Questions: Using a constant of variation of 6/7, complete the table of values for the relationship between x and y. Write your answers in the spaces provided. x 0 14 □ y 6 18 24

Using a constant of variation of 6/7, complete the table of values for the relationship between x and y. Write your answers in the spaces provided. x 0 14 □ y 6 18 24
Transcript text: \$ 8 Using a constant of variation of $\frac{6}{7}$, complete the table of values for the relationship between $x$ and $y$. Write your answers in the spaces provided. \begin{tabular}{|c|c|c|c|c|c|} \hline$x$ & 0 & & 14 & & $\square$ \\ \hline$y$ & & 6 & & 18 & 24 \\ \hline \end{tabular} Copying permitted for classroom use.
failed

Solution

failed
failed

Solution Steps

To solve this problem, we need to use the concept of direct variation, where \( y = kx \) and \( k \) is the constant of variation. Given \( k = \frac{6}{7} \), we can find the missing values in the table by applying this formula. For each pair of \( x \) and \( y \), if one value is missing, we can solve for it using the equation \( y = \frac{6}{7}x \).

Step 1: Determine the Constant of Variation

The constant of variation is given as \( k = \frac{6}{7} \).

Step 2: Calculate Missing \( y \) Values

Using the formula \( y = kx \):

  • For \( x = 0 \): \[ y = \frac{6}{7} \cdot 0 = 0 \]
  • For \( x = 14 \): \[ y = \frac{6}{7} \cdot 14 = 12 \]
Step 3: Calculate Missing \( x \) Values

Using the formula \( x = \frac{y}{k} \):

  • For \( y = 6 \): \[ x = \frac{6}{\frac{6}{7}} = 7 \]
  • For \( y = 18 \): \[ x = \frac{18}{\frac{6}{7}} = 21 \]
  • For \( y = 24 \): \[ x = \frac{24}{\frac{6}{7}} = 28 \]

Final Answer

The completed table of values is: \[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & 0 \\ 7 & 6 \\ 14 & 12 \\ 21 & 18 \\ 28 & 24 \\ \hline \end{array} \] Thus, the final answers are: \[ \boxed{(x = 0, y = 0), (x = 7, y = 6), (x = 14, y = 12), (x = 21, y = 18), (x = 28, y = 24)} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Position three pulleys at the angles assigned for F1, F2 and the equilibrant force FE, exp = -FR of 3 and recorded in Table 1, and attach the masses corresponding to these forces to the ends of the strings passing over these pulleys. Add the force, F3, to the proper position and record its magnitude and position in Table 9. Determine the uncertainties δm and δθ by making an adjustment to the mass and the angle, respectively, until the ring shifts, but doesn't touch the pin, then calculate the uncertainty δF by using Eq. (5) and record all these values in Table 9. Write your result in the box below in the form F3 ± δF (in N) at θ3 ± δθ (in degrees) Compare the experimental and theoretical values for the F3 clearly stating the quantitative value you are comparing.
failedAnswered
Native American nations often allied themselves with rivaling European settlers. These alliances affected their relationships with one another. Which statements best describes one way these alliances affected Native Americans? A. Native Americans formed one nation to fight European settlers. B. Native American introduced other Native Americans to the concept of religion. C. Native Americans captured other Native Americans for the slave trade. D. Native Americans fought other Native Americans for control of the colonists.
failedAnswered
With the information shown above, we can also determine that BC is congruent to BC. Therefore, which of the following theorems affirms that triangle GCB is congruent to triangle HCB? Choose two. A Side-Side-Side Congruence. B Angle - Side - Angle Congruence. C Side - Side - Angle Congruence. D Side - Angle - Side Congruence.
failedAnswered
Find the horizontal intercepts of the function f(x)=3x-4-1 The intercepts are at x=
failedAnswered
Who should PPPO and PPSO personnel contact first with contract and contract surveillance questions?