Math / Algebra

QuestionFor each Expression below Evaluate for $x=2, y=4, a=3, b=-2$ (6) $-3 A+2 b-8=$ (7) $5 x+2 y-8=$ (8) $-3 x+2 y+50=$ (a) $x^{2}+y^{2}-4=$ (10) $a^{2}+b+15=$ (11) $2 x+3 y+2 a=$ (12) $x^{2}-a^{2}+5=$ (13) $2 x+2 y+2 a+2 b=$ (14) $b^{2}+b-2=$ (15) $-2 x+4 y-4 a+b$

Studdy Solution

STEP 1

1. We are given specific values for the variables: $x = 2$ , $y = 4$ , $a = 3$ , and $b = -2$ .
2. Each expression needs to be evaluated by substituting these values into the expression.
3. Basic arithmetic operations will be used to simplify each expression after substitution.

STEP 2

1. Substitute the given values into each expression.
2. Simplify the expression to find the numerical result.

STEP 3

Expression (6): $-3a + 2b - 8$
Substitute $a = 3$ and $b = -2$ :
$-3(3) + 2(-2) - 8$

STEP 4

Simplify the expression:
$-9 - 4 - 8 = -21$

STEP 5

Expression (7): $5x + 2y - 8$
Substitute $x = 2$ and $y = 4$ :
$5(2) + 2(4) - 8$

STEP 6

Simplify the expression:
$10 + 8 - 8 = 10$

STEP 7

Expression (8): $-3x + 2y + 50$
Substitute $x = 2$ and $y = 4$ :
$-3(2) + 2(4) + 50$

STEP 8

Simplify the expression:
$-6 + 8 + 50 = 52$

STEP 9

Expression (a): $x^2 + y^2 - 4$
Substitute $x = 2$ and $y = 4$ :
$(2)^2 + (4)^2 - 4$

STEP 10

Simplify the expression:
$4 + 16 - 4 = 16$

STEP 11

Expression (10): $a^2 + b + 15$
Substitute $a = 3$ and $b = -2$ :
$(3)^2 + (-2) + 15$

STEP 12

Simplify the expression:
$9 - 2 + 15 = 22$

STEP 13

Expression (11): $2x + 3y + 2a$
Substitute $x = 2$ , $y = 4$ , and $a = 3$ :
$2(2) + 3(4) + 2(3)$

STEP 14

Simplify the expression:
$4 + 12 + 6 = 22$

STEP 15

Expression (12): $x^2 - a^2 + 5$
Substitute $x = 2$ and $a = 3$ :
$(2)^2 - (3)^2 + 5$

STEP 16

Simplify the expression:
$4 - 9 + 5 = 0$

STEP 17

Expression (13): $2x + 2y + 2a + 2b$
Substitute $x = 2$ , $y = 4$ , $a = 3$ , and $b = -2$ :
$2(2) + 2(4) + 2(3) + 2(-2)$

STEP 18

Simplify the expression:
$4 + 8 + 6 - 4 = 14$

STEP 19

Expression (14): $b^2 + b - 2$
Substitute $b = -2$ :
$(-2)^2 + (-2) - 2$

STEP 20

Simplify the expression:
$4 - 2 - 2 = 0$

STEP 21

Expression (15): $-2x + 4y - 4a + b$
Substitute $x = 2$ , $y = 4$ , $a = 3$ , and $b = -2$ :
$-2(2) + 4(4) - 4(3) + (-2)$

STEP 22

Simplify the expression:
$-4 + 16 - 12 - 2 = -2$

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Studdy Solution

STEP 1

STEP 2

1. Substitute the given values into each expression.2. Simplify the expression to find the numerical result.

STEP 3

Expression (6): −3a+2b−8-3a + 2b - 8−3a+2b−8Substitute a=3 a = 3 a=3 and b=−2 b = -2 b=−2:−3(3)+2(−2)−8 -3(3) + 2(-2) - 8 −3(3)+2(−2)−8

STEP 4

Simplify the expression:−9−4−8=−21 -9 - 4 - 8 = -21 −9−4−8=−21

STEP 5

Expression (7): 5x+2y−85x + 2y - 85x+2y−8Substitute x=2 x = 2 x=2 and y=4 y = 4 y=4:5(2)+2(4)−8 5(2) + 2(4) - 8 5(2)+2(4)−8

STEP 6

Simplify the expression:10+8−8=10 10 + 8 - 8 = 10 10+8−8=10

STEP 7

Expression (8): −3x+2y+50-3x + 2y + 50−3x+2y+50Substitute x=2 x = 2 x=2 and y=4 y = 4 y=4:−3(2)+2(4)+50 -3(2) + 2(4) + 50 −3(2)+2(4)+50

STEP 8

Simplify the expression:−6+8+50=52 -6 + 8 + 50 = 52 −6+8+50=52

STEP 9

Expression (a): x2+y2−4x^2 + y^2 - 4x2+y2−4Substitute x=2 x = 2 x=2 and y=4 y = 4 y=4:(2)2+(4)2−4 (2)^2 + (4)^2 - 4 (2)2+(4)2−4

