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
seropon [69]
3 years ago
13

In triangle △ABC, ∠ABC=90°, BH is an altitude. Find the missing lengths. AH=HC+2 and BC=2, find HC.

Mathematics
2 answers:
Sergio039 [100]3 years ago
4 0

Answer:

  HC = 1

Step-by-step explanation:

AC = HC +AH = HC +(HC+2) = 2·HC +2

The altitude divides the triangle into similar triangles, so the ratio of hypotenuse to short side is the same for all. That is ...

  BC/HC = AC/BC

  2/HC = (2HC +2)/2

  4 = 2(HC)(HC +1) . . . . . cross multiply

  0 = HC² +HC -2 . . . . . . divide by 2, subtract 2

  0 = (HC -1)(HC +2) . . . . factor. Solutions are those values of HC that make the factors be zero.

The useful solution is ...

  HC = 1

mylen [45]3 years ago
4 0

Answer:

The measure of HC is 1 unit.

Step-by-step explanation:

Given,

In triangle ABC,

∠ABC = 90°, BC = 2,

Also, H∈ AC such that ∠BHC = 90°,

And, AH = HC + 2

We have to find : HC

∵ ∠ABC = ∠BHC ( right angles )

∠ACB = ∠HCB

By the AA similarity postulate,

\triangle ABC\sim \triangle BHC

∵ The corresponding sides of similar triangles are in same proportion,

\implies \frac{BC}{HC}=\frac{AC}{BC}

\frac{2}{HC}=\frac{AH+HC}{2}

4=HC(HC+2+HC)

4=HC(2HC+2)

4=2HC(HC+1)

2=HC(HC+1)

\implies HC^2+HC-2=0

HC^2+2HC-HC-2=0

HC(HC+2)-1(HC+2)=0

(HC+2)(HC-1)=0

By zero product property,

HC = -2 ( not possible ) or HC = 1  

Hence, the measure of HC is 1 unit.

You might be interested in
Ten times the sum of half a number and 6 is 8​
Digiron [165]

Answer:

I think it's 7

Step-by-step explanation:

I'm guessing I think

3 0
3 years ago
Read 2 more answers
A veterinarian does research on the causes of enteroliths, stones that develop in the colon of horses. She suspects that feeding
dsp73

Answer:

On average, horses with and without enteroliths are fed the same amount of alfalfa per month

Step-by-step explanation:

Hello!

The veterinarian wants to research if eating alfalfa causes horses to have enteroliths.

The study variables are:

X₁: number of alfalfa flakes eaten over a month by a horse with enteroliths.

X₂: number of alfalfa flakes eaten over a month by a horse free of enteroliths.

She calculated a CI interval, with level 1 - α and the interval contained the cero.

With a significance level α, the hypotheses are:

H₀: μ₁ - μ₂ = 0

H₁: μ₁ - μ₂ ≠ 0

To decide whether you should reject or not the null hypothesis using a Confidence Interval is the following:

If the CI contains the number stated in the null hypothesis, the decision is to not reject the null hypothesis.

If the CI doesn't contain the number stated in the null hypothesis, then the decision is to reject the null hypothesis.

Since the interval contains the cero, if 1 - α and α are complementary, the decision is to reject the null hypothesis.

This means that at a level of significance of α, you can conclude that there is no difference between the population means of the numbers of alfalfa flakes eaten by horses with or without enteroliths.

I hope it helps!

7 0
3 years ago
On a certain hot​ summer's day, 391 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for
Tomtit [17]

127 children and 264 adults swam at the public pool that day

Step-by-step explanation:

On a certain hot​ summer's day

  • 391 people used the public swimming pool
  • The daily prices are $1.25 for children and $2.25 for adults
  • The receipts for admission totaled $752.75

We need to find how many children and how many adults swam at the public pool that​ day

Assume that the number of children is x and the number of adult is y in that day

∵ x children swam that day

∵ y adults swam that day

∵ 391 people used the swimming pool that day

- Add x and y, then equate the sum by 391

∴ x + y = 391 ⇒ (1)

∵ The daily price for children is $1.25 per child

∵ The daily price for an adult is $2.25

∵ The receipts for admission totaled $752.75

- Multiply x by 1.25 and y by 2.25, then add the products and

  equate the sum by 752.75

∴ 1.25x + 2.25y = 752.75

- Divide each term by 1.25 to simplify the equation

∴ x + 1.8y = 602.2 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate x

∵ (x - x) + (1.8y - y) = 602.2 - 391

∴ 0.8y = 211.2

- Divide both sides by 0.8

∴ y = 264

- Substitute the value of y in equation (1) to find x

∵ x + 264 = 391

- Subtract 264 from both sides

∴ x = 127

127 children and 264 adults swam at the public pool that day

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

6 0
3 years ago
I can't find the right answer
OlgaM077 [116]

Answer:

x10

Step-by-step explanation:

x^2 > 100\\\\\mathrm{For\:}u^n\:>\:a\\\mathrm{,\:if\:}n\:\mathrm{is\:even}\mathrm{\:then\:}u\:\:\sqrt[n]{a}\\\\x\sqrt{100}\\\\\sqrt{100}=10\\\\x10

7 0
3 years ago
A bacterial cell can double in number every 20 minutes. If one bacterial cell was present at the start of an experiment. How man
kakasveta [241]
There would be 4096 bacteria cells present.

2^12 = 4096
7 0
3 years ago
Read 2 more answers
Other questions:
  • In a game of football outdoors on a cold day, a player will begin to feel exhausted after using approximately 8.0 × 105 J of int
    8·1 answer
  • What is the midpoint of EC ?
    9·1 answer
  • Which statement is true about the data set?<br> [3,4,5,6,7,7,10)
    8·2 answers
  • Cedar Point Amusement Park charges $51.99 for an adult admission and $26.99 for a junior admission. One Thursday, the park colle
    13·1 answer
  • I need help on this can u plsssssss
    6·1 answer
  • The explicit formula for the geometric sequence Negative one-ninth, one-third, negative 1, 3, negative 9, ellipsis is f (x) = ne
    10·1 answer
  • Bradley and Andrew mow lawns to earn spending money. Together they earn $16.50 per hour working for 6 hours. they share their ea
    13·2 answers
  • Please help I’m confused
    9·1 answer
  • BRAINLIEST, THANKS, 5 STARS ! Correct and fast answers needed!!!!
    6·1 answer
  • The regular price of a blanket is seven dollars and 89 my cousin has a coupon for six dollars and 16 are how much will she pay f
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!