Algebra

The area of a triangle is

(1/2) x (length of the base) x (height of the triangle).

You ought to be able to handle it from this point.

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240

x + 2y <12

2x + y < 10

Solve this system of equations. 5x+3y+z=-29 x-3y+2z=23 14x-2y+3z=-18 Write the solution as an ordered triple.

maximum value of 6y+10y

x + y = 5

y = -x + 5

The graph is a straight line, with [ slope = -1 ], passing through the point [ y = 5 ] on the y-axis.

Find the coordinates of the vertices of triangle a'b'c' after triangle ABC is dilated using the given scale factor then graph triangle ABC and its dilation

A (1,1) B(1,3) C(3,1) scale factor 3

Reflecting the the x-axis (line y=0) leaves the x-coordinate unchanged and negates the y-coordinate:

(x, y) -> (x, -y)

For example:

(1, 2) -> (1, -2)

(3, -4) -> (3, 4)

An ordered pair that has a negative x-coordinate and a positive y-coordinate (-,+) would be plotted in which quadrant?

42

Example: if you have a point with the coordinates (2,4), a reflection over the y-axis will result in the point with coordinates (-2,4).

Sensible but hard to explain

-3(x + y + z)

You draw a number line. Then put a dot at the point at x. Happy graphing!

x + y + z = 12

y = 1

x - y - z = 0

Substitute y = 1 in the other two equations:

x + 1 + z = 12 so that x + z = 11

and

x - 1 - z = 0 so that x - z = 1

Add these two equations: 2x + 0z = 12 which implies that x = 6

and then x + z = 11 gives z = 5

So the solution is (x, y, z) = (6, 1, 5)

The answer depends on what the feasible region is and on what operator is between 6x and 8y.

The graph of an inequality is a region, not a line.

The answer depends on the feasible region and there is no information on which to determine that.