The local ice cream shop offers a deal on Wednesday where you can pay $4 for a plain ice cream sundae and $1 per topping you choose (maximum of 10 toppings). Which of the following graphs best models the cost someone could pay using this offer? (1 point)

Answer 1

To model the cost of an ice cream sundae based on the number of toppings chosen, we can define the variables:

• Let \( x \) be the number of toppings (where \( x \) can range from 0 to 10).
• The cost of the plain ice cream sundae is $4.
• Each topping costs an additional $1.

The total cost \( C \) can be expressed with the equation: \[ C = 4 + x \]

Here, the minimum cost when no toppings are added (when \( x = 0 \)) is $4, and the maximum cost when 10 toppings are added (when \( x = 10 \)) is $14, calculated as follows:

• When \( x = 10 \): \[ C = 4 + 10 = 14 \]

This relationship shows a linear function with a slope of 1 (for each additional topping, the cost increases by $1) and a y-intercept at 4 (the cost of the sundae without any toppings).

Graph Characteristics:

1. The x-axis represents the number of toppings (from 0 to 10).
2. The y-axis represents the total cost (ranging from $4 to $14).
3. The graph should be a straight line starting at the point (0, 4) and extending to (10, 14).

Conclusion:

To find the correct graph, look for:

• A linear line beginning at (0, 4) and ending at (10, 14).
• The line should have a positive slope, indicating that cost increases with the number of toppings chosen.

This description should guide you to identify the correct graph representing the cost of the ice cream sundae with toppings.

Answer 2

A car has 86,391 miles on its odometer and accumulates an average of 260 more each week. What is the function rule that represents the total number of M miles the car will have on the odometer after w weeks? (1 point)
Responses

M(w)=86,391+260w

M(w)=86,391w+260w

M(w)=86,391+260

M(w)=86,391w+260

Answer 3

To find the function rule that represents the total number of miles \( M \) the car will have on the odometer after \( w \) weeks, we need to consider the initial mileage and the mileage accumulated over time.

1. Initial mileage: The car currently has 86,391 miles.
2. Mileage accumulated per week: The car accumulates 260 miles each week.

Thus, after \( w \) weeks, the total mileage \( M \) will be the initial mileage plus the mileage gained from the weeks:

\[ M(w) = 86,391 + 260w \]

Conclusion:

The correct function rule is: \[ M(w) = 86,391 + 260w \]

So the answer is: M(w) = 86,391 + 260w.

Answer 4

(3 points)
The value of a motorcycle changes according to the equation V(t)=5,000(1.03)^t
, where V(t) = value in dollars and t= time in years.


In the equation, the number 5,000 represents the (Blank) of the motorcycle.

What does V(t)=9000 mean in the context of this problem? (Blank)

What does a value of t = 3 mean in the context of this problem? (Blank)

Answer 5

Certainly! Let's break down each part of your question based on the equation \( V(t) = 5,000(1.03)^t \).

1. In the equation, the number 5,000 represents the (Blank) of the motorcycle.

   The number 5,000 represents the initial value of the motorcycle or its value at time \( t = 0 \) years.

2. What does \( V(t) = 9000 \) mean in the context of this problem? (Blank)

   The equation \( V(t) = 9000 \) means that the value of the motorcycle is $9,000 at a certain time \( t \). To find the specific time, you would solve for \( t \) when \( V(t) = 9000 \).

3. What does a value of \( t = 3 \) mean in the context of this problem? (Blank)

   A value of \( t = 3 \) means that 3 years have passed since the initial value was recorded. Thus, \( V(3) \) represents the value of the motorcycle after 3 years.

Summary:

1. In the equation, the number 5,000 represents the initial value of the motorcycle.
2. \( V(t) = 9000 \) means the value of the motorcycle is $9,000.
3. A value of \( t = 3 \) means that 3 years have passed since the initial value was recorded.

Answer 6

Select the domain and range of the function below. You must pick one of each for credit.

(2 points)
Responses

{y | −∞<y ≤−2}

{y | −2≤y <∞}

{x | −∞<x <∞}

{y | −∞<y<∞}

{x | −2≤x <∞}

Answer 7

To determine the domain and range of a function, we need to have the specific function you are referring to. However, since you haven't provided that function, I'll explain how to assess the provided options for domain and range.

1. Domain refers to all the possible input values (usually represented as \( x \)).
2. Range refers to all the possible output values (usually represented as \( y \)).

Based on the options you've given, here’s how they can be interpreted:

Options for the Domain:

1. {x | −∞ < x < ∞} : This indicates all real numbers; the function accepts any real number as an input.
2. {x | −2 ≤ x < ∞} : This indicates that the function accepts all real numbers \( x \) that are greater than or equal to -2.

Options for the Range:

1. {y | −∞ < y ≤ −2} : This indicates all \( y \) values less than or equal to -2.
2. {y | −2 ≤ y < ∞} : This indicates all \( y \) values greater than or equal to -2.
3. {y | −∞ < y < ∞} : This indicates all real numbers, meaning the function can produce any output value.

