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
sveticcg [70]
3 years ago
15

△ABC is a right triangle with right angle C. Side AC¯¯¯¯¯¯¯¯ is 6 units longer than side BC¯¯¯¯¯¯¯¯. If the hypotenuse has lengt

h 217−−√ units, find the length of AC¯¯¯¯¯¯¯¯.
Mathematics
1 answer:
Vladimir [108]3 years ago
6 0

Given:

In △ABC is a right angle triangle.

AC is 6 units longer than side BC.

Hypotenuse=2\sqrt{17}

To find:

The length of AC.

Solution:

Let the length of BC be x.

So, Length of AC = x+6

According to the Pythagoras theorem, in a right angle triangle

Hypotenuse^2=Base^2+Perpendicualar^2

△ABC is a right angle triangle and AC is hypotenuse, so

(2\sqrt{17})^2=(x)^2+(x+6)^2

68=x^2+x^2+12x+36            [\because (a+b)^2=a^2+2ab+b^2]

Subtract 68 from both sides.

0=2x^2+12x+36-68

0=2x^2+12x-32

0=2(x^2+6x-16)

Divide both sides by 2.

x^2+6x-16=0

Splitting the middle term, we get

x^2+8x-2x-16=0

x(x+8)-2(x+8)=0

(x+8)(x-2)=0

x=-8,2

Side cannot be negative, so x=2 only.

Now,

AC=x+6

AC=2+6

AC=8

Therefore, the length of AC is 8 units.

You might be interested in
Simplify 7(x - 1) - 2(x + 1) + 3(x - 4)<br><br> 8x - 21<br> 8x - 4<br> 8x + 21
Anna007 [38]

Answer:

all work is shown and pictured

7 0
3 years ago
Alex is 4 years younger than 2 times his sister's age. Write a rule that represents Alex's age x as a function of his sister's a
Vesna [10]

Answer:

y = 2x - 4; Alex is 18.

Step-by-step explanation:

Since Alex is 4 years younger than 2 times his sister's age, and his sister is y and Alex is x, the function of y to x must be y = 2x - 4.

According to the rule, if Alex's sister is 11, Alex is 2 times that minus four. If you calculate that, you get

11 * 2 = 22

22 - 4 = 18

So Alex is 18 if his sister is 11.

6 0
3 years ago
Read 2 more answers
Leo's bank balances at the end of months 1, 2, and 3 are $1500, $1530, and $1560.60,
grandymaker [24]

Leo's balance after 9 months will be: $1757.49

Step-by-step explanation:

It is given that the balances follow a geometric sequence

First of all, we have to find the common ratio

Here

a_1 = 1500\\a_2 = 1530\\a_3 = 1560.60

Common ratio is:

r = \frac{a_2}{a_1} = \frac{1530}{1500} = 1.02\\r = \frac{a_3}{a_2} = \frac{1560.60}{1530} = 1.02

So r = 1.02

The general form for geometric sequence is:

a_n = a_1r^{n-1}

Putting the first term and r

a_n = 1500 . (1.02)^{n-1}

To find the 9th month's balance

Putting n=9

a_9 = 1500 . (1.02)^{9-1}\\= 1500.(1.02)^8\\=1757.4890

Rounding off to nearest hundredth

$1757.49

Hence,

Leo's balance after 9 months will be: $1757.49

Keywords: Geometric sequence, balance

Learn more about geometric sequence at:

  • brainly.com/question/10772025
  • brainly.com/question/10879401

#LearnwithBrainly

5 0
3 years ago
Distribute and evaluating <br> (X + 6) (x - 3)
sesenic [268]

Answer:

x^2+3x-18

Step-by-step explanation: hoped I helped

7 0
3 years ago
Read 2 more answers
NO ONE WILL HELP IN ENGLISH CAN SOMEONE HELP HERE!! GIVING AWAY 20 PNTS AND GIVING BRAINLIEST TO THE BEST ANSWER!!!!!!!!!!!
olchik [2.2K]
Are these true and false? I think it's true for both
6 0
3 years ago
Other questions:
  • Find the LCD that would eliminate the fractions in the equation 5x/6-x/3+1=8/9
    7·1 answer
  • The combined sales tax rate for your county is 7.25%. How much would you pay to purchase a new video game system with a listed p
    8·2 answers
  • Whats the value of 5y if -2(3y+5)=-4
    13·2 answers
  • I need to know exponets
    11·1 answer
  • Which of the following values is between 7 and 8
    15·2 answers
  • The temperature on mars ranges widely from -207 to 80 find the average of the temperature extremes on mars.With work
    12·1 answer
  • Gavin wants to buy a bike which costs 1,000 dollars. He raised 250 so far from his shoe shop. How much more does Gavin need to r
    7·2 answers
  • 2 hours 17 minutes 2 hours 48 minutes 1 hour 53 minutes 2 hours 19 minutes 1 hour 38 minutes what it the team's score​
    14·2 answers
  • Find all the real square roots of -49
    12·2 answers
  • When I did it I didn't get any of the answer choices so I know i'm Incorrect please help me find the correct answer
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!