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NemiM [27]
3 years ago
13

Use the elimination method to solve the system of equations

Mathematics
1 answer:
Lady bird [3.3K]3 years ago
4 0

Answer:

D

Step-by-step explanation:

2x + 3y = 18

3x - 3y = 12

the 3y and -3y cancel and you add the other like terms

5x = 30

x = 6

plug x back into any of the equations

2(6) + 3y = 18

12 + 3y = 18

3y = 6

y = 2

answer is (6,2)

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Solve for x x-23=17 NEED TO KNOW FAST PLEASE!!!!
Angelina_Jolie [31]

Answer:

x = 40

Step-by-step explanation:

Adding 23 to both sides gives us:

x - 23 + 23 = 17 + 23

x = 40

7 0
3 years ago
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A surveyor sights the top of a building with a handheld range finder. the top of the building is 148 feet 2 inches away. the ang
Leokris [45]

see the attached figure to better understand the problem


we know that

in the right triangle ABC

cos 56°=AC/AB

where

AC is the adjacent side to angle 56 degrees------> the distance from the surveyor to the building

AB is the hypotenuse-----> 148 ft 2 in

56 degrees------> is the angle of elevation

so

cos 56°=AC/AB---------> solve for AC

AC=AB*cos 56°

AB=148 ft 2 in

convert 2 in to ft

1 ft -----> 12 in

x ft------> 2 in

x=2/12-----> x=0.17 ft

AB=148 ft 2 in-----> 148 ft+0.17 ft------> AB=148.17 ft


AC=AB*cos 56°----> AC=148.17*cos 56°------> AC=82.86 ft


convert 0.86 ft to in

0.86 ft=0.86*12-----> 10.32 in

distance AB=82 ft 10 in


the answer is

the distance from the surveyor to the building is 82 ft 10 in

8 0
3 years ago
Use estimate to check for reasonableness of 25 cent plus 4 cent
Vedmedyk [2.9K]
29 cents..............................
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3 years ago
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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

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Hcf of 14 154 and 28​
anyanavicka [17]

Answer:

14

Step-by-step explanation:

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3 years ago
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