Jack and Tyler ate a total of 35 cupcakes Tyler ate 5 more than jack how many did each person eat
2 answers:
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Start by setting the function equal to 0 and then moving the -5.4 over to the other side of the equals sign. 
. The first rule for completing the square is that the leading coefficient be a +1. Ours is a -.2. So we need to factor it out. 
. Now we will take half the linear term, square it, and add it to both sides. Our linear term is 14. Half of 14 is 7, and 7 squared is 49. So we add 49 in to the left side just fine, but we cannot forget about that -.2 hanging around out front as a multiplier. What we have actually "added" in is -.2*49 which is -9.8. Now here's what we have after all that: 
. In that process, we have created a perfect square binomial on the left. Along with expressing that binomial we will do the math on the right: 
. Now we will move the -4.4 back over by addition, and it will then be apparent as to what our vertex is. The y coordinate of the vertex will give us the max height of the water. 
. As you can see, our work matches choice C from above.
Answer:
Part 1: 31.4 feet
Part 2: 61 feet
Part 3: 99,000 stalks of corn
Step-by-step explanation:
<u>Part 1:</u>
Diagram attached.
You can follow the problem closely and draw a diagram like this. The RED LINE is the distance we are looking to find.
The red line is the hypotenuse of a right triangle we can create (see the dotted line). We can now use the pythagorean theorem to solve for the distance.
Pythagorean Theorem is hypotenuse^2 = leg^2 + leg^2
Let red line [what we want to find] be h and the other 2 sides are 10-5=5 ft & 25 + 6 = 31ft. So we have:
Hence Bethany has to walk 31.4 feet
<u>Part 2:</u>
See 2nd diagram attached.
The blue line is the path of Bethany and the green line is path of Ben. The RED line is what we are looking to find, the shortest distance between them.
We use Pythagorean Theorem twice on the two triangles and add up the results.
<u>Left Triangle:</u>
If we make a triangle, we have base (one leg) = 30 and the other leg is 20-10=10. So we have:
<u>RightSide triangle:</u>
two legs are 25 and 15 respectively, so we use the pythagorean theorem again:
Thus, the shortest distance = 31.62 + 29.15 = 60.77 = 61 feet (rounded to nearest whole number)
<u>Part 3:</u>
The area of the Maize MINUS the area of the path is the Area of the Corn [what we are looking for].
Area of Maze:
100 * 100 = 10,000 sq. yd.
Area of Path = 1.5 * 3000 = 4,500 sq. yd.
Area of Corn = 10,000 - 4,500 = 5,500 sq. yard of land.
Now, each sq. yd. holds 18 stalks, so 5,500 sq. yd. will hold:
18 * 5,500 = 99,000 stalks of corn
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