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If Varies Directly As X, and When, Find y When (1 Point)

The document contains a series of mathematical problems involving direct and inverse variations, simplifications, and equations to solve. It also includes word problems related to work rates and mixtures. Each problem is assigned a point value indicating its difficulty or importance.

Uploaded by

Jasmina Angelevska Kostadinoska
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© © All Rights Reserved
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36 views6 pages

If Varies Directly As X, and When, Find y When (1 Point)

The document contains a series of mathematical problems involving direct and inverse variations, simplifications, and equations to solve. It also includes word problems related to work rates and mixtures. Each problem is assigned a point value indicating its difficulty or importance.

Uploaded by

Jasmina Angelevska Kostadinoska
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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NAME:_________________________________________

1. If y varies directly as x, and y=35 when x=7 , find y when x=9. (1

point)

2. If t varies inversely as r , and r =2 when t=−6 , find r when t=−11.


(1 point)

3. Simplify:

2
5 10
a. (1 (
point) ( m−3 )2 : m−3 )

3 a+2 6
b. (1 point) +
a+b 3 a+3 b

7 6
c. (1 point) y−8 − 8− y

1
w 2−11 w+ 24 w 2−15 w+50
d. (2 point) w2 −18 w+80 ∙ w2 −9 w+20

m 2 n2
6
e. (2 point) m−n
4

a 6a
f. (2 point) a+5 − a2−25

4. Solve each equation:


y+ 1 y−1 4
a. (1 point) 2
+
2
=
3

1 1 1
b. (1 point) 3 + a = a 2

15
c. (2 point) x + x
−8=0

2
x2 −4 x−2 1
d. (2 point) x −2 = x +2 + x−2

x−3 x−2 1
e. (2 point) 2x
= −
2 x +1 2

(1 point)Suppose y varies jointly as x and z. find y when x=6 and z=8,


if y=12 when z=3 and x=4.

1. Simplify:
p2 +7 p
3p
a. (1 point) 49− p2
3 p−21

−1
( a2−8 a+7 ) ( a−7 )−1
b. (2 point) :
( a−3 )−1 ( a−1 )−1 ( a−3 )−1

3
c. (2 point)
(x+ y) ( 1x − 1y )
1 1
(x− y )( + )
x y

x−1 2 x
d. (2 point) x+ 1 + x−4 + x 2−3 x−4

2. Solve:
1 x
a. (1 point) 2−x =2− x−2

x 2 1
b. (2 point) x2 −1 + x+1 = 2 x−2

4
5. (4 point)Working together, it takes Sam, Jenna and Francisco
two hours to paint one room. When Sam is working alone, he
can paint one room in 12 hours. When Jenna works alone, she
can paint one room in 3 hours. Determine how long it would
take Francisco to paint one room on his own.

6. (4 point)Melissa walks 6 miles to the house of a friend and


returns home on a bike. She averages 3 miles per hour faster
when cycling than when walking, and the total time for both
trips is two hours. Find her walking speed.

5
C: You have 10 liters of a juice blend that is 70% juice.
a. (3 point)How many liters of pure juice need to be added in
order to make a blend that is 75% juice?
b. (3 point)How many liters of pure juice to be added in order
to make a blend that is 90% juice?

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