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Let's say you have a function called f(x) which is equal to 4x² + 3x + 5

Now let's say you have another function called g(x) which is equal to 2x + 3

Now to find the composition f and g ((f ° g)(x)) you need to substitute the x value in the function f(x) with the function g(x).

You will get 4(2x + 3)² + 3(2x + 3) + 5. You can further simplify this if needed, but that is what (f ° g)(x) equals.

On the other hand, if you want to find (g ° f)(x) then you would need to substitute the x value in the function g(x) with the function f(x).

You will get 2(4x² + 3x + 5) + 3 and you can simplify this if needed.

That is the basics of compositions of functions.

R=2GM/c^2 is used.

R=[2 x 6.67E-11 x 1.989E30 x 100] / {[299,792,458^2] . 1,000}

R=295.22 Km - Schwarzchild's Radius.

In order to do this problem you need to covert the percent to a decimal. That means you need to move the decimal point to the left twice to get 0.21

Now multiply 0.21 by $24.58

Take the answer to that and add it to $24.58

To subtract these two numbers, you will need to make the exponents equal each other. 

So let's look at the second term: 3 x 10^-2

We want to change that exponent to 10². Since we're increasing the exponents by 4 powers of ten (from -2 to 2), that means we need to reduce the number on the left (3) by 4 powers of ten. So that means we divide 3 by 10 four times. 3/10 = .3 ----> .3 / 10 = .03 ----> .03 / 10 = .003 ----> .003 / 10 = .0003 (You can do this process more easily by moving the decimal point to the left 4 times).

Now you have 0.0003 x 10²

Now just subtract 0.0003 from 9 to get 8.9997 x 10²

1)  First term  =  1337  and the common ratio is  -1/2:

Terms are:  1337,  -668.5,  334.25,  -167.125,  83.5625,  -41.78125,  20.890625,  -10.4453125,  5.22265625,

                    -2.611328125,  1.3056640625, -0.65283203125

and all the remaining terms are smaller than 1.

So, to find the answer, add the positive terms in the list above.

2)  a₁ + a₃ + a₅ + a₇ + a₉  =  17    

      --->     a₁ + (a₁​ + 2d) + (a₁​ + 4d) + (a₁​ + 6d) + (a₁​ + 8d)  =  17

      --->     5a₁ + 20d  =  17

     a₂ + a₄ + a₆ + a₈ + a₁₀  =  15   

     --->   (a₁ + d) + (a₁​ + 3d) + (a₁​ + 5d) + (a₁​ + 7d) + (a₁​ + 9d)  =  15

     --->     5a₁ + 25d  =  15

Combining these answers:          5a₁ + 20d  =  17

                                                    5a₁ + 25d  =  15

Subtracting down:                                 -5d  =  2

                                                                 d  =  -2/5

Since  5a₁ + 20d  =  17     --->     5a₁ + 20(-2/5)  =  17    

                                          --->     5a₁ - 8 =  17

                                          --->     5a₁ =  25

                                          --->        a₁ =  5

The empirical rule basically states that 68% of the data falls within one standard deviation from the mean, 95% of the data falls within two standard deviations from the mean, and 99.7% of the data falls within three standard deviations from the mean.

So to find the percentage of IQ scores between 86 and 122, you need to find how far each of these numbers is from the mean in terms of the standard deviation. Luckily, if you subtract the standard deviation from the mean, you receive 86, and if you add the standard deviation to the mean, you receive 122. This means that both of these numbers are within one standard deviation from the mean meaning according to the empirical rule, that means 68% of the IQ scores are between 86 and 122.

1) How large is the Schwarzschild Radius for a 100 solar mass black hole? (in km)

Vesc = velocity needed to escape, in m/s

G = a constant, 6.67 x 10-11 N m2/kg2

M = mass of the object you are escaping from, in kg

R = radius of the object you are escaping from, in m

R = 300 Km

2) what formula is correct for the question above 

B) 

__________________________

Please show your work (optional)

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I'm assuming you want to simplify the expression. Use the distributive property to distribute the -3 to the two terms inside the parenthesis. In other words, you will need to multiply -3 by 5a and then -3 by 3.

