Question

evaluate the expressions. each number will match to a color with the same answer.
v = 3, w = -2, x = 4, y = -5, z = 8
number 1
2v² = 18
light gray
y² + 2w = -29
number 2
6y + 4 = -26
blue gray
5w + 2y - v - x =
number 3
x³ = 64
light blue
-6w³ =
number 4
v - 9w = 21
dark blue
wy + z =
number 5
vwx = -24
green
z² =
number 6
y + 2z = 11
bright pink
6y - 3w =
number 7
-3wz = 48
yellow
11w - x =
number 8
y² + w² = 29
red
vw - 7y =
number 9
-v³ = -27
orange
-y - w + 1 =
number 10
v + w + x + y + z =
purple
3w² - 1 =

Explanation:

Step1: Evaluate Light Gray's \( y^2 + 2w \)

Substitute \( y = -5 \), \( w = -2 \): \( (-5)^2 + 2(-2) = 25 - 4 = 21 \)

Step2: Evaluate Blue Gray's \( 5w + 2y - v - x \)

Substitute \( w = -2 \), \( y = -5 \), \( v = 3 \), \( x = 4 \): \( 5(-2) + 2(-5) - 3 - 4 = -10 -10 -3 -4 = -27 \)

Step3: Evaluate Light Blue's \( -6w^3 \)

Substitute \( w = -2 \): \( -6(-2)^3 = -6(-8) = 48 \)

Step4: Evaluate Dark Blue's \( wy + z \)

Substitute \( w = -2 \), \( y = -5 \), \( z = 8 \): \( (-2)(-5) + 8 = 10 + 8 = 18 \)

Step5: Evaluate Green's \( z^2 \)

Substitute \( z = 8 \): \( 8^2 = 64 \)

Step6: Evaluate Bright Pink's \( 6y - 3w \)

Substitute \( y = -5 \), \( w = -2 \): \( 6(-5) - 3(-2) = -30 + 6 = -24 \)

Step7: Evaluate Yellow's \( 11w - x \)

Substitute \( w = -2 \), \( x = 4 \): \( 11(-2) - 4 = -22 - 4 = -26 \)

Step8: Evaluate Red's \( vw - 7y \)

Substitute \( v = 3 \), \( w = -2 \), \( y = -5 \): \( 3(-2) - 7(-5) = -6 + 35 = 29 \)

Step9: Evaluate Orange's \( -y - w + 1 \)

Substitute \( y = -5 \), \( w = -2 \): \( -(-5) - (-2) + 1 = 5 + 2 + 1 = 8 \) (Wait, correction: Original expression? Wait, the table's Orange is \( -y - w + 1 \)? Wait, no, the user's table: Orange is \( -y - w + 1 \)? Wait, the given table for Number 9 Orange: \( -y - w + 1 \)? Wait, no, the user's image: Number 9 Orange: \( -y - w + 1 \)? Wait, no, let's recheck. Wait, the user's table: Number 9 Orange: \( -y - w + 1 \)? Wait, original problem: Number 9 Orange: \( -y - w + 1 \)? Wait, no, the user's image: Number 9 Orange: \( -y - w + 1 \)? Wait, maybe I misread. Wait, the user's table: Number 9 Orange: \( -y - w + 1 \)? Wait, no, let's do it again. Wait, \( y = -5 \), \( w = -2 \): \( -(-5) - (-2) + 1 = 5 + 2 + 1 = 8 \)? But maybe the expression is different. Wait, no, the user's table: Number 9 Orange: \( -y - w + 1 \)? Wait, perhaps a typo, but proceed with given values. Wait, no, let's check all:

Wait, Number 10 Purple: \( 3w^2 - 1 \), \( w = -2 \): \( 3(4) -1 = 11 \)

Number 10 left: \( v + w + x + y + z = 3 + (-2) + 4 + (-5) + 8 = 8 \)

Now, matching answers:

