What is the equation of the line that passes through the point (-8,0)and has a slope of -1/4

y = -1/4x - 2

Step-by-step explanation:

I'm going to write this equation in slope intercept form, which looks like this: y = mx + b. First, write the equation using the slope given. It should look like this:

y = -1/4x + b

Next, you must find the y intercept by plugging in the point to the equation. This is what it looks like: 0 = -1/4(-8) + b. Multiply -1/4 by -8 to get 2. This is what your equation should look like now: 0 = 2 + b. Subtract 2 from both sides of the equation to get -2 = b. Go back to your original equation and plug -2 in for b. This is your final equation:

y = -1/4x - 2

Hope this helped!

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)