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
Aleonysh [2.5K]
2 years ago
5

The length of a rectangle is 4 m less than the diagonal and the width is 5 m less than the diagonal. If the area is 82 m^2, how

long is the diagonal in meters? Round your answers to the nearest tenth.​
Mathematics
1 answer:
nikklg [1K]2 years ago
5 0

I hate rounding.

Let's call the diagonal x.  It's the hypotenuse of the right triangle whose legs are the rectangle sides.

According to the problem we have a length x-4 and a width x-5 and an area

82 = (x-4)(x-5)

82 = x^2 - 9x + 20

0 = x^2 - 9x - 62

That one doesn't seem to factor so we go to the quadratic formula

x = \frac 1 2(9 \pm \sqrt{9^2-4(62)}) = \frac 1 2(9 \pm \sqrt{329})

Only the positive value makes any sense for this problem, so we conclude

x = \frac 1 2(9 \pm \sqrt{329})

That's the exact answer.  Did I mention I hate rounding?  That's about

x = 13.6 meters

Answer: 13.6

----------

It's not clear to me this problem is consistent.  By the Pythagorean Theorem the diagonal satisfies

x^2 = (x-4)^2 + (x-5)^2

which works out to

x=9 \pm 2\sqrt{10}

That's not consistent with the first answer; this problem really has no solution.  Tell your teacher to get better material.

You might be interested in
Which of the following values of x is a solution to the equation negative 2 x plus 8 equals 14?
andreev551 [17]

Answer:

x= -3

Step-by-step explanation:

-2 x 3 =6 so 6+8=14

5 0
3 years ago
The sum of the first ten terms of a linear sequence is 145. the sum of the next ten term is 445. find the sum of the first four
chubhunter [2.5K]

The sum of the first four terms of the sequence is 22.

In this question,

The formula of sum of linear sequence is

S_n =\frac{n}{2}(2a+(n-1)d)

The sum of the first ten terms of a linear sequence is 145

⇒ S_{10} =\frac{10}{2}(2a+(10-1)d)

⇒ 145 = 5 (2a+9d)

⇒ \frac{145}{5} =2a+9d

⇒ 29 = 2a + 9d  ------- (1)

The sum of the next ten term is 445, so the sum of first twenty terms is

⇒ 145 + 445

⇒ S_{20} =\frac{20}{2}(2a+(20-1)d)

⇒ 590 = 10 (2a + 19d)

⇒ \frac{590}{10}=2a+19d

⇒ 59 = 2a + 19d -------- (2)

Now subtract (2) from (1),

⇒ 30 = 10d

⇒ d = \frac{30}{10}

⇒ d = 3

Substitute d in (1), we get

⇒ 29 = 2a + 9(3)

⇒ 29 = 2a + 27

⇒ 29 - 27 = 2a

⇒ 2 = 2a

⇒ a = \frac{2}{2}

⇒ a = 1

Thus, sum of first four terms is

⇒ S_4 =\frac{4}{2}(2(1)+(4-1)(3))

⇒ S_4 =2(2+(3)(3))

⇒ S₄ = 2(2+9)

⇒ S₄ = 2(11)

⇒ S₄ = 22.

Hence we can conclude that the sum of the first four terms of the sequence is 22.

Learn more about sum of sequence of n terms here

brainly.com/question/20385181

#SPJ4

6 0
1 year ago
Select the correct answer.<br> Solve
Molodets [167]

Answer:

B 1 1/7

Step-by-step explanation:

- 9 2/7 - ( -10 3/7)

We know subtracting a negative is like adding

- 9 2/7 +10 3/7

10 3/7 - 9 2/7

Putting this vertical

10  3/7

-9  2/7

-----------------

1   1/7

5 0
3 years ago
What is the slope and y intercept of y=-7x+12
MrRissso [65]
Hi there!

So the format of slope-intercept form is:

y= mx+b

m= your slope
x = just a variable
b= your y- intercept

Using those hints, see if you can figure out the answer! :)

Hope this helped!

---------------------------

DISCLAIMER: I am not a professional tutor or have any professional background in your subject. Please do not copy my work down, as that will only make things harder for you in the long run. Take the time to really understand this, and it'll make future problems easier. I am human, and may make mistakes, despite my best efforts. Again, I possess no professional background in your subject, so anything you do with my help will be your responsibility. Thank you for reading this, and have a wonderful day/night!

~~~~~~~~~~~~~~~~





























If you're super stuck, your answer would be:

Slope: -7
Y- intercept: 12

3 0
3 years ago
16 is 4% of what number?
IrinaK [193]
16 is 4% of 400 

Change the percentage into a decimal by dividing the decimal over 100:
\frac{4}{100} = 0.04

Divide 16 by the decimal (0.04):
16 \div 0.04 = 400
3 0
3 years ago
Other questions:
  • Is 5/8 greater than 6/16
    7·1 answer
  • if the minimum wage in 2017 was $13.15 and in 2018 it is $14.45, what percent did minimum wage increase
    11·1 answer
  • Situation:
    5·1 answer
  • How to do vertical and horizontal lines in a graph
    15·2 answers
  • What is the solution to the given system of equations?​
    10·1 answer
  • A flagpole casts a shadow 15 feet long. Brad is 6 feet tall. If Brad casts a 4.5ft shadow, how tall is the flag pole?
    5·1 answer
  • Four students, Kaylee, Xavier, Ruby, and Brandon, line up one behind the other. How many different ways can they stand in line?
    12·1 answer
  • HELP HELP HELP PLEASSSEEEE!!!!!!! THIS IS MAKING MY MIND GO NUTS!
    15·1 answer
  • Light travels at a speed of approximately Light travels at a speed of approximately 1,000,000,000 kilometers per second (621,118
    14·1 answer
  • Seven friends go to the local sandwich shop. All six people order the combination meal, which includes a drink and a veggie wrap
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!