geno3141

If a triangle has an hypotenuse, it must be a right triangle.

If a right triangle has one anlge of 45°, the other acute angle must also be 45°.

Therefore, the triangle is an isosceles right triangle.

One way to solve this is to use the Pythagorean Theorem:  a²+ b²  =  c²

c is the hypotenuse   --->   c = 10

Since it's isosceles, a = b, call each one x:     x² + x²  =  10²

                                                                   2x²  =  100

                                                                     x²  =  50

                                                                       x  =  √50  =  √25√2  =  5√2

2x  =  10 - y

y - x  =  -2     --->   (solve for y)   --->   y  =  x - 2

Replace this into the other equation:  2x  =  10 - (x - 2)

                (distribute)                           2x  =  10 - x + 2 

                (add x to both sides)            3x  =  12

                (divide by 3)                           x  =  4

Replace this into the equation  y  =  x - 2     --->     y  =  4 - 2     --->     y  =  2

Are you doing it by computer or by calculator?

If computer, what program are you using?

If calculator, what calculator are you using?

One answer:  -52.07 radians (approx)

Graph it.

-100 - 3x  =  -9x + 26

Add 9x to both sides:

-100 + 6x  =  26

Add 100 to both sides:

     6x  =  126

Divide both sides by 6:

   x  =  21

Not even close to infinity!

0.8(12.5x + 7)  =  2(5x + 11)

Distributing:

10x + 5.6  =  10x + 22

Subtracting 10x from both sides:

    5.6  =  22

Impossible!  This is not an equation ... No answer ...

If the scale factor is 2.5, then every dimension (length, width) is multiplied by 2.5.

30% written as a decimal is 0.30

"of" is interpreted as "times"

30% of $50,000.00

0.30 x 50000  =  ???

If you factor 234:     234  =  2 x 117

                                         =  2 x 3 x 39

                                         =  2 x 3 x 3 x 13

If you factor 341:     341  =  11 x 37

They have no common factors, they are relatively prime; the fraction does not reduce.

(x - 3) / (2x - 4) = x / (x - 2) + 2

[Since 2 makes the denominator zero, 2 cannot be an answer.]

Notice that  2x - 4  = 2(x - 2)

--->   (x - 3) / ( 2(x - 2) ) = x / (x - 2) + 2

The lowest common denominator is:  2(x - 2)

Multiply each term by 2(x - 2):

2(x - 2) · [ (x - 3) / ( 2(x - 2) ) ]  =  2(x - 2) · [ x / (x - 2)] + 2(x - 2) · [ 2 ]

Simplify:

--->   x - 3  =  2x + 4x - 8

Subtract x from both sides and simplify:

--->       -3  =  5x - 8

Add 8 to both sides:

--->         5  =  5x

Divide by 5:

--->         x  =  1