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krok68 [10]
3 years ago
6

Y varies directly as z, y=180, z=10 , find ywhen z=14

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
7 0

<h2>y = 252</h2>

Step-by-step explanation:

To find the value of y when z = 14 we must first find the relationship between them

The statement

y varies directly as z is written as

y = kz

where k is the constant of proportionality

when y = 180

z = 10

180 = 10k

Divide both sides by 10

k = 18

The formula for the variation is

y = 18z

When z = 14

y = 18(14)

<h3>y = 252</h3>

Hope this helps you

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Simplify 4/9 + 1/3<br> A 5/12<br> B 7/9<br> C 1 1/9<br> D 15/9
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Answer:

B) 7/9

Step-by-step explanation:

<h3>Fraction addition:</h3>
  • If the denominators are not same, find the LCM of the denominators.

          LCM of 3 and 9 is 9.

  • Now, find equivalent fractions with denominator as 9.

          \sf \dfrac{1}{3}=\dfrac{1*3}{3*3}\\\\

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  • Now add.

      \sf \dfrac{4}{9}+\dfrac{1}{3}=\dfrac{4}{9}+\dfrac{3}{9}\\\\

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In preperation for an easter egg hunt, 4 blue eggs are filled for every 7 green. How many green eggs will be filled if 100 blue
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Answer:

1. Typed question: 175 green eggs

2. Attached: 22 tables

Step-by-step explanation:

For the question you typed down, it is a ratio and proportion problem. You need to solve for the ratio proportional to the first ratio given.

4 blue eggs are filled for every 7 green. This means that the ratio between blue eggs and green eggs is 4:7.

Now yo need to figure out a ratio proportional to 4:7 if 100 blue eggs were filled. Below is how this is set up:

\dfrac{4\;blue\;eggs}{7\;green\;eggs} = \dfrac{100\;blue\;eggs}{x\;green\;eggs}

Now let's solve for x:

\dfrac{4\;blue\;eggs}{7\;green\;eggs} = \dfrac{100\;blue\;eggs}{x\;green\;eggs}\\\\or\\\\\dfrac{4}{7}=\dfrac{100}{x}\\\\Cross-multiply\\\\4x = (7)(100)\\\\4x = 700\\\\Divide\;both\;sides\;by\;4\\\\\dfrac{4x}{4}=\dfrac{700}{4}\\\\x=175

For your attached problem:

You have a total of 175 people, you need to figure out how many round tables you need if here are 8 chairs for each table You just need to divide the number of people by the number of chairs per table.

175 ÷ 8 = 21.9 tables

Now since you cannot have half a table, you round up to the nearest whole number. (we round up because you need to make sure that all of them are seated)

21.9 ≅ 22 tables.

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