3 years ago

Compare these rational expressions.......

Mathematics

1 answer:

Svet_ta [14]3 years ago

4 0

8 over 32 is double 2 over 16

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Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AC =16 and DC=5 what is the length of BC in the simplest ra

Nana76 [90]

The length of BC is $4 \sqrt{5}$ .

Solution:

Given ABC is a right triangle.

AC is the hypotenuse and BD is the altitude.

AB and BC are legs of the triangle ABC.

AC = 16 and DC = 5

<u>Leg rule of geometric mean theorem:</u>

$\frac{\text { hypotenuse }}{\text { leg }}=\frac{\text { leg }}{\text { part }}$

$\Rightarrow \frac{AC}{BC}=\frac{BC}{DC}$

$\Rightarrow \frac{16}{x}=\frac{x}{5}$

Do cross multiplication.

$\Rightarrow 16\times 5 = x\times x$

$\Rightarrow 80= x^2$

$\Rightarrow 16\times 5= x^2$

Taking square root on both sides.

$\Rightarrow \sqrt{16\times 5} = \sqrt{x^2}$

$\Rightarrow \sqrt{4^2\times 5} = \sqrt{x^2}$

square and square roots get canceled, we get

$\Rightarrow 4\sqrt{ 5} = x$

The length of BC is $4 \sqrt{5}$ .

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3 years ago

Take 9.5 gallons 6 1/3 poured out how much water is left in the tank

elena55 [62]

We can first convert 9.5 into fraction :

9.5= 9 1/2

Then we can use deduction to find out the answer:

9 1/2 - 6 1/3

=19/2 - 19/3

We change it to the same denominator:

=19×3/6 - 19×2/6

= 57/6 - 38/6

= 19/6

Therefore there are 19/6 or 3 1/6 gallons left in the tank.

Hope it helps!

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answer is probably ice cream

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2 years ago

Find the roots of f(x)=2x^2+7x+3 by using the quadratic formula

Oksana_A [137]

Answer:

f(x) = 2 ( x + 7/4)2 - 25/8

Step-by-step explanation:

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Bone dry, sorry nothing I can do about that

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