17. It looks like the funky symbol is averaging. I'll render it as #. Then a#b = (a+b)/2.
4 # 8 = 6
-5 # 0 = -2.5
2 # 2 = 2
18.
A and D are complementary. In degrees,
A+D=90
A and E are supplementary
A+E=180
Eliminating A,
A=90-D
90-D+E = 180
E=D+90
Answer: We conclude E is bigger than D by 90 degrees
19.
4x + 3(2 - x) = 8 - 2x Given
4x + 6 - 3x = 8 - 2x distributive law
x + 6 = 8 - 2x collect like terms
x + 2x = 8 + - 6 add equals to both sides
3x = 2 like terms
x = 2/3 divide both sides by 3
Answer: x=2/3
[tex]\dfrac{19 - 2(3x-1)}{5} = x + 2[/tex]
Multiply by 5
[tex]19-2(3x-1) = 5(x+2)[/tex]
Distribute
[tex]19 - 6x + 2 = 5x + 10[/tex]
Add 6x to both sides. Add -10 to both sides.
[tex]19 + 2 - 10 = 5x + 6x[/tex]
Collect terms,
[tex]11 = 11x[/tex]
Divide by 11,
[tex]x = 1[/tex]
Answer: x=1
20.
I'll let you make the chart, I'll just write.
We assume that each person likes a single color with no overlap.
We have girls B,C boys D,J colors g,p,r,y.
No person's name has the same length as their color. Let's write the lengths
B5,C5,D4,J3 g5,p4,r3,y6
So B and C don't like g, D doesn't like p, J doesn't like r
Cathy's in a different grade means C doesn't like p
A boy likes red means B and C don't like r.
That leaves only y for C. C likes y
That leaves only p for B. B likes p
That leaves only g for J. J likes g
That leaves: D likes r
Answer: Becky-pink, Cathy-yellow, Dck-red, Joe-green
