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Musya8 [376]
3 years ago
13

Given that LM is a midsegment of IJK, find JK. A. 7 B. 8 C. 14 D. 16

Mathematics
2 answers:
Leno4ka [110]3 years ago
8 0

Answer: Option D. 16

Solution:

If LM is a midsegment of IJK, it is joining the midpoint of the sides IJ and IK, and it's half the length of the base of the triangle (JK), then:

L is the midpoint of the side IJ, and divides it into two congruent parts:

IL=LJ

Replacing IL by 7x and LJ by 3x+4:

7x=3x+4

Solving for x: Subtracting 3x both sides of the equation:

7x-3x=3x+4-3x

Subtracting:

4x=4

Dividing both sides of the equation by 4:

4x/4=4/4

Dividing:

x=1

Then we can determine the length of LM:

LM=2x+6

Replacing x by 1 in the equation above:

LM=2(1)+6

LM=2+6

LM=8

and because LM is half the length of the base of the triangle (JK)

LM=(1/2) JK

Replacing LM by 8:

8=(1/2) JK

Multiplying both sides of the equation by 2:

2(8)=2(1/2) JK

16=(2/2) JK

16=(1) JK

16=JK

JK=16

Ad libitum [116K]3 years ago
7 0

<u>Answer:</u>

16

<u>Step-by-step explanation:</u>

We know that segment LM is the mid-segment of the triangle IJK which means ILM is half the size of IJK.

So, IL = LJ.

We know that IL = 7x and LJ = 3x+4 so putting these values equal to each to find the value of x:

7x = 3x + 4

7x - 3x = 4

x =4/4

x = 1

Now, if x = 1, then the segment LM will be:

2x + 6 = 2(1) + 6 = 8

If LM is half the length of JK, then JK is two times the length og LM.

Therefore, JK = 2 * 8 = 16.

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What is the value of x in this triangle?
gizmo_the_mogwai [7]

Answer:

  x = 33.49°

Step-by-step explanation:

The relevant trig ratio is the sine:

  Sin = Opposite/Hypotenuse

  siin(x) = 32/58

The angle measure is found using the inverse function:

  x = arcsin(32/58) ≈ 33.49°

8 0
2 years ago
Differentiate f and find the domain of f. (enter the domain in interval notation.)f(x) = ln(x2 − 12x)derivative f '(x) = 2x−12x2
guajiro [1.7K]
F(x) = ln(x² - 12x)
The derivative is
f'(x)= \frac{2x-12}{x^{2}-12x}

f(x) is undefined when x² - 12x = x(x - 12) = 0
That is, when x = 0 or x = 12.
Therefore the domain is (-∞, 0)∪(0,12)∪(12, ∞)

Answer:
The derivative is
f'(x) =  \frac{2x-12}{x^{2}-12x}
The domain is
(-∞, 0)∪(0, 12)∪(12,∞)



3 0
3 years ago
365x + 125 = 250x + 175
maxonik [38]
First, set up the equation. 
365x + 125 = 250x + 175 

Second, combine like terms on the same side by subtracting 250x and 125 from both sides.

365x +125 = 250x + 175  
-250x  -125   -250x -125 
__________________
115x = 50

Third, divide both sides by 115 to solve for x.

115x = 50
----      ----
115     115 

Fourth, simplify. 

x=50/115=10/23 or 0.435

7 0
3 years ago
the rectangle shown has an area of 105 square inches. the width is x+ 16 inches and the length is x. find the dimensions of the
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Answer:

Length = 5

Width = 21

Step-by-step explanation:

(x)(x + 16) = 105

x^2 + 16x = 105

x^2 + 16x - 105 = 0

(x - 5) x ( x + 21) = 0

x - 10 = 0

x = 5

x + 21 = 0

x = -21

Now that we have the zeroes.

We have to find the most viable one to put in.

Using -21 would not make sense, so we will use 5.

Plug it in:

x = 5

(5) (5 + 16) = 105

5 ( 21) = 105

6 0
3 years ago
6.<br> Find the measure of a.<br> 115°
Volgvan
Do you have a picture? i can help if you have one
4 0
3 years ago
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