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NikAS [45]
3 years ago
11

The area of a rectangular television screen is 3456 in^2. The width of that screen is 24 inches longer than the length. What is

a quadratic equation the represents the area of the screen? What are the dimensions of the screen?
Mathematics
1 answer:
shutvik [7]3 years ago
4 0
1. The problem says that the television has a rectangular shape. So, the formula for caculate the area of a rectangle is:

 A=LxW

 "A" is the area of the rectangle (A=3456 inches²).
 "L" is the the length of the rectangle.
 "W" is the width of the rectangle.

 2. The <span>width of the screen is 24 inches longer than the length. This can be expressed as below:

 W=24+L

 3. Then, you must substitute </span>W=24+L into the formula A=LxW:
<span>
 </span>A=LxW
<span> 3456=L(24+L)
 3456=24L+L</span>²
<span>
 4. The quadratic equation is:

 L</span>²+24L-3456=0

 5. When you solve the quadratic equation, you obtain:

 L=48 inches

 6. Finally, you must substitute the value of the length, into W=24+L:

 W=24+L
 W=24+48
 W=72 inches

 7. Therefore, the dimensions of the screen are:

 L=48 inches
 W=72 inches<span> </span>
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The product of two consecutive positive integers is 29 more than their sum. Find the integers
Rina8888 [55]
The consecutive positive integers would be: x and (x+1),
We would have to solve the following equation to find these numbers:
x(x+1)-[x+(x+1)]=29
x²+x-2x-1=29
x²-x-30=0
x=[1⁺₋√(1+120)]/2
x=(1⁺₋11)/2
We have two possible solutions:
x₁=(1-11)/2=-5    then: (x+1)=-5+1=-4  This is not the solution.
x₂=(1+11)/2=6    then: (x+1)=6+1=7    This solution is right.

Answer: the numbers would be 6 and 7. 
7 0
2 years ago
A warehouse is 55 yards long, 35 yards wide, and 5 yards high. What is the area of the warehouse floor? If the warehouse is fill
amid [387]

Answer:

The area of the warehouse floor is 1925yd²

The volume of the boxes is 4812.5yd³

Step-by-step explanation:

First we have to calculate the area, for this we must multiply the length by the width

a = area

l = long = 55yd

w = width = 35yd

a = l * w

a = 55yd * 35yd

a = 1925yd²

to calculate the volume we have to multiply the area by the height

asks us for the volume for half the height so we have to divide the height by 2

a = area = 1925yd²

h = height = 5yd/2 = 2.5yd

v = volume

v = a * h

v = 1925yd² * 2.5yd

v = 4812.5yd³

The area of the warehouse floor is 1925yd²

The volume of the boxes is 4812.5yd³

5 0
3 years ago
Is 1,341,491 divisible by 9?
zheka24 [161]

Answer:

no

Step-by-step explanation:

you would get this: 149054.555556

8 0
2 years ago
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Nd the 52nd term and the term named in the problem <br>40, 140, 240, 340, ...<br>Find a 32​
Galina-37 [17]

Answer:

5140 and 3140

Step-by-step explanation:

Note there is a common difference d between consecutive terms in the sequence, that is

d = 140 - 40 = 240 - 140 = 340 - 240 = 100

This indicates the sequence is arithmetic with n th term

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 40 and d = 100, thus

a_{52} = 40 + (51 × 100) = 40 + 5100 = 5140

a_{32} = 40 + (31 × 100) = 40 + 3100 = 3140

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