You should end up with: -15a - 9 + 6a - 4

Now simply add the like terms together for the final answer.

1. The fast freight train left at noon and arrived at 6Pm. The slow freight train made the same trip in 8 hours. What was the speed of the slow freight train if the speed of the fast freight train was 60 mph?

2. Henry can ride his horse at 4 mph to get to the field on time. If he stops for 1 hour to make a speech to his troops, he must ride at 5mph for the whole trip to get to the battlefield on time. How far is it to the battlefield?

Thank you so much

1) 60 x 6 =360 miles- the distance the fast freight train travelled.

360 / 8 =45 mph-the speed of slow freight train.

2) Since the Least Common Multiple of 4 and 5 =20, therefore the distance to the battlefield is:

20 miles. If Henry rides at 4 mph, it will take him 5 hours to get to the battlefield. If Henry rides at 5 mph, it will take him 4 hours to get to the battlefield.

4x² - 81     --->     (2x + 9)(2x - 9)

Using the formula:  d  =  r · t:

1)  The fast freight train left at noon and arrived at 6 pm   --->   it traveled form 6 hours   --->   t  =  6

     The fast freight train's speed was 60 mph   --->   r  =  60

     d  =  r · t   --->    d  =  60 · 6  =  360 miles.

     The slow freight train made the trip is 8 hours   --->   t  =  8

     Since it made the same trip as the fast freight train   --->   d  =  360 

     d  =  r · t   --->    360  =  r · 8   --->   r  =  360/8   --->   r   =  45 miles per hour.

2)  Henry can ride his horse to get to the field on time at 4 mph   --->   r =  4     and     time = t

     d  =  r · t   --->    d  =  4 · t  --->   t  =  d / 4

     If he stops for one hour he must ride at 5 mph   --->   r  =  5    

     This time is one hour more than the previous time   --->   t  =  d / 5 + 1

     Since the times are equal:     d / 4  =  d / 5 + 1

     Multiply both sides by 20:        5d  =  4d + 20

     Subtract 4d from both sides:      d  =  20 miles

Use a book from school or look it up on youtube. 

When JOHN CENA emerges from his cave

You distribute the #'s in the ( ) with a 1 and get 4g-5h-2h-3 and then you combine -5h and -2h and leave the rest the same with a final answer of -7h+4g-3. 

4/5 is = to 8/10, which as a fraction is 0.8.  Multiplying that by one does nothing, so your answer is 0.8.

If you are confused about the order of operations, for multiplication and division, just go left to right.

Ok so for the first question it is simple because all you have to do is crunch the number which can be simplified which will equal 83 terms that are 1

3 1/3 = 9/3 + 1/3 = 10/3

2 3/4 = 8/4 + 3/4 = 11/4

10/3 * 11/4 = (10*11)/(3*4)

=110/12

=55/6

what is -30m+12=18m ?

-30m + 12 = 18m

-48m = -12

m =  \(\frac {1}{4}\)

An aircraft has a liftoff speed of v = 33m/s. What minimum acceleration a does this require if the aircraft is to be airborne after a takeoff run of s = 240m? Please help I really don't understand this!!!!!

\(s=\frac{a}{2}\times t^{2} \)

\(s=v \times t\)     

\(t=\frac{s}{v}=\sqrt{\frac{2s}{a} } \)

\(\frac{s^{2} }{v^{2}}=\frac{2s}{a} \) 

\(a= \frac{2v^{2} }{s} \)

\(a=\frac{2\times 33^{2}m^{2} }{240m\times s^2} \)

\( a=9.075\frac{m }{s^{2} } \)

The aircraft has to start with an acceleration of at least \(\) \(9.075\frac{m }{s^{2} } \)

\( \)asinus :- )  !

No line is parallel to a point; it is parallel to a line.

What is the equation of the original line; the line that passes through the point (6,5)?

the answer is $3443

Leo has raised  0.8%  of  $5,687.50.     Since  0.8%  =  0.008,

                          0.008 x $5,687.50  =  $ 45.50