Simplify x + 4 - 5x

In a 30-60-90 triangle, if the the side opposite 30 degrees has a length

son4ous [18]

Might Want to draw this and Its very long but Hope it helped :)

Answer:

The sides are all of the same length - let's say a. The angles are all the same too, and since the angles must add up to 180∘, we conclude that the three angles in the equilateral triangle are equal to 180∘/3=60∘.

Now we do something sneaky. We draw a line all the way down from the top vertex of the triangle to the midpoint of the bottom line.

This new line cuts our equilateral triangle in half. What are the angles in one half?

The angle at the bottom is 90∘.

One of the angles is the same as one of the angles in the original equilateral triangle, so it is 60∘.

So the third angle must be 180∘−90∘−60∘=30∘.

Now the hypotenuse of this new triangle is a, the side length of the equilateral triangle. And the length of the shortest side is a/2, since the line we drew cut the bottom line in half.

8 0

3 years ago

If f(x)=x^2+2x-3 and g(x)=x^2-9, find (f/g)(4) and (f+g)(4)

Likurg_2 [28]

Answer:

Part 1: Find (f/g)(4) = 3

Part 2: Find (f+g)(4) = 28

Step-by-step explanation:

Part 1: Find (f/g)(4):

(f/g)(4) means divide f function by g function and simplify it. Then plug in 4 into x of that simplified function.

Let's do this:

$\frac{x^2+2x-3}{x^2-9}\\=\frac{(x+3)(x-1)}{(x-3)(x+3)}\\=\frac{x-1}{x-3}$

Plugging in 4 into x gives us:

$\frac{x-1}{x-3}\\=\frac{4-1}{4-3}\\=\frac{3}{1}\\=3$

The answer is 3

Part 2: Find (f+g)(4):

(f+g)(4) means add f function and g function and simplify it. Then plug in 4 into x of that simplified function.

Let's do this:

$(x^2+2x-3)+(x^2-9)\\=2x^2+2x-12$

Plugging in 4 into x gives us:

$2x^2+2x-12\\=2(4)^2+2(4)-12\\=28$

The answer is 28

5 0

3 years ago

Which statements must be true? Select each correct answer

kupik [55]

Answer:

Options (1), (3) and (5)

Step-by-step explanation:

By the property of midsegment,

Segment joining midpoints of two sides of a triangle measures the half of the third side of the triangle and midsegment is parallel to the third side.

Since, points U, V and W are the midpoints of the sides JK, KL and LJ,

UW = $\frac{1}{2}(KL)$