots, counted with multiplicity. Using repeated polynomial division, it can be shown that the two claims are equivalent.

A (single-variable) polynomial's number of solutions is equal to its highest exponent, or the polynomial's "degree," according to the fundamental theorem of algebra.

So, there are four solutions because this polynomial is of the fourth degree.

The algebraic fundamental theorem states that there are four solutions to the equation [tex]f(x) = 3x^4+x+2[/tex] .

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2.5 > -8 + v Solve the inequality for v.
Simplify your answer as much as possible.

Answers

Answer: 10.5 > v

Step-by-step explanation:

Add both sides by 8 to isolate the right side to just v. You would get 10.5 > v as a result.

(ANSWER ALL)(Need This Today Or Will Be Marked As Overdue) Solve Equations by Substitution Please Help Just Answer The Questions No Explanation Needed Thanks(WILL MARK BRAINLIEST)

Answers

The answers of the questions are as follows,

(a) b = 1

(b) x/3 + 5 = 6 , 9 - 3x = 0 and 2x + 4 = 10 has the solution x = 3

(c) x = 3

(d) x = 4

(e) 9 - x = 14/x , 65 - 2x = 6x + 9 and 3 + 4x = 5x - 4 has the solution x = 7

(a) 6 + 7(b - 1) = 5 + b

6 + 7b - 7 = 5 + b

7b - 1 = 5 + b

7b - b = 5 + 1

6b = 6

b = 1

(b) x/3 + 5 = 6 has the solution x = 3

as, 3/3 + 5 = 6

1 + 5 = 6

6 = 6

also, 9 - 3x = 0 has the solution x = 3

as, 9 - 3(3) = 0

9 - 9 = 0

0 = 0

also, 2x + 4 = 10 has the solution x = 3

as, 2(3) + 4 = 10

6 + 4 = 10

10 = 10

(c) 7x - 4 = 3x + 8

7x - 3x = 8 + 4

4x = 12

x = 3

(d) 6x - 9 = 15

6x = 15 + 9

6x = 24

x = 4

(e) 9 - x = 14/x has the solution x = 7

as, 9 - 7 = 14/7

2 = 2

also, 65 - 2x = 6x + 9 has the solution x = 7

as, 65 - 2(7) = 6(7) + 9

65 - 14 = 42 + 9

51 = 51

also, 3 + 4x = 5x - 4 has the solution x = 7

as, 3 + 4(7) = 5(7) - 4

3 + 28 = 35 - 4

31 = 31

Hence, The answers of the questions are as follows,

(a) b = 1

(b) x/3 + 5 = 6 , 9 - 3x = 0 and 2x + 4 = 10 has the solution x = 3

(c) x = 3

(d) x = 4

(e) 9 - x = 14/x , 65 - 2x = 6x + 9 and 3 + 4x = 5x - 4 has the solution x = 7

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to learn about the tv viewing habits of all the children attending oakbridge school, professor hull randomly selected and interviewed 50 of the school students. in this instance, all the children attending the school are considered to be a(n) population. representative sample. independent variable. control condition.

Answers

Answer:

representative sample

Step-by-step explanation:

ik things

f(x) = 2x² + 7x + 18
Find f(-4)

Answers

Answer:

f(- 4) = 22

Step-by-step explanation:

substitute x = = - 4 into f(x)

f(- 4) = 2(- 4)² + 7(- 4) + 18 = 2(16) - 28 + 18 = 32 - 10 = 22

confidence intervals for the means provide an estimate for where the true mean lies.

Answers

It is true that the confidence intervals for the mean provide an estimate for where the true mean lies.

In statistics, a confidence interval denotes the likelihood that a population parameter will fall between a set of values for a given proportion of the time. A confidence interval depicts the likelihood that a parameter will fall between two values near the mean. Confidence intervals quantify the degree of uncertainty or certainty in a sampling procedure.

