one positive number is 12 times another positive number. The difference between the two numbers is 143

2 answers:

8 0

Let x is one positive number
One positive number is 12 times another positive number 12x
12x - x = 143
11x = 143
x = 143/11
x = 13

12x = 12(13) = 156

answer: 2 numbers are 13 and 156

double check:

difference between the two numbers is 143
156 - 13 = 143

Natali [406]3 years ago

5 0

Let x be the unknown number and let's set up an equation.
12x - x = 143
Now solve for x:
11x = 143
x = 13
The positive number is 13.

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Find the value of y.

snow_tiger [21]

Answer:

y = √55

Step-by-step explanation:

All the triangles are similar, so the ratio of short side to hypotenuse is the same for all:

5/y = y/(5+6)

y^2 = 55

y = √55

_____

Comment on the geometry

There are three "geometric mean" relationships that apply to this geometry.

the altitude BD is the geometric mean of BC and BA (√30)
the long side of the large triangle is the geometric mean of the longer segment of the hypotenuse and the whole hypotenuse (x = √66)
the short side of the large triangle is the geometric mean of the shorter segment of the hypotenuse and the whole hypotenuse (y = √55)

If you were aware of the last of these relationships, you could write down the answer without any "work."

y = √(5(5 +6)) = √55

The geometric mean is the n-th root of the product of n numbers. When there are 2 numbers, it is the square root of their product.

4 0

3 years ago

What is the product of three square root of eight times four square root of three? Simplify your answer.

igor_vitrenko [27]

$The\ product\ of 3 \sqrt{8}*4 \sqrt{3}\ is\ 24 \sqrt{6}.$

First, recognize that all the numbers can be moved around because they are being multiplied together.
Next, rearrange the expression so that the whole-number coefficients are together:

$3\sqrt{8}*4\sqrt{6}$
$3*4*\sqrt{8}*\sqrt{3}$

Now try to simplify the square-roots to find any squares inside that can be reduced and taken out of the square-root:

$3*4*\sqrt{(2*2*2)}*\sqrt{3}$
$3*4*\sqrt{4*2}*\sqrt{3}$

Multiply the square roots together:
$3*4*\sqrt{(4*2*3)}$
$3*4*\sqrt{(4*6)}$

Now take out the square-root of 4 and simplify
$3*4*\sqrt{4}*\sqrt{6}$
$3*4*(2)*\sqrt{6}$
$24\sqrt{6}$

$Thus,\ your\ answer\ is\ 24\sqrt{6}$