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
melamori03 [73]
3 years ago
10

How many right triangles have a hypotenuse that measures 2x + 3 meters and legs that measure 2x - 5 meters and x + 7 meters? Wha

t are their dimensions?
Mathematics
1 answer:
Lady_Fox [76]3 years ago
3 0

Answer:

Two right angled triangle are possible.

Step-by-step explanation:

We are given the following in the question:

Measure of hypotenuse in meters = 2x + 3

Measure of legs in meters = 2x -5 \text{ and }x+7

In a hypotenuse triangle:

(\text{Hypotenuse})^2 = (\text{leg}_1)^2 + (\text{leg}_2)^2

Putting the values, we get,

(2x+3)^2 = (2x-5)^2 + (x+7)^2\\4x^2 + 9+12x = (4x^2 + 25 - 20x) + (x^2 + 49 +14x)\\4x^2 + 9 +12x = 5x^2 -6x +74\\x^2-18x +65 = 0\\x^2 - 13x - 5x + 65 = 0\\x(x-13)-5(x-13) = 0\\(x-13)(x-5) = 0\\x = 13, x = 5

Thus, there are two triangles possible with dimension:

Triangle 1:

\text{Hypotenuse} = 2x + 3 = 2(13) + 3  = 29\\\text{leg}_1 = 2x-5 = 2(13) - 5 = 21\\\text{leg}_2 = x + 7 = 13 + 7 = 20\\

Triangle 2:

\text{Hypotenuse} = 2x + 3 = 2(5) + 3  = 13\\\text{leg}_1 = 2x-5 = 2(5) - 5 = 5\\\text{leg}_2 = x + 7 = 5 + 7 = 12\\

You might be interested in
3x+y=1/3<br> 2x-3y=8/3<br><br> Solve the system of linear equation using any method.
krek1111 [17]
3x + 1y = ¹/₃   ⇒ 9x + 3y = 1
2x -  3y = 2²/₃ ⇒ 2x -  3y = 2²/₃
                                 11x = 3²/₃
                                  11     11
                                     x = ¹/₃
                             3x + y = ¹/₃
                         3(¹/₃) + y = ¹/₃
                               1 + y = ¹/₃
                             - 1        - 1
                                     y = ⁻²/₃
                              (x, y) = (¹/₃, ⁻²/₃)
4 0
4 years ago
A pick-up weighing 1.4 t is loaded with 40 bags of cement each weighing 50 kg. What in the total weight of the pick-up and its l
mixer [17]

Answer:

3.4 tonnes

Step-by-step explanation:

Kg --> tonnes = / 1000

50 x 40 / 1000 = 2. 2 + 1.4 = 3.4.

5 0
2 years ago
Please show me what formula to use to solve equation <br> x2-6x=13
makvit [3.9K]
X^2-6x=13
(x-3)^2-9=13
(x-3)^2=22
(x-3)= +-sqrt22
x = sqrt22+3 or x = -sqrt22+3
3 0
4 years ago
Question is in attached file
Nonamiya [84]

The rate of the passenger train is 81.67 MPH and the rate of the freight train is 66.67 MPH.

<h3>What is a linear equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

The distance traveled by passenger train = 245 miles

The distance traveled by freight train = 245 miles

The time takes for both trains is the same.

Let's suppose the rate of the passenger train is x and the rate of the freight train is y;

As we know,

Distance = speed×time

245/x = 200/y

200x = 245y

200x - 245y = 0 ..(1)

x = 15 + y ..(2)

Equations (1) and (2) represent the situation.

After solving equations (1) and (2):

\rm x=\dfrac{245}{3}= 81.67\\\\\\\:y=\dfrac{200}{3}=66.67

Thus, the rate of the passenger train is 81.67 MPH and the rate of the freight train is 66.67 MPH.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

5 0
2 years ago
Please HELP! URGENT!! <br> Lets say that if 1cm represent 1m in real life, what will 1mm represent?
Ghella [55]
1 mm = 0,1 cm

1 cm - 1 m
0,1 cm - x  m

x=\dfrac{0,1\cdot1}{1}=0,1 \text{ m}=10\text{ cm}
 
4 0
3 years ago
Other questions:
  • Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of op
    8·1 answer
  • PLZ HELP!
    14·2 answers
  • Which is the best description of 4 (21x÷7)
    6·1 answer
  • What number is 120% of 80
    11·1 answer
  • A rectangular filed is 190m by 270m . A rectangular barn is 23 m by 40 m is built in the field .
    7·1 answer
  • 13. Let f(x) = 5x + 10 and g(x) = 2*<br> a) Find f(2)<br> b) Find g(2)<br> c) Find f(2) + g(2)
    12·1 answer
  • WILL MARK BRANLIEst
    14·1 answer
  • Plss can someone help me out with thissss!!!!!!!!!!!
    10·1 answer
  • 6 times the difference of d and 5
    12·2 answers
  • What is the area of a rectangle with a length of 3 1/3 feet and a width of 1 2/3 feet?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!