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Aleonysh [2.5K]
3 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]3 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.

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Answer:

<h2>$66</h2>

Step-by-step explanation:

Step one:

given data

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$4 per bag

$10 weekly fee

let the number of bag be x

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Step two:

the independent variable is the weekly fee of $10

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6 0
3 years ago
9) Nancy starts a race at the start line and she is running 3 meters per second. Juan starts the same race 3 meters ahead of Nan
Travka [436]

Given:

Nancy is running 3 meters per second.

Juan starts the same race 3 meters ahead of Nancy but he is going at 2 meters per second.

To find:

The equations for Nancy and Juan.

Solution:

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Nancy is running 3 meters per second. So, the total distance covered by Nancy in the race is

y=3x

Juan starts the same race 3 meters ahead of Nancy but he is going at 2 meters per second. So, the total distance covered by Juan in the race is

y=3+2x

Therefore, the equations of Nancy and Juan are y=3x and y=3+2x respectively.

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3 years ago
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3 years ago
Which is a true statement about 10 days of production?
aalyn [17]
The answer to this question is C
5 0
3 years ago
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Pls pls pls helppp<br> ------------------
aliina [53]

Answer:

\fbox {x-intercepts : (1, 0) and (-3, 0)}

\fbox {Roots : x = 1, x = -3}

Step-by-step explanation:

<u>Given</u> :

  • y = 4x² + 8x - 12

4 cancels throughout.

  • <u>y = x² + 2x - 4</u>

<u>Solving by quadratic formula</u> :

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  • x = -8 ± √256 / 8
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∴ Hence, the x-intercepts are (1, 0) and (-3, 0). The roots of the equation are 1 and -3.

7 0
2 years ago
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