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2 years ago

PLZ HELP

1 answer:

8 0

Answer: Find the equation of a line with a given slope and containing the given point. Write the equation in slope-intercept form.

m = − 3/4, point (8, −4)

Find the equation of a line with a given slope and containing the given point. Write the equation in slope-intercept form.

m = − 7/2, point (−8, −4)

Find the equation of a line with a given slope and containing the given point. Write the equation in slope-intercept form.

m = −6, point (−1, −4)

Find the equation of a line with a given slope and containing the given point. Write the equation in slope-intercept form.

a horizontal line containing (−3, -5). #2

avatar+51

I'm going to answer the solution in Point-Slope and Slope-Intercept.

Slope - Intercept form is this: y = mx + b

We know that (x, y) is a point on the line, m is the slope, and b is the y-intercept.

From the given information we have that it has a slope of 2 (m = 2), and one of the points on the line is (3, 9) which means that (x = 3, y = 9)

Plugging in we get:

y = mx + b

9 = 2*3 + b

9 = 6 + b

b = 3

Therefore the y-intercept is 3. After having this information we can construct our equation.

We now have to put this in the point-slope form which is: (y - y1) = m(x - x1)

Transferring what we had before we can plugin and get y - 9 = 2(x - 3)

Comment down if you have any queries or any questions on the solution. Tell me as soon as possible. Good luck in your Algebra Pursuit!! :)

Enjoy!! I put the answer in both point-slope and slope-intercept if you haven't noticed!! :)

So our answer is:

y - 9 = 2(x - 3).

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A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.

mario62 [17]

Answer:

$(x-7)^2+(y-5)^2=1$

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

Center of the circle:

The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)$

$(x_m, y_m) = (7,5)$

This is the center coordinate of our circle.

Radius:

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}$

$r = \sqrt{(6-7)^2+(5-5)^2}$

$r = \sqrt{1^2}$

$r = 1$

Equation of the circle:

The equation is written as:

$(x-a)^2+(y-b)^2=r^2$

here, (a,b) are the center points of the circle

in our case this is $(a,b)=(x_m,y_m)=(7,5)$

and r = 1

$(x-7)^2+(y-5)^2=1^2$

$(x-7)^2+(y-5)^2=1$

This is the equation of the circle!

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A circular chicken house has an area of 40m². What length of chicken wire is required to fence the house without any wire left o

Lyrx [107]

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2 years ago

A 5-gallon jug of cleaning solution contains 6% bleach. How much pure water should be added to it to dilute to 4% bleach?

mihalych1998 [28]

Let's bear in mind that 5 gallons with a solution of 6% bleach, contains some water plus some bleach, how much bleach? well, is just 6% of 5 gallons or namely (6/100) * 5 gallons, or 0.30 gallons.

if we use "x" gallons of water, well pure water has no bleach, so is 0% bleach, and it has a (0/100) * x or 0x gallons of bleach.

the mixture will be say "y" gallons, and is 4% bleach, so (4/100) * y is 0.04y gallons in the mixture of bleach.

$\bf \begin{array}{lcccl}
&\stackrel{gallons}{quantity}&\stackrel{\textit{\% of bleach}}{amount}&\stackrel{\textit{gallons of bleach}}{amount}\\
&------&------&------\\
\textit{pure water}&x&0.00&0x\\
\textit{6\% solution}&5&0.06&0.3\\
-----&------&------&------\\
mixture&y&0.04&0.04y
\end{array}
\\\\\\
\begin{cases}
x+5=\boxed{y}\\
0x+0.3=0.04y\\
---------\\
0.3=0.04\left( \boxed{x+5} \right)
\end{cases}
\\\\\\
0.3=0.04x+0.2\implies 0.1=0.04x\implies \cfrac{0.1}{0.04}=x\implies 2.5=x$

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Aleksandr [31]

Answer:

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Step-by-step explanation:

what do you mean

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