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3 years ago

Given the function defined in the table below, find the average rate of

Mathematics

1 answer:

AURORKA [14]3 years ago

7 0

Answer:

Average rate of change = $\frac{2}{5}$

Step-by-step explanation:

Average rate of change of a function 'f' in the interval a ≤ x ≤ b is given by,

Average rate of change = $\frac{f(b)-f(a)}{b-a}$

We have to find the average rate of change in the interval 20 ≤ x ≤ 65

From the table attached,

f(65) = 32

f(20) = 14

Average rate of change = $\frac{32-14}{65-20}$

= $\frac{18}{45}$

= $\frac{2}{5}$

Therefore, average rate of change in the given interval is $\frac{2}{5}$ .

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Daniel and his children went into a bakery and where they sell cupcakes for $3.75 each and donuts for $1 each. Daniel has $20 to

grigory [225]

The system of inequalities are x + y ≥ 7 and 3.75x + 1y ≤ 20 The one possible solution is 4 cupcakes and 3 donuts.

<u>Solution:</u>

Given, Daniel and his children went into a bakery and where they sell cupcakes for $3.75 each and donuts for $1 each.

Daniel has $20 to spend and must buy a minimum of 7 cupcakes and donuts altogether.

⇒ "x" represents the number of cupcakes purchased

⇒ "y" represents the number of donuts purchased,

we have to write and solve a system of inequalities graphically and determine one possible solution.

Now, he should buy minimum 7 items, then x + y ≥ 7 ⇒ (1)

And, he has $20, so his maximum purchase is $20 then, 3.75x + 1y ≤ 20 ⇒ (2)

Now, suppose that he took 5 cupcakes, then he must take at least 2 donuts to satisfy (1)

So, substitute x and y values in (2)

⇒ 3.75(5) + 1(2) ≤ 20

⇒ 20.75 ≤ 20 ⇒ condition failed

So he can take maximum of 4 cupcakes only, and subsequently he has to take minimum of 3 donuts.

Hence, the one possible solution is 4 cupcakes and 3 donuts

7 0

3 years ago

If angle B measures 120 degrees, find

SpyIntel [72]

Answer:

C. 120°

Step-by-step explanation:

There are two paralell lines, one is part of Angle B, and the other of Angle Q. Then there is a diagonal line, coming at the same angle from B all the way to Q, because the other two lines are paralell. It basically means if you were to slide the flat line which is connected to Q up the diagonal line, it would fit perfectly with it's parallel. So the two angles; Angle B and Angle Q; are the exact same.

Hope this helped! Good luck with future math problems :)

7 0

3 years ago

Read 2 more answers

1,034 / 95 as a mixed number

tia_tia [17]

Answer:

10 and 84/95

Step-by-step explanation:

First, you divide 1034 by 95 to see how many times it fits in there. Then, after it comes out to a ten with a lot of decimal points, you multiply 95 times 10, and then subtract the product from 1034 to see what the leftover fraction is. 95×10=950. 1034-950=84. Then, you look at 84/95 and see if it can be simplified-which it can't, so your final answer is 10 84/95.

(hope this helps, sry if its badly written)

7 0

3 years ago

4x+3y=-5 -2x+2y=6 elimination method

Semenov [28]

X=-6.5
Y=7

Hope this helps