The value of a baseball card in dollars has been found to be 0.15y + 0.35, where y is the number of years since it was released. By how much is the baseball card's value increasing per year?

Question

A.
$0.15

B.
$0.35

C.
15%

D.
35%
.

Answer 1

The value of the baseball card is given by the equation \( V(y) = 0.15y + 0.35 \), where \( V \) is the value in dollars and \( y \) is the number of years since it was released.

To find out how much the value of the baseball card is increasing per year, we can look at the coefficient of \( y \) in the equation. The coefficient \( 0.15 \) represents the increase in value for each additional year.

Therefore, the baseball card's value is increasing by $0.15 per year.

The correct answer is:

A. $0.15

Answer 2

Manipulate the equation y=5x-11 so that it is written in terms of x. Which equation is equivalent to y=5x-11?
A.
x=(y/11) -5
B.
x= y+11/5

C.
y-11/5
D.
x=(y/5) +11

Answer 3

To manipulate the equation \( y = 5x - 11 \) in terms of \( x \), we can follow these steps:

1. Add 11 to both sides of the equation: \[ y + 11 = 5x \]

2. Divide both sides by 5 to isolate \( x \): \[ x = \frac{y + 11}{5} \]

Now let's match this with the answer options you provided:

A. \( x = \frac{y}{11} - 5 \)

B. \( x = \frac{y + 11}{5} \)

C. \( x = \frac{y - 11}{5} \)

D. \( x = \frac{y}{5} + 11 \)

The equivalent equation derived from the manipulation of \( y = 5x - 11 \) is:

B. \( x = \frac{y + 11}{5} \).

Answer 4

Charity is buying peaches at the store. The cost of the peaches are $1.30 per pound. If she has $6.50 to spend on peaches, how many pounds (x) can she buy?
Set up an equation to solve the problem.
A.
1.30x=6.50
B.
1.30+x=6.50
C.
1.30/6.50 =x
D.
6.50x=1.30

Answer 5

To find out how many pounds of peaches Charity can buy with $6.50, we need to set up an equation based on the cost per pound.

Given that the cost of peaches is $1.30 per pound, we can denote the number of pounds of peaches she can buy as \( x \). The total cost of the peaches will then be the cost per pound multiplied by the number of pounds. This gives us the following equation:

\[ 1.30x = 6.50 \]

This equation states that the cost of the peaches (at $1.30 per pound) multiplied by the number of pounds \( x \) is equal to her total budget of $6.50.

Therefore, the correct answer is:

A. \( 1.30x = 6.50 \).

Answer 6

Jackson solved the problem 3x-8=2(2x-7) using the following steps:
STEP 1: Use Distributive Property to get 3x-8=4x-14
STEP 2: Use Addition Property of Equality to get 3x = 4x-14+8
STEP 3: Combine Like Terms to get 3x = 4x-6
STEP 4: Use Subtraction Property of Equality to get 3x-4x= -6
STEP 5: Combine Like Terms to get (-x)=-6
What is the last step?
A.
Use Property of Equality to get x= (-6)
B.
Divide both sides by -1 to get x=6
C.
Divide both sides by -1 to get x= (-6)
D.
Use Multiplication Property of Equality to get x=6

Answer 7

Let's analyze Jackson's steps to find the last step in solving the equation.

From Jackson’s last step, he ended with:

\[ -x = -6 \]

To isolate \( x \), we need to divide both sides of the equation by \(-1\):

\[ \frac{-x}{-1} = \frac{-6}{-1} \]

This simplifies to:

\[ x = 6 \]

Therefore, the last step is:

B. Divide both sides by -1 to get \( x = 6 \).

Answer 8

A computer technician charges a fixed amount for a repair, plus an additional amount per hour. The equation below describes y, the total amount the technician charges, in dollars, based on x hours for the repair.

What is the meaning of the initial amount for the equation?

A.
It means the technician charges $45 per hour for the repair.

B.
It means the technician charges a fixed amount of $45 for the repair.

C.
It means the technician charges a fixed amount of $75 for the repair.

D.
It means the technician charges $75 per hour for the repair.

Answer 9

To determine the meaning of the initial amount in the equation, we first need to recognize that the initial amount typically refers to the fixed charge for the service, which is independent of the number of hours worked.

If the equation describing the total amount charged by the technician is structured like this:

\[ y = mx + b \]

where \( m \) is the amount charged per hour and \( b \) is the fixed initial charge, then the initial amount can be referred to as \( b \).

Without the specific equation provided, you would typically interpret the initial amount as the fixed charge for the repair.

Given the options you provided, if we assume the initial fixed amount is $75, then the correct interpretation would be:

C. It means the technician charges a fixed amount of $75 for the repair.

If it were $45, the statement would be:

B. It means the technician charges a fixed amount of $45 for the repair.

Please confirm the specific equation or values to provide a precise answer!