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
77julia77 [94]
3 years ago
14

The lengths of the legs of a right triangle are consecutive even integers. The hypotenuse is 58 inches. What is the sum of the l

engths of the legs in inches?
Mathematics
1 answer:
miskamm [114]3 years ago
3 0

Answer:

82 inches

Step-by-step explanation:

The difference between consecutive even integers is 2, thus

let the legs be n and n + 2

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

n² + (n + 2)² = 58² ← expand and simplify left side

n² + n² + 4n + 4 = 3364 ( subtract 3364 from both sides )

2n² + 4n - 3360 = 0 ( divide all terms by 2 )

n² + 2n - 1680 = 0 ← in standard form

(n + 42)(n - 40) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 42 = 0 ⇒ n = - 42

n - 40 = 0 ⇒ n = 40

But n > 0 ⇒ n = 40

and n + 2 = 40 + 2 = 42

Thus sum of legs = 40 + 42 = 82 inches

You might be interested in
How do you figure out 9/10 of 50
zepelin [54]
9/10 of 50....." of " means multiply
9/10 * 50 = 450/10 = 45
3 0
3 years ago
Read 2 more answers
The fastest recorded speed for an eastern gray kangaroo is 40 mph. What was the
Ludmilka [50]

The kangaroo's speed in feet per second is 58.67 feet per second

<h3>What was the kangaroo's speed in feet per second?</h3>

The speed is given as:

Speed = 40 mph

Rewrite properly as

Speed = 40 miles per hour

1 mile = 5280 feet

So, we have

Speed = 40 * 5280 feet per hour

Evaluate

Speed = 211200 feet per hour

1 hour = 3600 seconds

So, we have:

Speed = 211200 feet per 3600 seconds

Evaluate the quotient

Speed = 58.67 feet per seconds

Hence, the kangaroo's speed in feet per second is 58.67 feet per seconds

Read more about speed at:

brainly.com/question/4931057

#SPJ1

3 0
1 year ago
The function f(x) = x2 has been translated 9 units up and 4 units to the right to form the function g(x). Which represents g(x)?
Inga [223]
For this case , the parent function is given by [tex f (x) =x^2
[\tex]
We apply the following transformations
Vertical translations :
Suppose that k > 0
To graph y=f(x)+k, move the graph of k units upwards
For k=9
We have
[tex]h(x)=x^2+9
[\tex]
Horizontal translation
Suppose that h>0
To graph y=f(x-h) , move the graph of h units to the right
For h=4 we have :
[tex ] g (x) =(x-4) ^ 2+9
[\tex]
Answer :
The function g(x) is given by
G(x) =(x-4)2 +9
8 0
3 years ago
Read 2 more answers
Mary spent half of her allowance going to the movies. She washed the family car and earned seven dollars. What is her weekly all
Nata [24]

Answer:If Mary spent half of her allowance the equation will begin with 1/2x or 0.5x where x is her allowance and 0.5 is half of her allowance spent. Mary also earned 7 dollars by washing the car so this will be added to her allowance spent.

The problem says that after Mary has spent half of her allowance at the movies she was left with 18 dollars so that means that the equation must be equal to 18.

The equation you want to set up is

0.5x+7=18

Where, 18-7=11

0.5x=11

11/.5 = x

x = $22

Thus, Mary has a weekly allowance of 22 dollars.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Please help I’ll give you points and mark you brainliest
elixir [45]
ANSWER:

i think it’s c
5 0
3 years ago
Other questions:
  • The price for a TV was decreased by 20% and then by 10%. By what percent was the new price lower than the original?
    6·1 answer
  • Express 607.409 in words
    9·2 answers
  • For free points and a brainliest write an inequality that represents the description, and then solve. (Q5).Dave has $15 to spend
    12·2 answers
  • Which of the following is the solution to
    7·2 answers
  • Michael is 17 years older than John. In 4 years, the sum of there ages will be 49. Find Michaels present age.
    5·1 answer
  • Plz guys help me with that questions plz<br><br>plz guys help me
    7·2 answers
  • Point slope form for (-10,3) and (-2,-5)
    14·2 answers
  • Please help me !!!!?
    14·1 answer
  • What's the missing measurement ? pls help :]
    11·2 answers
  • REWARDING BRAINLY TO CORRECT ANSWER
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!