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)
During 7 hours: 28 parts assembled
during 14 hours: 56 parts assembled
during 21 hours: 84 parts assembled
during 28 hours: 112 parts assembled
during 35 hours: 140 parts assembled
She worked as a carpenter for 12 hours and as a blacksmith for 18 hours.
Assuming you mean she earned $20 as a carpenter and $25 as a blacksmith per hour, with a total of 30 hours for $690,
let c represent carpenter hours and b for blacksmith hours.
20c + 25b = 690
c + b = 30
Subtract b from each side so that c = 30 - b
Plug this value into the first equation
20(30 - b) + 25b = 690
600 - 20b + 25b = 690
600 + 5b = 690
5b = 90
b = 18
To find c, plug this value of b into the other equation
c + 18 = 30
c = 12
Answer:
11 cakes
Step-by-step explanation:
so you know each cup can make 3 cakes so multiply that by 3 then add 2(from the 2/3 cups)
Answer:
We know that lines AB and CD are parallel because if you expand them, we know they will never touch.
Step-by-step explanation:
