Simplify this problem

In isosceles right triangle ABC, point is on hypotenuse \overline{BC} such that \overline{AD} is an altitude of \triangle ABC an

Dmitriy789 [7]

Answer:

Area of triangle is 25.

Step-by-step explanation:

We have been given an isosceles right triangle

Isosceles triangle is the triangle having two sides equal.

Figure is shown in attachment

By Pythagoras theorem

$BC^2=AC^2+AB^2$

AD is altitude which divides the triangle into two parts

DC=5 implies BC =10 since D equally divides BC

Let AC=a implies AB=a being Isosceles

On substituting the values in the Pythagoras theorem:

$10^2=a^2+a^2$

$100=2a^2$

$\Rightarrow a^2=50$

$\Rightarrow a=\pm5\sqrt{2}$

WE can find area of right triangle by considering height AB and AD

Area of triangle ABC is:

$\frac{1}{2}\cdot BC\cdot AD$ (1)

$\Rightarrow \frac{1}{2}\cdot 10\cdot AD$

And other method of area of triangle is:

$\frac{1}{2}\cdot AB\cdot BC$ (2)

Equating (1) and (2) we get:

$\frac{1}{2}\cdot 10\cdot AD=\frac{1}{2}\cdot a\cdot a$

$\Rightarrow AD=\frac{a^2}{10}$

$\Rightarrow AD=\frac{50}{10}=5$

Using area of triangle is: $\frac{1}{2}\cdot BC\cdot AD$

Now, the area of triangle ABC= $\frac{1}{2}\cdot 5\cdot 10$

$\Rightarrow 25$

4 0

3 years ago

You usually buy a 16.5-ounce bottle of shampoo. There is a new bottle that says it gives you 30% more free.

Katarina [22]

Answer:

$\frac{x-16.5}{16.5}=0.30$

Hopefully, this is your desired setup. (I noticed the formula you have to fill in there.)

Have a good day.

Step-by-step explanation:

Hi.

You could use the percent change formula.

Since we know it is a percent increase then we will do new-old instead of old-new:

$\frac{\text{new}-\text{old}}{\old}$

x is the new amount of shampoo.

16.5 is the original amount (old) of shampoo.

The percent increase is 30%=0.30 .

So we have the following equation:

$\frac{x-16.5}{16.5}=0.30$

We could have found the equation like this:

$16.5+16.5(0.30)=x$

Subtract 16.5 on both sides:

$16.5(0.30)=x-16.5$

Divide both sides by 16.5:

$0.30=\frac{x-16.5}{16.5}$

By us of symmetric property of equality:

$\frac{x-16.5}{16.5}=0.30$

5 0

3 years ago

Read 2 more answers

A jet travels 4680 miles against the wind in eight hours and 5720 miles in the wind in the same amount of time what is the rate

Kryger [21]

9514 1404 393

Answer:

jet: 650 mph
wind: 65 mph

Step-by-step explanation:

The speed against the wind is ...

4680 mi/(8 h) = 585 mi/h

The speed with the wind is ...

5720 mi/(8 h) = 715 mi/h

The speed of the airplane in still air is the average of these speeds:

(585 +715)/2 = 650 mi/h . . . speed in still air

The speed of the wind is the difference between the airplane speed and the speed in the wind:

715 -650 = 65 mi/h . . . speed of the wind

_____

<em>Additional comment</em>

If p and 'a' represent the speeds of the plane and the air, the speeds with and against the wind are ...

p + a = with

p - a = against

If we average these, we get ...

((p +a) +(p -a))/2 = (with + against)/2

p = (with + against)/2 . . . . . . . the formula we used above

8 0

2 years ago

What is the solution to the equation 13.7y = 6.2y + 30?

ICE Princess25 [194]

Answer:

it's 4

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

What is the range of the averages in this class? histogram group of answer choices 65 points 80 points 30 points none of the abo

natulia [17]

The range of the averages in a class with a maximum point of 100 point and a minimum point of 20 point is 80 points

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Range is the difference between the maximum value and minimum value of a data set. Hence:

Range = Maximum - Minimum

Let us assume that the maximum point is 100 point and the minimum point is 20 point, hence:

Range = 100 - 20 = 80 points

The range of the averages in a class with a maximum point of 100 point and a minimum point of 20 point is 80 points

Find out more on equation at: brainly.com/question/2972832

#SPJ1

8 0

2 years ago