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natali 33 [55]
3 years ago
14

The Jones family traveled 314 miles each day until they reached their destination, which is 1,256 miles away from their starting

point. How many days did they drive until they arrived at their destination?
Mathematics
2 answers:
skelet666 [1.2K]3 years ago
8 0
1256/314= 4 days until arrival
algol133 years ago
6 0
In this case, you want to divide the total distance (1,256) by the amount of distance travelled each day (314).

Think of division like I do, using A, B, and C. It may sound confusing at first but labelling them is quite easy.

My equation would go something like this:
A x B = C
Or:
C = A × B (or B x A)
Then:
C ÷ B = A (or A = B)

A is the amount of distance travelled per day and C is the total amount of distance travelled. We need to find B, which is the number of days it took to drive 1,256 miles.

Plot it like this:
314 x B = 1,256

By that point, you start dividing like the equation I mentioned before.
C ÷ A = B
1,256 ÷ 314 = B

If you calculate it the right way, you should get a solid 4 as the answer.

The equation will look like:
314 x 4 = 1,256.

The process I explained may sound a bit complex, but it's actually much simplier. Just plot A, B and C, and make an equation that makes sense with multiplication and division.

I really hope this helps you in the future!
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Answer:

1.) x=8\sqrt{3};y=16

2.) x=1;y=\frac{\sqrt{3}}{2}

3.) x=28 ; y=14\sqrt{3}

4.) x=24 ; y=12\sqrt{3}

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Step-by-step explanation:

Use the 30°-60°-90° formulas:

a. longer leg=\sqrt{3}*shorter leg

b. hypotenuse=2*shorter leg

1.) Insert values for a:

x=\sqrt{3}*8

Simplify:

x=8\sqrt{3}

Insert values for b:

y=2*8

Simplify:

y=16

2.) Insert values for a:

y=\sqrt{3}*\frac{1}{2}

Simplify:

y=\frac{\sqrt{3}}{2}

Insert values for b:

x=2*\frac{1}{2}

Simplify:

x=1

3.) Insert values for a:

y=\sqrt{3}*14

Simplify:

y=14\sqrt{3}

Insert values for b:

x=2*14

Simplify:

x=28

4.)Insert values for a:

y=\sqrt{3}*12

Simplify:

y=12\sqrt{3}

Insert values for b:

x=2*12

Simplify:

x=24

5.) Insert values for a:

12=\sqrt{3}*x

Divide both sides by \sqrt{3} and rationalize:

\frac{12}{\sqrt{3}}=\frac{\sqrt{3}*x}{\sqrt{3}}\\\\\frac{12}{\sqrt{3}}=x\\\\\frac{\sqrt{3}}{\sqrt{3}}*\frac{12}{\sqrt{3}}\\\\\frac{12\sqrt{3}}{\sqrt{9}}\\\\\frac{12\sqrt{3}}{3}\\\\4\sqrt{3}=x

Flip:

x=4\sqrt{3}

Insert values for b:

y=2*4\sqrt{3}

Simplify:

y=8\sqrt{3}

6.) Insert values for a:

8=\sqrt{3}*x

Divide both sides by \sqrt{3} and rationalize:

\frac{8}{\sqrt{3}}=\frac{\sqrt{3}*x}{\sqrt{3}}\\\\\frac{8}{\sqrt{3}}=x\\\\\frac{\sqrt{3}}{\sqrt{3}}*\frac{8}{\sqrt{3}}\\\\\frac{8\sqrt{3}}{\sqrt{9}}\\\\\frac{8\sqrt{3}}{3}=x

Flip:

x=\frac{8\sqrt{3}}{3}

Insert values for b:

y=2*\frac{8\sqrt{3}}{3}

Simplify:

y=\frac{16\sqrt{3}}{3}

Finito.

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