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John received $112.5 and Joan received $157.5 respectively as per the given ratio.

John and Joan share the amount in the ratio: 5:7

it is given that Joan had $45 more amount than John, therefore

Let the amount with John be x, so the amount with Joan will be x + 45

Formulating the equation we get:

Amount with John/Amount with Joan = Ratio of money with John/Ratio of money with Joan

x/(x + 45) = 5/7

7x = 5x + 225

2x = 225

x = 112.5

Amount with John  = 112.5

Amount with Joan = 157.5

So, amount John received $112.5 and Joan received $157.5 respectively.

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Answer:

60 percent

I think it is 60 but you might need a more certifyd answer

==================================================

Explanation:

A is 40% of B

This translates to the equation A = 0.40B or A = 0.4B

This is because 40% converts to 0.40 in decimal form

Let's divide both sides by 0.4 to isolate B

A = 0.4B

A/0.4 = B

B = (1/0.4)A

B = 2.5A

This shows that B is 250% of A

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

Another approach:

40% = 40/100 = 2/5

"A is 40% of B" is the same as "A is 2/5 of B

So,

A = (2/5)*B

5A = 2B

2B = 5A

B = 5A/2

B = (5/2)A

B = 2.5A

which is another way to show that B is 250% of A

10

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8

Step-by-step explanation:

corect me if i wrong

Answer:

Part A is 63-7.5

Step-by-step explanation:

Answer:

- 4(4z + 3)

Step-by-step explanation:

- 16z - 12 ← factor out - 4 from each term

= - 4(4z + 3)

The length of each side of the chip is 9 centimeters.

A square is an object that has four sides and four equal sides. All the four sides of a square are of equal length. A square has two diagonal that bisect each other at 90°.

The area of a square = length²

Given the area of a square, the length can be determined by calculating the square root of the area of the square. The square root of a number divides a number into two equal halves.

Length = √area

√81 = 9cm

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Answer:

17. (2/5)

19. (-7/3)

21. (2/3)

Step-by-step explanation:

17.

    5            5             1

- -------n + ------n = - ------

    2            4             2

    5 (2)       5             1 (2)

- -------n + ------n = - ------

    2 (2)       4             2 (2)

   10            5             2

- -------n + ------n = - ------

    4            4             4

   10            5             2

(- -------n + ------n = - ------) (4)

    4            4             4

-10n + 5n = -2

-5n = -2

÷ -5 ÷-5

n = (2/5)

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

19.

 3           15           21

-------n - -------n = -------

 2             4           4

 3 (2)      15           21

-------n - -------n = -------

 2 (2)       4            4

  6           15           21

(-------n - -------n = -------) (4)

  4             4           4

6n - 15n = 21

-9n = 21

÷-9   ÷-9

n = (-7/3)

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

21.

     1                    5

- -------n - n =  - -------

     4                   6

   1 (3)               5 (2)

- -------n - n =  - -------

   4 (3)               6 (2)

     3                   10

- -------n - n =  - -------

    12                   12

     3                      10

(- -------n - n =  - -------) (12)

    12                      12

-3n - 12n = -10

--15n = -10

÷-15    ÷-15

n = (2/3)

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

I hope this helps!

Answer:

A: 2

B: 5

C: 4

D: 3

E: 1

Step-by-step explanation:

Looks right to me :)

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

Work below. Enjoy!

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

A simple way to determine the scale factor is to measure a segment's size in units and compare it to the original.

Segment XW = 6 units

Segment EF = 2 units

Now, simply divide the larger (6) by the smaller (2) and you get your answer (3).

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

Good luck! :)

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~pinetreee

Answer:

36 = 69

Step-by-step explanation:

45

No

Step-by-step explanation:

All numbers that are prime are odd and If the number is divisible by 2 it would be a composite number

Using linear functions, we have that:

a) The system is composed by these following equations: 175 + 55x, 325 + 25x.

b) The graph is given at the end of the answer.

c) From the point of intersection on the graph, both services will have the same cost of $450 for 5 hours of work.

A linear function is modeled by:

y = mx + b

In which:

For each function, we have that:

Hence the linear equations that compose the system are given by:

175 + 55x, 325 + 25x.

The graph is given at the end of the answer, and from it, the intersection point is at (5,450), meaning that both services will have the same cost of $450 for 5 hours of work.

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Tom and Ben received 650 and 780 respectively.

Let the amount paid to each for every hour they work be x. Now, forming the equation as per the given information in question.

5x + 6x = 1430

Performing addition to find the value of x.

11x = 1430

Shifting 11 to Right Hand Side of the equation

x = 1430 ÷ 11

Performing division to find the value of x

x = 130

Now finding the amount received by Tom and Ben based on the number of hours they worked.

