MATHEMATICS
MIDDLE SCHOOL

Answer: 3.2 × 10^−4 m/hr(100cm/m) = 3.2 x 10^-2 cm/hr

3.2 x 10^-2 cm/hr/(3600 sec/hr) = 8.889 x 10^-6

choice (A)

3.2 x 10^-2 cm/hr/(3600 sec/hr) = 8.889 x 10^-6

choice (A)

HIGH SCHOOL

Water coming out from a fountain is modeled by the function: f(x)=−x2+6x+6

Where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.

What does the average rate of change of f(x) from x = 2 to x = 5 represent?

a.The water travels an average distance of 4 feet from 2 seconds to 5 seconds.

b.The water travels an average distance of 1 foot from 2 seconds to 5 seconds.

c.The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds.

d. The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

Average rate of change from x = 2 to x = 5 is (f(5) - f(2))/(5 - 2) = ((-(5)^2+6(5)+6) - (-(2)^2+6(2)+6))/3 = ((-25+30+6) - (-4+12+6))/3 = (11 - 14)/3 = -3/3 = -1

Therefore, the water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

Therefore, the water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

Average speed = change in position / change in time.

m = (f( b ) - f ( a )) / ( b - a )

a = 2, b = 5

f ( a ) = f ( 2 ) = - 4 + 12 + 6 = 14

f ( b ) = f ( 5 ) = - 25 + 30 + 6 = 11

m = (11-14) / (5-2) = -3/3 = -1

Answer: D ) The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

m = (f( b ) - f ( a )) / ( b - a )

a = 2, b = 5

f ( a ) = f ( 2 ) = - 4 + 12 + 6 = 14

f ( b ) = f ( 5 ) = - 25 + 30 + 6 = 11

m = (11-14) / (5-2) = -3/3 = -1

Answer: D ) The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

HIGH SCHOOL

(25 to the power of 9) + (5 to the power of 17) is divisble by 30. Prove the divisibility.

Blank x 30

Answer should be exponent with a base.

Answer:

5^16

Step-by-step explanation:

25^9 + 5^17

Replace 25 with 5^2

5^2^9 + 5^17

We know that a^b^c = a^(b*c)

5^(2*9)+ 5^17

5^18+ 5^17

We can factor out 5^17

5^17 (5+1)

5^17(6)

But we need 30 so I need one more 5 inside 5^17 = 5^16 *5

5^16 *5 *6

5^16(30)

HIGH SCHOOL

A rectangular rug is 12.5 feet long and 10 feet wide. The rug needs to be reduced by a factor of es026-1.jpg to be placed near a door. What is the area of the reduced rug in square feet?

The reducing factor is 1/5. The rectangular rug 12.5 feet long and 10 feet wide needs to be reduced by a factor of 1/5.

The area of the reduced rug will be the new long times the new wide.

New long = 12.5 feet * 1/5 = 2.5 feet

New wide = 10 feet * 1/5 = 2.0 feet

New area = 2.5 feet * 2.0 feet = 5.0 feet^2.

Answer: 5.0 ft^2

The area of the reduced rug will be the new long times the new wide.

New long = 12.5 feet * 1/5 = 2.5 feet

New wide = 10 feet * 1/5 = 2.0 feet

New area = 2.5 feet * 2.0 feet = 5.0 feet^2.

Answer: 5.0 ft^2

Answer:

A) 5

Step-by-step explanation:

MIDDLE SCHOOL

In pattern number 9,12,15,18,21 what come next

After 21 comes 24 and just keep adding three

The pattern is 3 so after 24 you add 3 more and so on and so on