geno3141

If the three numbers represent the sides of a triangle, then call 'c' the length of the largest side, and 'a' and 'b' the lengths of the other two sides.

∠C is the angle opposite side 'c' and since side c is the largest side of the triangle, ∠C will be the largest angle of the triangle.

If c²  =  a² + b², then the triangle is a right triangle because ∠C is a right angle.

If c²  >  a² + b², then the triangle has an obtuse angle at ∠C.

If c²  <  a² + b², then the triangle has an acute angle at ∠C, making all the angles acute.

y  =  9x     --->     y  =  9x + 0

It is a linear equation which, when graphed, has a slope of 9 and a y-intercept of 0 (passes through the origin).

F  =  (9/5)C + 32

F  =  (9/5)(-50) + 32  =  -90 + 32  =  -58°F

The slope-intercept form for a straight line is:  y  =  mx + b

where m is the slope and b is the y-intercept.

The equation  y  =  -6  can be written as  y  =  0x - 6,

showing that m (the slope) is 0 and that b (the y-intercept) is -6.

There is a formula that I use for problems like this:

(Percent)·(Amount) + (Percent)·(Amount)  =  (Final Percent)·(Final Amount)

If you have 10 liters divided into two parts, call the amount of one part 'x' and the amount of the other part '10 - x':

(10%)·(x) + (40%)·(10 - x)  =  (30%)·(10)

(0.10)·(x) + (0.40)·(10 - x)  =  (0.30)·(10)

0.10x - 4.00 - 0.40x  =  3.00

-0.30x - 4.00  =  3.00

-0.30x  =  -1.00

x  =  -1.00 / -0.30  =  3.33 liters

Just as GL said!

(x + 3)² = (x + 3)(x + 3)

Using FOIL:  First, Outside, Inside, Last:

(x + 3)(x + 3)  =  x·x  +  x·3  +  3·x  +  3·3  =  x²  +  3x  +  3x  +  9  =    x²  +  6x  +  9 

Even though we don't know how many originally were in that town and we don't know how many are there now, we do know that there are 6 x 115 = 690 fewer people in the town now than were there 6 years ago.

When you take calculus, you study situations which approach ∞/∞.

The expression, ∞/∞, is called "indeterminate" because the the problem that created it determines its value.

The value might be ∞, might be zero, might be 23.5, might be -12.75, etc.

So, without knowing the problem that created this situation, you don't really know what the answer should be, and it could be any number, or even ∞.

What is the question?

I believe that there will be two such points.

One point is 3/4ths of the way from (3,5) to (8,-3).

  To find this point:  the x-distance from 3 to 8 is 5; 3/4ths of 5 is 15/4, or 3.75, adding 3.75 onto 3 is 6.75

                             the y-distance from 5 to -3 is -8; 3/4ths of -8 is -6, adding -6 to 5 is -1

          this point is (6.75, -1)

          Checking:  the distance from 3 to 6.75 is 3.75; the distance from 6.75 to 8 is 1.25; 3.75 = 3 x 1.25

                          the distance from 5 to -1 is -6; the distance from -1 to -3 is -2; -6 = 3 x -2

The other point is past (8,-3).

   To find this point: the x-distance from 3 past 8 must have value 3, the x-distance from 8 away from 3 must                                have value 1.   Dividing the distance from 3 to 8 into 2 parts, each part has value 2.5;                                 add 2.5 onto 8 gives 10.5.

                              the y-distance from 5 to -3 has 2 parts, each part having value -4; add -4 onto -3 gives                                 -7

            this point is (10.5,-7)

          Checking:  the distance from 3 to 10.25 is 7.25; the distance from 8 to 10.25 is 2.25; 7.25 = 3 x 2.25

                          the distance from 5 to -7 is -12; the distance from -7 to -3 is -4; -12 = 3 x -4