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nika2105 [10]
3 years ago
13

A baker, in 70 minutes, iced 40 cupcakes and, in 49 minutes, iced 28 cupcakes. What is the constant of proportionality?

Mathematics
1 answer:
Zinaida [17]3 years ago
8 0

Answer:

\frac{4}{7}

Step-by-step explanation:

The constant of proportionality is the slope of the line joining the two points

(70,40) and (49,28).

Recall the slope formula:

m =  \frac{ y_2 -  y_1 }{ x_2 - x_1}

We substitute the point to get:

m =  \frac{28 - 40}{49 - 70}  =  \frac{ - 12}{ - 21}  =  \frac{4}{7}

<u>Alternatively</u>:

A proportional relation is given by

y = kx

where k is the constant of proportionality.

Using any point, we substitute and solve for k.

40 = 70k

k =  \frac{40}{70} = \frac{4}{7}

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Find the midpoint of the line segment with endpoints at the given coordinates (-6,6) and (-3,-9)
JulsSmile [24]

The midpoint of the line segment with endpoints at the given coordinates (-6,6) and (-3,-9) is \left(\frac{-9}{2}, \frac{-3}{2}\right)

<u>Solution:</u>

Given, two points are (-6, 6) and (-3, -9)

We have to find the midpoint of the segment formed by the given points.

The midpoint of a segment formed by \left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \text { and }\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right) is given by:

\text { Mid point } \mathrm{m}=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)

\text { Here in our problem, } x_{1}=-6, y_{1}=6, x_{2}=-3 \text { and } y_{2}=-9

Plugging in the values in formula, we get,

\begin{array}{l}{m=\left(\frac{-6+(-3)}{2}, \frac{6+(-9)}{2}\right)=\left(\frac{-6-3}{2}, \frac{6-9}{2}\right)} \\\\ {=\left(\frac{-9}{2}, \frac{-3}{2}\right)}\end{array}

Hence, the midpoint of the segment is \left(\frac{-9}{2}, \frac{-3}{2}\right)

6 0
3 years ago
Some friends played a board game. During the​ game, one unlucky player had to move back 8 spaces 5 turns in a row. Find a number
mojhsa [17]

Answer:

I think that it would be -40

Step-by-step explanation:

I think this because they had to go back 40 spaces because 8 x 5 = 40.

7 0
3 years ago
Amelia drives 10 miles in 20 minutes. If she drove three hours in total at the same rate, how far did she go? subquestion - how
olga nikolaevna [1]

Answer:

Amelia drove 90 miles in 3 hours.

Step-by-step explanation:

she drove 10 miles in 20 minutes

we multiply this by 3, and get

30 miles in an hour ( 60 minutes)

then we multiply this by 3 and get

90 miles in 4 hours (180 minutes) :)

5 0
3 years ago
I need with #10, please?
777dan777 [17]

Answer:

h=7ft

Step-by-step explanation:

sinФ=opposite/hypotenuse

sin45°=5/h

0.71=5/h

multiply via by h

0.71h=(5/h)h

h cancel h it remains 5

0.71h=5

divide through by 0.71

0.71h/0.71=5/0.71

h=7.04ft

h=7ft approximately



4 0
3 years ago
Of equations to answer the questions.
iren [92.7K]
2x + 3(8 - 3x) = 3
2x + 24 -9x = 3
-7x = -21
x = 3

y = 8 - 3x
y = 8 - 3(3)
y = 8-9
y = -1

Check the math:
2(3) + 3(-1) = 6 - 3 = 3
4 0
3 years ago
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