How do you solve 1/4(x+5)^2-1=3 in steps?

x = -1, -9

Step-by-step explanation:

given:

1/4(x+5)^2-1=3

rewriting:

add 1 to both sides:

divide both sides by 1/4:

square root both sides:

subtract 5 from both sides, we now have two equations to solve:

x = - 5 - 4                     x = - 5 + 4

x = -9                                x = - 1

x = -1, -9

Hopefully this helps, have a nice day! :D

Edit: The other answer forgot to solve for when 4 is negative

Edit #2: They have fixed it now

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240