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3 years ago

The sum if three consecutive even numbers is 78 What is the smallest of the three numbers ?

1 answer:

5 0

Let the smallest number equal n. Therefore, the other numbers are (n+2) and (n+4).

The sum of the three numbers are:

$n + (n+2) + (n+4)$

$=3n+6$

Since the sum equals 78,

$3n+6=78$

Divide both sides by 3,

$n+2=26$

$n=24$

Therefore, the smallest number is 24.

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Given that D(x) = 2x, select all of the following that are true statements

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Answer:

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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 $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem

$D(x)=2x$

D(x) is a direct variation (linear function)

The variable x is the independent variable or input value

The variable D(x) is the dependent variable or output value

<u><em>Verify each statement</em></u>

case 1) D(x) is a function

The statement is true

see the explanation

case 2) x is the dependent variable

The statement is false

The variable x is the independent variable or input value

case 3) D(x) is a direct variation

The statement is true

see the explanation

case 4) D(x) is a rule for the set of points (5.10). (6, 12) and (-2,-4)

The statement is true

Because

For x=5

substitute in the linear equation

$D(x)=2(5)=10$ ---> is ok

For x=6

substitute in the linear equation

$D(x)=2(6)=12$ ---> is ok

For x=-2

substitute in the linear equation

$D(x)=2(-2)=-4$ ---> is ok

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3 years ago

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(n-10)

Step-by-step explanation:

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2 years ago

Solve the system of equations by graphing: -1/3x + y=-1, y=4+1/3x

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$-\frac{1}{3}x$ + y = -1 ⇒ y = $\frac{1}{3}x$ - 1

To graph this line, plot a point at the y-intercept (0, -1), than plot the next point using the rise over run from the slope $(\frac{1}{3})$ by counting up 1 and to the right 3 of the y-intercept. This gives you a second point of (3. 0). Draw a line through those two coordinates.

Answer: Plot (0, -1) and (3, 0) and draw a line through them.

***************************************************************************************

y = 4 + $\frac{1}{3}x$ ⇒ y = $\frac{1}{3}x$ + 4

Same as above. Plot the y-intercept (0, 4) and then use rise over run from the slope to plot (3, 5).

Answer: Plot (0, 4) and (3, 5) and draw a line through them.

***********************************************************************************

You should end up with two PARALLEL lines. Since the lines never intersect, there are no solutions to this system of equations.

Answer: No Solution

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3 years ago