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Allushta [10]
3 years ago
13

How do i solve x-3/18 = 12/9? (Proportions and Ratios)

Mathematics
1 answer:
neonofarm [45]3 years ago
5 0

Hey there!

\bold{x-\frac{3}{18}=\frac{12}{9}}

  • <em>Firstly, you have to simplify both sides of your equation </em>
  • \bold{x+\frac{-1}{6}=\frac{4}{3}}
  • <em>Secondly, you have to \bold{add} by  \bold{\frac{1}{6}} on each of your sides that you're working with </em>
  • \bold{x+\frac{-1}{6}+\frac{1}{6}=\frac{4}{3}+\frac{1}{6}}
  • \bold{Cancel:\frac{-1}{6}+\frac{1}{6}} because it gives you the result of  \bold{0}
  • \bold{Keep:\frac{4}{3}+\frac{1}{6}} because it gives you the answer for \bold{x}
  • \boxed{\boxed{\bold{Answer:x=\frac{3}{2}}}}

Good luck on your assignment and enjoy your day!

~\bold{LoveYourselfFirst:)}

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Among the fractions given in this question 11/18 and 5/14,  the largest fraction is: 3/5.

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To find out which fraction is the largest, just divide the numerator by the denominator of the ratio and make the comparisons between them, thus defining which is the largest by decimal places or the largest number.

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Answer:

a) the common difference is 20

b) x_8=115 , x_{12}=195

c) the common difference is -13

d) a_{12}=52, a_{15}=13

Step-by-step explanation:

a) what is the common difference of the sequence xn

Looking at the table, we get x_3=16, x_4=36 and x_5= 56

Deterring the common difference by subtracting x_4 from x_3 we get

36-16 =20

So, the common difference is 20

b) what is x_8? what is x_12

The formula used is: x_n=x_1+(n-1)d

We know common difference d= 20, we need to find x_1

Using x_3=16 we can find x_1

x_n=x_1+(n-1)d\\x_3=x_1+(3-1)d\\15=x_1+2(20)\\15=x_1+40\\x_1=15-40\\x_1=-25

So, We have x_1 = -25

Now finding x_8

x_n=x_1+(n-1)d\\x_8=x_1+(8-1)d\\x_8=-25+7(20)\\x_8=-25+140\\x_8=115

So, \mathbf{x_8=115}

Now finding x_{12}

x_n=x_1+(n-1)d\\x_{12}=x_1+(12-1)d\\x_{12}=-25+11(20)\\x_{12}=-25+220\\x_{12}=195

So, \mathbf{x_{12}=195}

c) what is the common difference of the sequence a_m

Looking at the table, we get a_7=104, a_8=91 and a_9= 78

Deterring the common difference by subtracting a_7 from a_8 we get

91-104 =-13

So, the common difference is -13

d) what is a_12? what is a_15?

The formula used is: a_n=a_1+(n-1)d

We know common difference d= -13, we need to find a_1

Using a_7=104 we can find x_1

a_n=a_1+(n-1)d\\a_7=a_1+(7-1)d\\104=a_1+7(-13)\\104=a_1-91\\a_1=104+91\\a_1=195

So, We have a_1 = 195

Now finding a_{12} , put n=12

a_n=a_1+(n-1)d\\a_{12}=a_1+(12-1)d\\a_{12}=195+11(-13)\\a_{12}=195-143\\a_{12}=52

So, \mathbf{a_{12}=52}

Now finding a_{15} , put n=15

a_n=a_1+(n-1)d\\a_{15}=a_1+(15-1)d\\a_{15}=195+14(-13)\\a_{15}=195-182\\a_{15}=13

So, \mathbf{a_{15}=13}

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