CPhill

Sorry, Anonymous.....but Q can't possibly be "26"

This would imply that :

26 + l 16.4 l  = 9.6      which definitely isn't true......adding an absolute value to 26 has to result, at the very least, in a value of 26....and this cannot equal 9.6  !!!!!

7^3-4•3+8

Sorry, Anonymous, but the first operation is to exponentiate.....so 7^3  = 343

Then, we would multiply 4*3  =12    and we have....

343 - 12 + 8     =   339

I assume you want the angle of elevation at the bottom of the hill....We can use the sine inverse to find this....we have........

sine^-1 (550 /1750) = about 18.3°  = 18°   (to the nearest degree)

Q + |16.4| = 9.6     notice that the absolute value of a positive number is just the number itself.....so we have

Q + 16.4 = 9.6    subtract 16.4 from both sides

Q =  - 6.8

This is known as the "Pigeonhole" principle.....Melody is correct......if we pull out all different ones on the first three tries, we must have a matching pair after the fourth  one is selected.....!!!!

Let Noah's rate = R .....  then Grady's rate is  R + .60R 

And Rate * Time = Distance    ...so....

R(2) + 12 =  [R + .60R](2)   ....   simplify

2R  + 12  = 2R + 1.2R       subtract 2R from each side

12 = !.2R      divide both sides by 1.2

R = 10 mph  ......and this is Noah's rate

Note that Grady's rate = 10 + .60(10)   = 16 mph

And, as Anonymous has pointed out, Grady rides 32 miles and Noah rides 20 miles

The answer is B......if the number of dimes = d , then the number of quarters  = 3d

And each dime is worth 10 cents and each quarter is worth 25 cents.....so....the total sum (amount) of money is given by :

The value of each dime (in cents) * their number + the value of each quarter (in cents) * their number  =

10*d + 25*(3d)  =   10d + 25(3d)

Ok....look at this....the first term [ n = 1 ] is just:

 (-1)^1 * (1/2)^(1 - 1) = -1 * (1/2)^0   = -1 * 1 = -1

And the third term is just:

(-1)^3 * (1/2)^(3 -1)  = -1 * (1/2)^2 = -1 * (1/4) = -1/4

So...the 4th term  is  just:

(-1)^4 * (1/2)^(4 - 1)   =  1 * (1/2)^3 =   1 * (1/8)   = 1/8

Does that help???

The "formula" for the nth term of the series is given by:

a_n  = a₁  + d(n -1)       where a1 is the first term, (-5), and d is the common difference between successive terms  = (4)..so we have

a_n = -5 + 4(n - 1)   =  -5 + 4n - 4   =   -9 + 4n  ....or just...    4n -9 .... so...the answer is (B)

The answer is C → (-2, 3)......reflecting across the y axis only changes the sign on the x coordinate...