All categories

2 years ago

Solve the following problem, round your answer to the nearest 2 decimal places if needed.

Mathematics

1 answer:

blondinia [14]2 years ago

5 0

Applying the midsegment theorem, the value of x = 5

Recall:

The midsegment theorem of a triangle states that the length of the mid-segment (DE) which is parallel to the third side (AC), is half the length of the third side AC of triangle BAC.

Thus:

DE = 1/2(AC)

Substitute

2x - 3 = 1/2(x + 9)

Multiply both sides by 2

2(2x - 3) = x + 9

4x - 6 = x + 9

Combine like terms

4x - x = 6 + 9

3x = 15

Divide both sides by 3

x = 5

Therefore, applying the midsegment theorem, the value of x = 5

Learn more about the midsegment theorem on:

brainly.com/question/7423948

You might be interested in

What does the x-intercept sometimes represent in a real world problem

UNO [17]

I think it represents where something is starting from, like something growing up (a chart with rising numbers)

3 0

3 years ago

Find the value of x so that the function has the given value.

nataly862011 [7]

For h(x) = -7x + 10, x =1

For r(x) = 4/5x+ 7 , x = -15

Step-by-step explanation:

in order to find the value of x on which the functions will have given values, we will put the functions equal to the given values

So,

h(x) = -7x + 10; h(x) = 3

$h(x) = -7x+10\\3 = -7x+10\\3-10 = -7x+10-10\\-7 = -7x$

Dividing both sides by -7

$\frac{-7x}{-7} = \frac{-7}{-7}\\x = 1$

r(x) = 4/5x+7; r(x) = -5

$r(x) = \frac{4}{5}x +7\\-5 = \frac{4}{5}x +7\\-5-7 = \frac{4}{5}x\\-12 = \frac{4}{5}x\\x = -12 * \frac{5}{4}\\x = -15$

Keywords: Functions

Learn more about functions at:

#LearnwithBrainly

3 0

3 years ago

What is the length of BC , rounded to the nearest tenth?

Arte-miy333 [17]

Step $1$

In the right triangle ADB

Find the length of the segment AB

Applying the Pythagorean Theorem

$AB^{2} =AD^{2}+BD^{2}$

we have

$AD=5\ units\\BD=12\ units$

substitute the values

$AB^{2}=5^{2}+12^{2}$

$AB^{2}=169$

$AB=13\ units$

Step $2$

In the right triangle ADB

Find the cosine of the angle BAD

we know that

$cos(BAD)=\frac{adjacent\ side }{hypotenuse}=\frac{AD}{AB}=\frac{5}{13}$

Step $3$

In the right triangle ABC

Find the length of the segment AC

we know that

$cos(BAC)=cos (BAD)=\frac{5}{13}$

$cos(BAC)=\frac{adjacent\ side }{hypotenuse}=\frac{AB}{AC}$

$\frac{5}{13}=\frac{AB}{AC}$

$\frac{5}{13}=\frac{13}{AC}$

solve for AC

$AC=(13*13)/5=33.8\ units$

Step $4$

Find the length of the segment DC

we know that

$DC=AC-AD$

we have

$AC=33.8\ units$

$AD=5\ units$

substitute the values

$DC=33.8\ units-5\ units$

$DC=28.8\ units$

Step $5$

Find the length of the segment BC

In the right triangle BDC

Applying the Pythagorean Theorem

$BC^{2} =BD^{2}+DC^{2}$

we have

$BD=12\ units\\DC=28.8\ units$

substitute the values

$BC^{2}=12^{2}+28.8^{2}$

$BC^{2}=973.44$

$BC=31.2\ units$

therefore

the answer is

$BC=31.2\ units$

8 0

3 years ago

Read 2 more answers

You need a loan for $1000, and you can take this loan out with Company A or Company B. Company A charges an 8% interest rate and

Wittaler [7]

Answer: Company b

Step-by-step explanation:

because company B is only 5percent it is better and can pay in 8 years

5 0

2 years ago

Andresssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss

Leviafan [203]

Answer:

Anderess?

Step-by-step explanation:

3 0

2 years ago