1. A company that manufactures drinking glasses packages 100 glasses per container for shipping. During the packaging process, an average of 3 glasses are broken per container. If the company needs to package and ship 14,000 drinking glasses that are not broken, EXACTLY how many glasses must the company manufacture?
2. What is the value of the larger of the zeros of the function?
g (x) = (x-2) (x+9)
3. The function f(x)=-1/8^2+3/2x represents the height in the air of a T-shirt after is it released from a launcher during a baseball game. Let f(x) represent the height, in yards, of the T-shirt after x seconds. What is the height, in yards, of the T-shirt after 2 seconds, written as an improper fraction. (Or you could just do it and I'll do the fraction myself)
4. The equation f (x) = 4x^2 - 12x + 13 is written as the equivalent function f (x) (2x-3)^2 + k. What is the vale of k?
.97x = 14000
well, the zeros are -9 and 2, so ...
Or, you could just do it yourself
f(x)=-1/8 x^2+3/2 x
f(2) = -1/8 (2^2) + 3/2 (2)
...
well, (2x-3)^2 = 4x^2 - 12x + 9
so, ...
I need someone to dumb the answers for 3 and 4 waaaayyyy down. Could anyone do this?
Nvm, just 4
Wait, so the answer to #4 is 9? Somebody plz help! This is a really important benchmark and I don't have a lot of time to finish it, then I have another one to do! I have to have them both turned in in just a few hours.
1. To find the number of glasses that the company must manufacture, we need to calculate the total number of containers required to package 14,000 glasses.
Since each container holds 100 glasses and 3 glasses are broken per container, the number of glasses that make it to the container is 100 - 3 = 97 glasses.
Let's calculate the number of containers required by dividing the total number of glasses (14,000) by the number of glasses per container (97):
Containers = 14,000 / 97 ≈ 144.33
Since we can't have a fraction of a container, we need to round up to the next whole number. Therefore, the company needs to package 145 containers.
To find the number of glasses the company must manufacture, we multiply the number of containers by the number of glasses per container:
Number of glasses = Containers * Glasses per container
Number of glasses = 145 * 100 = 14,500 glasses
Therefore, the company must manufacture exactly 14,500 glasses.
2. To find the value of the larger zero of the function g(x) = (x-2)(x+9), we need to find the values of x where g(x) equals zero.
Setting g(x) equal to zero and factoring the equation, we get:
(x-2)(x+9) = 0
To determine the values of x that make the equation true, we set each factor equal to zero:
x-2 = 0 or x+9 = 0
Solving these equations, we get:
x = 2 or x = -9
The larger zero between these values is x = 2.
Therefore, the value of the larger zero of the function is 2.
3. To find the height of the T-shirt after 2 seconds, we need to substitute 2 into the function f(x) = -1/8^2 + 3/2x.
f(x) = -1/8(2)^2 + 3/2(2)
Simplifying the equation, we get:
f(x) = -1/8(4) + 3/2(2)
= -1/2 + 6/2
= 5/2
So, the height of the T-shirt after 2 seconds is 5/2 yards, which is also equal to 2 1/2 yards as an improper fraction.
4. To find the value of k in the equation f(x) = 4x^2 - 12x + 13 = (2x-3)^2 + k, we can compare the given equation with the standard form for a perfect square trinomial:
f(x) = (2x-3)^2 + k
Given that f(x) = 4x^2 - 12x + 13, we can equate the corresponding terms:
4x^2 - 12x + 13 = (2x-3)^2 + k
Expanding (2x-3)^2 and simplifying the equation, we get:
4x^2 - 12x + 13 = 4x^2 - 12x + 9 + k
Comparing the like terms, we find that the equation is satisfied if:
13 = 9 + k
To find the value of k, we subtract 9 from both sides:
k = 13 - 9
k = 4
Therefore, the value of k in the equation f(x) = (2x-3)^2 + k is 4.