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GREYUIT [131]
2 years ago
13

Scenario: Kevin is baking cupcakes for a fundraiser at his school. Yesterday, he prepared 30 cupcakes in 45 minutes. Today, he p

repared 20 cupcakes in 30 minutes.
A) Does the scenario represent a direct variation?
B) If yes, explain the meaning of the constant of proportionality in the scenario.

take your time if you want :)

Mathematics
1 answer:
attashe74 [19]2 years ago
5 0

a) As the constants are equal, the situation represents a proportional relationship.

b) The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.

<h3>What is a proportional relationship?</h3>

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, the constants for each situation are:

k = 30/45 = (30/15)/(45/15) = 2/3 = 20/30.

Since the constants are equal, the situation represents a proportional relationship.

The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.

More can be learned about proportional relationships at brainly.com/question/10424180

#SPJ1

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What is the slope of the line NP
Luba_88 [7]

Answer:

The slope of NP is \frac{-5}{7} ⇒ B

Step-by-step explanation:

  • In any square, every two opposite sides are parallel and every two consecutive sides are perpendicular
  • Parallel lines have the same slope
  • The product of the slopes of the perpendicular lines is -1, which means if the slope of one m, then the slope of the other is \frac{-1}{m} (reciprocal m and change its sign)
  • The rule of the slope of the line which passes through the points (x1, y1) and (x2, y2) is m = \frac{y2-y1}{x2-x1}

In square MNPR

∵ MN and NP are adjacent sides

∴ MN ⊥ NP

∵ M = (3, 8) and N = (-2, 1)

∴ x1 = 3 and y1 = 8

∴ x2 = -2 and y2 = 1

→ Use the rule of the slope above to find the slope of MN

∴ m(MN) = \frac{1-8}{-2-3}

∴ m(MN) = \frac{-7}{-5}

∴ m(MN) = \frac{7}{5}

∵ MN ⊥ NP

∴ The product of their slopes = -1

→ Reciprocal the slope of MN and change its sign

∴ m(NP) = \frac{-5}{7}

∴ The slope of NP is \frac{-5}{7}

8 0
3 years ago
You are making fruit baskets using 54 apples, 36 oranges, and 73 bananas. a. Explain why you cannot make identical fruit baskets
GrogVix [38]
Question 1:
73 is a prime number. It can only be divided by 1 and by itself. 

The GCF of the three numbers:
 54                               36                            73
1×54                           1×36                          1×73
2×27                          2×18
3×18                           3×12
6×9                            4×9
                                   6×6

GCF of 54, 36 and 73  is 1

GCF of 54 and 36 is 18

If we divide 54 apples into 18 baskets, we have 3 apples in each basket
If we divide 36 oranges into 18 baskets, we have 2 oranges in each basket
If we divide 73 bananas into 18 baskets, we have 4 bananas in each basket + one banana left over.

So the greatest number of identical fruit baskets we can make with the least amount of fruit left over is 18 baskets
6 0
3 years ago
1.Sam has a piggy bank full of quarters, dimes, nickels, and pennies. Describe two ways he could make $0.78 using only two kinds
insens350 [35]
3 quarters and 3 pennies, or 7 dimes 1 nickel and 3 pennies

Hope this helps

6 0
3 years ago
Read 2 more answers
Please help quickly
Crank

Answer:25 m

Step-by-step explanation:

3 0
3 years ago
Which of these relations on {0, 1, 2, 3} are equivalence relations? Determine the properties of an equivalence re- lation that t
slava [35]

Answer:

The relations that are equivalence relations are a) and c)

Step-by-step explanation:

A relation on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive

We are going to analyze each one.

a){ (0,0), (1,1), (2,2), (3,3) }

Is an equivalence relation because it has all the properties.

b){ (0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3) }

Is not an equivalence relation. Not reflexive: (1,1) is missing, not transitive: (0,2) and (2,3) are in the relation, but not (0,3)

c){ (0,0), (1,1), (1,2), (2,1), (2,2), (3,3) }

Is an equivalence relation because it has all the properties.

d){ (0,0), (1,1), (1,3), (2,2), (2,3), (3,1), (3,2) (3,3) }

Is not an equivalence relation. Not transitive: (1,3) and (3,2) are in the relation, but not (1,2)

e){ (0,0), (0,1) (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3) }

Is not an equivalence relation. Not symmetric: (1,2) is present, but not (2,1)Not transitive: (2,0) and (0,1) are in the relation, but not (2,1)

5 0
3 years ago
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