The mean is a basic mathematical average of two or more values. There are two sorts of means that may be calculated: the arithmetic mean and the geometric mean. A mean tells you the average of a bunch of values, which helps you contextualize each data point.

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Find the length of the third side. If necessary, write in simplest radical form

Answers

Answer:

5

Step-by-step explanation:

By the Pythagorean Theorem:

[tex] {x}^{2} + {10}^{2} = {(5 \sqrt{5} )}^{2} [/tex]

[tex] {x}^{2} + 100 = 125[/tex]

[tex] {x}^{2} = 25[/tex]

[tex]x = 5[/tex]

Graph the points of the given function with the x-values x=−2 , x = 2, and x = 7. f(x)=−3x+2−−−−√

Answers

By evaluating the linear function we will get the 3 points:

A. (-2, 8)

B. (2, -4)

C. (7, -19)

You can see the graph on the image at the end.

How to graph the points?

Well, the first thing we need to do is get these points, to do so, we need to evaluate the linear function in the given values.

We have f(x) = -3x + 2

if x = 2

f(2) = -3*2 + 2 = -4

if x = -2

f(-2) = -3*-2 + 2 = 8

if x = 7

f(7) = -3*7 + 2 = -19

So we have the points (-2, 8), (2, -4), and (7, -19)

The graph of these 3 points can be seen in the image below.

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Spiral Review A room is 15 feet long and 12 feet wide. A scale drawing of the room is 10 inches by 8 inches. What is the scale of inc
in the drawing to inches in the actual room?
Enter the correct answer in the box.

Answers

The scale of increase in the drawing to inches in the actual room is 18

A room is 15 feet long and 12 feet wide. A scale drawing of the room is 10 inches by 8 inches

1 feet = 12 inches

Initially the room's length = 15 feet = 15 x 12 = 180 inches

On scale drawing the length = 10 inches

Let the  scale of inc in the drawing to inches in the actual room be k

10 x k = 180

k = 180 / 10 = 18

Initially the room's width = 12 feet = 12 x 12 =144 inches

On scale drawing the width = 8inches

8 x k = 144

k = 18

Therefore,  the  scale of inc in the drawing to inches in the actual room is 18

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10 cars are washed in 75 minutes by dave. joe can wash 6 cars in 30 minutes. find how long it would take to wash 20 cars if dave and joe work together.

Answers

As per the unitary method, the time taken by Dave and joe work together to wash 20 cars is 125 minutes.

Unitary method:

In math, the method in which first we find the value of one unit and then the value of the required number of units is referred as unitary method.

Given,

10 cars are washed in 75 minutes by Dave. joe can wash 6 cars in 30 minutes.

Now, we need to find the time taken to wash 20 cars if Dave and joe work together.

Here we know that,

10 cars are washed in 75 minutes by Dave. joe can wash 6 cars in 30 minutes.

So, for 1 minute, the can wash,

Dave's works for 1 car  = 75/10 =  7.5

And Joe's time for one car = 30/6 = 5

So, together they can wash the car at,

=> (7.5 + 5)/2

=> 6.25 minutes.

So, for 20 cars they take the time,

=> 6.25 x 20

=> 125

Therefore, they take 125 minute to wash 20 cars.

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Ken and hamid run around a track
it take ken 80 econd to complete a lap. It take hamid 60 econd to complete a lap
ken and hamid tart running at the ame time from the tart line
how many lap will they each have run when they next meet on the tart line?

Answers

Ken will run 3 laps and Hamid will run 4 laps in 80 and 60 seconds.

To find this, we first find the number of seconds that will have passed when they meet again.  We use the LCM, or least common multiple, for this.  First we find the prime factorization of each number:

LCM of 80 and 60 = 2X2X5X4X3

                             = 4X5X4X3

                             = 240

Now, divide the respective seconds from the total 240, we get

for Ken, 240÷ 80 = 3 laps

For Hamid, 240÷ 60 = 4 laps

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