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How do you write 1 is to 2 as 5 is to x as a proportion in fractional notation?

A. 2/1 = 5/x
B. 1/2 = 5/x
C. 1 : 2 = 5 : x
D. 1 : 3 :: 5 : x

11 answers

The correct answer to express "1 is to 2 as 5 is to x" in fractional notation is:

B. \( \frac{1}{2} = \frac{5}{x} \)

This representation shows the proportion clearly, stating that the ratio of 1 to 2 is the same as the ratio of 5 to x.

Determine if 2.25/10 ?= 9/40' 2.5/10 ?= 90/40' or 2.25/12 ?= 90/40 is a proportion.

A. None of these sets of ratios is a proportion.
B. 2.25/10 = 9/40
C. 2.25/12 = 90/40
D. 2.5/10 = 90/40

To determine whether each set of ratios is a proportion, we need to check if the cross products are equal for each pair of ratios:

  1. For the ratio \( \frac{2.25}{10} \) and \( \frac{9}{40} \):

    • Cross Multiply: \( 2.25 \times 40 \) and \( 10 \times 9 \)
    • Calculate: \( 2.25 \times 40 = 90 \) and \( 10 \times 9 = 90 \)
    • Since \( 90 = 90 \), this is a proportion.

  2. For the ratio \( \frac{2.5}{10} \) and \( \frac{90}{40} \):

    • Cross Multiply: \( 2.5 \times 40 \) and \( 10 \times 90 \)
    • Calculate: \( 2.5 \times 40 = 100 \) and \( 10 \times 90 = 900 \)
    • Since \( 100 \neq 900 \), this is not a proportion.

  3. For the ratio \( \frac{2.25}{12} \) and \( \frac{90}{40} \):

    • Cross Multiply: \( 2.25 \times 40 \) and \( 12 \times 90 \)
    • Calculate: \( 2.25 \times 40 = 90 \) and \( 12 \times 90 = 1080 \)
    • Since \( 90 \neq 1080 \), this is not a proportion.

From this analysis, the only correct proportion is from the first set:

The answer is B. \( \frac{2.25}{10} = \frac{9}{40} \).

Meters Feet
7 23.03
6 19.74
5 16.45
4 13.16

Determine the number of feet in 1 meter.

A. 3.29 feet
B. 4/13.16 foot
C. 161.21 feet
D. 0.304 feet

To determine the number of feet in 1 meter, we can use the given data from the table and find the conversion factor.

From the table, we can see that 7 meters corresponds to 23.03 feet. To find how many feet are in 1 meter, we can set up the following equation using the data from the table:

\[ \text{Feet per meter} = \frac{\text{Total feet}}{\text{Total meters}} = \frac{23.03 \text{ feet}}{7 \text{ meters}} \]

Calculating that:

\[ \text{Feet per meter} = \frac{23.03}{7} \approx 3.290 \]

So, there are approximately 3.29 feet in 1 meter.

Thus, the correct answer is:

A. 3.29 feet.

You made 280.00 for working 40, which is described by 40y = $280.00x. Determine your earnings per hour.

A. $0.14
B. $70.00
C. $11,200
D. $7.00

To determine your earnings per hour, you can simply divide your total earnings by the total hours worked.

From the information provided:

  • Total earnings = $280.00
  • Total hours worked = 40 hours

Calculating the earnings per hour:

\[ \text{Earnings per hour} = \frac{\text{Total earnings}}{\text{Total hours}} = \frac{280.00}{40} = 7.00 \]

Therefore, your earnings per hour is $7.00.

The correct answer is:

D. $7.00.

(10, 5)
(8, 4)
(4, 2)

The proportional relationship is shown on the graph. Derive the equation of the line y = mx through the origin.

A. y = 4x
B. y = 1/2x
C. y = 2x
D. y = 8x

To derive the equation of the line \(y = mx\) through the origin, we need to determine the slope \(m\) of the line using the points provided.

Given Points:
(10, 5)
(8, 4)
(4, 2)

We can calculate the slope \(m\) using any two points. The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Let's calculate the slope using the points (10, 5) and (4, 2):

\[ m = \frac{2 - 5}{4 - 10} = \frac{-3}{-6} = \frac{1}{2} \]

Now that we have the slope, the equation of the line through the origin is:

\[ y = \frac{1}{2}x \]

Thus, the answer to the question is:

B. \(y = \frac{1}{2}x\).

Graph the proportional relationship y = x by plotting points.

A.
(0, 0)
(1, -1)
(2, -2)
B.
(2, 2)
(0, 0)
(1, 1)
C.
(2, 4)
(1, 2)
(0, 0)
D.
(3, 1)
(0, 0)

(0, 0)
(100, 5)
(200, 10)
(300, 15)

The equation \( y = x \) represents a proportional relationship where the output is equal to the input. The points on this line will include pairs where the y-coordinate matches the x-coordinate.

Let's evaluate the provided options:

A.

  • (0, 0)
  • (1, -1)
  • (2, -2)
    (This is incorrect because the y-values should equal the x-values, not their negatives.)

B.

  • (2, 2)
  • (0, 0)
  • (1, 1)
    (This is correct because all points fit the equation \( y = x \).)

C.

  • (2, 4)
  • (1, 2)
  • (0, 0)
    (This is incorrect because the points do not fit \( y = x \). The y-values are twice the x-values.)

D.

  • (3, 1)
  • (0, 0)
    (This is incorrect because (3, 1) does not fit \( y = x \).)

Thus, the correct set of points that represent the proportional relationship \( y = x \) is:

B.

  • (2, 2)
  • (0, 0)
  • (1, 1)