geno3141

If  s  represents the value of each side of an isosceles right triangle and  h  represents the value of the hypotenuse,

then  h = s·√(2)  and  s = h/√(2)  or  s = h·√(2) /2

So:

if h = 4   --->   s  = 4·√(2) /2  =  2·√(2)

if h = 5   --->   s  = 5·√(2) /2 

if h = 3·√(2)   --->    h  =  3·√(2)·√(2) /2  =  3

Complementary angles are angles that sum to 90°, so:

(x - 5) + (4x)  =  90°

            5x - 5  =  90°

                  5x  =  95°

                    x  =  19°

x - 5  =  19 - 5  =  14°

4x  =  4(19)  =  76°

Without the uppercase T, you may need to give all the answers, which is done by adding (and subtracting) all whole number multiples of 180° (or π/2).

For instance:  T  =  21.80° ± k·180° (where k is any whole number)

Tan(Y) = 4/10

--->   Y  =  Tan^-1(4/10)

--->   Y  =  21.80°  or  0.38^r  (approximately)

(Assuming that the uppercase T in Tan means that you want only the principal value.) 

Assuming that the main operation is the division, we get:

6 to the second is 6² = 6 x 6 = 36

2 times 3 plus 4 is 2 x 3 + 4  =  6 + 4  =  10

36 divided by 10 is 3.6

However, just starting from the left to the right, using the order of operations, we get:

6² ÷ 2 x 3 + 4

=  36 ÷ 2 x 3 + 4

=  18 x 3 + 4

=  54 + 4

= 58

178/8 can be reduced to 89/4.

1.8 + 0.7 can be reduced to 2.5 which can be written as 5/2.

(89/4) / (5/2)  =  (89/4) x (2/5)                  (change from division to multiplication)

                        =  (89/2) x (1/5)                  (cancel the 2s)

                        =  89/10  or 8.9

3xy² - 48x

Factor out the common terms, 3 and x:

3x(y² - 16)

Look at what remains inside the parentheses, a difference of squares:

3x(y - 4)(y + 4)

Thank you, Alan!

  x + y  =  10     --->    -x - y  =  -10

2x + y  =  13     --->   2x + y  =  13

Add down the columns:  x  =  3

Substituting into the first equation:  y = 7

x² - y²  =  (3)² - (7)² =  9 - 49  =  -40