1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
AlexFokin [52]
3 years ago
12

Find the missing lengths: LK=15 and KH=9, find KI and HI.

Mathematics
1 answer:
Luda [366]3 years ago
3 0

Answer:

KI=11.25 and HI=6.75

Step-by-step explanation:

Consider the below figure attached with this question.

According to Pythagoras Theorem:

base^2+perpendicular^2=hypotenuse^2

Use Pythagoras in triangle HKL

LH^2+KH^2=LK^2

(LH)^2+9^2=15^2

(LH)^2+81=225

(LH)^2=144

Taking square root on both sides.

LH=12

Let length of HI be x.

LI = 12+x

Use Pythagoras theorem in ΔKLI,

(KI)^2+15^2=(12+x)^2

(KI)^2+225=x^2+24x+144

(KI)^2=x^2+24x+144-225

(KI)^2=x^2+24x-81...(1)

Use Pythagoras theorem in ΔHKI,

(KI)^2=x^2+9^2

(KI)^2=x^2+81...(2)

From (1) and (2) we get

x^2+81=x^2+24x-81

24x=162

x=\dfrac{162}{24}=6.75

Hence, the measure of HI is 6.75 units.

Substitute x=6.75 in equation (2).

(KI)^2=(6.75)^2+81

(KI)^2=126.5625

Taking square root on both sides.

KI=\sqrt{126.5625}

KI=11.25

Hence, the measure of KI is 11.25 units.

You might be interested in
A dollar bill is worth _____ pennies. When written in decimal format, each penny can be written as ______ of a dollar.
VMariaS [17]
A dollar bill is worth 500 pennies. 1$ = 100 pennies.
3 0
3 years ago
Read 2 more answers
What is the answer to 10k-9=9k + 10?
oee [108]
K=19 which would leave the equation 181=181. The first step to solving this is subtracting 9k from each side.
after you do that it should be k-9=10
now you add 9 to both sides leave k=19. plug k into the equation and get 181=181
7 0
3 years ago
a patients dose of medication increased from 100mg to 150mg. What is the percent increase in medication?
lord [1]

Answer:

The answer is 50% increase. Hope this helped!

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A researcher asks participants to taste each of three meals and to choose the one they like best. The same foods are in each mea
Margarita [4]

Answer:

D. All of the above

Step-by-step explanation:

By the given data, some persons were in the experiment and each of them was given with three meals, Low Calorie, Moderate Calorie and High Calorie. They results for the meal they liked is as below:

Low Calorie Meal got likes = 6

Moderate Calorie Meal got likes = 7

High Calorie Meal got likes = 17

so,

Option A is correct as High Calorie meal got 17 likes while Low Calorie meal got 6 likes.

Option B is also correct as Low Calorie meal got 6 likes while Moderate Calorie meal got 7 likes.

Option C is correct too as High Calorie meal got largest number of likes even more than the double of Low calorie and Moderate calorie meal so it was more than expected.

3 0
3 years ago
an item is regularly sold at $40. kala bought it at a discount of 35% off the regular price. how much did kala pay
KonstantinChe [14]

To solve this problem, we must first find the discount amount, and then subtract this amount from the total price of the item.

To find the discount amount, we must find 35% of $40. To do this, we must first convert 35% to its decimal equivalent by dividing 35/100. We do this because percentages are parts out of a total 100 percent, thus this fraction represents an equivalent value that we can multiply by other numbers. Using our knowledge that 35/100 = 0.35, we can now set up our expression:

35% of $40 (keep in mind that the word "of" refers to multiplication in math)

0.35 * 40

To solve, we just multiply these two numbers together, which gives us 14.

This means that Kala got a discount of $14 off of the original price of $40. To find out how much she paid for it, we must subtract $14 from $40, as modeled below:

$40 - $14 = $26

Therefore, Kala paid $26 for the item.

Hope this helps!

5 0
3 years ago
Other questions:
  • Roberto decorates rectangular signs. One sign is 2/3 foot long and 1/4 foot wide. Another sign is 1/2 foot long and 1/3 foot wid
    7·1 answer
  • A 2-digit number with x units and 7 less units than tens.
    12·1 answer
  • What ordered pair is a solution of the equation 2x-y=9
    14·2 answers
  • Which function in vertex form is equivalent to f(x) = x2 + 6x + 3?
    11·2 answers
  • An animal shelter houses ferrets, cats, and dogs. There are 108 animals at the shelter. Of the
    11·1 answer
  • 1. Which of the following relations is a function?
    5·1 answer
  • Which is an example of a trinomial?
    6·2 answers
  • 2/3&lt; x/8 &lt;7/8 what number could replace x to make a true statement<br><br> 3<br> 4<br> 5<br> 6
    6·2 answers
  • Deena took six final exams and received these scores:<br> 65, 72, 79, 86, 93, 100.
    15·1 answer
  • Compute the following without using a calculator. You must show your work to receive full credit.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!