Answer:
h(x) = (1/2)(x - 3)^2 + 2
Step-by-step explanation:
Start with y = x^3.
Multiply x^3 by the dilation factor (1/2); this compresses the graph vertically.
Next, replace the x in x^3 with (x - 3). This shifts the graph 3 units to the right.
Last, starting with your g(x) = (1/2)(x - 3)^2, add 2
You will end up with h(x) = (1/2)(x - 3)^2 + 2.
Answer:
These lines are perpendicular.
Step-by-step explanation:
Put both equations in the slope intercept form of a line.
y = -6x - 8 This is already in the slope intercept form for a line
-x + 6y = 12 Add x to both sides of the equation
6y = x + 12 Divide through the whole equation by 6
y = 1/6x +2
Now we compare the two slopes of -6 and 1/6. They are negative reciprocals of each other. That means that the line are perpendicular.
Answer:
probability of getting no heads: 1/ 8
probability of at least two tails: 1/4
Step-by-step explanation:
To calculate the probability of getting no heads, multiply the probability of not getting heads for each coin. A coin has two sides: heads and tails; the probability of not getting heads would be 1/2.
1. Multiply the probabilities for each coin
1/2 · 1/2 · 1/2 = 1/8
To calculate the probability of getting at least two tails, multiply the probability of getting tails for two coins and the probability of flipping either heads or tails for the remaining coin. Because it is at least two tails, the remaining coin can flip to either heads or tails.
1. Multiply the probabilities for each coin
1/2 · 1/2 · 2/2 = 1/4
Answer: It will take Damon 6 weeks to save the money he needs to buy the snowboard
Step-by-step explanation:
First, let's see what the problem is giving us:
-The variable X will represent the number of weeks it will take Damon to save the money he needs.
- Damon has $40
- Damon is going to safe $20 weekly
- The snowboard costs $160
Therefor:
Our equation will be: $40 + $20X = $160
Step 1
We need to isolate the variable by subtracting in both sides of the equation 40 in order to maintain the equality.
40 - 40 + 20X = 160 - 40
This will let us with 20X = 120
Step 2
We have to isolate the variable again, but this time (because the variable is being multiplied by 20) we have to divide on both sides of the equation.
20X/20 = 120/20
Therefore: X=6
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The answer is 3125........
