Let the number be x.
x - 25 = -50
x = -50 + 25
x = -25
Hence, the number is -25.
Answer:
sqrt(882) or 29.698
Step-by-step explanation:
AD^2 + DC^2 = AC^2
sqrt(21^2+21^2) = 29.698
y = m x + b is a linear equation.
This equation is in the slope - intercept form, where m is the slope and b is y - intercept.
For example: y = 2 x + 5
In this equation: m = 2 ( the slope ) and b = 5 ( the line intercepts y-axis at the point ( 0, 5 ) ).
Answer:
Height: 3/2 inches
Length: 12 inches
Width: 4 inches
Step-by-step explanation:
Let x is the side length of the square
The height of the box by cutting squares off :x
- The new length of the cardboard = 15 -2x (because we cut from 4 corners)
- The new width of the cardboard = 7 -2x (because we cut from 4 corners)
The new volume of it is:
V = (15 -2x) (7 -2x) x
<=> V =
To maximum volume, we use the first derivative of the volume
<=> 
<=> 
<=> 2x -3 = 0 or 6x -35 = 0
<=> x = 3/2 or x = 35/6
To determine which value of x gives a maximum, we evaluate
= 24x -88
= 24(3/2) -88 = -52
= 24(35/6) -88 = 52
We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.
So the dimensions (in inches) of the box is:
Height: 3/2 inches
Length: 15-2(3/2) = 12 inches
Width: 7 - 2(3/2) = 4 inches