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
tekilochka [14]
3 years ago
15

The area of a right triangle is sixty square centimetres. Its base is one centimetre less than twice its height. If the base and

height of the right triangle are both decreased by 2 centimetres, how much will the hypotenuse of the right triangle decrease?
1. 2 centimetres

2. 17 centimetres

3. sqrt(205) centimetres

4. 4 centimetres

5. None of the above
Mathematics
1 answer:
NemiM [27]3 years ago
3 0

Answer:

5. None of the above

Step-by-step explanation:

We have this information:

A = 60 cm2

b = 2*h - 1

Let's find out b and h:

The equation of the are of a triangle is A = (b*h)/2, if we replace it with our information, we have

60 = ((2*h - 1) * h)/2\\ 120 = 2*h^2 - h\\ 0 = 2*h^2 - h - 120

Let's find h with the quadratic formula:

\fbox {Quadratic formula:}  \frac{-b\pm\sqrt{b^2-4ac}}{2a}

h = \frac{-(-1)\pm\sqrt{(-1)^2-4*2*(-120)}}{2*2} = \frac{1\pm\sqrt{961}}{4} = \frac{1\pm\ 31}{4}

h = 8 or h = -7.5

But h represents the height of the triangle, so it has to be a positive number, that's h = 8.

If we replace this in the equation we had for b, we have that b = 2*8 - 1 = 15.

Now we can calculate the hypotenuse with the Pythagorean equation  

\fbox {Pythagorean equation:} <em>The square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the two legs (the two sides that meet at a right angle). </em>

The base and the height are our legs. We will use "H" for the hypotenuse

H^2 = b^2 + h^2 = 15^2 + 8^2 = 289\\ H = \sqrt {289} = 17

H = 17

If we decrease the base and the height by 2 centimeters, we have  

b' = 15 - 2 = 13 and h' = 8 - 2 = 6

With this, let's calculate the new hypotenuse:

H'^2 = b'^2 + h'^2 = 13^2 + 6^2 = 205\\ H' = \sqrt {205} \approx 14.3

H' \approx 14.3

So, the hypotenuse decreases H - H' \approx 17 - 14.3 = 2.7

You might be interested in
M m m m basically what does x equal i guess i dont know for 3x+4
andrey2020 [161]

Answer:

<u>x = -4/3</u>

Step-by-step explanation:

3x + 4 = 0

3x = -4

<u>x = -4/3</u>

3 0
3 years ago
Read 2 more answers
This is stupid I know lol but I'm having a hard time remembering the difference between a histogram and a bar graph. Can someone
Y_Kistochka [10]

<u>In Bar Graphs;</u>

- Bars have equal space

- One the y-axis, we have numbers & on the x-axis, we have data which can be anything.

<u> In Histograms;</u>

- Bars are fixed

- On the y-axis, we have numbers & and on the x-axis, we have data which in continuous & will always be number.

<u>An easy way you can remember the difference is looking at the spaces of the bars. </u>

<em>A bar graph has gaps</em>

<em>A histogram has no gaps.</em>

6 0
2 years ago
Some body please help me!!!!!!
VladimirAG [237]

Surface area of a cube = 486 square inches

Solution:

Given each side of a cube = 9 inches

Net of a cube has 6 squares.

Area of square = side × side

Area of 1 square = 9 × 9 = 81 square inches

Surface area of a cube = Area of 6 squares

                                      = 6 × (side × side)

                                      = 6 × 81

                                      = 486 square inches

Hence, surface area of a cube is 486 square inches.

7 0
3 years ago
At an university 70% of the students who attend stay on campus. If 1,380 of the students who attend live off campus, what is the
Alborosie

Answer:

4600

Step-by-step explanation:

We can write a proportion to find the total amount who attend university using the information given. A proportion is two equivalent ratios set equal to each other. Since 70% live on campus, then 30% live off campus and we are told that number is 1,380.

\frac{30}{100}=\frac{1380}{y}

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

30y=100(1380)

30y=138000

y=4600.

There are 4600 students who attend the university.

7 0
2 years ago
Circle C has radius 5 and center C(6,-2). What is the equation of circle C ?
Delvig [45]

Answer:

i guess it is d

Step-by-step explanation:

make it braintliest please

4 0
3 years ago
Other questions:
  • You've just received an order of silk flower arrangements from your wholesaler. You paid $20.00 each for them. Your store uses a
    13·2 answers
  • Write an equation of the graph:
    12·1 answer
  • Choose the equation of the horizontal line that passes through the point (-8 -7)
    13·1 answer
  • Given the speeds of each runner below, determine who runs the fastest. \text{Katie runs 10 feet per second.} Katie runs 10 feet
    9·1 answer
  • Calcular la velocidad de propagación de una onda que tiene una frecuencia de 60Hz y una longitud de onda de 0.2 m
    9·1 answer
  • A whole number rounded to the nearest ten thousand is 620,000. What is the least possible value for that number?
    14·1 answer
  • What is 30 percent of 210​
    7·1 answer
  • I need help fast please
    14·1 answer
  • PLs answer the question in the picture. I will give a thanks, 5 stars, and BRAINLIEST for a good and applicable answer.
    14·2 answers
  • The current price of a school t-shirt is $10.58. Next year the cost of a t-shirt will be $15.35.
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!