Find the equation of the linear function represented by the table below in slope-intercept form.
X: -4 1 6 11
Y: -21 -1 19 39
To find the equation of a linear function in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
Let's first find the slope (m) using the formula:
m = (change in y) / (change in x)
For the points (-4, -21) and (1, -1):
m = (-1 - (-21)) / (1 - (-4))
m = 20 / 5
m = 4
Now, let's use the slope-intercept form of a linear function (y = mx + b) and substitute the slope we found:
y = 4x + b
To find the y-intercept (b), we can choose any point from the table and substitute its coordinates into the equation. Let's use the point (1, -1):
-1 = 4(1) + b
-1 = 4 + b
b = -1 - 4
b = -5
Now substitute the value of b back into the equation:
y = 4x - 5
Therefore, the equation of the linear function represented by the table is y = 4x - 5 in slope-intercept form.
Adrian is going to an amusement park. The price of admission into the park is $35, and once he is inside the park, he will have to pay $3 for every ride he rides on. How much money would Adrian have to pay in total if he goes on 12 rides? How much would he have to pay if he goes on r rides?
Cost with 12 rides:
Cost with r rides:
To find the total cost if Adrian goes on 12 rides, we need to calculate the cost of admission plus the cost of the rides.
The cost of admission is $35.
The cost of each ride is $3.
So, the total cost if Adrian goes on 12 rides would be:
Total cost = Admission cost + (Cost per ride x Number of rides)
Total cost = $35 + ($3 x 12)
Total cost = $35 + $36
Total cost = $71
Therefore, Adrian would have to pay $71 in total if he goes on 12 rides.
To find the cost if Adrian goes on r rides, we can use the same formula.
Total cost = Admission cost + (Cost per ride x Number of rides)
Total cost = $35 + ($3 x r)
Total cost = $35 + $3r
Therefore, if Adrian goes on r rides, he would have to pay $35 + $3r in total.
Nora is taking a multiple choice test with a total of 100 points available. Each question is worth exactly 2 points. What would be Nora's test score (out of 100) if she got 6 questions wrong? What would be her score if she got x questions wrong?
Score with 6 questions wrong:
Score with x questions wrong:
If Nora got 6 questions wrong, she would lose 6 points because each question is worth 2 points. Since each question is worth 2 points, her score would be:
Total score = Total points available - Points lost
Total score = 100 - (6 * 2)
Total score = 100 - 12
Total score = 88
Therefore, Nora's test score would be 88 out of 100 if she got 6 questions wrong.
If Nora got x questions wrong, she would lose x * 2 points because each question is worth 2 points. Her score would be:
Total score = Total points available - Points lost
Total score = 100 - (x * 2)
Total score = 100 - 2x
Therefore, Nora's test score would be 100 - 2x out of 100 if she got x questions wrong.
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
3, 12, 48, ...
Answer
Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.
3, 12, 48, ...
Attempt 1 out of 3
This is….sequence and the…is equal to…
To determine whether the sequence is arithmetic or geometric, we need to look for a pattern in the differences or ratios between consecutive terms.
Let's look at the differences between consecutive terms:
12 - 3 = 9
48 - 12 = 36
The differences between consecutive terms are not constant, so the sequence is not arithmetic.
Now let's look at the ratios between consecutive terms:
12 / 3 = 4
48 / 12 = 4
The ratios between consecutive terms are constant (4), so the sequence is geometric.
The common ratio in this sequence is 4.