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Jlenok [28]
2 years ago
14

WORD PROBLEMS

Mathematics
1 answer:
garri49 [273]2 years ago
8 0

Answer:

The answer is

Step-by-step explanation:

Step by step

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Jimmy threw a baseball in the air from the roof of his house. The path followed by the baseball can be modeled by the function f
erastovalidia [21]

Answer:

Step-by-step explanation:

The first part of A is easy. Look at the quadratic function, and the constant, the very last number with no t stuck to it represents the height from which the object in question was originally launched. Our constant is 40, so the height of the roof from which the baseball was thrown is 40 feet. Part 2 of A is not quite as simple because it requires factoring using the quadratic formula.Before we do that, let's make our numbers a bit more manageable, shall we? Let's factor out a -8 to get

f(t) = -(t^2-6t-5) and a = 1, b = -6, c = -5.

Filling in the quadratic formula now looks like this:

t=\frac{6+-\sqrt{6^2-4(1)(-5)} }{2(1)} and

t=\frac{6+-\sqrt{36+40} }{2} and

t=\frac{6+-\sqrt{56} }{2} so the 2 solutions are

t=\frac{6+\sqrt{56} }{2}=6.74sec and

t=\frac{6-\sqrt{56} }{2}=-.742sec and since we know time can NEVER be negative, the time it takes for the baseball to hit the ground from a height of 40 feet is 6.74 seconds. Onto part B.

In order to determine exactly how high the baseball did go, we have to find the vertex of the function. We do this by completing the square and getting the function into vertex, or work, form. Begin by setting the quadratic equal to 0, moving over the constant, and then factoring out the leading coefficient. The rule for completing the square are kinda picky in that you have to have a 1 as the leading coefficient, and righ now ours is a -8. So following the rules I stated above:

-8(t^2-6t)=-40 Next is the take half the linear term, square it, and then add it to both sides. Our linear term is a -6. Half of -6 is -3, and -3 squared is 9, so we add 9 into the parenthesis first:

-8(t^2-6t+9)=-40+??

Because this is an equation, we can't add 9 to one side without adding the equivalent to the other side. But, we cannot forget about that -8 sitting out front there, refusing to be ignored. We didn't just add in a 9, we actually added in a -8 times 9 which is -72. That's what goes on the right side in place of the ??.

-8(t^2-6t+9)=-40-72

The reason we complete the square is found on the left side of the equals sign. We have, in the process of completing the square, formed a perfect square binomial that will serve as the h in our vertex (h, k) where h is the number of seconds it takes for the baseball to reach its max height of k, whatever k is. That's what we have to find out. Putting the left side into its simplified perfect square binomial and adding the numbers on the right gives us:

-8(t-3)^2=-112

For the last step, add over the -112 and set it back equal to f(t):

-8(t-3)^2+112=f(t) From that we determine that the vertex is (3, 112). The max height of this baseball was 112 feet...so no, it did not make it up to the height of 120 feet that Jimmy wanted for the baseball.

6 0
2 years ago
How many solutions will this system have?
Natalka [10]
Indefinitely many

The lines are on each other so every solution is correct
4 0
2 years ago
Read 2 more answers
An amusement park manager determined that about 23 of all customers would wait in long lines to ride the new roller coaster. Whi
laiz [17]

Answer:

Top Left in I.M.

Step-by-step explanation:

Trust me

4 0
2 years ago
Read 2 more answers
For a club gathering you were having, you bought a total of 50 burgers, and spent $90. You paid $2 per turkey burger, and $1.50
Sedaia [141]

Answer:

<u></u>

  • <u>No. You would have to cut the number of veggie burgers in more than half.</u>

Explanation:

<u>1. Model the situation with a system of equations</u>

<u />

<u>a) Name the variables:</u>

  • number of turkey burgers: t
  • number of veggie burgers: v

<u />

<u>b) Number of burgers:</u>

  • 50 = t + v

<u />

<u>c) Cost of the 50 burgers:</u>

  • $90 = 2t + 1.50v

<u>2. Solve that system of equations:</u>

<u />

<u>a) System</u>

  • 50 = t + v
  • 90 = 2t + 1.50v

<u>b) Mutliply the first equation by 2 and subtract the second equation</u>

  • 100 = 2t + 2v
  •  90 = 2t + 1.50v

  • 10 = 0.5v
  • v = 20 ⇒ t = 50 - 20 = 30

<u />

<u>c) How much would you spend if the next year you buy the double of 20 turkey burgers (40) and the half of 30 veggie burgers (15)</u>

  • $2(40) + $1.50(15) = $80 + $22.50 = $102.50

Then, you if you double the number of turkey burgers, and cut the number burgers in half, you would spend more than $90 ($102.50).

6 0
3 years ago
A bag has 8 bagels. Three of the bagels r cranberry. What % of the bagels r cranberry?
Solnce55 [7]
It'll will be 24% because it's like a fraction so three cranberry in a bag of 8 so 3/8 8x3 will be 24 then just add the percents
5 0
3 years ago
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