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Nat2105 [25]
2 years ago
13

Farmer Hanson is putting together fruit baskets. He has 240 apples and 150 pears. What is the largest number of baskets he can p

ut together so that he can have the same number of apples and same number of pears in each basket considering no fruit is left out?
Mathematics
1 answer:
Tomtit [17]2 years ago
4 0

Answer: 30 baskets.

<u>Step-by-step explanation:</u>

You need to find the Greatest Common Factor (GCF).

240 (apples) = 2 x 2 x 2 x 2 x 3 x 5

150 (pears) = 2 x 3 x 5 x 5

GCF (240, 150) = 2 x 3 x 5

                         = 30

You can make 30 baskets containing 240/30 = 8 apples and 150/30 = 5 pears.

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Complete the square to rewrite y = x2 - 6x + 15 in vertex form. Then state
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Since x^2 is the square of x and 6x is twice the product between x and 3, the second square must be 3 squared, i.e. 9.

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x^2-6x+9+6 = (x-3)^2+6

Which is the required vertex form. This form tells us imediately that the vertex is the point (3,6).

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2 years ago
(1 Convert the integral below to polar coordinates and evaluate the integral. ∫4/2√0∫16−y2√yxydxdy∫04/2∫y16−y2xydxdy Instruction
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Answer:

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4 0
2 years ago
Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval.Tiles
Ugo [173]

By definition, the average rate of change is given by:

AVR = \frac{f(x2)-f(x1)}{x2-x1}

We evaluate each of the functions in the given interval.

We have then:

For f (x) = x ^ 2 + 3x:

Evaluating for x = -2:

f (-2) = (-2) ^ 2 + 3 (-2)\\f (-2) = 4 - 6\\f (-2) = - 2

Evaluating for x = 3:

f (3) = (3) ^ 2 + 3 (3)\\f (3) = 9 + 9\\f (3) = 18

Then, the AVR is:

AVR = \frac{18-(-2)}{3-(-2)}

AVR = \frac{18+2}{3+2}

AVR = \frac{20}{5}

AVR = 4


For f (x) = 3x - 8:

Evaluating for x =4:

f (4) = 3 (4) - 8\\f (4) = 12 - 8\\f (4) = 4

Evaluating for x = 5:

f (5) = 3 (5) - 8\\f (5) = 15 - 8\\f (5) = 7

Then, the AVR is:

AVR = \frac{7-4}{5-4}

AVR = \frac{3}{1}

AVR = 3


For f (x) = x ^ 2 - 2x:

Evaluating for x = -3:

f (-3) = (-3) ^ 2 - 2 (-3)\\f (-3) = 9 + 6\\f (-3) = 15

Evaluating for x = 4:

f (4) = (4) ^ 2 - 2 (4)\\f (4) = 16 - 8\\f (4) = 8

Then, the AVR is:

AVR = \frac{8-15}{4-(-3)}

AVR = \frac{-7}{4+3}

AVR = \frac{-7}{7}

AVR = -1


For f (x) = x ^ 2 - 5:

Evaluating for x = -1:

f (-1) = (-1) ^ 2 - 5\\f (-1) = 1 - 5\\f (-1) = - 4

Evaluating for x = 1:

f (1) = (1) ^ 2 - 5\\f (1) = 1 - 5\\f (1) = - 4

Then, the AVR is:

AVR = \frac{-4-(-4)}{1-(-1)}

AVR = \frac{-4+4}{1+1}

AVR = \frac{0}{2}

AVR = 0


Answer:

from the greatest to the least value based on the average rate of change in the specified interval:


f(x) = x^2 + 3x interval: [-2, 3]

f(x) = 3x - 8 interval: [4, 5]

f(x) = x^2 - 5 interval: [-1, 1]

f(x) = x^2 - 2x interval: [-3, 4]


4 0
2 years ago
Matthew ran 3/8 mile and then walked 7/10 mile. Which pair of fractions can he use to find how far he went in all? (A 15/40 and
Strike441 [17]
Before we could add these numbers, 3/8 and 7/10 need a common denominator. Both 8 and 10 go into 40.

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10 goes into 40 four times
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ANSWER: A) 15/40 and 28/40

Hope this helps! :)
7 0
2 years ago
Read 2 more answers
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