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3 years ago

Solve for a: 3/5a = 1/4

Mathematics

2 answers:

GrogVix [38]3 years ago

7 0

3a/5=1/4 multiply both sides by 5

3a=5/4 divide both sides by 3

a=5/12

liberstina [14]3 years ago

6 0

3/5a = 1/4....multiply both sides by 5/3, cancelling out the 3/5 on the left
a = 1/4 * 5/3
a = 5/12

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What should be subtracted from 13/(-56) to get 11/28

zloy xaker [14]

Answer:

-5/8

Step-by-step explanation:

13/ -56 -x = 11/28

Add 13/56 to each side

13/ -56 + 13/56 -x = 11/28+ 13/56

-x = 11/28 + 13/56

Get a common denominator

-x = 11/28 *2/2 +13/56

-x = 22/56 + 13/56

-x = 35/56

Divide top and bottom by 7

-x = 5/8

Multiply both side by -1

x = -5/8

8 0

3 years ago

How to get the answers?

beks73 [17]

By inclusion/exclusion,

$n(P' \cup Q) = n(P') + n(Q) - n(P' \cap Q)$

We have

$n(\xi) = n(P) + n(P') \implies n(P') = 28 - n(P)$

so that

$n(P' \cup Q) = (28 - n(P)) + n(Q) - 2n(P) = 28 - 3n(P) + n(Q)$

Now,

$n(\xi) = 28 \implies n(P \cup Q) = 28 - 7 = 21$

and by inclusion/exclusion,

$n(P \cup Q) = n(P) + n(Q) - n(P \cap Q)$

Decompose $Q$ into the union of two disjoint sets:

$Q = (P \cap Q) \cup (P' \cap Q)$

Since they're disjoint,

$n(Q) = n(P\cap Q) + n(P'\cap Q) \implies n(Q) = n(P\cap Q) + 2n(P)$

$\implies n(P \cup Q) = n(P) + (n(P\cap Q) + 2n(P)) - n(P \cap Q)$

$\implies 21 = 3n(P)$

$\implies n(P) = 7$

From the Venn diagram, we see there are 3 elements unique to $P$ - by the way, this is the set $P \cap Q'$ - so $n(P\cap Q) = 7-3 = 4$ , and it follows that

$n(Q) = n(P\cap Q) + 2n(P) = 4 + 2\times7 = 18$

Finally, we get for (a)

$n(P' \cup Q) = 28 - 3n(P) + n(Q) = 28 - 3\times7 + 18 = \boxed{25}$

For (b), we have by inclusion/exclusion that

$n(P \cup Q') = n(P) + n(Q) - n(P \cap Q') = 7 + 18 - 3 = \boxed{22}$

5 0

2 years ago

A quarterback is sacked for a loss of 5 yard in Th e next play, his team loses 15yards then Th e team gain12yards on Th e third

Lera25 [3.4K]

First Play: loses 5 yards ( -5 )
Second Play: loses 15 yards ( -15 )
Third Play: gains 12 yards ( +12 )

-5yd + (- 15yd) + 12yd

= -20yd + 12yd

= -8yd

4 0

3 years ago

Help!!! i don’t understand this chart

Tatiana [17]

hope it helps

5 0

3 years ago

Simplify 5e+8f+7e-f

kipiarov [429]

Answer:

12e+7f

Step-by-step explanation:

you gather like terms

5e+7e =12e

8f-f=7f

12e + 7f

8 0

3 years ago