The length of a rectangle is five inches less than twice its width. If the rectangle has a perimeter of 80 inches, findthe length and width.
Answers
50 + 30 = 80
Related Questions
A charity fair raised $6,000 by selling 500 lottery tickets. There were two types of lottery tickets: A tickets cost $10 each, and B tickets cost $60 each. How many tickets of each type were sold?
Expand and simplify the following expression:
Sin78 ×cos42+cos78×sin42 evaluate without the use of a calculator
What's does 2 alternate interior angle equals?
Answers
Answer:
Step-by-step explanation:
To maximize the area of the two identical rectangular pens, we need to find the dimensions that will allow us to enclose the largest possible area using the given 480 feet of fencing.
Let's start by assigning variables to the dimensions of the rectangular pen. Let's say the length of the pen is "L" and the width is "W". Since the two pens share one wall, we can divide the available fencing equally between the two long sides and the two short sides.
The equation for the perimeter of a rectangle is: P = 2L + 2W.
In this case, we have two pens, so the total perimeter is 480 feet: 2L + 2W = 480.
We can simplify this equation by dividing both sides by 2: L + W = 240.
To maximize the area, we need to find the dimensions that satisfy this equation while maximizing the product of L and W, which represents the area.
Since the pens are identical, we can express one dimension in terms of the other. Let's solve the equation for L: L = 240 - W.
Now, substitute this expression for L in the equation for the area: A = L * W = (240 - W) * W.
To find the maximum area, we need to find the value of W that maximizes the expression (240 - W) * W.
One way to do this is by graphing the equation or using calculus, but since this is likely a high school-level problem, we can use the concept of symmetry.
Since the equation for the area is quadratic, the maximum area will occur at the midpoint of the symmetry axis. In this case, the symmetry axis is given by W = 240/2 = 120.
So, to maximize the area, each pen should have a width of 120 feet.
Substituting this value back into the equation for the perimeter, we can find the length of each pen: L + 120 = 240, L = 240 - 120 = 120.
Therefore, the dimensions of each pen that will maximize the area are 120 feet by 120 feet.
Keep in mind that this is just one possible answer, as there may be other valid dimensions that also maximize the area. However, for a symmetrical solution, both pens should have equal dimensions.
Answers
x + (x + 2) = 236
solve for x
2x + 2 = 236
subtract 2 from each side of the equation
2x = 234
divide both sides by 2
x = 117
117 is the first odd integer. to find the other integer (x + 2), substitute 117 for x, and you have 117 + 2, which equals 119
The two consecutive odd integers that add up to 236 are 117 and 119.
Answers
Answers
Answers
Answer:
The residual value is -0.75
Step-by-step explanation:
we know that
The residual value is the observed value minus the predicted value.
RESIDUAL VALUE=[OBSERVED VALUE-PREDICTED VALUE]
where
Predicted value.--> the predicted value given the current regression equation
Observed value. --> The observed value for the dependent variable.
in this problem
we have the point (1,4)
so
The observed value is 4
Find the predicted value for x=1
predicted value is 4.75
so
RESIDUAL VALUE=(4-4.75)=-0.75
Answer:
-0.75
Step-by-step explanation:
Answers
First part: when (6x + 2) is positive
6x + 2 < 10
6x < 10 - 2
6x < 8
x < 8/6
x < 4/3
Second part: when (6x + 2) is negative.
-(6x + 2) < 10 Divide both sides of inequality by -1 and change the sign.
(6x + 2) > -10
6x + 2 > -10
6x > -10 - 2
6x > -12 Divide both sides by 6.
x > -12/6
x > -2.
Combined solution: x < 4/3 and x > -2
-2 < x < 4/3.
Graph is a line on the number line between -2 and 4/3.
-2 and 4/3 are excluded from solution.