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vodka [1.7K]
2 years ago
12

Aleesia has a box of 52 muffins. She wants to put out plates that each have the same number of muffins. What is one possible way

Aleesia could put an equal number of muffins on each plate so there are no muffins leftover
Mathematics
1 answer:
Brums [2.3K]2 years ago
8 0

Answer:

4 muffins per plate (13 plates)

Other answers are possible. See below

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

Explanation:

The factors of 52 are: 1, 2, 4, 13, 26, 52

If Aleesia picks any of those values, then she will divide the muffins up equally.

For example, if she puts 4 muffins per plate, then that means she'll have 13 plates since 4*13 = 52.

Or she could put 2 muffins per plate to get 26 plates (because 2*26 = 52).

Side note: A prime factor tree might be helpful.

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a cube-shaped box has a volume of 125 cubic inches. if a box is packed full of cubes with edge lengths of 1 inch how many cubes
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A minigolf ball is on a perfectly horizontal surface, x = 2 m away from the center of the hole. There is a small obstacle in the
nika2105 [10]
<h3>Answer:</h3><h3>Two possible smallest and largest angles are 11.78° and 78.22°.</h3>

Step-by-step explanation:

Minigolf ball will follow a trajectory to get into the hole.

Since range of a trajectory is calculated by the formula,

R=\frac{u^{2}sin2\theta}{g}

Where u = initial speed of the ball

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g = gravitational pull

Now we plug in the values in the formula,

2=\frac{7^{2}sin(2\theta)}{9.8}

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Hence two possible smallest and largest angles are 11.78° and 78.22°.

6 0
3 years ago
Find the value of k for which the line y = kx + 6 is a tangent to the curve x^2 + y^2 – 10x + 8y = 84
guajiro [1.7K]

Answer:

k = 1/2

Step-by-step explanation:

input y = kx +6 into the equation of the curve x² + y² – 10x + 8y = 84

x² + (kx + 6)² - 10x + 8(kx + 6) = 84

expand:

x² + k²x² + 12kx + 36 - 10x + 8kx + 48 = 84

simplify by collecting like terms:

x² + k²x² + 20kx - 10x + 84 = 84

subtract 84 on both sides to bring it to the left:

x² + k²x² + 20kx - 10x + 84 - 84 = 0

x² + k²x² + 20kx - 10x = 0

factorise out x:

x²(1 + k²) + x(20k - 10) = 0

using the discriminant b² - 4ac where b is 20k - 10, a is 1 + k² and c is 0, substitute them in the formula b² - 4ac:

b² - 4ac

(20k - 10)² - 4(1 + k²)(0) = 0

the part highlighted in bold is gone because it's all multiplied by 0, so we are left with (20k - 10)² = 0

(20k - 10)² is the same as

(20k - 10)(20k - 10)

equate both to 0

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add 10 on both sides

20k = 10 and 20k = 10

divide 20 on both sides

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10/20 is simplified to 1/2

k = 1/2

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The constant of proportionality is 5/9

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y = 5/9 x

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