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w=12

how to read this number

1,758,500,000

It is read: One billion, seven hundred and fifty eight million, five hundred thousand(s).

5^18 - 25^8=5^18 - 5^16 mod 120 =0. It is divisible evenly by 120!!.

What is the product of the x−intercept and y−intercept of the equation 6x−8y=24

How do I solve this problem?

Please do not send the answer, just help me figure out what I'm supposed to do, please!

\(\begin{array}{|rcll|} \hline 6x-8y &=& 24 \qquad & | \qquad : 24 \\ \frac{6}{24}x-\frac{8}{24}y &=& 1 \\ \frac{x}{4}-\frac{y}{3} &=& 1 \\ \frac{x}{4}+\frac{y}{-3} &=& 1 \\ \frac{y}{\underbrace{-3}_{y-intercept}}+ \frac{x}{\underbrace{4}_{x-intercept}} &=& 1 \\ \hline \end{array} \)

y−intercept * x−intercept  = -3 * 4 = -12

Question 4:  Use the slope-intercept form:  y - y₁  =  m(x - x₁)

m = 7  and  x₁= -4  and  y₁ = -3   --->    y - -3  =  7(x - -4)   --->   y + 3  =  7x + 28   --->   y  =  7x + 25

Question 5:  Lines are parallel when their slopes are parallel.

      Slope formula:  m  =  (y₂ - y₁) / (x₂ - x₁)

A:  (1,6) & (4,-3)   --->   m  =  (-3 - 6) / (4 - 1)   --->   m  =  -9/3  =  -3

     (6,4) & (9,-5)   --->   m  =  (-5 - 4) / (9 - 6)   --->   m  =  -9/3  =  -3      <---  These lines are parallel.

You should also check the rest ...

If Carolyn Tan's regular rate is 75.00, then her overtime rate is 75.00 x 1.5  =  112.50.

Her regular work week consists of 40 hours; this amount is 75.00 x 40  =  3000.00

If she worked 5 3/4 hours of overtime, this amount is (5 3/4) x 112.50  =  646.88.

The total amount is:  3000.00 + 646.88  =  3646.88.

How many primes less than 100 are divisible by 3?

One, just the number 3.

Any other number that is divisible by 3 can't be a prime!

Find the remainder when  f(x) = 2x^3 − x^2 + x + 1  is divided by  2x + 1.

The remainder theorem states that f(x) / (x - a)  will have a remainder of  f(a).

However, this doesn't apply if the coefficient of the x-term isn't 1.

So first, let's divide both  f(x)  and  2x + 1  by 2:

         ---   This is legal because  f(x) / (x - a)  =  [ f(x) / 2 ]  /  [ (x - a) / 2) ].

     f(x) / 2  =  (2x^3 − x^2 + x + 1) / 2  =  x^3 − (1/2)x^2 + (1/2)x + (1/2)

     (2x + 1) / 2  =  x + (1/2)

Now, the coefficient of the x-term is 1.

So, to find the remainder when  x^3 − (1/2)x^2 + (1/2)x + (1/2)  is divided by  x + (1/2),  replace  x  with  -(1/2):

     --->     (-1/2)^3 − (1/2)(-1/2)^2 + (1/2)(-1/2) + (1/2)

     --->     -1/8 - 1/8 - 1/4 + 12

     --->     -1/8 - 1/8 - 2/8 + 4/8

     --->     0

Therefore, the remainder will be  0.

A hint:  

1)  Draw the picture of the triangle and the circle; then, modify the circle to include only the area of the circle that is within the triangle

2)  Find the area of the triangle.

3)  Find the area of the circle; now modify this area to be only that part that is within the triangle.

4)  Divide the answer to step 3 by the answer to step 2.

5^18 - 25^8 
= 5^18 - 5^16 
= 5^16(5² – 1) 
= 5^16(24) 
= 24 × 5 × 5^15 
divide by 120 = 120 × 5^15/120 divisible 
= 5^15 

38^9 - 38^8 
= 38^8(38 –1) 
= 38^8 × 37 
divisible by 37 

To prove that 5¹⁸ - 25⁸ is divisible by 120, write 25 as 5² and:

     5¹⁸ - 25⁸  =  5¹⁸ - (5²)^{8  =}  5¹⁸ - 5¹⁶

Now, factor out 5¹⁶:

     5¹⁸ - 5¹⁶   =    5¹⁶(5² - 1)    =    5¹⁶(25​ - 1)    =     5¹⁶(24) 

Since  120  =  24 x 5:

    5¹⁶(24)  /  (24 x 5)    =    5¹⁵

what is the simplest form of 25/54?

25/54 Cannot be reduced any further.

how do i prove that "5^18 - 25^8" is divisible by 120

For large numbers such as these, the easiest way is to do the Math on a calculator and find out that way:"5^18 - 25^8" is divisible by 120

5^18=3,814,697,265,625 - (25^8)=152,587,890,625=3,662,109,375,000 / 120=30,517,578,125.

This way, you don't have to guess.

Did you try the calculator here? Try it and see what you get.

What does "equilateral" mean? It means "equal sides", doesn't it. So if one side is 15, the perimeter would have to be: 15 x 3=45, or 15+15+15=45.

I can help you with the first 3 questions, but I'm not competent enough to answer the last 2.

1) At the rule you are given, the object falls at a rate of 3 times the previous second.

So, in the 4th second only, the object will fall 3 x 81 =243 meters. And the total distance covered in all 4 seconds is: 9 + 27 +81 + 243 =360 meters, or "B"

2) In question 2, you have 2 geometric series going in parallel. The first is from week 1 to 29 inclusive, skipping every 2nd week, for a total of 15 weeks. The 2nd is from week 2 to 30 inclusive, skipping every 2nd week, for a total of 15 weeks. If you use the geometric series formula, you will see that the answer is "A"

3) In question 3, it is also a geometric series, with the first term being $29,100, number of terms 27(2014 -1988 +1), and the ratio is 1.04. If you do the Math, you will see that the answer is "A"

Simplify the following:
f(x)=(2 x^3-x^2+x+1)/(2 x+1)

The possible rational roots of 2 x^3-x^2+x+1 are x = ±1/2, x = ±1. Of these, x = -1/2 is a root. This gives 2 x+1 as all linear factors:
(((2 x+1) (2 x^3-x^2+x+1))/(2 x+1))/(2 x+1)

 | |
2 x | + | 1 | | x^2 | - | x | + | 1
2 x^3 | - | x^2 | + | x | + | 1
2 x^3 | + | x^2 | | | |
 | | -2 x^2 | + | x | |
 | | -2 x^2 | - | x | |
 | | | | 2 x | + | 1
 | | | | 2 x | + | 1
 | | | | | | 0:
(x^2-x+1 (2 x+1))/(2 x+1)

((2 x+1) (x^2-x+1))/(2 x+1) = (2 x+1)/(2 x+1)×(x^2-x+1) = x^2-x+1:
Answer: |x^2-x+1

about 13

Step 1 isn't so much wrong as incomplete. There is an additional solution, namely -(81)^(1/4)

(-3)^4 = 81 as well as 3^4 = 81

.

Or simply:  y = 2^(x-1)

.

Set y equal to zero and find the corresponding value of x.  This gives you the x-intercept.

Set x equal to zero and find the corresponding value of y.  This gives you the y-intercept.

Then multiply the two results together.

A graph often helps in these sort of problems:

Yep.......round to the nearest tenth......