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4 years ago

The variable Z is directly proportional to X. when X is 15, Z has the value of 45. what is the value of Z when X=23

1 answer:

8 0

$If\ Z\ is\ directly\ proportional\ to\ X\ then\ \frac{Z}{X}=const.\\------------------------\\X=15\ and\ Z=45\\\\X=23\ and\ Z=?\\\\\frac{Z}{23}=\frac{45}{15}\to\frac{Z}{23}=3\ \ \ \ |multiply\ both\ sides\ by\ 23\\\\\huge\boxed{Z=69}$

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Answer:

9 students chose duck

Step-by-step explanation:

The question says "6 more students chose duck than chose penguin"

This means that you would add 6 to the number that chose penguin, which is 3.

6 + 3 = 9

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3 years ago

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4 years ago

the equation of line cd is y = 3x − 3. write an equation of a line perpendicular to line cd in slope-intercept form that contain

liberstina [14]

Answer:

The required equation is $y=-\frac{1}{3}x+2$ .

Step-by-step explanation:

The equation of line cd is

$y=3x-3$

Slope intercept form of a line is

$y=mx+b$

Where, m is slope and b is y-intercept.

Slope of line cd is 3.

The product of slopes of two perpendicular lines is -1.

$m_1\times m_2=-1$

$3\times m_2=-1$

$m_2=-\frac{1}{3}$

Therefore slope of perpendicular line is $-\frac{1}{3}$ .

Point slope form of a line is

$y-y_1=m(x-x_1)$

Slope of perpendicular line is $-\frac{1}{3}$ and line passing through the point (3,1).

$y-1=-\frac{1}{3}(x-3)$

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

$y=-\frac{1}{3}x+2$

Therefore the required equation is $y=-\frac{1}{3}x+2$ .

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3 years ago

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What is the vertex of the graph of this equation y=2x^2+8x-24

sdas [7]

Answer:

The vertex would be D) (-2, -32)

Step-by-step explanation:

To find the vertex , start by find the x-value. For this we can use the equation below.

x = -b/2a

In which a is the coefficient of x^2 and b is the coefficient of x.

x = -b/2a

x = -(8)/2(2)

x = -8/4

x = -2

Now that we have x, we find y by plugging -2 in for each x.

y = 2x^2 + 8x - 24

y = 2(-2)^2 + 8(-2) - 24

y = 2(4) - 16 - 24

y = 8 - 16 - 24

y = -32

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3 years ago

What is the slope of the line that passes through the points (1,-5) and (3,5)?

Lana71 [14]

Answer:

a) 5

Step-by-step explanation:

Put them into slope intercept form AKA y=mx+b: -5=m1+b and 5=m3+b

Subtract the equations to get -10=-2m

Divide both sides by two to get: 5=m

Hope this helps! (^-^)

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3 years ago