- \( 2v^2 = 18 \) (Number 1) matches Dark Blue \( wy + z = 18 \)
- \( 6y + 4 = -26 \) (Number 2) matches Yellow \( 11w - x = -26 \)
- \( x^3 = 64 \) (Number 3) matches Green \( z^2 = 64 \)
- \( v - 9w = 21 \) (Number 4) matches Light Gray \( y^2 + 2w = 21 \)
- \( vwx = -24 \) (Number 5) matches Bright Pink \( 6y - 3w = -24 \)
- \( y + 2z = 11 \) (Number 6) matches Number 10 Purple \( 3w^2 -1 = 11 \)
- \( -3wz = 48 \) (Number 7) matches Light Blue \( -6w^3 = 48 \)
- \( y^2 + w^2 = 29 \) (Number 8) matches Red \( vw - 7y = 29 \)
- \( -v^3 = -27 \) (Number 9) matches Blue Gray \( 5w + 2y -v -x = -27 \)
- \( v + w + x + y + z = 8 \) (Number 10 left) matches Orange \( -y - w + 1 = 8 \) (if \( -y - w + 1 = -(-5) - (-2) +1 = 5 +2 +1 =8 \))

But the task is to evaluate each expression. Let's list all evaluated:

- Light Gray: \( y^2 + 2w = 21 \)
- Blue Gray: \( 5w + 2y - v - x = -27 \)
- Light Blue: \( -6w^3 = 48 \)
- Dark Blue: \( wy + z = 18 \)
- Green: \( z^2 = 64 \)
- Bright Pink: \( 6y - 3w = -24 \)
- Yellow: \( 11w - x = -26 \)
- Red: \( vw - 7y = 29 \)
- Orange: \( -y - w + 1 = 8 \) (assuming expression)
- Purple: \( 3w^2 - 1 = 11 \), \( v + w + x + y + z = 8 \)

But the user's table has some pre-filled answers (like Number 1: 18, Number 2: -26, etc.). Let's confirm each:

For example, Number 1: \( 2v^2 = 2*(3)^2 = 18 \) (correct). Number 2: \( 6y +4 = 6*(-5)+4 = -30 +4 = -26 \) (correct). Number 3: \( x^3 = 4^3 = 64 \) (correct). Number 4: \( v -9w = 3 -9*(-2) = 3 +18 =21 \) (correct). Number 5: \( vwx = 3*(-2)*4 = -24 \) (correct). Number 6: \( y + 2z = -5 + 2*8 = -5 +16 =11 \) (correct). Number 7: \( -3wz = -3*(-2)*8 = 48 \) (correct). Number 8: \( y^2 + w^2 = (-5)^2 + (-2)^2 =25 +4=29 \) (correct). Number 9: \( -v^3 = -27 \) (correct, \( v=3 \), \( -3^3 = -27 \)). Number 10 left: \( 3 + (-2) +4 + (-5) +8 = 8 \). Number 10 Purple: \( 3*(-2)^2 -1 = 3*4 -1=11 \).

Now, the expressions to evaluate (the ones without pre-filled answers):

1. Light Gray: \( y^2 + 2w = (-5)^2 + 2*(-2) =25 -4=21 \)
2. Blue Gray: \( 5w + 2y -v -x =5*(-2)+2*(-5)-3-4= -10-10-3-4=-27 \)
3. Light Blue: \( -6w^3 = -6*(-2)^3 = -6*(-8)=48 \)
4. Dark Blue: \( wy + z = (-2)*(-5)+8=10+8=18 \)
5. Green: \( z^2 =8^2=64 \)
6. Bright Pink: \( 6y -3w =6*(-5)-3*(-2)= -30+6=-24 \)
7. Yellow: \( 11w -x =11*(-2)-4= -22-4=-26 \)
8. Red: \( vw -7y =3*(-2)-7*(-5)= -6+35=29 \)
9. Orange: \( -y -w +1 = -(-5)-(-2)+1=5+2+1=8 \)
10. Number 10 left: \( v + w + x + y + z =3 + (-2) +4 + (-5) +8=8 \)
10. Purple: \( 3w^2 -1 =3*(-2)^2 -1=12-1=11 \)

Answer:

• Light Gray: \( 21 \)
• Blue Gray: \( -27 \)
• Light Blue: \( 48 \)
• Dark Blue: \( 18 \)
• Green: \( 64 \)
• Bright Pink: \( -24 \)
• Yellow: \( -26 \)
• Red: \( 29 \)
• Orange: \( 8 \)
• Number 10 (left): \( 8 \)
• Purple: \( 11 \)