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This is very simple problem:

1 - Multiply 1000 shares by the purchase price + $14 commission.

2 - Bond price is the face value of $2,500.

3 - $5,000 fund has the same face value at purchase or $5,000

4- Add up 1 to 3 and that is the value of her acct. at the beginning of the year.

AT THE END OF THE YEAR:

1 - Multiply 1000 shares by the sale price - $14 commission

2 - Multiply $2,500 bond x 7/100 or 0.07 to get the interest for 1 year + $2,500 principal

3 - Do the same with $5000 fund at 3.5% + $5,000 principal.

4 - Add up 1 to 3 and that is the value of the account at the YEAR END.

5 - Subtract the total at the beginning of the year from the total at the end of year and that is her GAIN or LOSS.

Doubling of her fund from $5000 to $10,000 would take:

10,000 = 5,000 x 1.035^n

Divide both sides by 5,000

2 = 1.035^n

n = log(2) / log(1.035) =20.15 years to double her money @ 3.5%.

We can easily tell that the new line's y intercept is 1

Therefore, in y=mx+b, we know that b is 1.

So we only need to know the slope.

We put 4x+2y=8 into slope-intercept form, which is y=-2x+4

Parrelel lines have the same slope.

So our new line equation is y=-2x+1

In these problems, ALWAYS know that the slope of two parrelel lines are the same.

Once you have the slope plugged into y=mx+b you can plug in y and x from a given coordinate to find b

THen you can make your equation

Welcome back Nickolas!
 

Just remember to post off-topic though

Yes, that makes sense.

Because 2^10 is slightly over 1000

So 2^20 is kinda slightly over 1,000,000

We know that 2^19 is NOT over 1,000,000 because 2^20 divided by 2 will be significantly under 1,000,000

I suppose you could do it in your head by knowing that 2^10 is just over 1,000. So, 2^20 would be 1,000 x 1,000 +.

The only factors it has are 2s. You can multiply 2 by itself ANY number of times up to 95 times and the results will all be factors of 95.

This should be extremely easy...

Have you learned how to solve systems of equations?
 

Whenever you try to find the intersect of two lines, just solve the systems of equations of the graph.

So... we will use elimination

9x - 4y = 6

7x + y = 17

Notice how the second equation can be multiplied by 4 to match the coefficient of y in the first equation.

So we have

9x - 4y = 6

28x + 4y = 68

Now we add the equations

37x = 74

x = 2

So we know that y = 3

So our answer is (2, 3)

Thank you!

YES! Very good. You can always confirm it by using actual powers such as:16^5  vs  24^5. And the difference is:3 x 5^2.

I'm sorry, I wasn't allowed to use a calculator for this type of problem.

I knew that at some point 2^n was going to be over 1,000,000.

Is there a method to get there without using a calculator?

The problem can be super easy after you find out 2^n is larger than 1,000,000

39614081257132168796771975168 = 2^95 (95 prime factors, 1 distinct)

It has 96 DIVISORS (factors) and 76 of them are over 1,000,000.  You obtain them as follows:

2^0, 2^1, 2^2, 2^3, 2^4...........and so on until you get to: 2^20 = 1,048,576. So, the powers of 2 from 0 to 19 =20 factors(divisors) that are under 1,000,000.

Seemewd easiest to just graph it:

These are both the same question:

Been there, done that !  

Thanks....I messed that up!!

Amplitude is   4   (Hecticar forgot to divide by 2)

2)   the function is negative where the graph is below the x- axis

(-inf, 3) U (1,4)

3. What is the amplitude of the function graphed?

amplitude  =  maximum y-value  -  minimum y-value   =   6 - (-2)   =   6 + 2   =   8

Here is 1)   https://web2.0calc.com/questions/need-some-helpp

The others have been posted and ansewered before also.....just try searching for them.....   G'Luck !

1. The function shown in the graph is vertically stretched by a factor of 4 to produce a new graph. Which function represents the new graph?

The graph in the picture has a period of  1  and amplitude of  1  , so it is a graph of  y = sin(2π x)

y  =  sin(2π x)     stretched vertically by a factor of  4  is     y  =  4sin(2π x)

2x + 5y  =  -8          Multiply both sides of this equation by  3.

6x + 15y  =  -24

6x  =  16 + a - 15y          Add  15y  to both sides of this equation.

6x + 15y  =  16 + a

So now our two equations are:

6x + 15y  =  -24

6x + 15y  =  16 + a

The system will have infinitely many solutions when both equations are identical.

So the system will have infinitely many solutions when....

-24  =  16 + a          Subtract  16  from both sides of this equation.

-40  =  a

a  =  -40