To put an equation into (x+c)^2, we need to see if the trinomial is a perfect square.
General form of a trinomial: ax^2+bx+c
If c is a perfect square, for example (1)^2=1, 2^2=4, that's a good indicator that it's a perfect square trinomial.
Here, it is, because 1 is a perfect square.
To ensure that it's a perfect square trinomial, let's look at b, which in this case is 2.
It has to be double what c is.
2 is the double of 1, therefore this is a perfect square trinomial.
Knowing this, we can easily put it into the form (x+c)^2.
And the answer is: (x+1)^2.
To do it the long way:
x^2+2x+1
Find 2 numbers that add to 2 and multiply to 1.
They are both 1.
x^2+x+x+1
x(x+1)+1(x+1)
Gather like terms
(x+1)(x+1)
or (x+1)^2.
Answer:
Step-by-step explanation:
You have the right answer
Answer:
Step-by-step explanation:
This is for the first question.
Slope-intercept is:
m - slope
b - y-intercept
We are given the slope of 
and a y-intercept of 2.
Plug in the values:
Hope this helps.
Since the triangle is an equilateral triangle we know all of it's sides must be the same length, with that in mind the angles that make up the triangle must be equal as well. Knowing that a triangle's three interior angles make up 180 degrees we know that the size of each angle must be one third of this (as each angle must be equal).
180/3 = 60
then we may split the triangle along it's altitude into two special right triangles
more specifically two 30-60-90 triangles.
this means that the side with 30 degrees will be some value "x" where the side for 60 degrees will be related as it is "x*sqrt(3)" and the hypotenuse (which would be the side of the triangle) would be proportionally "2x"
this would mean that the altitude is the side associated with the 60 degree angle as such we can solve for "x" using this.
12= x*sqrt(3)
12/sqrt(3)=x
4sqrt(3)=x (simplifying the radical we get "x" equals 4 square root 3)
now we may solve for the side length of the triangle which is "2x"
2*4sqrt(3) -> 8sqrt (3)
eight square root of three is the answer.
Subtract the number she completed from what she had left to paint originally.
The fractions have different denominators so first step is to rewrite the fractions with a common denominator.
23/25 can be rewritten as 92/100
Now you have 78 21/100 - 34 92/100
Because 21/100 is smaller than 92/100 subtract 1 whole number from 78 and rewrite 1 as 100/100 and add that to the fraction.
78 21/100 becomes 77 121/100
Now subtract :
77 121/100 - 34 92/100
77-34 = 43
And 121/100 - 92/100 = 29/100
Combine to get 43 and 29/100
