the first item is 1 and the second item is -3 , the difference  between these two numbers are -3/1 =-3

the second item is  3 and the third item is 9, the difference between these two numbers are 9/-3=-3

so the common difference is -3 , the fourth  item should be =3x9=27 and the fifth item 81=-3x-27

so you can find the others by yourself .......... 

BTW, students may contend that the result does not look any simpler than what we started with, but to a mathematician it is. Really!

Taking out a common factor is always considered simplifying an expression.  

Assume the 8 working hrs are inclueded with the 30 mins lunch break , the total paid working hrs are 7.5, you work for 5 days a week with $15 per hr , so you should get 7.5x$15x5=$562.5

In each case, the distance, d, that a girl is from the tower is related by:

tan(Θ) = 85 / d

Where Θ is the angle of elevation, and 85 is the tower's height....so....

d = 85/tan(Θ)

And the total distance is given by

[85 / tan(32)] + [85 / tan(54)] = 197. 8 ft

Assuming that we have 20 weights of each type

5 , 15,  25, 50

Here are all the combinations

(1 x 50) + (7 x 5)          (4 x 15) + (5 x 5)         (1 x 50) + (1 x 25) + (2 x 5)

(1 x 25) + (4 x 15)        (3 x 15) + (8 x 5)         (1 x 50) + (1 x 15) + (4 x 5)

(1 x 25) + (12 x 5)        (2 x 15) + (11 x 5)        (1 x 50) + (2 x 15) + (1 x 5)

(2 x 25) + (7 x 5)          (1 x 15) + (14 x 5)        (2 x 25) + (2 x 15) + (1 x 5)

(3 x 25) + (2 x 5)          (17 x 5)                        (2 x 25) + (1 x 15) + (4 x 5)

(5 x 15) + (2 x 5)                                              (1 x 25) + (3 x 15) + (3 x 5)

                                                                        (1 x 25) + (2 x 15) + (6 x 5)

                                                                        (1 x 25) + (1 x 15) + (9 x 5)

I think that's it.......   

√3 + √51 

recognize that 51 has some factors

= √3 + √(3 x 17)

= √3 + √3 x √17

= √3 x 1 + √3 x √17

now, taking out the common factor √3,

= √3 (  ......... )

Can you finish by working out what goes inside those brackets?  🍦🍦🃏

I should point out that I'm using unknown "a" for the price of one adult ticket, and "y" to stand for the price of a youth ticket. 

😼😼

Using the information given, form your two equations:

134 = 2a + 3y

146 = 3a + 2y

Now, how to solve by eliminating one of the unknowns?

Perhaps multiply ALL terms in the first equation by 3,

and multiply ALL terms in the second equation by -2, and see how that looks. I think you should now be able to finish it.  🙌🙌

21.8x  =  -124.26

Divide both sides by 21.8:

      x  =  -124.26/21.8     <--- calculator time!

A  =  ½·b·h

This is a monomial because it has only one term (terms are separated by plus or minus signs).

A monomial may have several variables if they are combined by multiplication.

There are many possibilities (provided they have enough weights of each size). I'll let you figure out the number of 5 gram weights needed in each possibility:

50 gm     25 gm    15 gm     5 gm

   1             1                         ?

   1                           1           ?

   1                           2           ?

   1                                        ?

                   3                        ?

                   2                        ?

                   2           1            ?

                   1           1            ?

                   1           2            ?

                   1           3            ?

                   1           4            ?

                                1            ?

                                2            ?

                                3            ?

                                4            ?

                                5            ?

                                              ?

This is a compound problem:  A  =  P(1 + r)^t

A = final amount = 305 million         P = beginning amount = 281 million

r = rate per year (as a decimal)         t = number of years = 8 years

--->   305,000,000  =  281,000,000(1 + r)⁸

Divide both sides by 281,000,000

--->   1.4663  =  (1 + r)⁸

Now, find the 8^th root of both sides:

--->   1.0103  =  1 + r

Subtract 1 from both sides:

--->   r  =  0.0103   --->   r  =  1.03%

First, find the amount of increase:

--->   1, 120, 000, 000, 000 - 700, 000, 000, 000  =  420, 000, 000, 000

Then divide this answer by the original number.

--->   420, 000, 000, 000 ÷ 700, 000, 000, 000  =  0.60

Finally, turn this into a percentage by multiplying by 100 and attaching a % sign.

--->   0.60 x 100  =  60%

Since A = (-4,5) and A' is the reflection image wrt y-axis, A' = (4, 5).

Since B = (-5,-4) and B' is the 90° anticlockwise rotation, B' = (4,-5)

To determine whether or not A'B is perpendicular to AB', find the slopes of A'B and AB'. If they are negative reciprocals, then the lines will be perpendicular.

Is this enough help?

well, you're adding a positive number and a negative number, when you do that, you're really subtracting. Just subtract 208 from 617 and you have your answer.

617 - 208

The mean is found by summing the values and then dividing by the number of them.

There is no number that occurs more than any other....thus, there is no mode

~ Sorry for taking so long to check your awswers. I emailed a friend who took the same test and 3/15 was marked correct on hers, so I went with that. Thanks for the help!

4(x-1)≤4x   simplify on the left

4x - 4 ≤ 4x  subtract 4x from both sides

-4 ≤ 0       

This answer may be puzzling....but notice.......since this answer is always true.....then, we have an identity and any real number value of x will solve the inequality

magnesium metal burns in a jar of chlorine gas to form clouds of ....    

😻

As for all right-angled triangles, hypotenuse = sqrt( base^2 + altitude^2 )

so just apply that formula here.          🐎

We can find this using the Law of Sines

 336.58 / sin(67.5)  = s / sin(45)      where s is the side length  ... solving for s, we have

s = 336.58 * sin (45) / sin(67.5) = about  257. 6 m

This isn't linear.....let's see if it could be a quadratic in the form of ax^2 + bx + c

We have the following system of equations

a + b + c = 40     (1)

4a + 2b +  c  = 68   (2)

9a + 3b + c = 116    (3)

Subtracting (1) from (2)  gives us      3a + b  = 28      (4)

Subtracting (2) from (3)  gives us      5a + b  = 48       (5)

Subtracting (4) from (5)  gives us  2a = 20   ...so..   a = 10    

And substituting this into (4) gives us that b = -2     

And substituting these two values into (1) we have that c = 32

So our function is

f(x)  = 10x^2  - 2x + 32

The diagonal length is given by

d = √(s^2 + s^2)  =  √(2s^2) = √2s = s√2     where s is the side length

Therefore

s√2 = 15√2 

So, s must equal 15 cm.

Be careful, here...

-8^2  = (-1)*8*8 = (-1)*64 =  -64  ...  but

(-8)^2  = (-8)*(-8)   = 64

The moral of the story is that parentheses do matter....