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3 years ago

Proportional constant

Mathematics

1 answer:

Jobisdone [24]3 years ago

5 0

Answer:

The value of the proportionality constant (y to x) is: 3/10

Step-by-step explanation:

We know the slope of any graph where 'y' varies directly with 'x' gives us the constant of proportionality 'k'.

i.e. y = kx

and k = y/x

Given the points

(100, 30)

(300, 90)

(500, 150)

We know that the proportionality constant (y to x) is:

k = y/x

For the point (100, 30)

k = 30/100=3/10

For the point (300, 90)

k = 90/300=3/10

For the point (500, 150)

k = 150/500=3/10

As the value of proportionality constant (y to x) is the same.

i.e. k = 3/10

Thus, the value of the proportionality constant (y to x) is: 3/10

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Using FOIL method. Multiply the terms. (X^2 -7)(x^2 -4)

murzikaleks [220]

Answer:

x^4-11x^2+28

Step-by-step explanation:

Set it up

x^2(x^2-4) -7(x^2-4)

2. Multiply

x^4-4x^2-7x^2+28

3. Simplify

x^4-11x^2+28

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3 years ago

Write the equation in slope-intercept form through the point (-4, -7) and is perpendicular to the line y = -(7/4)x + 4 and graph

Scilla [17]

You have to write the equation for a line that crosses the point (-4, -7) and is perpendicular to the line

$y=-\frac{7}{4}x+4$

When you have to determine a line that is perpendicular to a known line, you have to keep in mind that the slope of the perpendicular line will be the negative inverse of the first one.

If for exampla you have two lines, the first one being:

$y_1=mx+b$

And the second one, that is perpedicular to the one above:

$y_2=nx+c$

The slope of the second one is the negative inverse of the first one:

$n=-\frac{1}{m}$

The slope of the given line y=-7/4+4 is m=-7/4

So the slope of the perpendicular line has to ve the inverse negative of -7/4

$\begin{gathered} n=-(-\frac{4}{7}) \\ n=\frac{4}{7} \end{gathered}$

Considering it has to pass through the point (-4,-7) and that we already determined its slope, you can unse the point slope formula to determine the equation of the perpendicular line:

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

replace with the coordinates of the point and the slope and calculate:

$\begin{gathered} y-(-7)=\frac{4}{7}(x-(-4)) \\ y+7=\frac{4}{7}(x+4) \\ y+7=\frac{4}{7}x+\frac{16}{7} \end{gathered}$

Subtract 7 to both sides of the equation to write it in slope-intercept form:

$\begin{gathered} y+7-7=\frac{4}{7}x+\frac{16}{7}-7 \\ y=\frac{4}{7}x-\frac{33}{7} \end{gathered}$

Now you can graph both lines

8 0

1 year ago

Writing in Math Stacy multiplied 5 x 9 and said the nswer was 44. What two patterns could you use to show nat her answer is not

marusya05 [52]

Answer:

5*9= 45

Step-by-step explanation

Well using your hands you can put down your fifth finger and that will give you four fingers on the left and five on the right that then equals 45

6 0

3 years ago

the volume v of a tank varies directly with its height h a tank 12 ft High holds 300 cubic feet write an equation relating v &am

Liula [17]

v varies directly with height means

v/h=k were k is a constant

or also h/v=k where k is a constant (this is a different k than previous)

so if h=12 and v=300 then

h/v=12/300=1/25=k

so the relationhip could be h/v=1/25

if you di v/h, then

v/h=300/12=25/1=25=k

so the relationship could be v/h=25

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3 years ago

If x= eighth root of y and y= z^16 how is x proportionate to z ?

ankoles [38]

$x= \sqrt[8]{y}
\\ y = z^{16}

$

Plug "y" into the first equation.

$x = \sqrt[8]{z^{16}} = (z^{16})^{1/8} = z^{16/8} = z^2$

8 0

3 years ago