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2 years ago

1. Which of the following questions has a constant of

Mathematics

1 answer:

garik1379 [7]2 years ago

4 0

Answer:

In B) y = x/7 , the constant of proportionality is 7.

Step-by-step explanation:

Two quantities X and Y are said to be in proportion if and only if

X = kY or, $\frac{X}{Y} = k$ ,

where k = Proportionality Constant.

Here, 7 is the constant of proportionality. Then,

A . y = 14x

here, $\frac{y}{x} = 14$ ≠ 7

B . y = x/7

here, $\frac{x}{y} = 7$ = constant of proportionality .

C. y = x

here, $\frac{y}{x} = 1$ ≠ 7

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3.1 Find the equation of the line passing through (4, 5) and parallel to the line 3x – 2y = 4.

valentinak56 [21]

$\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}$

Find the equation of the line passing through (4, 5) and parallel to

3x-2y=4.

$\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}$

First of all, We need to convert this equation from standard form (ax+by=c) into slope-intercept form (y=mx+b).

$\rightarrow$ First, add 2y on both sides:-

$\Large\textsf{3x+2y=4}$

$\rightarrow$ Now, subtract 3x on both sides:-

$\Large\textsf{2y=-3x+4}$

$\rightarrow$ Divide by 2 on both sides

$\Large\text{$y=-\displaystyle\frac{3}{2}x +2$}$

$\rule{300}{3}$

Now, let's find the equation of the line that's parallel to the given line.

Remember, if lines are parallel to each other, then their slope's the same.

So the slope of the line that's parallel to the line whose equation we just found, is

$\Large\text{$-\displaystyle\frac{3}{2}$}$

Now let's write the equation in point-slope form:-

$\hookrightarrow\sf{y-y_1=m(x-x_1)}$

Replace numbers with letters, as follows:-

$\sf{y-5=-\displaystyle\frac{3}{2} (x-4)}$

The equation above is the equation in point-slope form.

Incase you need it converted to slope intercept form, refer to the steps below ~

Multiply -3/2 times x and -4:-

$\hookrightarrow\sf{y-5=-\displaystyle\frac{3}{2} x-6}$

Now, Add 5 on both sides:-

$\hookrightarrow\sf{y=\displaystyle\frac{3}{2} x+1}$

$\Uparrow\sf{Our\:equation\:in\:slope\;intercept\;form}$

<h3>Good luck with your studies.</h3>

#TogetherWeGoFar

$\rule{300}{1}$

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makvit [3.9K]

Cccccccccccccccccccccccccccccccc

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2 years ago

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Lostsunrise [7]

Answer:

largest 4 digit number × largest 3 digit number

=9999 × 999

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2 years ago

Miguel buys 100 feet of fence to enclose a rectangular area of his backyard so his dog can run freely. What is the maximum area,

sdas [7]

Suppose the length of the triangle is x, if the perimeter of the rectangle is 100 ft, the width of the rectangle will be (50-x) ft.
Area of rectangle will be:
A=length*width
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A=50x-x^2
at maximum area, dA/dx=0
thus
dA/dx=50-2x=0
solving for x we get
2x=50
x=25
thus for maximum area length=25 ft
the size of the width will be
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thus the maximum area will be:
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2 years ago

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Dmitrij [34]

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2 years ago