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True [87]
2 years ago
15

The sum of 3 consecutive multiples of 4 is 180.

Mathematics
1 answer:
Paul [167]2 years ago
7 0

9514 1404 393

Answer:

  56, 60, 64

Step-by-step explanation:

The middle of the three numbers is their average: 180/3 = 60. The other two will be 4 more or less than this.

The numbers of interest are 56, 60, 64.

_____

<em>Additional comment</em>

For "consecutive integer" problems, it is often useful to work with the average of the numbers. The average will be the middle number of an odd number of numbers (as here), or will be halfway between the two middle numbers if their number is even.

Even if you bother to write equations, it can work to do that in terms of the average value (middle number): (x -4) +(x) +(x +4) = 180 in this case.

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Divide $960 into a ratio of 3:5 using the unitary method.
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Answer:

$360 : $600

Step-by-step explanation:

If I'm understanding the problem right, you're looking for this to be put into a 3:5 ratio.

When doing problems like these, I'll add the two numbers in the ratio together, then divide the number (in this case 960) by the sum of the ratios, which in this case is 8.

From there you'd divide 960/8, which is 120. Based on that, you can assume 120 is equal to "1" in the ratio. Then multiply the base unit 1 by each one of the ratios.

120 x 3 = 360

120 x 5 = 600

The ratio will look like this: 360:600

hope this helps u and brainliest is always nice

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6

Step-by-step explanation:

Bruno(B)= 4.5× Charles(C)

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A cell phone company charges $20 for registration and $0.5 for every minute call, write an equation to model the cost C(x) for u
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Step-by-step explanation:

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A home gardener estimates that 24 apple trees will have an average yield of 104 apples per tree. But because of the size of the
d1i1m1o1n [39]

Answer:

The farmer should plant 14 additional trees, for maximum yield.

Step-by-step explanation:

Given

Trees = 24

Yield = 104

x \to additional\ trees

So, we have:

Trees = 24 + x

Yield = 104 - 2x

Required

The additional trees to be planted for maximum yield

The function is:

f(x) = Trees * Yield

f(x) = (24 + x) * (104 - 2x)

Open bracket

f(x) = 24 * 104 + 104x - 24 * 2x - x * 2x

f(x) = 2796 + 104x - 48x - 2x^2

f(x) = 2796 + 56x - 2x^2

Rewrite as:

f(x) = - 2x^2 + 56x + 2796

Differentiate

f'(x) = -4x + 56

Equate f'(x) = -4x + 56 to 0 and solve for x to get the maximum of x

-4x + 56 = 0

-4x =- 56

Divide by -4

x =14

The farmer should plant 14 additional trees, for maximum yield.

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