MATHEMATICS HIGH SCHOOL

Subtract 3 from 4/9 of 20

Answers

Answer 1

Answer:

Answer:

5 8/9

Step-by-step explanation:

20*4/9=8 8/9

8 8/9–3=5 8/9

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I sell cookies for $3 and muffins for $7. Yesterday, I made $129. I sold a total of 27 items. How many of each did I sell?

Answers

You sold 15 cookies and 12 muffins.

c - cookies
m - muffins

c + m = 27

3c + 7m = 129

I don’t know how to explain how to do efficiently but I just plugged in numbers until it worked:

3(15) + 7(12) = 129

45 + 84 = 129

Answer:

You sold 15 cookies and 12 muffins

Step-by-step explanation:

So you're given that 1 cookie is sold for $3 and 1 muffin is sold for $7

You're also given that in total you made $129, and sold 27 items

Let's make equations from that, letting c stand for amount of cookies and m for amount of muffins.

3c + 7m = 129 (equation for amount of money made)
c + m = 27 (equation for amount of items sold)

Now we can use the second equation to find m:

c + m = 27

m = 27 - c

Not we can substitute m into the first equation to find c:

3c + 7m = 129

3c + 7(27-c) = 129 [substitute m for (27-c)]

3c + 189 -7c = 129 [distribute 7 into (27-c)]

-4c + 189 = 129 [combine like terms]

-4c = -60 [subtract 189 from both sides]

c = 15 [divide both sides by -4]

Now we can substitute c into the second equation to find m:

c + m = 27

15 + m = 27

m = 12

Find the area of the circle given the diameter is 8. Use 3.14 for pi

Answers

Answer:

A = 50.265482457437 or A = 50.27 or A = 50.265

Step-by-step explanation:

Given that a, b, and c are non-zero real numbers and a + b ≠ 0, solve for x.ax + bx - c = 0

Answers

$ax+bx-c=0 \ \ \ |+c \nax+bx=c \n(a+b)x=c \ \ \ |/ (a+b), a+b \not= 0 \n\boxed{x=(c)/(a+b)}$

$ax+bx-c=0\nx(a+b)=c\nx=(c)/(a+b)$

If PQ = 21 cm and QR = 5, then what are the possible lengths for PR so that PQ,QR and PR can form a triangle? Explain your reasoning

Answers

Please see the pic, I'd solved in it.

So we are given the measurements of two sides of a Triangle:
(write down the given to be clear)
PQ=21 cm
QR=5 cm
But one very important thing:
As Aman said, the length of PR would definitely not be greater than the sum of the other two sides/legs....
Why? Because then it gives a STRAIGHT LINE!
which means: PR will be less than that sum
PR<sum of PQ and QR
PR<21+5
PR<26
Time for Pythagoras Theorem!
We can now split it into Two ways, since we dont know if PR is just a leg or the hypotenuse of the triangle:
And therefore:
Assuming PR is a leg:
(PQ seems to be the larger number)
PQ²=PR²+QR²
21² =PR²+5²
21²-5²=PR²
√21²-5²=PR
20.396 cm=PR
≈20.4 cm
20.4≤PR<26 (which means it can be 20.4 as well, but not any lower as it is very obvious)
Assuming that PR is the hypotenuse:
PR²=PQ²+QR²
PR²=21²+5²
PR=√21²+5²
PR=21.587 cm≈ 21.6 cm
21.6≤PR<26
So basically, the length can be 21.6 itself or higher.

Find the range of the following piecewise function.[0,11)
(-4,6]
(0,11]
[-4,6)