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Question Use the table to answer the question. ($) Cost of Candy Bar A Quantity ($) Cost 1 1.25 2 2.50 3 3.75 4 5.00 5 6.25 The cost of Candy Bar A is displayed in the table. The proportional relationship between the cost and quantity for Candy Bar B is represented by the equation y=x . Which candy bar is the cheapest cost per bar? Enter 1 for Candy Bar A. Enter 2 for Candy Bar B. (1 point) Skip to navigation

11 answers

To find out which candy bar is the cheapest cost per bar, we need to calculate the cost per bar for both Candy Bar A and Candy Bar B.

Cost per bar for Candy Bar A:

  • For 1 bar: $1.25 = $1.25 per bar
  • For 2 bars: $2.50 = $1.25 per bar
  • For 3 bars: $3.75 = $1.25 per bar
  • For 4 bars: $5.00 = $1.25 per bar
  • For 5 bars: $6.25 = $1.25 per bar

The cost per bar for Candy Bar A is consistently $1.25.

Cost per bar for Candy Bar B: According to the equation \(y = x\), the cost is equal to the quantity. So:

  • For 1 bar: Cost = $1.00 (1 x $1.00)
  • For 2 bars: Cost = $2.00 (2 x $1.00)
  • For 3 bars: Cost = $3.00 (3 x $1.00)
  • For 4 bars: Cost = $4.00 (4 x $1.00)
  • For 5 bars: Cost = $5.00 (5 x $1.00)

The cost per bar for Candy Bar B is $1.00.

Conclusion:

  • Candy Bar A costs $1.25 per bar.
  • Candy Bar B costs $1.00 per bar.

Thus, Candy Bar B is cheaper.

The answer is 2 for Candy Bar B.

Use the image to answer the question. Use the graph to derive the equation of the line in slope-intercept form. (1 point) Skip to navigation

To derive the equation of a line in slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), you'll typically need to follow these steps:

  1. Identify the Slope:

    • Pick two points on the line. Let’s say these points are \((x_1, y_1)\) and \((x_2, y_2)\).
    • The formula for slope \(m\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

  2. Identify the Y-Intercept:

    • Find the point where the line crosses the y-axis. This point will have the coordinates \((0, b)\), where \(b\) is the y-intercept.

  3. Write the Equation:

    • Substitute the slope \(m\) and y-intercept \(b\) into the slope-intercept form \(y = mx + b\).

If you can provide me with the specific coordinates or a description of the graph, I can help you derive the equation accurately!

Write y−6x=5 in slope-intercept form(1 point) y=

To write the equation \(y - 6x = 5\) in slope-intercept form (\(y = mx + b\)), we need to isolate \(y\).

Here are the steps:

  1. Start with the original equation:

    \[ y - 6x = 5 \]

  2. Add \(6x\) to both sides to isolate \(y\):

    \[ y = 6x + 5 \]

Now, the equation is in slope-intercept form, where the slope \(m = 6\) and the y-intercept \(b = 5\).

Thus, the final slope-intercept form is:

\[ y = 6x + 5 \]

Describe what makes a proportion. Give an example of a proportion.(2 points)

A proportion is an equation that states that two ratios are equal. It is typically written in the form \( \frac{a}{b} = \frac{c}{d} \), where \( a \), \( b \), \( c \), and \( d \) are numbers, and \( b \) and \( d \) are not zero. For a proportion to hold true, the cross products (the product of the means and the product of the extremes) must be equal, which means that \( a \cdot d = b \cdot c \).

Properties of Proportions:

  1. Cross Product Property: If \( \frac{a}{b} = \frac{c}{d} \), then \( a \cdot d = b \cdot c \).
  2. Equivalent Ratios: If two ratios are equivalent, they can be expressed as a proportion.

Example of a Proportion:

Consider the following ratios:

\[ \frac{1}{2} = \frac{3}{6} \]

In this case:

  • The first ratio \( \frac{1}{2} \) means for every 1 part, there are 2 total parts.
  • The second ratio \( \frac{3}{6} \) means for every 3 parts, there are also 6 total parts.

To verify that these two ratios form a proportion, we can use the cross product property:

  • Cross multiplying gives us: \[ 1 \cdot 6 = 2 \cdot 3 \] which simplifies to: \[ 6 = 6 \]

Thus, since both sides are equal, this confirms that \( \frac{1}{2} \) and \( \frac{3}{6} \) are indeed in proportion.

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Use the image to answer the question. Find the coordinates of the intersection point that solves the system of these two linear equations in two variables: 2x+y=15 and y=−x+5 . (1 point) Responses (5,−10) left parenthesis 5 comma negative 10 right parenthesis (−10, 5) left parenthesis negative 10 comma 5 right parenthesis (−5, 10) left parenthesis negative 5 comma 10 right parenthesis (10,−5) left parenthesis 10 comma negative 5 right parenthesis Skip to navigation

To find the intersection point that solves the system of the equations \(2x + y = 15\) and \(y = -x + 5\), we can substitute the second equation into the first equation.

  1. Start with the first equation:
    \[ 2x + y = 15 \]

  2. Substitute \(y\) from the second equation into this equation:
    \[ y = -x + 5 \]
    Substitute for \(y\) in the first equation:
    \[ 2x + (-x + 5) = 15 \]

  3. Solve for \(x\):
    \[ 2x - x + 5 = 15 \]
    \[ x + 5 = 15 \]
    \[ x = 10 \]

  4. Now, substitute \(x = 10\) back into the second equation to find \(y\):
    \[ y = -10 + 5 \]
    \[ y = -5 \]

So, the coordinates of the intersection point are \((10, -5)\).

Thus, the correct response is: \[ (10, -5) \text{ (10, -5)} \]