Jake made punch by combining 2.75 liters of orange juice, 1.25 liters of pineapple juice, and 3.5 liters of soda. He then poured equal amounts of all the punch into 3 different containers. How much punch did Jake pour into each container?

Step-by-step explanation:

the key is x = 0.

also I see in the first table no "run-away" effect of some values, so my first suspicion is : it is linear.

let's test it.

a linear function is a line :

y = ax + b

remember, x = 0 is a key element.

y = a×0 + b

-3 = a×0 + b

-3 = b

so, we know, the line function is

y = ax - 3

now, for the a. let's use the next xy pair (1, 1).

1 = a×1 - 3

4 = a

aha ! our line function is therefore

y = 4x - 3

verify with the next 2 points (2, 5) and (3, 9)

5 = 4×2 - 3 = 5 correct

9 = 4×3 - 3 = 9 correct

linear type and equation confirmed.

the second table :

yes, we see relatively big y values compared to the x values.

and the y values follow the powers of 2

so it seems to to be exponential.

64 = 2⁶

32 = 2⁵

16 = 2⁴

8 = 2³

so, while x increases, the powers of 2 decrease. so, we must build something like y = 2^x, but it must run contrary to the increase in x.

the old trick : c-x.

again, x= 0 is key. when x = 0 we get the biggest y (64). that means that gives us c.

64 = 2^(c-x) = 2^(c-0) = 2^c = 2⁶

=> c = 6

so, we suspect the exponential function

y = 2^(6-x)

let's verify with the other points

(1, 32)

32 = 2^(6-1) = 2^(5) = 32 correct

(2, 16)

16 = 2^(6-2) = 2^(4) = 16 correct

(3, 8)

8 = 2^(6-3) = 2^(3) = 8 correct

so, yes, it is the exponential function

y = 2^(6-x)

Answer:

Angle, Lengths

Step-by-step explanation:

Angle measurements and segment lengths are preserved as the transformations neither change the scale factor nor change the angle measurements

Answer:

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Step-by-step explanation:

According to the question, therefore, the maximum number of grams of fat he should consume will be 76.3 grams.

Directly divide 687 by 9 as both are fat content. Therefore, by dividing them, we get to know about how grams of fat can be consumed.

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Answer:

24

Step-by-step explanation:

the area formula for a triangle is

base x high

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

   2

so 6x8=48 and divided by 2 is 24

Answer:

24

Step-by-step explanation:

8×6 then Divide by 2........

Answer:

first answer = 2

second answer = 12

third answer = - 12

fourth answer = 2

The number of cyclists the group needs to raise at least $57,000 must be at least 1000 cyclists

Let x represent the number of cyclists.

Since, the activists receive $60 per cyclist entry and $15,000 in donations, hence:

Revenue = 60x + 15000

Also, the cost of the race is $18 per entry, hence:

Cost = 18x

They need to raise at least $57,000, hence:

Profit ≥ 57000

Revenue - Cost ≥ 57000

(60x + 15000) - 18x ≥ 57000

42x ≥ 42000

x ≥ 1000

Therefore the number of cyclists the group needs to raise at least $57,000 must be at least 1000 cyclists

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Answer:

Dekalb: 3500+40x = F

Sycamores : 12,040 - 100x = F

Step-by-step explanation:

These expressions can be used to explain each population

X = number of years for both expression

F = Final population

Dekalb: 3500+40x = F

Sycamores : 12,040 - 100x = F

The current population if 3500 if no years have gone by, plug in the year of numbers for X to find final population after the amount of years.

Answer:i think 24

Step-by-step explanation:

Answer:

where is the equation please put it

94

Answer:

718

Step-by-step explanation:

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Answer:

88

Step-by-step explanation:

all the options are wrong it is 88

Answer:

Each month he will save $ 50

Each month he will spend $1,250

Raking will have $600 in his checking account at the end of the year.

Step-by-step explanation:

1300 - 500 - 750 = $50

$50 x 12 month = $600

The required amount Rakim saves and sped each month is $50 and $1250.

