Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:
. Now we factor out the -2:
. Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:
. Simplifying gives us this:
On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:
From this form,
you can determine the coordinates of the vertex to be (1, 3)
The best answer to go with is b
Answer:
y = -7 and x = -36
Step-by-step explanation:
x - 4y = -8
5y - 1 = x
→ Substitute 5y - 1 into x - 4y = -8
5y - 1 - 4y = -8
→ Simplify
y - 1 = -8
→ Add 1 to both sides
y = -7
→ Substitute y = -7 into 5y - 1
( 5 × -7 ) - 1 = -36
1.
558 can be rounded to 600.
44 can be rounded to 40.
600 x 40 = 24,000
2.
9 x 802 = 9 (800 +2) =7200 + 18 = 7218
3.
3699 x 7 = (3700-1) x 7 = 25,900 - 7 = 25,893
4.
34 x 93 = 34 x (100-7) = 3400 - 238 = 3162
5.
678 x 87 = 58,986
This is 6P4
the number of permutations of 4 from 6. 6! / 2!
= 6*5*4*3* 2 / 2 = 360
