Avoid repeating the question as it can be perplexing.
Given 100 cookies and 20 brownies,
What is the highest number you can divide them equally by?
To find the greatest common factor,
Factor them:
100 = 2*2*5*5
20 = 2*2*5
Thus, the greatest common factor, which is shared between them, is 2*2*5 or 20.
Calculating further, 100/20=5
20/20=1
This means there are 20 groups, each containing 5 cookies and 1 brownie.
20 groups
The expression at hand is:
(-4a ^ -2 b ^ 4) / (8a ^ -6b ^ -3)
Using the laws of exponents, we can transform this expression.
This leads to:
(-4/8) * ((a ^ (- 2 - (- 6))) (b ^ (4 - (- 3))))
Rearranging gives us:
(-2/4) * ((a ^ (- 2 + 6)) (b ^ (4 + 3)))
(-1/2) * ((a ^ 4) (b ^ 7))
-1 / 2a ^ 4b ^ 7
Final Answer:
The exponent for b in Marina's simplification must be 7
If the point (4,-1) is part of the graph of y = f(x), then the related point on the graph of y = g(x) would be: (4,-1/2), (2,-1), (-1,-1), (1,4), (4,-4), (-12,1)
=> (4,-1/2)
=> (2,-1)
=> (-1,-1)
=> (1,4)
=> (4,-4)
=> (-12,1)
Further explanation
-
Dividing the function by 2 results in all the y-values being halved as well. Thus, to determine the new point, we take the y-value (-1) and halve it to arrive at -1/2. Hence, the new point is (4,-1/2).
- When 2 is subtracted from the function's input, it shifts all x-values up by 2. Therefore, to adjust the x-value (4), we add 2 to get 2. Thus, the new point is (2,-1).
- Making the function's input negative alters each x-value by multiplying by -1. Consequently, to find the new point, we take x-value (4) and apply -1 to get -1. Therefore, the new point is (-1,-1).
- Multiplying the function's input by 4 results in each x-value being divided by 4. To find the new x-value from 4, we divide by 4 to get 1. Hence, the new point becomes (1,4).
- When multiplying the entire function by 4, each y-value is increased fourfold. Thus, the original value of 4 becomes -4, making the new point (4,-4).
- By multiplying the entire function by -1, each y-value is also multiplied by -1. As a result, the new y-value becomes 1, leading to the new point (-12,1).
Learn more
- Learn more about corresponding point
- Learn more about point on the graph
- Learn more about the graph
Answer details
Grade: 9
Subject: mathematics
Chapter: corresponding point
Keywords:
corresponding point, the graph, point on the graph