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
grigory [225]
3 years ago
14

The longest side of a triangle is 4 more than twice the shortest. The third side is 3 more than the shortest. The perimeter is 3

1. Find all sides of the triangle.
Mathematics
1 answer:
kondaur [170]3 years ago
7 0

Answer:

The shortest side = 6

The third side = 9

The hypotenuse (the longest side) = 16

Step-by-step explanation:

First, let's establish the following based on the information given:

The shortest side = x

The third side = (x + 3)

The hypotenuse (the longest side) = (2x + 4)

The perimeter = 31

Since the perimeter is the total of all 3 sides, we are left with this equation:

(x) + (x + 3) + (2x + 4) = 31

From here, combine like-terms and solve for x.

(x) + (x + 3) + (2x + 4) = 31

(4x + 7) = 31

4x = 24

x = 6

Now that we know the value of x, we can apply this to the predetermined formulas to find the measurements of the remaining two sides.

The shortest side = 6

The third side = (x + 3) = 9

The hypotenuse (the longest side) = (2x + 4) = (2(6) + 4) = (12 + 4) = 16

To check, add all of the sides together to make sure they equal 31.

6 + 9 + 16 = 31

~Hope this Helps!~

You might be interested in
If tan of angle theta = 11/60 , what is the value of cot angle theta?
UkoKoshka [18]
The tangent and cotangent functions of the angle are related such that one is the reciprocal of the other. From the given tan theta = 11 / 60. The reciprocal of this number is 60 / 11. This value is also the cotangent of the angle. Thus, the cotangent angle theta is 60 / 11. 
5 0
3 years ago
Read 2 more answers
In a batch of 890 calculators, 12 were found to be defective. What is the probability that a calculator chosen at random will be
jarptica [38.1K]
890 times 12 equals 10680
4 0
3 years ago
Which definite integral approximation formula is this: the integral from a to b of f(x)dx ≈ (b-a)/n * [<img src="https://tex.z-d
Stella [2.4K]

The answer is most likely A.

The integration interval [<em>a</em>, <em>b</em>] is split up into <em>n</em> subintervals of equal length (so each subinterval has width (<em>b</em> - <em>a</em>)/<em>n</em>, same as the coefficient of the sum of <em>y</em> terms) and approximated by the area of <em>n</em> rectangles with base (<em>b</em> - <em>a</em>)/<em>n</em> and height <em>y</em>.

<em>n</em> subintervals require <em>n</em> + 1 points, with

<em>x</em>₀ = <em>a</em>

<em>x</em>₁ = <em>a</em> + (<em>b</em> - <em>a</em>)/<em>n</em>

<em>x</em>₂ = <em>a</em> + 2(<em>b</em> - <em>a</em>)/<em>n</em>

and so on up to the last point <em>x</em> = <em>b</em>. The right endpoints are <em>x</em>₁, <em>x</em>₂, … etc. and the height of each rectangle are the corresponding <em>y </em>'s at these endpoints. Then you get the formula as given in the photo.

• "Average rate of change" isn't really relevant here. The AROC of a function <em>G(x)</em> continuous* over an interval [<em>a</em>, <em>b</em>] is equal to the slope of the secant line through <em>x</em> = <em>a</em> and <em>x</em> = <em>b</em>, i.e. the value of the difference quotient

(<em>G(b)</em> - <em>G(a)</em> ) / (<em>b</em> - <em>a</em>)

If <em>G(x)</em> happens to be the antiderivative of a function <em>g(x)</em>, then this is the same as the average value of <em>g(x)</em> on the same interval,

g_{\rm ave}=\dfrac{G(b)-G(a)}{b-a}=\dfrac1{b-a}\displaystyle\int_a^b g(x)\,\mathrm dx

(* I'm actually not totally sure that continuity is necessary for the AROC to exist; I've asked this question before without getting a particularly satisfying answer.)

• "Trapezoidal rule" doesn't apply here. Split up [<em>a</em>, <em>b</em>] into <em>n</em> subintervals of equal width (<em>b</em> - <em>a</em>)/<em>n</em>. Over the first subinterval, the area of a trapezoid with "bases" <em>y</em>₀ and <em>y</em>₁ and "height" (<em>b</em> - <em>a</em>)/<em>n</em> is

(<em>y</em>₀ + <em>y</em>₁) (<em>b</em> - <em>a</em>)/<em>n</em>

but <em>y</em>₀ is clearly missing in the sum, and also the next term in the sum would be

(<em>y</em>₁ + <em>y</em>₂) (<em>b</em> - <em>a</em>)/<em>n</em>

the sum of these two areas would reduce to

(<em>b</em> - <em>a</em>)/<em>n</em> = (<em>y</em>₀ + <u>2</u> <em>y</em>₁ + <em>y</em>₂)

which would mean all the terms in-between would need to be doubled as well to get

\displaystyle\int_a^b f(x)\,\mathrm dx\approx\frac{b-a}n\left(y_0+2y_1+2y_2+\cdots+2y_{n-1}+y_n\right)

7 0
3 years ago
17) x =<br> (6x-7)<br> (103-x)
Firlakuza [10]

Answer:

6B = F8

Step-by-step explanation:

5 0
3 years ago
PLEASE HELP ITS ABOUT TO BE DUE
Jlenok [28]

Answer:

x=-1

Step-by-step explanation:

4(x-3(-2))=6(x-3(-2)) => 4(x+6)=6(x+6) => 4x+24=6x+26 => -2=2x => x=-1

6 0
3 years ago
Other questions:
  • The answer please ?????
    5·1 answer
  • Alexis has a rectangular piece of red paper that is 4 centimeters wide. It’s length is 8 centimeters. She glued a rectangular pi
    5·1 answer
  • I need help with this can you type what I need to type in
    11·1 answer
  • Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m² by increasing the w
    15·1 answer
  • A rider sits on a motorcycle. The motorcycle has a mass of 237kg. The rider has a mass of 89kg. What is the total mass of the mo
    5·1 answer
  • Write an equation in slope-intercept form for the line with slope 8 and y-intercept -8.​
    11·1 answer
  • Pls answer……………………..
    13·1 answer
  • Jennifer and Micaela are selling pies for a school fundraiser. Customers can buy apple pies and pumpkin pies. Jennifer sold 4 ap
    14·1 answer
  • Find the product of 7×1/2
    11·1 answer
  • If every 5 minutes I get 3 coins then how long will it take for me to get 75 coins?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!