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
V125BC [204]
3 years ago
8

The longer leg of a right triangle is 7 cm longer than the shorter leg. the hypotenuse is 8 cm longer than the shorter leg. what

is the perimeter of the triangle?
Mathematics
1 answer:
notsponge [240]3 years ago
3 0
First we define a variable:
 x: length of the shortest side of the triangle.
 Then, using the Pythagorean theorem we have:
 (x + 8) ^ 2 = x ^ 2 + (x + 7) ^ 2
 Rewriting we have:
 x ^ 2 + 16x + 64 = x ^ 2 + x ^ 2 + 14x + 49
 Clearing x we have:
 64 - 49 = 2x ^ 2 - x ^ 2 + 14x - 16x
 64 - 49 = 2x ^ 2 - x ^ 2 + 14x - 16x
 15 = x ^ 2 - 2x
 x ^ 2 - 2x - 15 = 0
 The roots of the polynomial are:
 x = -3
 x = 5
 We discard the negative root because it is a dimension.
 Then, the perimeter is:
 P = (x + 7) + (x + 8) + x
 P = (5 + 7) + (5 + 8) + 5
 P = 30
 Answer:
 
the perimeter of the triangle is:
 
P = 30
You might be interested in
Solve for x, given the equation Square root of x-5+7=11
denis-greek [22]

\sqrt{x-5+7} = 11\\x-5+7 = 11^2\\x-5+7 = 121\\x + 2 = 121\\x = 119

Check the answer:

\sqrt{119-5+7} \\\sqrt{114+7} \\\sqrt{121} \\11

This answer is correct,

x = 119

6 0
3 years ago
Four resistors are connected in series such that their total resistance is 50ohm . If the resistance of resistors is 5 ohm , 10o
Katyanochek1 [597]
<h2>Answer:</h2>

\boxed{R_{4}=20\Omega}

<h2>Step-by-step explanation:</h2>

If resistors are in series, so the current  I is the same in all of them. In this problem we have four resistors. So, we can get a relationship between the Equivalent resistance  of series combination and the four resistors as follows:

R_{eq}=R_{1}+R_{2}+R_{3}+R_{4}

R_{eq} is the total resistance 50\Omega. Moreover:

R_{1}=5\Omega \\ R_{2}=10\Omega \\ R_{3}=15\Omega

Therefore:

50=5+10+15+R_{4} \\ \\ R_{4}=50-(5+10+15) \\ \\ R_{4}=50-30 \\ \\ \boxed{R_{4}=20\Omega}

7 0
3 years ago
Sketch the graph by hand using asymptotes and intercepts, but not derivatives. Then use your sketch as a guide to producing grap
Arisa [49]

The local minima of f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2} are (x, f(x)) = (-1.5, 0) and (7.980, 609.174)

<h3>How to determine the local minima?</h3>

The function is given as:

f\left(x\right)=\ \frac{\left(2x+3\right)^2\left(x\ -2\right)^5}{x^3\left(x-5\right)^2}

See attachment for the graph of the function f(x)

From the attached graph, we have the following minima:

Minimum = (-1.5, 0)

Minimum = (7.980, 609.174)

The above means that, the local minima are

(x, f(x)) = (-1.5, 0) and (7.980, 609.174)

Read more about graphs at:

brainly.com/question/20394217

#SPJ1

7 0
1 year ago
Which of these is the correct root of the word judicial?
Kobotan [32]
Pretty sure law. judicial means of, by, or appropriate to a court or judge.
6 0
2 years ago
Experimental verification of opposite side of parallelograms .
zloy xaker [14]
If you mean  proof that the opposite sides of a parallelogram are equal, you draw a diagonal then prove that the 2 triangles formed are congruent.
6 0
3 years ago
Other questions:
  • 8 + 6x - 10x = 16 - 8x
    5·1 answer
  • (27x4 - 18x3 + 9x 2) = 3x<br> Answer ASAP
    13·1 answer
  • If m angle b=(3x-16) degrees, what is the measure of the supplement of angle b
    15·1 answer
  • 4,400 is 10 times as much as 440
    13·1 answer
  • mr. Morgan owns an ice cream shop.His shop made 1,380 last weekend.mr Morgan charges $2 for each scoop of ice cream.about how ma
    8·2 answers
  • 248 is equal to 65 added to w
    15·2 answers
  • The angle measurements in the diagram are represented by the following expressions.
    13·1 answer
  • Jesse found 5 seashells on the beach today. This is 1 less than one-third he found yesterday. Which equation, when solved for x,
    14·1 answer
  • Help !!! i will mark brainliest if u have the correct answer!!
    12·2 answers
  • Бу — 7 = 7<br> 3х — 8y = — 31
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!