Given that,
Rakim's goal is to have at least $500 in his checking account at the end of the year. The table shows his activity for the month of January. Will Rakim make his goal.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
According to the question,
Total money he has = 1300
Total money spend = 750 + 500 = 1250
Money he save = 1300 - 1250 = 50
For the condition of at end of the year he must have at least $500
So,
Yearly saving = 50 × 12 = $600, which greater than $500.

The required amount Rakim saves and sped each month is $50 and $1250.

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Answer:

15 hours

Step-by-step explanation:

Let h = numbers of hour worked, x = tips, t = Thomas' pay, and m = Marie's pay

We can set up an equation for this question:

t = 4h + x

Now plug in 120 for x

t = 4h + 120

Now we set up Marie's pay:

m = 12h

Since Thomas and Marie made the same amount of money over the same number of hours, we can say:

4h + 120 = 12h

       120 = 8h

           h = 15

This means they both worked for 15 hours.

Answer:

A,D and E

Step-by-step explanation:

6 14 miles in 5 days.

In 1 day Tom rides 6 14/5 = 1 228 miles

1 week has 7 days

5 weeks have 35 days

1 day Tom rides 1 228 miles

35 days Tom rides for 1 228 * 35 = 42 98miles.

Step-by-step explanation:

45 6

13 6

_____ +

02 6

1

________

6 /..8

..... -6

_______

..... 2

0

_______

6/5

...5

_____

0

The volume of a cylinder is found by using the formula V = pi x r^2 x h where r is the radius and h is the height.

Using the given volume and radius calculate the height:

169.56 = pi x 1.5^2 x h

169.56 = pi x 2.25 x h

169.56 = 7.065 x h

H = 169.56/7.065

H = 24 inches

The answer is the height is 24 inches

Answer:

b

Step-by-step explanation:

Answer:

1 hour equals 18 bucks

144 divided by 18 equals 8 so she works for 8 hours to get 144 bucks

Step-by-step explanation:

144 divided by 18 equals 8

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Answer:

A right triangle needs to have all the sides of the same length. Since this obviously does not, it is not a right triangle. Infact, this is a scalene triangle because all of its sides are unequal.

Answer: ite will be 3 bc i done that all ready

Step-by-step explanation:

The number of individuals that work for the company is 272 workers.

Given,

The Parker company employs 68 part-time workers.

This represents 4% of the total workforce.

We need to find out how many individuals work for the company.

Percentage is a fraction or a ratio in which the value of whole is always 100.

Find the total workforce.

Total workforce = 100%

We have,

4% = 68 workers

Multiply 25 on both sides.

25 x 4% = 4 x 68 workers

100% = 272 workers.

This means the number of individuals that work for the company is 272 workers.

Thus the number of individuals that work for the company is 272 workers.

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Answer:

b.15%

Step-by-step explanation:

Answer:

In order to calculate the slope, you'll need 2 ordered pairs (x, y).

The formula for calculating the slope is:

[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

where m = slope

(x1, y1) = first ordered pair

(x2, y2) = second ordered pair

Regardless of which values for the (x1, y1) and (x2, y2) you choose, you would still end up with the same slope (as long as it's done correctly).

As an example, let's say you have the following set of points:

(2, 4) (8, 1)

Let (x1, y1) =  (2, 4)

     (x2, y2) = (8, 1)

Plug these values into the slope formula:

[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

[tex]m = \frac{1 - 4}{8 - 2} = \frac{-3}{6} = -\frac{1}{2}[/tex]

Therefore, the slope of the line is - 1/2.

To prove that you'll end up with the same value for the slope:

This time, let (x1, y1) =  (8, 1)

                     (x2, y2) = (2, 4)

[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

[tex]m = \frac{4 - 1}{2 - 8} = \frac{3}{-6} = - \frac{1}{2}[/tex]

Therefore, the value of the slope is still -1/2.

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Answer:

7x-11

Step-by-step explanation:

Answer:

7x-11=

X= 11/7

Step-by-step explanation:

Answer:

75.02 ft and 64.62 ft.

Answer:

[tex]25 = \frac{25}{100} [/tex]

so answer is

[tex]a) \: \: \frac{25}{100} [/tex]