Check if my answers are correct. will mark brainliest to whoever comments first! you, and god bless.

2. how is the graph of y equals -8x^2 - 2. different from the graph of y equals negative 8x squared.? (1 point)

it is shifted 2 units to the left
it is shifted 2 units to the right. ***
it is shifted 2 units up.
it is shifted 2 units down.

a model rocket is launched from a roof into a large field. the path of the rocket can be modeled by the equation y equals negative 0.06 x squared plus 9.6 x plus 5.4 where x is the horizontal distance, in meters, from the starting point on the roof and y is the height, in meters, of the rocket above the ground. how far horizontally from its starting point will the rocket land? round your answer to the nearest hundredth.

4.30 m
160.56 m
160.23 m
13.94 m ***

a physics student stands at the top of hill that has an elevation of 37 meters. he throws a rock and it goes up into the air and then falls back past him and lands on the ground below. the path of the rock can be modeled by the equation y equals negative 0.02 x squared plus 0.8 x plus 37 where x is the horizontal distance, in meters, from the starting point on the top of the hill and y is the height, in meters, of the rock above the ground. how far horizontally from its starting point will the rock land? round your answer to the nearest hundredth.

37.00 m ***
67.43 m
27.43 m
37.78 m

find the solutions to the system. y= x^2 - 5x + 2 y= -6x + 4

(2,8) and (-1, 2)
(-2, 8) and (1, -2)
(-2, 16) and (1, -2) ***
no solution

find the solutions to the system y=x^2-2x-2 y=4x+5

(-1, 1) and (7, -23)
(-1, 1) and (7, 33)
(-1, 33) and (7, 1)***
no solution

if an object is dropped from a height of 85 feet, the function h(t)= -16t^2 + 85 gives the height of the object after t seconds. approximately, when will the object hit the ground?

85.00 seconds
69.00 seconds
0.33 seconds
2.30 seconds ***

a ball is thrown into the air with an upward velocity of 28 ft/s. its height (h) in feet after t seconds is given by the function h= -16t^2 + 28t + 7. how long does it take the ball to reach its maximum height? what is the ball’s maximum height? round to the nearest hundredth, if necessary.

reaches a maximum height of 7 feet after 1.75 seconds. ***
reaches a maximum height of 43.75 feet after 0.88 seconds.
reaches a maximum height of 17.5 feet after 0.88 seconds.
reaches a maximum height of 19.25 feet after 0.88 seconds.

a catapult launches a boulder with an upward velocity of 148 ft/s. the height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 148t + 30. how long does it take the boulder to reach its maximum height? what is the boulder’s maximum height? round to the nearest hundredth, if necessary.

reaches a maximum height of 30 feet after 9.25 second.
reaches a maximum height of 640.5 feet after 4.63 seconds.
reaches a maximum height of 1,056.75 feet after 4.63 seconds. ***
reaches a maximum height of 372.25 feet after 4.63 seconds.

a community group is planning the expansion of a square flower garden in a city park. if each side of the original garden is increased by 3 meters, the new total area of the garden will be 225 square meters. find the length of each side of the original garden.

15m ***
3 m
12 m
square root of 12m

19. what is the value of c so that y = x^2 + 15x + c is a perfect square trinomial?

30
15/2***
15/4
225/4

solve the equation by completing the square. round to the nearest hundredth if necessary.
x^2 + 10x = 18

-11.56, 1.56
11.56, 1.56***
-11.56, -1.56
11.56, -1.56

solve the equation by completing the square. x^2 + 9x - 14 = 0

10.35, 1.35
10.35, -1.35
-10.35, -1.35
-10.35, 1.35 ***

1. It is shifted 2 units down.

The graph of is shifted 2 units down with respect to the graph of . We can prove this by taking, for instance, x=0, and calculating the value of y in the two cases. In the first function:

In the second function:

So, the first graph is shifted 2 units down.

2. 160.56 m

The path of the rocket is given by:

The problem asks us to find how far horizontally the rocket lands - this corresponds to find the value of x at which the height is zero: y=0. This means we have to solve the following equation

Using the formula,

which has two solutions: and . The second solution is negative, so it has no physical meaning, therefore the correct answer is 160.56 m.

3. 27.43 m

The path of the rock is given by:

The problem asks us to find how far horizontally the rock lands - this corresponds to find the value of x at which the height is zero: y=0. This means we have to solve the following equation

Using the formula,

which has two solutions: and . In this case, we have to choose the second solution (27.43 m), since the rock was thrown backward from the initial height of 37 m, so the negative solution corresponds to the backward direction.

4. (-2, 16) and (1, -2)

The system is:

(1)

(2)

We can equalize the two equations:

which becomes:

Solving it with the formula, we find two solutions: x=-2 and x=1. Substituting both into eq.(2):

x=-2 -->

x=1 -->

So, the solutions are (-2, 16) and (1, -2).

5. (-1, 1) and (7, 33)

The system is:

(1)

(2)

We can equalize the two equations:

which becomes:

Solving it with the formula, we find two solutions: x=7 and x=-1. Substituting both into eq.(2):

x=7 -->

x=-1 -->

So, the solutions are (-1, 1) and (7, 33).

6. 2.30 seconds

The height of the object is given by:

The time at which the object hits the ground is the time t at which the height becomes zero: h(t)=0, therefore

By solving it,

7. Reaches a maximum height of 19.25 feet after 0.88 seconds.

The height of the ball is given by

The vertical velocity of the ball is equal to the derivative of the height:

The maximum height is reached when the vertical velocity becomes zero: v=0, therefore when

from which we find

And by substituting these value into h(t), we find the maximum height:

8. Reaches a maximum height of 372.25 feet after 4.63 seconds.

The height of the boulder is given by

The vertical velocity of the boulder is equal to the derivative of the height:

The maximum height is reached when the vertical velocity becomes zero: v=0, therefore when

from which we find

And by substituting these value into h(t), we find the maximum height:

9. 12 m

Let's call x the length of the side of the original garden. The side of the new garden has length (x+3), so its area is

Solvign this equation, we find

10. 225/4

In fact, if we write , we see this is equivalent to the perfect square:

11. -11.56, 1.56

The equation is:

By using the formula:

which has two solutions: x=-11.56 and 1.56.

12. -10.35, 1.35

The equation is:

By using the formula:

which has two solutions: x=-10.35 and 1.35.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5