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
kotykmax [81]
1 year ago
12

The area of a right triangle is given by the expression:

Mathematics
1 answer:
lorasvet [3.4K]1 year ago
6 0

The expression that models the length of the second leg of the triangle is <u>2x - 3.</u>

<u><em>Recall</em></u>:

The area of a triangle = \frac{1}{2} bh

<em><u>Given</u></em>:

Area of triangle = \frac{1}{2} (6x^2 - 7x - 3)

Length of one of the legs = 3x + 1

Therefore, it means that multiplying both legs should give us:

6x^2 - 7x - 3

To find the expression that models the other leg, divide 6x^2 - 7x - 3 by 3x + 1:

  • <em>Thus</em>:

\frac{6x^2 - 7x - 3}{3x - 1}

  • Factorize the numerator

\frac{6x^2 - 2x - 9x - 3}{3x - 1}\\\\\frac{2x(3x - 1) - 3(3x - 1)}{3x - 1}\\\\\frac{(2x- 3)(3x - 1)}{3x - 1}

  • Simplify

\frac{(2x- 3)(3x - 1)}{3x - 1} = 2x- 3

Therefore, the expression that models the length of the second leg of the triangle is <u>2x - 3.</u>

<u></u>

<u></u>

Learn more here:

brainly.com/question/20712284

You might be interested in
Zane each one eighth of a pizza later he is a half of the same Pizza to eat more the first time or the second time
Katyanochek1 [597]
Second time. hope this helped
3 0
3 years ago
Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study wa
4vir4ik [10]

Using the z-distribution, it is found that since the <u>test statistic is greater than the critical value</u>, it can be concluded that the mean length of jail time has increased.

At the null hypothesis, it is <u>tested if the mean length of jail time is still of 2.5 years</u>, that is:

H_0: \mu = 2.5

At the alternative hypothesis, it is <u>tested if it has increased</u>, that is:

H_1: \mu > 2.5

We have the <u>standard deviation for the population</u>, thus, the z-distribution is used. The test statistic is given by:

z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}

The parameters are:

  • \overline{x} is the sample mean.
  • \mu is the value tested at the null hypothesis.
  • \sigma is the standard deviation of the sample.
  • n is the sample size.

For this problem, the values of the <u>parameters</u> are: \overline{x} = 3, \mu = 2.5, \sigma = 1.5, n = 26

Hence, the value of the <u>test statistic</u> is:

z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{3 - 2.5}{\frac{1.5}{\sqrt{26}}}

z = 1.7

The critical value for a <u>right-tailed test</u>, as we are testing if the mean is greater than a value, with a <u>significance level of 0.05</u>, is of z^{\ast} = 1.645

Since the <u>test statistic is greater than the critical value</u>, it can be concluded that the mean length of jail time has increased.

A similar problem is given at brainly.com/question/24166849

5 0
2 years ago
Translate into algebraic terms...7 less than 5 times a number
Nutka1998 [239]

Answer: 5x-7


Step-by-step explanation:


5 0
3 years ago
Prove: an odd plus an odd equals an even
Brums [2.3K]

Answer:

Step-by-step explanation:

1+1=2

1+3=4

3+3=6

3+5=8

3+7=10

8 0
2 years ago
Read 2 more answers
Is 2.95 less than 2.949
BabaBlast [244]
It is equal when you round it off.
7 0
3 years ago
Read 2 more answers
Other questions:
  • When two so sided dice are rolled there are 36 outcomes. Find the probability that the sum is not 4.
    6·1 answer
  • Evaluate the expression:<br> 3(a + b - 3) - 212a + b - 4) when a = 2 and b = 1
    7·1 answer
  • at a baseball game, a vender sold a combined total of 221 sodas and hot dogs. the number of hot dogs sold was 59 less than the n
    5·1 answer
  • What is -8.9 x 1.4 = equal to
    10·2 answers
  • Select the correct answer.
    11·1 answer
  • Solve for x.<br> 75°<br> 11x-2
    14·1 answer
  • Hey bro's help me!!​
    6·2 answers
  • What is the answer to this question?​
    5·1 answer
  • The adjacent sides of a rectangle are (2x – 1) and (x + 5). Find its area.
    8·1 answer
  • Explain the steps <br><br> 3(2y + 5) = -21
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!