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
Licemer1 [7]
3 years ago
12

The area of a door is 3024 square inches. If

Mathematics
1 answer:
olasank [31]3 years ago
7 0

Answer:

Lets take all factors into consideration first

The door is a rectangle and the area of a rectangle is length times width

Let the width be w

Let the length be l

Equation length × breadth = area

(w+48)w = 3024

w^2 + 48w = 3024

w^2 + 48w - 3024 = 0

w^2 + 84w - 36w - 3024 = 0

w(w + 84) -36 ( w + 84) = 0

(w + 84) (w - 36) = 0

w + 84 = 0 AND w - 36 =0

w = -84 and w = 36

Since width cannot be negative, the right answer is 36

How did I get 84 and 36? Well, I had to factorize 3024 and since 84 times 36 is 3024 and 84 minus 36 is 48, I chose them.

You might be interested in
A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the flo
Arada [10]

Answer:

The parabolic shape of the door is represented by y - 32 = -\frac{2}{49}\cdot x^{2}. (See attachment included below). Head must 15.652 inches away from the edge of the door.

Step-by-step explanation:

A parabola is represented by the following mathematical expression:

y - k = C \cdot (x-h)^{2}

Where:

h - Horizontal component of the vertix, measured in inches.

k - Vertical component of the vertix, measured in inches.

C - Parabola constant, dimensionless. (Where vertix is an absolute maximum when C < 0 or an absolute minimum when C > 0)

For the design of the door, the parabola must have an absolute maximum and x-intercepts must exist. The following information is required after considering symmetry:

V (x,y) = (0, 32) (Vertix)

A (x, y) = (-28, 0) (x-Intercept)

B (x,y) = (28. 0) (x-Intercept)

The following equation are constructed from the definition of a parabola:

0-32 = C \cdot (28 - 0)^{2}

-32 = 784\cdot C

C = -\frac{2}{49}

The parabolic shape of the door is represented by y - 32 = -\frac{2}{49}\cdot x^{2}. Now, the representation of the equation is included below as attachment.

At x = 0 inches and y = 22 inches, the distance from the edge of the door that head must observed to avoid being hit is:

y -32 = -\frac{2}{49} \cdot x^{2}

x^{2} = -\frac{49}{2}\cdot (y-32)

x = \sqrt{-\frac{49}{2}\cdot (y-32) }

If y = 22 inches, then x is:

x = \sqrt{-\frac{49}{2}\cdot (22-32)}

x = \pm 7\sqrt{5}\,in

x \approx \pm 15.652\,in

Head must 15.652 inches away from the edge of the door.

8 0
3 years ago
Help math math math ASAP
STALIN [3.7K]
<h3><u>Solution</u>:-</h3>

The equation of any straight line can be written as in slope intercept form as -

\green{ \underline { \boxed{ \sf{y=mx+c}}}}

where,

  • m is its slope
  • c is its y-intercept.

<em><u>Given equation:- </u></em>

\begin{gathered}\\\implies\quad \sf 5x+y = 10 \\\end{gathered}

<u>Arranging it in slope intercept form by transposing 5x to RHS </u>

\begin{gathered}\\\implies\quad \sf y = 10 -5x \\\end{gathered}

\begin{gathered}\\\implies\quad \sf y =  -5x +10\\\end{gathered}

\leadstoComparing the equation y = -5x +10 with the standard form of the equation, we get -

\quad \bull\: \sf m= -5

\quad \bull \: \sf c= 10

Thus , 5 is our required answer.

4 0
2 years ago
Read 2 more answers
What’s 1 km 600m turned into meters
Art [367]
I'm pretty sure its 1600m
8 0
3 years ago
Read 2 more answers
Technically the elasticity number is negative because
Len [333]
<span>When price falls quantity demanded will rise, but for simplicity economists take the absolute value of the elasticity number.</span>
4 0
3 years ago
= ______units^3 <br><br> please help (:
Nat2105 [25]

Answer:

V = \frac{4}{3}π units^3

Step-by-step explanation:

The formula for the volume of a sphere is:

V = 4π\frac{r^{3} }{3}

Now, substitute 1 for r because the radius is 1:

V = 4π\frac{1^{3} }{3}

Next, simplify the fraction:

V = \frac{1}{3}(4π)

Finally, multiply \frac{1}{3} by 4π:

V = \frac{4}{3}π

8 0
3 years ago
Other questions:
  • Do not understand how to get the grades percent
    13·1 answer
  • Can someone answer this question please answer it correctly if it’s corect I will mark you brainliest
    7·2 answers
  • Which one please? Thanks for your help.
    15·1 answer
  • 3x = 21, then x = ? please help i dont really understand and te answer choices are 7, 18, 6
    7·2 answers
  • Help me pls thanks so much
    11·1 answer
  • Jenny makes 5 out of every 6 foul throw shots she attempts. If she missed 36 foul throw
    7·1 answer
  • −3x^2−4x+7 answer this problem please - algebra - factoring
    13·2 answers
  • một kho hàng có 927 chiếc quạt, đã chuyển đi 1/9 số quạt đó. Hỏi kho hnag còn lại bao nhiêu chiếc quạt?
    9·1 answer
  • Does this table represent a function or not? Why or why not?
    12·2 answers
  • In a sequnece u5=-3.7 and u15 =-52.3, what is the 19th term
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!