Not sure about number 1

2. 61 = 8x + 5

56 = 8x

7 = x

3. 2 (3x) = 7x – 5

6x = 7x – 5

-x = -5

x = 5

BC = AB = 3(5) = 15

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

6 = -2 + x

8 = x

1 = (4 + y)/2

2 = 4 + y

-2 = y

the coordinates of B are (8,-2)

1. have you ever sat in achair that is not stable – one with four legs? that is because four points do not necessarily lie in the same plane. but three points do. that is why 3-legged stools, or in this case a tripod, is stable. three points determine a unique plane, so three legs will always be stable; they must lie in the same plane.

2. if B is between A and C, AB + BC = AC. so now you can write an equation: (3x+4) + (5x+1) = 61.

combine like terms: 8x + 5 = 61

now, “undo” in the reverse order of operations; always “undo” addition or subtraction first, so subtract 5 from both sides: 8x = 56. now divide both sides by 8: x = 7.

3. if B is the midpoing, then 2AB = AC by the definition of midpoint; it means that b is in the exact middle so that AB is half of AC – or it takes two of them (two halves) to make the whole.

so 2(3x) = 7x-5

distribute: 6x = 7x-5

subtract 7x from both sides: -x = -5

divide both by -1: x = 5

substiture this back into the AB equation. since AB = BC (because B is the midpoint – exactly half way between A and C), BC will be the same length as AB.

AB = 3x, but x = 5, so AB = 3(5) = 15

so BC also = 15

4. midpoint: average the x’s to get the x coordinate of the midpoint and average the y’s to get the y coordinate of the midpoint.

let’s call B(x,y) then (-2+x)/2 is the average of the two x’s of the endpoints. but we know the x value of the midpoint is 3, so (-2+x)/2 = 3. cross multipy to solve: -2 + x = 6.

add 2 to both sides: x = 8

do the same for the y coordinate. the average is the y-coordinate of the midpoint, but the average also is (4+y)/2

so (4+y)/2 = 1. cross multipy: 4+y = 2. subtract 4 from both sides: y = -2

1) D, the base of the tripod is three noncolinear points, they are on a plane

2) x=3/2 —> 3x+4=5x+1 —> 3=2x —–> x=3/2

3) 2(3x)=7x-5

6x=7x-5 x=5

because B is the midpoint, Line Ab must be half the whole line, therefore if you multiply the half of the line by two you can set it equal to the value of the whole line.

becuase the two lines on either sides of the midpoint are equal BC=AB

AB=3x

AB=3(5)

AB=BC=15

get it?

4) B(4,-2) it is east if you graph it.

1. i don’t know, but i’m thinking d.

2. since b is between a and c, we can assume ab+bc=ac. given the equations, we subsitute.

(3x+4)+(5x+1)=61, remove parenthesis 3x+4+5x+1=61

now we can add the whole numbers and the variables.

8x+5=61, isolate the variable

8x+5-5=61-5

8x=56

8x/8=56/8

x=7

3. since we know b is the midpoint, we can assume that ab=bc and ab+bc=ac. since we know ab and ac, we want to use ab+ab=ac or 2ab=ac

2(3x)=7x-5

6x=7x-5

6x+5=7x-5+5, now we isolate the variable

6x+5=7x

6x+5-6x=7x-6x

5=1x or 5=x

4. I know there is a formula for this, but I forgot it. but let’s see, m is the midpoint of ab, so again we know am=mb. That’s all I can give you of that because I forgot the equation.

to respond to ur midpoit proble, persist with those steps: Set ur compass length to greater advantageous than 0.5 of the section, yet decrease than the completed element. place the compass factor on factor A Draw an arc it truly is above the section and one that is decrease than do no longer replace THE COMPASS placing!!! place the compass factor on factor B Draw an arc it truly is above the section (and intersects w/ the before made arc) and one that is decrease than (back, this is going to intersect with the before made arc). Now place ur straightedge so as that u could make a line from the intersections of the two arcs. the place this line crossed section AB is the midpoint of AB