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3 years ago

Triangle ABC is equilateral. Find the height of BD

Mathematics

2 answers:

Oksana_A [137]3 years ago

4 0

Answer:

C) 4√3

Step-by-step explanation:

The given triangle is an equilateral triangle. BD is angle bisector.

Triangle BCD is a 30-60-90 degree triangle in the ration of 1:√3:2

Here we are given BC, that is highest length of the side.

So 2x = 8

x = 8/2

x = 4.

BD = √3 x

Now plug in x =4, we get

Height (BD) = 4√3

Thank you.

MA_775_DIABLO [31]3 years ago

4 0

Answer:

Step-by-step explanation:

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What are the solutions to the equation 3(x – 4)(x + 5) = 0

Ne4ueva [31]

Answer:

x=4

x=-5

Step-by-step explanation:

in order for this to be equal to 0, 1 or both of the factors has to be 0, because anything multiplied by 0 is 0.

123 * 29382 * 8139* 0 = 0

x-4 = 0

x = 4

x+5 = 0

x=-5

7 0

3 years ago

Show that triangle MPT =Triangle MTP

exis [7]

Unusual notation. I won't fuss with it.

a. We have isosceles PRT, so angle RPT = angle RTP.

By the definition of angle bisector, angle MTP = angle MTF, and angle MPT = angle MPU.

We have m angle RTP = m angle MTF + m angle MTP = 2 m angle MTP

Similarly, m angle RPT = 2 m angle MPT

2 m angle MTP = 2 m angle MPT

angle MPT = angle MPT

That's the first part.

b. That makes MPT isosceles.

c. 2x+124=180

2x = 56

x = 28 degrees

MTP = 28 degrees

d. We have angle RPT=angle RTP=56 so PRT=180-2(56)=68 degrees

PUT = 180 - UTP - UPT = 180 - 28 - 56 = 96 degrees

Bad drawing, PUT looks acute.

angle PRT = 68 degrees, angle PUT = 96 degrees

3 0

3 years ago

Which equation best represents the line that is parallel to 3x -4y=7 and passes through the point (-4,-2)? Select two options.

katovenus [111]

Answer:

The equation that best represents the line that is parallel to 3x - 4y = 7 and passes through the point (-4, -2) is y = 3/4x + 1.

Step-by-step explanation:

3x - 4y = 7 and (-4, -2)

First, solve for y in the equation:

3x - 4y = 7

-4y = -3x + 7

4y = 3x - 7

y = 3/4x - 7/4

m = 3/4 (This will be the slope of the parallel line.) and (-4, -2)

Use the point-slope equation to find the equation that will best represent a parallel line:

y − y1 = m(x − x1)

y - -2 = 3/4(x - -4)

y + 2 = 3/4x + 3 (the 4s cancel out)

(3/4 x 4/1 = 3)

y = 3/4x + 1

The graph that I attached is what these two equations would look like graphed. I am not sure what you mean by two options, I'm sorry!

6 0

3 years ago

Tom and his best friend are going to join a gym. Tom saw that Platinum gym has a sale with a one time fee of $90 and a monthly f

worty [1.4K]

Answer:

Part 1:

For Platinum Gym:

90 + 30x

For Super Fit Gym:

200 + 20x

Part 2: $270

Part 3: $320

Part 4: 11 months

Part 5: See explanation below

Step-by-step explanation:

Part 1:

Let "x" be the number of months:

For Platinum Gym:

90 + 30x

For Super Fit Gym:

200 + 20x

Part 2:

We put x = 6 in platinum gym's equation and get our answer.

90 + 30x

90 + 30(6)

90 + 180

=$270

Part 3:

We put x = 6 into super fit's equation and get our answer.

200 + 20x

200 + 20(6)

200 + 120

=$320

Part 4:

To find the number of months for both gyms to cost same, we need to equate both equations and solve for x:

90 + 30x = 200 + 20x

10x = 110

x = 11

So 11 months

Part 5:

We know for 11 months, they will cost same. Let's check for 10 months and 12 months.

In 10 months:

Platinum = 90 + 30(10) = 390

Super Fit = 200 + 20(10) = 400

In 12 months:

Platinum = 90 + 30(12) = 450

Super Fit = 200 + 20(12) = 440

Thus, we can see that Platinum Gym is a better deal if you want to get membership for months less than 11 and Super Fit is a better deal if you want to get membership for months greater than 11.

4 0

3 years ago

Which of the following is the function F(x) if F^-1(x) = x+4/11?

Marianna [84]

Answer:

B. F(x) =X-4/11

Step-by-step explanation:

We are given the inverse function;

f^(-1)(x) = x + 4/11

Thus means, x was replaced with y and vise versa. Thus;

x = y + 4/11

Lets make y the subject;

y = x - 4/11

Thus,in inverse of a function we replace y with f(x) for the original function or f^(1)(x) for the inverse.

Thus, putting f(x) for y gives;

f(x) = x - 4/11

8 0

3 years ago