Making a Selection:

Without the specific function, I can't definitively tell you which domain and range apply. However, if we consider the most common cases:

• If the function is polynomial: The domain is usually all real numbers \({x | −∞ < x < ∞}\), and the range depends on the degree and leading coefficient of the polynomial.

• If the function is a linear function like a line that doesn't have restrictions: Domain could also be \({x | −∞ < x < ∞}\) and range would be \({y | −∞ < y < ∞}\).

• If it opens upwards or downwards with a vertex: Then the range would reflect the minimum or maximum point.

Recommended Allowed Selections:

If you are unsure, you might choose:

• For domain: {x | −∞ < x < ∞} (if the function is unrestricted).
• For range: {y | −∞ < y < ∞} (if the function is unrestricted and can take any output).

Please provide the specific equation of the function if you need accurate selections for the domain and range!

Answer 8

Which equation has the same zeros as the function graphed? (0, 2) (0, 5)

(1 point)
Responses

(x−2)^2=y

(x−2)^2=(x+5)^2+y

(x+5)(x + 2)=y

(x−2)(x−5)=y

Answer 9

To determine which equation has the same zeros as the function graphed at the points (0, 2) and (0, 5), we first need to identify the x-values that correspond to these y-values.

The zeros of a function are the values of \( x \) for which the function's output (\( y \)) equals zero.

From the points you provided (0, 2) and (0, 5), we can deduce:

1. The function has zeros (or roots) where \( y = 0 \), which means we need to find the x-values that make the equation equal to zero.

Now, let's analyze the given responses:

1. \( (x - 2)^2 = y \):

   • Zeros: Set \( y = 0 \): \((x - 2)^2 = 0\) gives \( x = 2 \).
   • Zero at 2 only, does not match.

2. \( (x - 2)^2 = (x + 5)^2 + y \):

   • This equation seems more complex, but we would set \( y = 0 \) to look for zeros.
   • Would need to be expanded and solved for specific zeros, not straightforward.

3. \( (x + 5)(x + 2) = y \):

   • Zeros: Set \( y = 0\): \((x + 5)(x + 2) = 0\) gives:
     • \( x + 5 = 0 \Rightarrow x = -5 \)
     • \( x + 2 = 0 \Rightarrow x = -2 \)
   • Zeros at -5 and -2, does not match.

4. \( (x - 2)(x - 5) = y \):

   • Zeros: Set \( y = 0\): \((x - 2)(x - 5) = 0\) gives:
     • \( x - 2 = 0 \Rightarrow x = 2 \)
     • \( x - 5 = 0 \Rightarrow x = 5 \)
   • Zeros at 2 and 5, which matches the requirement.

Conclusion:

The equation that has the same zeros as the function graphed at points (0, 2) and (0, 5) is:

\( (x - 2)(x - 5) = y \).

Answer 10

Look at the equation below.

−10x+13+12x=5x−8


Which of the following steps could be used to transform the equation into the form x=a
, where a
is a number, to show that the equation has one solution?

Select TWO options that apply.

(2 points)
Responses

Subtract 13 from both sides of the equation and then simplify.

Add 5x to both sides of the equation and then simplify.

Subtract 10x from both sides of the equation and then simplify.

Add 8 to both sides of the equation and then simplify.

Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.

Answer 11

To solve the equation \(-10x + 13 + 12x = 5x - 8\) and transform it into the form \(x = a\), let's analyze the steps provided in the options, focusing on simplifying the equation correctly.

Steps to Consider:

1. Combine Like Terms on the Left Side: \(-10x + 12x\) combines to \(2x\). Thus, the equation simplifies to: \[ 2x + 13 = 5x - 8 \]

2. Rearranging the Equation: Now, we want to isolate \(x\) by moving all \(x\) terms to one side and constant terms to the other side.

Analyzing the Options:

1. Subtract 13 from both sides of the equation and then simplify.

   • This will help isolate \(x\) and is a good step.
   • When you do this, you'll have: \[ 2x = 5x - 8 - 13 \Rightarrow 2x = 5x - 21 \]

2. Add 5x to both sides of the equation and then simplify.

   • Adding \(5x\) would result in: \[ 2x + 5x + 13 = -8 \Rightarrow 7x + 13 = -8, \] which is not necessary; you could accomplish the goal in other ways.

3. Subtract 10x from both sides of the equation and then simplify.

   • This means transferring \(10x\) to the right side: \[ 13 + 12x - 10x = 5x - 8 \Rightarrow 13 + 2x = 5x - 8. \] This is acceptable.

4. Add 8 to both sides of the equation and then simplify.

   • Adding \(8\) would not be directly useful to isolate \(x\) at this point in the equation.

5. Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.

   • This step is incorrect since \(10x\) and \(12x\) do not combine to \(22x\) (they combine to \(2x\)).

Conclusion:

The two appropriate steps that could be used to transform the equation into the form \(x = a\) are:

1. Subtract 13 from both sides of the equation and then simplify.
2. Subtract 10x from both sides of the equation and then simplify.

This will ultimately lead to the correct transformation isolating \(x\).