1.Mia charges $2.25 per hour when she babysits, plus $5.00 for transportation expenses.Which function rule represents the amount y mia charges to babysit for x hours?

A)Y = 2.25x + 5.00***
B)X = 5.00y + 2.25
C)Y = 5.00x + 2.25
D)Y = 7.25x

2.(So this one is my updated answer, because I did the work completely wrong the first time)
What are the first four terms of the sequence represented by the expression n(n-1)-5?
A)-7,-5,-3,-1
B)-5,-10,-15,-20
C)0,2,6,12
D)-5,-3,1,7***

3.Suppose you earn $10.00 each hour you babysit.Which function describes the relationship between your total earnings E and the number of hours you babysit, h?
A) E(h)= 10h***
B) E(h)= h + 10
C) E(h)= h - 10
D) E(h)= h = 10E

4.Which function rule represents the data in the table?
X:-3, -2, -1, 0, 1
Y:-1, 2, 5, 8, 11
A) Y = -3x - 8
B) Y = 1/3x - 8
C) Y = 1/3x + 8
D) Y = 3x + 8***

(The last 2 I actually need help with)

5.The data in the table illustrate a linear function
X: -3, 0, 3, 6
Y: -6, -2, 2, 6
A) -4/3
B) -3/4
C) 3/4
D) 4/3

6.Which quadratic rule represents the data in the table?(The up arrows indicate exponents)
X: -1, 0, 1, 2, 3
Y: 4, 5, 4, 1, -4
A) Y = -2x^2 + 5
B) Y = -x^2 + 5
C) Y = x^2 - 5
D) Y = x^2 + 5

your first 4 are correct

#5
you don't say what we are to find, looking at the choices, my guess is the slope
look at the last two ordered pairs (3,2) and (6,6)
slope= (6-2)/(6-3)
= 4/3

#5
Let's pick the easiest point, (1,4)
- it does NOT satisfy A), C) and D)
suggesting B
A quick mental check shows that the other points in your table also work in B

(notice -x^2 means that you have to square the number and them make the result negative, thus -x^2 will always produce a negative result)

Thank you SO MUCH Reiny

5. The data in the table illustrate a linear function.

To determine this, we can examine the change in y for each unit change in x.

From x = -3 to x = 0, y changes from -6 to -2, which is an increase of 4.
From x = 0 to x = 3, y changes from -2 to 2, which is an increase of 4.

Since the change in y for each unit change in x is the same (4), the data represents a linear function.

Therefore, the answer is (C) 3/4.

6. To find the quadratic rule represented by the data in the table, we need to determine the pattern.

Examining the y-values, we can see that they are symmetric around the middle value (x = 1). The pattern is "down 1, up 1, down 3, down 5." This suggests a quadratic relationship where the vertex (maximum or minimum point) is at x = 1.

To determine the specific quadratic rule, we can substitute the x-values and y-values into the general form of a quadratic equation (Y = ax^2 + bx + c) and solve for the coefficients a, b, and c.

Using the x = -1, y = 4:
4 = a(-1)^2 + b(-1) + c => 4 = a - b + c

Using the x = 0, y = 5:
5 = a(0)^2 + b(0) + c => 5 = c

Using the x = 1, y = 4:
4 = a(1)^2 + b(1) + c => 4 = a + b + c

Using the x = 2, y = 1:
1 = a(2)^2 + b(2) + c => 1 = 4a + 2b + c

Using the x = 3, y = -4:
-4 = a(3)^2 + b(3) + c => -4 = 9a + 3b + c

From the second equation, we found c = 5. Substituting this into the other equations, we can solve for a and b.

4 = a - b + 5 => a - b = -1 (Equation 1)
4 = a + b + 5 => a + b = -1 (Equation 2)
1 = 4a + 2b + 5 => 4a + 2b = -4 (Equation 3)
-4 = 9a + 3b + 5 => 9a + 3b = -9 (Equation 4)

Solving these equations simultaneously, we find a = -1 and b = 0.

Therefore, the quadratic rule represented by the data in the table is:
Y = -x^2 + 5

So, the answer is (B) Y = -x^2 + 5.

1. To determine the function rule that represents the amount Mia charges to babysit for x hours, we need to identify the fixed cost (transportation expenses) and the variable cost (hourly rate). The fixed cost is $5.00, and the variable cost is $2.25 per hour. We can write the function rule as Y = 2.25x + 5.00, where Y represents the amount charged and x represents the number of hours babysat. Therefore, the correct answer is A) Y = 2.25x + 5.00.

2. To find the first four terms of the sequence represented by the expression n(n-1)-5, we plug in the values of n and evaluate the expression.
For n = 1: 1(1-1) - 5 = 1(0) - 5 = -5
For n = 2: 2(2-1) - 5 = 2(1) - 5 = -3
For n = 3: 3(3-1) - 5 = 3(2) - 5 = 1
For n = 4: 4(4-1) - 5 = 4(3) - 5 = 7
Therefore, the first four terms of the sequence are -5, -3, 1, 7. The correct answer is D) -5, -3, 1, 7.

3. The relationship between earnings E and the number of hours babysat h can be described by the function E(h) = 10h. Since you earn $10.00 per hour you babysit, the function rule is E(h) = 10h, where E represents total earnings and h represents the number of hours babysat. Therefore, the correct answer is A) E(h) = 10h.

4. To determine the function rule that represents the data in the table, we need to find the relationship between the x-values and the y-values. The given x-values (-3, -2, -1, 0, 1) and y-values (-1, 2, 5, 8, 11) follow a pattern where the y-values increase by 3 for every increase of 1 in the x-values. Therefore, the function rule is Y = 3x + 8, where Y represents the y-values and x represents the x-values. Therefore, the correct answer is D) Y = 3x + 8.

5. The given data represents points on a coordinate plane. To determine if the data represents a linear function, we need to check if the ratio of the change in the y-values to the change in the x-values is constant.
Calculating the ratios for the given data:
(-2 - (-6)) / (0 - (-3)) = 4 / 3
(2 - (-2)) / (3 - 0) = 4 / 3
(6 - 2) / (6 - 3) = 4 / 3
Since the ratios are all equal to 4 / 3, the data represents a linear function. Therefore, the correct answer is A) 4/3.

6. To determine the quadratic rule that represents the data in the table, we need to identify the pattern in the y-values. By observing the table, we can notice that the y-values follow the pattern of decreasing squares of x-values.
The correct answer is B) Y = -x^2 + 5.