<h3>
Answer:</h3>
2xy
<h3>
Step-by-step explanation:</h3>
GCF stands for the greatest common factor.
Finding All Factors
To find the GCF you need to find the factors of each term. First, find the factors of the coefficients.
- The factors of 18 include: 1, 2, 3, 6, 9 and 18
- The factors of 32 include: 1, 2, 4, 8, 16, and 32
Next, lay out the variables that are factors.
- The variables of 18xy are x and y.
- The variables of 32xyz are x, y, and z.
Remember that variables count as factors
Greatest Common Factor
Now that we have all of the factors we can find the GCF. The GCF will be the largest number and the most variables that are a factor of both terms.
In this case, the largest factor of 18 and 32 is 2. Since both x and y are factors of both terms, the GCF is 2xy.
The parabolic motion is an illustration of a quadratic function
The equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
<h3>How to model the function?</h3>
Given that:
x stands for time and y stands for height in feet
So, we have the following coordinate points
(x,y) = (5,0), (11,0) and (10,80)
A parabolic motion is represented as:
y =ax^2 + bx + c
At (5,0), we have:
25a + 5b + c = 0
c= -25a - 5b
At (11,0), we have:
121a + 11b + c = 0
Substitute c= -25a - 5b
121a + 11b -25a - 5b = 0
Simpify
96a + 6b = 0
At (10,80), we have:
100a + 10b + c = 80
Substitute c= -25a - 5b
100a + 10b - 25a -5b = 80
75a -5b = 80
Divide through by 5
15a -b = 16
Make b the subject
b = 15a + 16
Substitute b = 15a + 16 in 96a + 6b = 0
96a + 6(15a + 16) = 0
Expand
96a + 90a + 96 = 0
This gives
186a = -96
Solve for a
a = -16/31
Recall that:
b = 15a + 16
So, we have:
b = -15 * 16/31 + 16
b =-240/31 + 16
Take LCM
b =(-240 + 31 * 16)/31
[tex]b =256/31
Also, we have:
c= -25a - 5b
This gives
c= 25*16/31 - 5 * 256/31
Take LCM
c= -880/31
Recall that:
y =ax^2 + bx + c
This gives
y = -16/31x^2 + 256/31x - 880/31
Hence, the equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31
Read more about parabolic motion at:
brainly.com/question/1130127
D. Distributive Property
The distributive property allow you to multiply a sum by multiplying each addend separately.
Answer:
(0.18 x 23.50) + 23.50
Step-by-step explanation:
First, find the percentage of 23.50 (equation in the parenthesis). 18% is equivalent to 0.18. Then, you add that to 23.50. That's the total amount Sam should pay. I hope this makes sense.
Please write your points by enclosing the x- and y-components inside parentheses: (2, 4) and (7,2). Use the distance formula. Do you know it?
Distance between (2,4) and (7,2) is Sqrt ( [7-2]^2 + [2-4]^2 )
Note: by "Quasstion" you most likely meant "question."
