1 year ago

Simplify these expressions. a. 4x + 7x + (–x) b. –5yz + yz + 2yz

Mathematics

1 answer:

salantis [7]1 year ago

4 0

Answer:A. 10x. B. -2yz

Step-by-step explanation:

A. 4x+7x=11x

11x+(-x) = 11x-1x=10x

B. -5yz+yz=-4yz

-4yz+2yz=-2yz

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A jet flies 425 km from Ottawa to Québec at rate v + 60. On the return flight, the

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Answer:

a. $\frac{- 42,500}{(v + 60)(v - 40)}$

Step-by-step Explanation:

Given:

Distance Ottawa to Québec = 425 km

Initial flight rate = v + 60

Return flight rate = v - 40

$t = \frac{d}{r}$

Required:

Flight times difference of the initial and return flights

Solution:

=>Flight time of the initial flight:

$t = \frac{d}{r}$

$t = \frac{425}{v + 60}$

=>Flight time of the return flight:

$t = \frac{425}{v - 40}$

=>Difference in flight times:

$\frac{425}{v + 60} - \frac{425}{v - 40}$

$\frac{425(v - 40) -425(v + 60)}{(v + 60)(v - 40)}$

$\frac{425(v) - 425(40) -425(v) -425(+60)}{(v + 60)(v - 40)}$

$\frac{425v - 17000 -425v - 25500}{(v + 60)(v - 40)}$

$\frac{425v - 425v - 17000 - 25500}{(v + 60)(v - 40)}$

$\frac{- 42,500}{(v + 60)(v - 40)}$

3 0

2 years ago

In a library, the ratio of maths books to science books is 3 : 2 and the ratio of science books to history books is 1 : 3. If th

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Answer:

60 maths books

Step-by-step explanation:

Let the following be:

Maths books = m
Science books = s
History books = h

And we have ratios and sum:

m/s = 3/2
s/h = 1/3
m+s+h = 220

From the ratios we get:

m = 3s/2
h= 3s

Considering the above in the sum of books:

m+s+h = 220
3s/2 + s + 3s = 220
3s + 2s + 6s = 2*220
11s = 440
s = 440/11
s = 40

Number of maths books:

m = 3s/2 = 3*40/2 = 60

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