geno3141

2.5% expresses a relationship, not an absolute amount.

2.5% of £100 is £2.5, less than £5.

2.5% of £1000 is £25, greater than £5.

2.5% of £200 is £5, the same.

If a, b, and c are the three lengths, add the shorter two lengths, this sum must be greater than the longest side.

If all three sides are the same length, it is an equilateral triangle.

Nope ---

The 3 multiplied times the 1/3 = 1; so ignore them, leaving:

y = log(10^x - 1) + 1

As x gets larger, 10^x - 1 approaches 10^x, so log(10^x - 1) + 1 approaches log(10^x) + 1.

Since log(10^x) = x, y approaches x + 1.

For your example:  first press the (2nd) key. This will turn the (sin) key into (asin). Press this key, then enter the numbers:  16/20  and press the equal (=) sign. This will give you the size of the angle.

"asin" means "arcsine" which is inverse sine, what you want.

Similarly, for cos and tan.

The only answer is:  3x + 8

and it can't be simplified any farther.

Rate is distance divided by time.

If Amy can run 3 miles in s minutes, her rate is her distance (3 miles) divided by her time (s minutes);

     her rates is (3 miles) / (s minutes)  =  (3/s) miles/minute

Distance is rate times time, so, if Amy ran for 50 minutes, the distance is:  

     (3/s) miles/minute x 50 minutes   =   150/s miles

(4/5)(x - 1) =  1 + x/2

Multiply both sides by 10:

10[ (4/5)(x - 1) ]  =  10[ 1 + x/2 ]

8(x - 1)  =  10 + 5x

8x - 8  =  10 + 5x

3x - 8  =  10

3x  =  18

x  =  6

The log, to the base x, of 16 equals 2 can be written in exponential form as x² = 16.

Solving that, x can either equal 4 or -4; however, negative bases aren't used for logs, so the answer is just 4.

If you are trying to factor this:

2[ x² - 14x + 49 - y² ]

Separate teh terms as follows:

2[ (x² - 14x + 49) - y² ]

Factor that section:

2[ (x - 7)(x - 7) - y² ]

2[ (x - 7)² - y² ]

Now factor  (x - 7)² - y²  as the difference of squares:

     Since  A² - B²  =  (A + B)(A - B), substituting (x - 7) for A and y for B, 

          (x - 7)² - y²   =  [(x - 7) + y][(x - 7) - y]  =  (x - 7 + y)(x - 7 - y)

2(x - 7 + y)(x - 7 - y)

Use the calculator to enter 70e^(-.25x5).

Make certain that you use the 'e' key on the calculator.