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AVprozaik [17]
3 years ago
14

The sum of two and the quotient of a number x and 5

Mathematics
1 answer:
Y_Kistochka [10]3 years ago
5 0

2+x/5 is the correct answer

2+x/5 is the correct answer

2+x/5 is the correct answer

2+x/5 is the correct answer

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Jennifer hit a golf ball from the ground and it followed the projectile ℎ(t)= −15t^2+100t, where t is the time in seconds, and ℎ
oksano4ka [1.4K]

Answer:

Step-by-step explanation:

In order to find the max height the ball reached, we have to complete the square on that quadratic. That will also, conveniently so, give us the number of seconds it will take the ball to reach that max height, that answer to part b. Let's begin to complete the square. Normally, you would move the constant over to the other side of the equals sign, but there is no constant here. The next step is to get the leading coefficient to be a 1, and ours right now is a -15. So we have to factor it out. Here's where we start the process of completing the square.

-15(t^2-\frac{20}{3}t)=0 Next step is to take half the linear term, square it, and add it to both sides. Our linear term is 20/3. Half of 20/3 is 20/6, and 20/6 squared is 400/36.

-15(t^2-\frac{20}{3}t+\frac{400}{36})=0+??? Because this is an equation, what we add to the left side also has to be added to the right. BUT we didn't just add in 400/36, because we have that -15 out front as a multiplier that refuses to be ignored. What we actually added in was -15(400/36):

-15(t^2-\frac{20}{3}t+\frac{400}{36})=0-\frac{500}{3}

The reason we do this is to create a perfect square binomial on the left which will serve as the number of seconds, h, in the vertex (h, k), where h is the number of seconds it takes the ball to reach its max height, k. Simplifying both sides then gives us:

-15(t-\frac{20}{6})^2=-\frac{500}{3} Finally, we will move the right side over by the left and set the quadratic back equal to h(t):

h(t)=-15(t^2-\frac{20}{3})^2+\frac{500}{3} and from that you can determine that the vertex is (\frac{20}{3},\frac{500}{3}).

The answer to a. is vound in the second number of our vertex: k, the max height. The max of the golf ball was 500/3 feet or 166 2/3 feet.

Part b is found in the first number of the vertex: h, the number of seconds it took the golf ball to reach that max height. The time it took was 3 1/3 seconds.

Part c. is to state the domain (the time) and the range (the height) of the ball.

Domain is

D: {x | 0 ≤ x ≤ 3 1/3} and

Range is

R: {y | 0 ≤ y ≤ 166 2/3}

8 0
3 years ago
Calculate 6 3/4 & on tax $2,305
drek231 [11]

6 (3/4) = .0675

2,305.00 * .0675 =155.59

Brainiest please  

5 0
3 years ago
M is the centroid (center of gravity) of △ABC, line k goes thru M and intersects AB and AC . The distances of the vertices B and
lana [24]

Answer:

  30

Step-by-step explanation:

The midpoint of BC will be a distance from line k that is the average of the distances of B and C: (17+13)/2 = 15. Call that midpoint P. We know distance MP is half of distance MA. This same relationship will hold with respect to the distances from P and A to any line through M. That is, the distance from line k (through M) is twice the distance from P to line k: 30 units.

5 0
3 years ago
124 ounces decreased by 67%
slavikrds [6]
40.92 ounces.
You can find it by multiplying 124 by 0.33
8 0
3 years ago
Read 2 more answers
How would you know if these are a positive or a negative 0,1) and (-3,6).
Ipatiy [6.2K]
Negative has the little dash in front of it

Thank you hope this helps
7 0
3 years ago
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