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Svet_ta [14]
3 years ago
13

(14-16). A new mattress at the Mattress Store cost $625. They are running a Christmas sale where I can save off the original pri

ce. Tax in Indiana is 7% ?
How much money did I save from the discount?

How much did I pay in tax?

What would be the final cost of the mattress after the discount and tax are applied?
Mathematics
2 answers:
Arada [10]3 years ago
8 0

Answer:

You pay 581.25, but you save 43.75. :))

Step-by-step explanation:

almond37 [142]3 years ago
7 0
581.25 is what your paying and you are saveing 43.75
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Kesha threw her baton up in the air from the marching band platform during practice. The equation h(t) = −16t² + 54t + 40 gives
lapo4ka [179]

Answer:

a) 40 feet

b) 54 ft/min

c) 4 mins

Step-by-step explanation:

Solution:-

- Kesha models the height ( h ) of the baton from the ground level but thrown from a platform of height hi.

- The function h ( t ) is modeled to follow a quadratic - parabolic path mathematically expressed as:

                           h ( t ) = −16t² + 54t + 40

Which gives the height of the baton from ground at time t mins.

- The initial point is of the height of the platform which is at a height of ( hi ) from the ground level.

- So the initial condition is expressed by time = 0 mins, the height of the baton h ( t ) would be:

                         h ( 0 ) = hi = -16*(0)^2 + 54*0 + 40

                         h ( 0 ) = hi = 0 + 0 + 40 = 40 feet

Answer: The height of the platform hi is 40 feet.

- The speed ( v ) during the parabolic path of the baton also varies with time t.

- The function of speed ( v ) with respect to time ( t ) can be determined by taking the derivative of displacement of baton from ground with respect to time t mins.

                        v ( t ) = dh / dt

                        v ( t )= d ( −16t² + 54t + 40 ) / dt

                        v ( t )= -2*(16)*t + 54

                        v ( t )= -32t + 54

- The velocity with which Kesha threw the baton is represented by tim t = 0 mins.

Hence,

                        v ( 0 ) = vi = -32*( 0 ) + 54

                        v ( 0 ) = vi = 54 ft / min

Answer: Kesha threw te baton with an initial speed of vo = 54 ft/min

- The baton reaches is maximum height h_max and comes down when all the kinetic energy is converted to potential energy. The baton starts to come down and cross the platform height hi = 40 feet and hits the ground.

- The height of the ball at ground is zero. Hence,

                     h ( t ) = 0

                     0 = −16t² + 54t + 40

                     0 = -8t^2 + 27t + 20

- Use the quadratic formula to solve the quadratic equation:

                     

                    t = \frac{27+/-\sqrt{27^2 - 4*8*(-20)} }{2*8}\\\\t = \frac{27+/-\sqrt{1369} }{16}\\\\t = \frac{27+/-37 }{16}\\\\t =  \frac{27 + 37}{16} \\\\t = 4

Answer: The time taken for the baton to hit the ground is t = 4 mins

3 0
3 years ago
Equation for the points (3,8) (2,6) on slope
Irina18 [472]
\frac{8-6}{3-2} = \frac{2}{1}=4

The slope is 2

y=2x + b

Plug in a point to solve for b
8 = 2(3) + b

8 = 6 + b
b = 2

The equation is y = 2x + 2
7 0
3 years ago
Read 2 more answers
Please help me with this I would give you 50 points.<br> FEET 1 4 5<br> INCHES 24 36
kipiarov [429]

Answer: feet: 1, 2, 3, 4, 5

          inches: 12, 24, 36, 48, 60

Step-by-step explanation:

There are 12 inches in a foot, therefore if you have 1 foot you have 12 inches, if you have 2 feet you have 24 inches becauase 2*12 = 24 and so on...

6 0
2 years ago
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Question is in the attachment
ruslelena [56]
Sorry I can’t see the pic
6 0
2 years ago
A ring is now reduced to £840. This is a saving of 40% of the original price.
gladu [14]
The original price of the ring is <span>£</span>1400
6 0
3 years ago
Read 2 more answers
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