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
Anastaziya [24]
3 years ago
13

The area of a right triangle is 16 square miles. One leg of the triangle is 4 miles longer than the other leg. Find the length o

f each leg.
Mathematics
2 answers:
faltersainse [42]3 years ago
7 0
-----------------------------------------------
Define x:
-----------------------------------------------
Let one of the leg be x and the other leg is x + 4.

-----------------------------------------------
Formula:
-----------------------------------------------
Area of triangle = 1/2 x base x height

-----------------------------------------------
Find x:
-----------------------------------------------
16 = 1/2 (x) (x+4)

-----------------------------------------------
Multiply by 2 on both sides:
-----------------------------------------------
32 = x(x+4)

-----------------------------------------------
Apply distributive property:
-----------------------------------------------
32 = x² + 4x

-----------------------------------------------
Subtract 32 from both sides:
-----------------------------------------------
x² + 4x - 32 = 0

-----------------------------------------------
Factorise:
-----------------------------------------------
(x - 4)(x + 8) = 0
x = 4 or x = -8 (rejected, length cannot be negative)

-----------------------------------------------
Find the length of the legs:
-----------------------------------------------
One leg = x = 4 miles
The other leg = x + 4 = 4 + 4 = 8 miles

--------------------------------------------------------------------
Answer: The 2 legs are 4 miles  and 8 miles.
--------------------------------------------------------------------
xxMikexx [17]3 years ago
4 0
First, define the area of a triangle: A = 1/2bh. Let A = 16, and since it’s a right triangle, the base and the height can easily be translated to its two legs. Let one leg = x, and the other = x + 4. So this would give you the equation: 16 = .5(x)(x+4). Distribute so 16 = .5x^2 + 2x. You might want to get rid of the decimal/fraction, so multiply everything by 2 and this would give you 32 = x^2 + 4x. Recognizing that this will be a quadratic equation let x = 0 and bring everything unto one side, so 0 = x^2 + 4x - 32. Factor. 0 = (x+8)(x-4). Since a leg cannot be negative, x can only equal 4. This means that one leg is 4 and the other is 8.
You might be interested in
3. Order the rational numbers from least to greatest:<br> 0.5, 0, - 1.5, 1, -0.5, -1
harina [27]

Answer:

-1.5,-1,0,0.5,1 is the answer

8 0
2 years ago
Suppose that prices of recently sold homes in one neighborhood have a mean of $215,000 with a standard deviation of $8900. Using
bonufazy [111]

Answer:

The minimum percentage of recently sold homes with prices between $197,200 and $232,800 is 75%.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by 100(1 - \frac{1}{k^{2}}).

In this question:

Mean of $215,000, standard deviation of $8900.

What is the minimum percentage of recently sold homes with prices between $197,200 and $232,800?

215000 - 2*8900 = 197200

215000 + 2*8900 = 232800

Within 2 standard deviations of the mean, so:

The minimum percentage of recently sold homes with prices between $197,200 and $232,800 is 75%.

4 0
3 years ago
24=−3(2a−14)−3a<br> what is A?
Lemur [1.5K]

Answer:

a = 2

Step-by-step explanation:

Hope this helps and have a nice day :)

3 0
2 years ago
Read 2 more answers
Write the domain as an inequality​
Pavlova-9 [17]

Answer:

x\leq 0

Step-by-step explanation:

The domain is the span of x-values covered by the graph.

From the graph, we can see that the x-values covered by the graph is all values to the left of zero including zero.

Therefore, the domain is all x-values less than or equal to 0:

x\leq 0

Further notes:

In interval notation, this is:

(-\infty,0]

4 0
3 years ago
Read 2 more answers
(PLEASE HELP) A local newspaper charges g dollars for a four-line classified ad. Each additional line costs d dollars. Write an
otez555 [7]

Answer:

g + 3d

Step-by-step explanation:

aaaaaaaaaaaaaaaaaa

4 0
2 years ago
Other questions:
  • Please Solve Quickly &amp; Show Work!! Please Hurry I'm Offering 15pts PLEASE BE ACCURATE
    9·2 answers
  • Given the points (10,-9) and (3, 5) find the slope.
    14·1 answer
  • Simplify (4x) · mn · 15 · 2.
    5·2 answers
  • What is not equivalent to 65%
    14·2 answers
  • Suppose a telephone poll is conducted by contacting U.S. citizens via landlines about their view of gay marriage. Suppose over 5
    10·1 answer
  • Consider the problem of utility over territory. Let’s start simply
    14·1 answer
  • What is value of x for which the equation 9^-6 x 9^x = 1
    7·2 answers
  • please help me with this math problem, the question is on the picture that i attached, ill mark brainliest if the answer is corr
    15·1 answer
  • A job fair was held at the Student Union. 25% of the students who attended received job offers. Of all of the students at the jo
    7·1 answer
  • Sole this addtion question by substituting numbers for the given letters, to find the value of START Each letter represents a un
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!