(URGENT) A dog is resting against a pole to which he is attached with a 24 meter chain. He watches a cat approach to within 8 meters of the pole and promptly gives chase. The dog runs at 12 meters per second and the cat runs at 10 meters per second. Which does the dog reach first, the car or the end of the chain?

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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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:

3 cans of tomato paste and 6 should be correct

Answer:

"Zero and its operation are first defined by [Hindu astronomer and mathematician] Brahmagupta in 628," said Gobets. He developed a symbol for zero: a dot underneath numbers.

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:

60 percent

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

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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

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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

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.)

Additional:

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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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Work below. Enjoy!

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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).

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Good luck! :)

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Answer:

Part A is 63-7.5

Step-by-step explanation:

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

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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Answer:

36 = 69

Step-by-step explanation:

45

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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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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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

Answer: the time taken by train to cover 50km per hour is equal to the time taken by it to cover the distance of 250km for 5 hours

Step-by-step explanation:

You divide then together

Answer:

x=18

Step-by-step explanation:

it is a proportion

8:12=x:27

you have to multiply the know external terms(8 and 27) and divide them by the 12

The coordinate of the midpoint of the segment with the given endpoints is (-1, 0)

The midpoint of a line is the point that divides the line into two equal parts.

The formula for calculating the midpoint is expressed as;

M(x, y) = (x₁+x₂/2, y₁+y₂/2)

Using the coordinate points (-6, 0) and (-4, 0)

M(x, y) = -6+(-4)/2

M(x, y) = -2/2

M(x, y) =-1

Hence the coordinate of the midpoint of the segment with the given endpoints is (-1, 0)

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

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:

here's the answer

Step-by-step explanation:

the total calls are 39 call

the remaining calls are 1530

the remaining rounds are 481

481+39=520

520x3= 1560

10

_

8

Step-by-step explanation:

corect me if i wrong

Answer:

connect the last point to the first point to complete the question

translate the figure in part

translate the figure in part 3 units horizontal y and 6 units vertically

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

14 1/2 fruits

Step-by-step explanation:

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

The equation for Rhett's Situation is 70x + 50 = 250 and the equation for Scarlett's Situation is 70x + 35 = 250. In Rhett's case equation their is no expense per car wash but in case of Scarlett' equation their is expense of $5 per car wash.

Total amount earned by Rhett = $250  

Let the number of cars Rhett washed = x

Rhett charges $70 per car and earned $50 in tips. So, we can write

Total amount earned by Rhett = 70x + 50

On comparing total amount earned by Rhett, we get

70x + 50 = 250

The equation for Rhett's Situation is 70x + 50 = 250.

Total amount earned by Scarlett = $250  

Let the number of cars  Scarlett washed = x

Scarlett charges $75 per car wash and earned $35 in tips but also had to pay $5. 00 in cleaning supplies per car wash.. So, we can write

Total amount earned by Scarlett = 75x + 35 - 5x = 70x +35

On comparing total amount earned by Scarlett, we get

70x + 35 = 250

The equation for Scarlett's Situation is 70x + 35 = 250.

In Rhett's case equation their is no expense per car wash but in case of Scarlett' equation their is expense of $5 per car wash.

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Answer:-150

Step-by-step explanation:

Step 1: Solve all the integers.

−115-35

Step 2: Add the numbers and keep the negative sign.

-150

Hope this helps!!

P.S: It as a fraction is the same thing as it being in decimal from lol.

Answer: 3.5

Step-by-step explanation:

A = 2, B = 7, C = 6

(7a + b)/c

=(7(2)+7)/(6)

=(14+7)/6

=21/6

=3.5