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4 years ago

Find an equation for the line that passes through the points (5, 2) and (-3,6).

Mathematics

1 answer:

RUDIKE [14]4 years ago

4 0

Answer:

y = -1/2x + 6

Step-by-step explanation:

Find the slope

( 5 , 2) ( -3 , 6)

m =( y2 - y1 )/ ( x2 - x1)

x1 = 5

y1 = 2

x2 = -3

y2 = 6

m = ( 6 -2)/(-3 - 5)

m = 4/-8

m = - 1/2

Substitute m into the equation of a line

y = mx + c.

y = -1/2x + c

Substitute any of the two points given into the equation

Let's pick (2 ,5)

x = 2

y = 5

y = -1/2x + c

5 = -1/2(2) + c

5 = -1*2/2 + c

5 = -2/2 + c

5 = -1 + c

c = 5 + 1

c = 6

y = -1/2x + 6

The equation of the line is

y = -1/2x + 6

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Step-by-step explanation:

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3 years ago

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Answer:

Step-by-step explanation:

12 + 2x - 12

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3 years ago

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Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 60 inches long and cuts it into

Alex_Xolod [135]

Answer:

a) the length of the wire for the circle = $(\frac{60\pi }{\pi+4}) in$

b)the length of the wire for the square = $(\frac{240}{\pi+4}) in$

c) the smallest possible area = 126.02 in² into two decimal places

Step-by-step explanation:

If one piece of wire for the square is y; and another piece of wire for circle is (60-y).

Then; we can say; let the side of the square be b

so 4(b)=y

b= $\frac{y}{4}$

Area of the square which is L² can now be said to be;

$A_S=(\frac{y}{4})^2 = \frac{y^2}{16}$

On the otherhand; let the radius (r) of the circle be;

2πr = 60-y

$r = \frac{60-y}{2\pi }$

Area of the circle which is πr² can now be;

$A_C= \pi (\frac{60-y}{2\pi } )^2$

$=( \frac{60-y}{4\pi } )^2$

Total Area (A);

A = $A_S+A_C$

= $\frac{y^2}{16} +(\frac{60-y}{4\pi } )^2$

For the smallest possible area; $\frac{dA}{dy}=0$

∴ $\frac{2y}{16}+\frac{2(60-y)(-1)}{4\pi}=0$

If we divide through with (2) and each entity move to the opposite side; we have:

$\frac{y}{18}=\frac{(60-y)}{2\pi}$

By cross multiplying; we have:

2πy = 480 - 8y

collect like terms

(2π + 8) y = 480

which can be reduced to (π + 4)y = 240 by dividing through with 2

$y= \frac{240}{\pi+4}$

∴ since $y= \frac{240}{\pi+4}$ , we can determine for the length of the circle ;

60-y can now be;

= $60-\frac{240}{\pi+4}$

= $\frac{(\pi+4)*60-240}{\pi+40}$

= $\frac{60\pi+240-240}{\pi+4}$

= $(\frac{60\pi}{\pi+4})in$

also, the length of wire for the square (y) ; $y= (\frac{240}{\pi+4})in$

The smallest possible area (A) = $\frac{1}{16} (\frac{240}{\pi+4})^2+(\frac{60\pi}{\pi+y})^2(\frac{1}{4\pi})$

= 126.0223095 in²

≅ 126.02 in² ( to two decimal places)

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4 years ago

1 quart of milk into 4 bottle i had 1/4 milk how many ounces pour into each bottle

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Answer:

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Step-by-step explanation:

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3 years ago

Use completing the square to solve the equation x2+16x=−44 . First determine the number you must add to both sides of the equati

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Answer:

We will add 64 to both sides.

x=8±√20

Step-by-step explanation:

Here we are given the equation:

$x^{2}+16x=-44$

Now we take half of the coefficient of x and add it to x.

Coefficient of x is 16, half of 16 is 8.

Also we add square of 8 to both sides.

So new equation becomes:

$x^{2}+16x+64=-44+64$

Completing the square:

$(x+8)^{2}=20$

NOw let us simplify it to get the value of x.

Taking square root on both sides:

$x+8=+/-\sqrt{20}$

Bringing 8 to the right side:

x=8±√20

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3 years ago