Question

question sheet
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: \( y^2 + 2w \)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Substitute \( y = -5 \), \( w = -2 \):
\( -(-5) - (-2) + 1 = 5 + 2 + 1 = 8 \) (Wait, original \( v + w + x + y + z = 3 + (-2) + 4 + (-5) + 8 = 8 \), so Orange matches Number 10? Wait, recheck: \( -y - w + 1 = 5 + 2 + 1 = 8 \), and \( v + w + x + y + z = 3 -2 +4 -5 +8 = 8 \). Correct.

Step10: Evaluate Purple: \( 3w^2 - 1 \)

Substitute \( w = -2 \):
\( 3(4) - 1 = 12 -1 = 11 \) (And \( y + 2z = -5 + 16 = 11 \), so Purple matches Number 6.

Now, match 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 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) Wait, \( -v^3 = -27 \), and Blue Gray was \( -27 \), so Number 9 matches Blue Gray.
• \( v + w + x + y + z = 8 \) (Number 10) matches Orange (\( -y - w + 1 = 8 \)).

(Assuming the task is to evaluate all, here are the results for each expression.)

Answer:

(For example, if asked for a specific one, say Light Gray: \( \boldsymbol{21} \), Blue Gray: \( \boldsymbol{-27} \), Light Blue: \( \boldsymbol{48} \), Dark Blue: \( \boldsymbol{18} \), Green: \( \boldsymbol{64} \), Bright Pink: \( \boldsymbol{-24} \), Yellow: \( \boldsymbol{-26} \), Red: \( \boldsymbol{29} \), Orange: \( \boldsymbol{8} \), Purple: \( \boldsymbol{11} \), and Number 1-10 as calculated.)

(If the question was to evaluate a specific expression, e.g., Light Gray: \( y^2 + 2w = \boldsymbol{21} \))