geno3141

And ∠g = 121°.

The "-" of -3/2 means that you need to flip the number into the denominator.

The "3" of -3/2 means that you need to cube the number.

The "2" of -3/2 means that you need to find the square root of the number.

You can do these in any order that you wish.

I'm going to find the square root first, then cube that answer, then flip the number.

49   --->   (square root)  --->  7   --->   (cube it)   --->   343   --->   (flip it)   --->   1/343

0/0 is an "indeterminate" expression.

The reason that 6/2 is 3 is because 2 x 3 = 6. (In other words, it "checks.")

When you divide 0/0, you might think that the answer is 0, because it checks:  0 x 0 = 0.

However, you might think that the answer is 6, because 6 also checks:  0 x 6 = 0.

Try -4:  0/0 = -4  --->  0 x -4 = 0, It also works!

In fact, every number works! That's why it's called "indeterminate"; there is no specific answer.

When you take calculus, you find that the problem that led to that "solution" determines the value of 0/0.

Sometimes, it is a number, like 6, or -4, or even 0.

Sometimes, it isn't a number, for instance, ∞.

Point D is (4, 1).

Slope of line AC:  m  =  (-2 - -1)/(6 - 1)  =  -1/5

Line through D parallel to AC:  y - 1  =  (-1/5)(x - 4)  --->  x + 5y  =  9

Distance from point B to that line must have a slope perpendicular to that line and pass through (3, -4):

                 y + 4  =  5(x - 3)   --->  5x - y  =  19

Find the point where the two lines intersect:  x + 5y = 9  and 5x - y = 19   --->   (4, 1)

Find the distance from (3, -4) to (4, 1)   --->   d = √[ (4 - 3)² + (1 - -4)² ]  =  √26

French, I believe ... but it seems to be a weather forecast ...

Use the distributive property:  -(x + 3y)  =  -1(x + 3y)  =  (-1)(x) + (-1)(3y)  =  -1x + -3y  =  -x - 3y

A simpler way is to realize that the minus sign in front of the parentheses changes the sign of all the terms inside the parentheses.

8 + 6 + 10 + 7 + x  =  45

One way:  Add the numbers 8, 6, 10, and 7 and subtract this answer from 45.

Another way: From 45, subtract 8, then subtract 6, then subtract 10, then subtract 7.

Choose a method to solve it ...

If the problem was:                            m³ =  1000

Find the cube root of both sides:   (m³)^1/3  =  (1000)^1/3

    --->                                               m  =  10 

Erica most likely divided by three instead of finding the cube root.

Choose a point on the graph which is clearly on one side of the line or the other.

Place both the x-value and the y-value into the original inequality.

If those values make the inequality true, shade the side of the line that includes that point; if those values don't make the inequality true, shade the other side of the line.

For example:

For the inequality:  y > 2x - 7

First, draw the line y = 2x + 7 (making it a dashed line; if the original inequality were y ≥ 2x + 7, you would make a solid line).

Then choose a point that is not on the line:  I'll choose the point (1, 5). Put in these values into the original inequality:

Since  5 > 2(1) - 7   --->  5 > 2 - 7   --->   5 > -5   is true, shade that side of the line (the upper side).

If I had chosen the point (10, 1) --->  1 > 2(10) - 7   --->   1 > 10 - 3   --->   1 > -7  is false, so I would not have chosen that side (the lower side), and I would have again shaded the upper side.

Specific questions?

-7(2x + 1) + 3(5x - 4)  =  0

Use the Distributive Property:  -7(2x) + (-7)(1) + 3(5x) + 3(-4)  =  0

Multiply:                                                  -14x - 7 + 15x - 12  =  0

Simplify:                                                                     x - 19  =  0

Add 21 to both sides:                                                          x  =  19