Amount received by Tom = 5x

Amount received by Tom = 5 × 130

Amount received by Tom = 650

Amount received by Ben = 6x

Amount received by Ben = 6 × 130

Amount received by Ben = 780

Therefore, the amount received by Tom and Ben are 650 and 780 respectively.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The problem is asking for the product, meaning we need to multiply.

-2 1/4 * 2 1/2

To make multiplying easier, we can convert the mixed numbers into improper fractions.

2 * 4 = 8, + 1 = 9/4

2 * 2 = 4, + 1 = 5/2

Now, we have this:

-9/4 * 5/2

Since the denominators are different, we can find the least common multiple of the denominators to make them the same. In this case, the least common multiple of 4 and 2 is 4.

-9/4 * 1 = -9/4

5/2 * 2 = 10/4

Now, we have this:

-9/4 * 10/4

We can now multiply!

-9 * 10 = -90

/4 * /4 = /16

= -90/16

You can simply the improper fraction if you'd like.

-90 / 16 = -5.625

So, our answer is -90/16, or -5.625.

The total change in the number of bushels he has for sale after 7 days = 116.2

In this question,

A farmer sells an average of 16 3/5 bushels each day.

We write above improper fraction 16 3/5 in proper fraction as 83/5

And the decimal form of given fraction 83/5 is:

83/5 = 16.6

After 7 days, he would sold (16 3/5) × 7 bushels.

We simplify an expression (16 3/5) × 7

(16 3/5) × 7 = 16.6 × 7

                  = 116.2

As a result, the farmer would have only 120 - 116.2 = 3.8 bushels for sale.

Therefore, the total change in the number of bushels he has for sale after 7 days = 116.2

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All of the coordinates in the attached screenshot are in the second quadrant.

Answer:

-5+6 = 1

6-5 = 1

therefore, the answer is D.

Answer:

D

Step-by-step explanation:

-5+6=+1

and 6-5=+1

since both are equal to 1

D is the answer

Answer:

13, 15,17

Step-by-step explanation:

Let x = the first number

Let x + 2 = the second number

Let x + 4 = the third number

Consecutive means in order like 1,2,3 or 20,21,22. Consecutive odd means that you want three numbers in order that are odd.  Each number would be 2 more than the number before.  For example 5 + 2 = 7.  We would have to add 4 to 5 to find the next consecutive odd number.

x + (x + 2) + (x +4)  = 45  I put the numbers in parentheses so you could see the first number plus the second number plus the third number equals 45

x + x+ 2 + x+ 4 = 45  Combine like terms

3x + 6 = 45  Subtract 6 from both sides of the equation.

3x = 39  Divide both sides by 3

x = 13

Add 2 to that to get the next odd number.

Add 4 to 13 to get the third odd number.

Answer: 13 cm

Step-by-step explanation:

Let the value of the shortest of the three side lengths is x.

Since the three sides of a triangle are consecutive odd

integers, hence: x, x+2, x+4.

Thus,

[tex]P=x+(x+2)+(x+4)\\45=x+x+2+x+4\\45=3x+6\\45-6=3x+6-6\\39=3x\\[/tex]

Divide both parts of the equation by 3:

[tex]13\ cm=x[/tex]

Answer:

if the cost for the luncheon was $558

and 24 attendees ordered the meat lunches , how many vegetarian lunches were

Step-by-step explanation:

Answer:

Step-by-step explanation:

In the first pair of numbers  15/x² + 6 is larger and in the second pair of numbers (s² + 2)/(s² + 1) is larger

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is two pairs of expressions. From the image given , we can write them as -

Pair 1 → f(x) = 15/x² + 6     and       h(x) = 15/x² + 7

Pair 2 → f(s) = (s² + 2)/(s² + 1)    and       h(s) = (s² + 4)/(s² + 3)  

We can compare which expression is larger in both the pairs without substituting any specific value as follows -

Pair 1 →  f(x) = 15/x² + 6     and       h(x) = 15/x² + 7.

The numerator is same in both the functions.

Now, for any value of x ∈ R →  x² + 6 < x² +7  by 1. Therefore, f(x) > h(x)

Pair 2 → f(s) = (s² + 2)/(s² + 1)    and      h(s) = (s² + 4)/(s² + 3)  

f(s) = (s² + 2)/(s² + 1) = [(s² + 1) + 1]/(s² + 1) = 1 + 1/(s² + 1)

h(s) =  (s² + 4)/(s² + 3) =  [(s² + 3) + 1]/(s² + 3) = 1 + 1/(s² + 3)  

So, we can write that -

f(s) = 1 + 1/(s² + 1)

h(s) = 1 + 1/(s² + 3)  

Now for any value of s →  (s² + 1) < (s² + 3)  by 2. So →  1/(s² + 1) > 1/(s² + 3). Therefore → 1 + 1/(s² + 1) > 1 + 1/(s² + 3). Finally, we can write -

(s² + 2)/(s² + 1) > (s² + 4)/(s² + 3)

Therefore, in the first pair of numbers  15/x² + 6 is larger and in the second pair of numbers (s² + 2)/(s² + 1) is larger.

