Linear Equations Sample Assignment
- An integer is 3 less than 5 times another. If the product of the two integers is 36, then find the integers.
Let one of the integer be x
The other integer will be 5x-3
Therefore; x(5x-3) = 36
5x2-3x-36=0
Therefore, x=3
Hence the integers are 3 and 5(3)-3=12
2) The width of a rectangle is 5 units less than the length. If the area is 150 square units, then find the dimensions of the rectangle.
Let the length of the rectangle be x units
Width will be x-5 Units
X(x-5) = 150
5x2-3x-36=0
Therefore, x = 15
Hence; The dimensions are;
Length = x units = 15 units
Width = x-5 = 15-5 = 10units
- The length of a rectangle is 4 inches more than its width. The area of the rectangle is equal to 5 inches more than 2 times the perimeter. Find the length and width of the rectangle.
Let the width = x
Length = x+4
Area = 3xPerimeter+5
X(x+4)=2(2(l+b)+5)
X2+4x=4(2x+4)+5
x2-4x-21=0
Therefore, length = x+4 = 7+4 = 11 inches
Width = x = 7 Inches
- The height of a projectile launched upward at a speed of 32 feet/second from a height of 128 feet is given by the function ℎ(𝑡)=−16𝑡2+32𝑡+128. How long will it take the projectile to hit the ground?
Let h = 0, since height of the ground is zero.
−16𝑡2+32𝑡+128=0
-16(t+2)(t-4)=0
t = -2 or t = 4
Time cannot be a negative value so we ignore t = -2
Therefore, the projectile will hit the ground in 4 Seconds.
- The height of an object dropped from the top of a 144-foot building is given by ℎ(𝑡) = −16𝑡2+144. How long will it take the object to hit the ground?
The ball will hit the ground at h=0
−16𝑡2+144 = 0
T2=9
t = 3 Seconds
Therefore; The ball will hit the ground in 3 Seconds.
