Not sure what algebra tiles are
not sure how to absolutely prove
I can prove it works at least most of the time by subsitute ing number for x
remember that 0,1,2 have special properties and are not very good for subsituting so
try 4
4+8(4)=4(2(4)+1)
true or false?
4+8(4)=4(2(4)+1)
multipily
4+32=4(8+1)
36=4(9)
36=36
this is treu at least for the number 4
another way is to believe in the distributive property where
a(b+c)=ab+ac so then
4(2x+1)=4(2x)+4(1)=8x+4=4+8x
Im pretty sure that it would be 4 but not sure
Answer:
(6,5), (3,-4) either one of those...
We can use linear combinations of the equations to eliminate variables.
3x - 4y = 1
-2x + 3y = 1
To eliminate y we'll make the linear combination of 3 times the first equation minus four times the second.
9x - 12y = 3
-8x + 12y = 4
Adding,
x = 7
We could solve for y directly but let's use another linear combination, twice the first plus three times the second:
2(3x - 4y) + 3(-2x + 3y)= 2(1)+3(1)
y = 5
Check: 3(7)-4(5)=1 good. -2(7)+3(5)=1 good.
Q18 Answer: (7,5)
y = -3x + 5
5x - 4y = -3
4y +1(5x - 4y) = 4(-3x + 5) + 1(-3)
5x = -12x + 20 -3
17 x = 17
x = 1
y = -3(1) + 5 = 2
Check: 5(1) - 4(2) = -3 good
Q19 Answer (1,2)
6x + 5y = 25
x = 2y + 24
6x = 12y + 144
5y = 25 - 12y - 144
17y = -119
y = -119/17= -7
x = 2y+24= 10
Check: 6(10)+5(-7)=25 good 2y+24=2(-7)+24=10=x good
Q20 Answer (10,-7)
3x + y = 18
-7x + 3y = -10
9x + 3y = 54
9x - -7x = 54 - -10
16x = 64
x=4
y = 18 -3x = 18-12=6
Check: 3(4)+6=18 good, -7(4)+3(6)=-10 good
Q21 Answer: (4,6)
Answer:
1. distance = sqrt( (7-7)^2+(2- -8)^2) = 10
2. check out desk (0,0 ) => distance = sqrt( (0- -9)^2+(0-0)^2) = 9
3. last corner ( -3, 4)
4. area = sqrt( (-10- -10)^2+(10-4)^2) x sqrt( (-3- -10)^2+(10-10)^2) = 6x7 =42
5. check desk (0,0), south direction = negative y axis => P_beginning (0,-20), P_end (0,-(20+25)) = (0,-45)
6. A(-2,-1) and B(4,-1) lie in y =-1. AB = sqrt( (-2- 4)^2+(-1- -1)^2) =6
=> area = 3.6x6 =21.6
=> peri = 2x(3.6+6) = 19.2
7. A(-5,4) and B(2,4), AB = sqrt( (-5- 2)^2+(4- -4)^2) = 7 => AB is base
=> p = peri = 7+ 8.3x2 = 23.6
=> area = sqrt[px(p-7)x(p-8.3)x(p-8.3)]
=sqrt[23.6x(23.6-7)x(23.6-8.3)x(23.6-8.3)] = 302.8