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The numbers ordered from least to greatest are- 2.14, 2.2, 2.221, 2.276, 2.26, 2.291.

Here, we are given 6 numbers-

2.2, 2.276, 2.291, 2.14, 2.26, 2.221

Now, we can add as many zeroes as we want after the decimal, it does not change the value of the number.

Thus, let us make all the numbers 3 digit decimal numbers

2.200,  2.276,  2.291,  2.140,  2.260,  2.221

Here, all the numbers have 2 in the units place, so we just need to compare the decimals

The first digit after decimal is 2 in all the numbers except 2.140, thus it is the smallest.

Then, the second digit after decimal is 0 in 2.200, thus it is the next smallest number.

By similar logic, looking at the second digit after the decimal only we can arrange the remaining numbers as 2.221, 2.276, 2.260, 2.291.

Thus, the numbers ordered from least to greatest are- 2.14, 2.2, 2.221, 2.276, 2.26, 2.291.

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Your question was incomplete. Please check for full content below-

Drag the numbers below to put them in order from least to greatest

2.2, 2.276, 2.291, 2.14, 2.26, 2.221

The equation to determine the week w when Gael and Kiara have the same amounts of money in their account is 45w + 250 = 75w + 310

An equation is used to show the relationship between numbers and variables. An equation can be linear, quadratic depending on the degree.

Let w represent the number of weeks.

For Kiara:

Money in account = (80 - 35)w + 250 = 45w + 250

For Gael:

Money in account = (95 - 20)w + 310 = 75w + 310

For both to have same amount of money:

45w + 250 = 75w + 310

The equation to determine the week w when Gael and Kiara have the same amounts of money in their account is 45w + 250 = 75w + 310

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Keiko used 83.5 pounds of type A coffee and 82.5 pounds of type B coffee in the blend.

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression

Given:

Type A coffee cost $5.35 per pound

Type B Coffee cost $4.05 per pound

Keiko made total 166 pound of the blend of $780.85

Therefore,

[tex]5.35x + 4.05y = 780.85 \;\;\;\;\; -------equation (1)[/tex]

[tex]x + y = 166 \;\;\;\; ---------equation (2)[/tex]

simplify the equation (2),

[tex]y = 166-x[/tex]

Substitute the value of y in equation (1),

[tex]5.35x + 4.05 (166-x) = 780.85[/tex]

[tex]5.35x + 672.3 - 4.05x = 780.85[/tex]

[tex]5.35x-4.05x=780.85-672.3[/tex]

[tex]1.3x=108.55[/tex]

Therefore,

[tex]Total\;pound\;of\;type\;A\;coffee\;is,\;x=83.5\;pounds[/tex]

Substitute the value of x in equation (2),

[tex]y=166-83.5[/tex]

Therefore,

[tex]Total\;pound\;of\;type\;B\;coffee\;is,\;y=82.5\;pounds[/tex]

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Answer: QV=31 units ==> 3rd option

Step-by-step explanation:

SV=QV   ==> Congruent segments are equal

4x-1=QV

TQ=TS   ==> Congruent segments are equal

26=3x+2

26-2=3x+2-2

3x=24

x=8

4x-1=QV

4(8)-1=QV

32-1=QV

QV=31 units ==> 3rd option

Answer: -104y^2 + 52y

Step-by-step explanation:

-13y(8y-4)=

-13y*8y - 4(-13y)= ==> distribution property

-13*8*y*y - (-52y)=-104y^2 + 52y    

Answer:

15.6 units (3 s.f.)

Step-by-step explanation:

The distance between 2 points is given by the formula below, where [tex](x_1, y_1)[/tex] is the first coordinate and [tex](x_2, y_2)[/tex] is the second coordinate.

[tex]\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}[/tex]

Using the distance formula above,

distance between A(-3, 1) and B(7, 13)

= [tex]\sqrt{(13-1)^{2} + [7-(-3)]^{2} } }}[/tex]

= [tex]\sqrt{12^2+(7+3)^2}[/tex]

= [tex]\sqrt{244}[/tex]

= 15.6 units (3 s.f.)

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Answer:

c) 5

Step-by-step explanation:

Solving for the value of x,

→ 3x - 8 - 4x = -13

→ 3x - 4x = -13 + 8

→ -x = -5

→ [ x = 5 ]

Thus, the value of x is 5.

Answer:

5

Step-by-step explanation:

Use PEMDAS

First you should do is to combine like terms

[tex] - x - 8 = - 13[/tex]

Haveing combined ike terms you need to add 8 to both sides (Like terms are terms that have the same variable like,x)

[tex] - x = - 5[/tex]

Then divide by a negative 1

(this is to get rid of negative x)

[tex]x = 5[/tex]

Hope this helps!

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