The old lion cage at the zoo was a square, with sides x meters long. For the part of the zoo's 50 birthday celecration, the zoo expanded the length and width. The expression for the total area of the new cage is (x^2+18x+81) square meters.
Part 1:Robert thinks that the cage's length had increased by 6 meters, and its width increased by 8 meters. Is Robert right?
Part 2:How much did the zoo expand the length and width?
Part 3:If the area of the old lion cage was 25 square meters, what is the area of the new cage?
I'm not sure what are the answers are. For part 1, I think Robert is wrong, because i used factoring and 6+8=14 and 6 x 8=48.
For part 2, I think the length and width are 9.
Part 3, i don't have an answer for that.
Since x^2 + 18 x + 81 = (x+9)^2, the cage must still be square and increased in length of each side by 9 meters. That answers (1) and (2).
(3) If the old area was 25 m^2, the old side length a was sqrt 25 = 5 m.
Now it is 5 + 9 = 14 m
You all suck an egg even you ms sue
Suck an egg
To find the answers to these questions, let's break down each part:
Part 1:
To determine if Robert is right, we need to compare the given expression for the total area of the new cage (x^2 + 18x + 81) with the dimensions he proposed. According to Robert, the length increased by 6 meters (x + 6) and the width increased by 8 meters (x + 8).
To determine if Robert's proposal matches the expression for the total area of the new cage, we need to expand the expression:
(x + 6) * (x + 8) = x^2 + 8x + 6x + 48 = x^2 + 14x + 48
Comparing this with the given expression (x^2 + 18x + 81) for the total area of the new cage, we can see that Robert's proposal does not match. Therefore, Robert is incorrect.
Part 2:
To find out how much the zoo expanded the length and width, we need to compare the given expression for the total area of the new cage (x^2 + 18x + 81) with the original square cage.
The original square cage has sides x meters long, so its area is x^2 square meters.
Subtracting the original square cage's area from the given expression for the total area of the new cage will give us the expansion:
(x^2 + 18x + 81) - x^2 = 18x + 81
Therefore, the zoo expanded the length and width of the cage by 18x + 81 meters.
Part 3:
To find the area of the new cage if the area of the old lion cage was 25 square meters, we need to substitute the value of the old cage's area (25) into the given expression for the total area of the new cage (x^2 + 18x + 81) and solve for x.
x^2 + 18x + 81 = 25
Rearranging the equation:
x^2 + 18x + 81 - 25 = 0
x^2 + 18x + 56 = 0
Now, we can either factor this quadratic equation or use the quadratic formula to solve for x. After finding the value of x, we can substitute it back into the expression x^2 + 18x + 81 to find the area of the new cage.
It seems like you haven't found an answer for Part 3 yet, since you stopped after factoring the quadratic equation. Once you solve the quadratic equation and find the value of x, substitute that value into the expression x^2 + 18x + 81 to determine the area of the new cage.