geno3141

There are many answers:

Since  71 x 1 = 71       71 / 1 = 71

Since  71 x 2 = 144     144 / 2 = 71

Etc.

Let's attack  4^34  first:

   4^1 = 4

   4^2 = 16

   4^3 = 64

   4^4 = 256   --->  This indicates that if the exponent is odd, the last digit will be a  4; if the exponent is even,                               the last digit will be a  6.

Now  7^35:

   7^1 = 7                         7^5 = 16807

   7^2 = 49                       7^6 = 117649

   7^3 = 343                     7^7 = 823543

   7^4 = 2401                   7^8 = 5764801

This indicates that it cycles in groups of 4, so you can keep doing this until you get to 7^35. (You really don't have to keep doing the multiplications.)

Another way is to divide the exponent by 4:

  if the remainder is 1, the answer ends in a 7;

  if the remainder is 2, the answer ends in a 9;

  if the remainder is 3, the answer ends in a 3; and

  if the remainder is 0, the answer ends in a 1.

Dividing 35 by 4, the remainder is 3; therefore the last digit is a  3.

Now, the problem is reduced to adding 1 to a number whose last digit is  6 to another number whose last digit is  3. So what is the last digit of  1 + 6 + 3? 

To add the fractions  1/2  and  1/4  get a common denominator.

Since  2  can be divided evely into  4, make the common denominator  4.

Since 2 x 2 = 4, multiply both the numerator and denominator of 1/2 by 2:

     (1/2) x (2/2)  =  (1 x 2) / (2 x 2)  =  2/4

---> 9 1/2  +  3 1/4  =  9 2/4  + 3 1/4

Now, add the whole numbers together (9 + 3  = 12)

and add the fractions (2/4  + 1/4  = 3/4)

So the answer is:  12 3/4

(When you add fractions with the same denominator together, add the numerators (2  + 1  = 3) and write this answer over the common denomintor. (Don't add the denominators together!) This is how  2/4  +  1/4 becomes 3/4.)   

Let  x  represent the measure of the angle.

Supplementary angles are angles that sum to 180°. Thus, if one angle is  x  the other angle will be  180° - x.

"An angle" becomes  x.

"measures" is a verb so it becomes  =.

" 104° less than" means subtract 104° from what follow those words.

"the measure of a supplementary angle" becomes 180° - x.

Replacing the original words with these symbols, we have:  x  =  (180° - x) - 104°

Combining  180° - 104°, this becomes 76°.

--->  x  =  -x + 76°

--->  2x  =  76°

--->  x = 38°

Then, find the supplement. 

Since the sun is approximately a sphere and the formula for the surface area of a sphere is:

     S.A.  =  4 π r²

and since the diameter of the sun is approximately 1, 392, 000 km.

first:  find the radius of the sun

second: place that value into the formula.

The formula for the equation of a circle with center=(h,k) and radius = r is:

     (x-h)²+(y-k)² =r³

For this problem h = 0, k = 3 and r = 6:

     x² + (y-3)² = 6²

Since y = 1.5x + 3, to find the points of intersection, replace y in the circle equation with this value:

     x² + (1.5x + 3 - 3)² = 6²

    --->      x² + (1.5x)² = 36           (simplify)

     --->    x² + 2.25x² = 36 

     --->     3.25x² = 36

     --->     x² = 36 / 3.25

     --->     x = ±√(36 / 3.25)

Now, find the corresponding value for y for each of these values for x and you will have the two points of intersection.

-4b/5 > -12

Multiply both sides by 5:

-4b > -60

Divide both sides by -4 

Rule: If you multiply or divide both sides of an inequality by a negative number, you must change the direction of the inequality. However, you do not change the direction of the inequality if you add or subtract negative numbers.

b < 12

Rate = (Final Position - Initial Position) / (Final Time - Initial Time)

Rate = (475 - 295) / (6:00 - 3:00)

Rate = 180 / 3

Rate = 60 miles per hour

One possible answer is  1 x 75285

Another possible answer is  3 x 25095

Etc.

The compound interest formula is: A = P(1 + r/n)^(nt)

where A = final amount, P = amount invested, r = decimal interest rate, n = number of times compounded per year, and t = number of years.

Entering the given values:    1050 = 850(1 + r/4)^(4*10)

---> 1050 = 850(1 + r/4)^40                  Divide bothsides by 850, to get:

--->  (1050/850) = (1 + r/4)^40             Find the 40th root of both sides, to get:    

--->  (1050/850)^(1/40) = 1 + r/4          Subtract 1 from both sides, to get:   

--->  (1050/850)^(1/40) - 1 = r/4            Multiply both sides by 4 to get:

--->  [ (1050/850)^(1/40) - 1 ] * 4 = r

r ≈ .02119  --> r  ≈ 2.119%