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
Assoli18 [71]
3 years ago
6

The sides of a triangle have lengths of x, x + 5, and 25. If the longest side is 25, which of the following values of x would ma

ke the triangle right? A. 10 B. 12 C. 15 D. 17
Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
6 0
In a right angle, the sum of the squares of the two shorter sides is equal to the square of the longest side.
Here, the longest side is 25, the shorter sides are x and x+5.

x^2+(x+5)^2=25^2 \\
x^2+x^2+10x+25=625 \\
2x^2+10x+25=625 \ \ \ |-625 \\
2x^2+10x-600=0 \ \ \ |\div 2 \\
x^2+5x-300=0 \\
x^2+20x-15x-300=0 \\
x(x+20)-15(x+20)=0 \\
(x-15)(x+20)=0 \\
x-15=0 \ \lor \ x+20=0 \\
x=15 \ \lor \ x=-20


The length of a side must be a positive number, so x=15.
The answer is C.
You might be interested in
What is the absolute value of 2
Anna71 [15]

Answer:The Absolute Value of a number tells us how far the number is from zero, on a Number Line. 2 is 2 units away from zero. Hence |2|=2.hope it helps

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What lowest terms 19/31
jonny [76]
The lowest terms for 19/31 would be 1
7 0
3 years ago
A research group needs to determine a 90% confidence interval for the mean repair cost for all car insurance small claims. From
lutik1710 [3]

Answer:

a) z = 1.645

b) The should sample at least 293 small claims.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.9}{2} = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645, which means that the answer of question a is z = 1.645.

Now, find  the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

(b) If the group wants their estimate to have a maximum error of $12, how many small claims should they sample?

They should sample at least n small claims, in which n is found when

M = 12, \sigma = 124.88. So

M = z*\frac{\sigma}{\sqrt{n}}

12 = 1.645*\frac{124.88}{\sqrt{n}}

12\sqrt{n} = 205.43

\sqrt{n} = \frac{205.43}{12}

\sqrt{n} = 17.12

\sqrt{n}^{2} = (17.12)^{2}

n = 293

The should sample at least 293 small claims.

8 0
3 years ago
What is the completely factored form of f(x) = 6x3 – 13x2 – 4x + 15?
lana66690 [7]

Answer:

= -4x + 7 is the correct answer

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
The following is an example of 5x2
beks73 [17]

Answer:

D.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • What is the perimeter of a rectangle if 2 sides are 5", and the other sides are both y?
    5·2 answers
  • Text the answer 770-765-3026
    15·2 answers
  • In a square in which the houses are evenly spaced around the outside, numbers 3 and 10 are opposite each other. What is the smal
    11·1 answer
  • A recipe that makes 6 servings calls for 1 1/5 cups of juice.
    9·1 answer
  • What is 9x-2?????????????
    8·1 answer
  • If ΔMNO ≅ ΔXYZ, then what corresponding parts are congruent?
    15·2 answers
  • Write a word problem that represents this equation 5s+6=46
    9·1 answer
  • Quickly please im very confused
    10·1 answer
  • 5x - 12 = 13, solve using algebra.
    12·2 answers
  • The height of a hot air balloon is tracked as it makes its trip from launch to the landing site. Look at the graph to determine
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!