STEP 10

Simplify the expression:4+16−4=16 4 + 16 - 4 = 16 4+16−4=16

STEP 11

Expression (10): a2+b+15a^2 + b + 15a2+b+15Substitute a=3 a = 3 a=3 and b=−2 b = -2 b=−2:(3)2+(−2)+15 (3)^2 + (-2) + 15 (3)2+(−2)+15

STEP 12

Simplify the expression:9−2+15=22 9 - 2 + 15 = 22 9−2+15=22

STEP 13

Expression (11): 2x+3y+2a2x + 3y + 2a2x+3y+2aSubstitute x=2 x = 2 x=2, y=4 y = 4 y=4, and a=3 a = 3 a=3:2(2)+3(4)+2(3) 2(2) + 3(4) + 2(3) 2(2)+3(4)+2(3)

STEP 14

Simplify the expression:4+12+6=22 4 + 12 + 6 = 22 4+12+6=22

STEP 15

Expression (12): x2−a2+5x^2 - a^2 + 5x2−a2+5Substitute x=2 x = 2 x=2 and a=3 a = 3 a=3:(2)2−(3)2+5 (2)^2 - (3)^2 + 5 (2)2−(3)2+5

STEP 16

Simplify the expression:4−9+5=0 4 - 9 + 5 = 0 4−9+5=0

STEP 17

Expression (13): 2x+2y+2a+2b2x + 2y + 2a + 2b2x+2y+2a+2bSubstitute x=2 x = 2 x=2, y=4 y = 4 y=4, a=3 a = 3 a=3, and b=−2 b = -2 b=−2:2(2)+2(4)+2(3)+2(−2) 2(2) + 2(4) + 2(3) + 2(-2) 2(2)+2(4)+2(3)+2(−2)

STEP 18

Simplify the expression:4+8+6−4=14 4 + 8 + 6 - 4 = 14 4+8+6−4=14

STEP 19

Expression (14): b2+b−2b^2 + b - 2b2+b−2Substitute b=−2 b = -2 b=−2:(−2)2+(−2)−2 (-2)^2 + (-2) - 2 (−2)2+(−2)−2

STEP 20

Simplify the expression:4−2−2=0 4 - 2 - 2 = 0 4−2−2=0

STEP 21

Expression (15): −2x+4y−4a+b-2x + 4y - 4a + b−2x+4y−4a+bSubstitute x=2 x = 2 x=2, y=4 y = 4 y=4, a=3 a = 3 a=3, and b=−2 b = -2 b=−2:−2(2)+4(4)−4(3)+(−2) -2(2) + 4(4) - 4(3) + (-2) −2(2)+4(4)−4(3)+(−2)

STEP 22

Simplify the expression:−4+16−12−2=−2 -4 + 16 - 12 - 2 = -2 −4+16−12−2=−2

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1. Substitute the given values into each expression.
2. Simplify the expression to find the numerical result.

Expression (6): $-3a + 2b - 8$
Substitute $a = 3$ and $b = -2$ :
$-3(3) + 2(-2) - 8$

Simplify the expression:
$-9 - 4 - 8 = -21$

Expression (7): $5x + 2y - 8$
Substitute $x = 2$ and $y = 4$ :
$5(2) + 2(4) - 8$

Simplify the expression:
$10 + 8 - 8 = 10$

Expression (8): $-3x + 2y + 50$
Substitute $x = 2$ and $y = 4$ :
$-3(2) + 2(4) + 50$

Simplify the expression:
$-6 + 8 + 50 = 52$

Expression (a): $x^2 + y^2 - 4$
Substitute $x = 2$ and $y = 4$ :
$(2)^2 + (4)^2 - 4$

Simplify the expression:
$4 + 16 - 4 = 16$

Expression (10): $a^2 + b + 15$
Substitute $a = 3$ and $b = -2$ :
$(3)^2 + (-2) + 15$

Simplify the expression:
$9 - 2 + 15 = 22$

Expression (11): $2x + 3y + 2a$
Substitute $x = 2$ , $y = 4$ , and $a = 3$ :
$2(2) + 3(4) + 2(3)$

Simplify the expression:
$4 + 12 + 6 = 22$

Expression (12): $x^2 - a^2 + 5$
Substitute $x = 2$ and $a = 3$ :
$(2)^2 - (3)^2 + 5$

Simplify the expression:
$4 - 9 + 5 = 0$

Expression (13): $2x + 2y + 2a + 2b$
Substitute $x = 2$ , $y = 4$ , $a = 3$ , and $b = -2$ :
$2(2) + 2(4) + 2(3) + 2(-2)$

Simplify the expression:
$4 + 8 + 6 - 4 = 14$

Expression (14): $b^2 + b - 2$
Substitute $b = -2$ :
$(-2)^2 + (-2) - 2$

Simplify the expression:
$4 - 2 - 2 = 0$

Expression (15): $-2x + 4y - 4a + b$
Substitute $x = 2$ , $y = 4$ , $a = 3$ , and $b = -2$ :
$-2(2) + 4(4) - 4(3) + (-2)$

Simplify the expression:
$-4 + 16 - 12 - 2 = -2$