Answer:
the first one is. hope helps
Answer:
- t = 1.5; it takes 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground.
Explanation:
<u>1) Explanation of the model:</u>
- Given: h(t) = -16t² + 48t
- This is a quadratic function, so the height is modeled by a patabola.
- This means that it has a vertex which is the minimum or maximu, height. Since the coefficient of the leading (quadratic) term is negative, the parabola opens downward and the vertex is the maximum height of the soccer ball.
<u>2) Axis of symmetry:</u>
- The axis of symmetry of a parabola is the vertical line that passes through the vertex.
- In the general form of the parabola, ax² + bx + c, the axis of symmetry is given by x = -b/(2a)
- In our model a = - 16, and b = 48, so you get: t = - ( 48) / ( 2 × (-16) ) = 1.5
<u>Conclusion</u>: since t = 1.5 is the axys of symmetry, it means that at t = 1.5 the ball reachs its maximum height and that it will take the same additional time to fall back to the ground, whic is a tolal of 1. 5 s + 1.5 s = 3.0 s.
Answer: t = 1.5; it takes 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground.
Answer:
- f = -2/5a +14
- 12.4 ≈ 12 fish for 4 algae blooms
Step-by-step explanation:
The 2-point form of the equation for a line is useful when you are given two points to work with:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
The independent variable (x) is apparently "algae blooms" and is to be represented by "a". The dependent variable (y) is "number of fish" and is to be represented by "f". So, we have ...
f = (4 -10)/(25 -10)(a -10) +10
f = -6/15(a -10) +10
f = -2/5a +14 . . . an equation for the scenario
Four a=4, the fish population is predicted to be ...
f = -2/5(4) +14 = 12.4
There will be about 12 fish when there are 4 algae blooms.
Answer: $2.55
Step-by-step explanation:
He bought the second shirt for half off the first shirt's price. He therefore bought it at:
= 19.99/2
= $10.00
Total paid for both shirts is therefore:
= 19.99 + 10
= $29.99
Sales tax is 8.5% so he paid:
= 29.99 * 8.5%
= 2.54915
= $2.55
Step-by-step explanation:
7. Since they are similar triangles we have:
So DF is 15
8. They are also similar. So:
So PR is 10
