6x2y – 2x2y – 10x2y + 8x2y =

The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 sq

lara [203]

Answer:

Part 1) The constant of variation is $k=1/9$

part 2) The equation is $y=\frac{1}{9}x$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

Let

x -----> the number of square feet

y -----> the number of square yards

Three square yards are equivalent to 27 square feet

so

we have the point (27,3)

Part 1) What is the constant of variation?

The constant of variation or proportionality is equal to

$k=y/x$

substitute the values

$k=3/27$

Simplify

$k=1/9$

Part 2) What is the equation representing the direct variation?

we know that

$y=kx$

substitute the value of k

$y=\frac{1}{9}x$

3 0

1 year ago

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Cynthia rounds a number, x,to one decimal place. the result is 6.3.

gladu [14]

The answer is: $6.25\leq6.3$

The explanation is shown below:

1. Cynthia rounds the number, which is identified as $x$ , to one decimal place and the result is 6.3.

2. Based on this, we know that $x$ could have been between 6.25 and 6.35. Therefore, the error interval for $x$ is given by:

$6.25\leq6.3$

Where $\leq$ indicates that the value 6.25 is included and indicates that the value 6.35 is not included (Because if $x$ had been exactly 6.35, Cynthia would round up to 6.4).

7 0

1 year ago

What is the solution to this system of equations? Y= 2x - 3.5 x - 2y = -14

goldfiish [28.3K]

Answer:

x=7

y=10.5

Step-by-step explanation:

1. You can apply the method of substitution, as you can see below:

- Substitute $y=2x-3.5$ into the other equation and solve fo x:

$x-2(2x-3.5)=-14\\x-4x+7=-14\\x=7$

- Substitute the value of x obtain into the first equation, then the value of y is:

$y=2(7)-3.5\\y=10.5$

6 0

1 year ago

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What is the average rate of change of f(x), represented by the graph, over the interval [-2, 2]?

Molodets [167]

To get the average rate of change (ARC) of f(x) over [x1, x2], we use the formula:
ARC = ( f(x2) - f(x2) ) / (x2 - x1)

From the graph
f(2) = 4
f(-2) = 4

Plugging in the values into the formula:
ARC = (4 - 4) / (2 - (-2) )
ARC = 0

The points connecting (-2,4) amd (2,4) is a horizontal line that is the rate of change is 0.

5 0

2 years ago

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A food company originally sells cereal in boxes with dimensions 25 cm by 14 cm by 10 cm. To make more profit, the company decrea

hjlf

Answer:

1.75 cm

Step-by-step explanation:

We are given that the dimensions of the box as 25 cm by 14 cm by 10 cm.

Now, to increase the profit, the dimensions of the box by 'x' cm.

Thus, the new dimensions are (25-x) cm by (14-x) cm by (10-x) cm.

Further, it is given that the volume of the new box is 2,208 $cm^{3}$