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name date skillz review (1 point each) graph. list all pairs of numbers…

Question

name
date
skillz review (1 point each)
graph. list all pairs of numbers that multiply to the given number. which number pair contains the largest perfect square?

  1. $x + y = 4$ 2) 60 3) use 60
  2. $2x - 5y = 10$ 5) 54 6) use 54

directions: simplify each expression.

  1. $(6n^2 - 5) - (3n^2 + 7)$
  2. $(13x^3 - 8x^2 - x^4) - (10x^4 - 9x^3 - 10x^2)$
  3. $(9g^3 + 5g + 16) + (9g^3 - 12g^2 + g)$

Explanation:

Response
SKILLZ REVIEW

Step1: Find intercepts for $x+y=4$

For x-intercept: set $y=0$, $x=4$. For y-intercept: set $x=0$, $y=4$. Plot points $(4,0)$ and $(0,4)$, draw line through them.

Step2: List factor pairs of 60

Positive pairs: $(1,60), (2,30), (3,20), (4,15), (5,12), (6,10)$; Negative pairs: $(-1,-60), (-2,-30), (-3,-20), (-4,-15), (-5,-12), (-6,-10)$

Step3: Identify largest square factor of 60

Perfect squares dividing 60: $1,4$. Largest is 4, from pair $(4,15)$ or $(-4,-15)$.

Step4: Find intercepts for $2x-5y=10$

For x-intercept: set $y=0$, $2x=10 \implies x=5$. For y-intercept: set $x=0$, $-5y=10 \implies y=-2$. Plot points $(5,0)$ and $(0,-2)$, draw line through them.

Step5: List factor pairs of 54

Positive pairs: $(1,54), (2,27), (3,18), (6,9)$; Negative pairs: $(-1,-54), (-2,-27), (-3,-18), (-6,-9)$

Step6: Identify largest square factor of 54

Perfect squares dividing 54: $1,9$. Largest is 9, from pair $(6,9)$ or $(-6,-9)$

Step1: Simplify $(6n^2 - 5) - (3n^2 + 7)$

Distribute negative sign: $6n^2 -5 -3n^2 -7$. Combine like terms: $(6n^2-3n^2)+(-5-7)$
$=3n^2 -12$

Step2: Simplify $(13x^3 -8x^2 -x^4) - (10x^4 -9x^3 -10x^2)$

Distribute negative sign: $13x^3 -8x^2 -x^4 -10x^4 +9x^3 +10x^2$. Combine like terms: $(-x^4-10x^4)+(13x^3+9x^3)+(-8x^2+10x^2)$
$=-11x^4 +22x^3 +2x^2$

Step3: Simplify $(9g^3 +5g +16) + (9g^3 -12g^2 +g)$

Remove parentheses: $9g^3 +5g +16 +9g^3 -12g^2 +g$. Combine like terms: $(9g^3+9g^3)-12g^2+(5g+g)+16$
$=18g^3 -12g^2 +6g +16$

Answer:

  1. Graph: Line through $(4,0)$ and $(0,4)$
  2. Factor pairs of 60: $(1,60), (2,30), (3,20), (4,15), (5,12), (6,10), (-1,-60), (-2,-30), (-3,-20), (-4,-15), (-5,-12), (-6,-10)$
  3. Pair with largest perfect square: $(4,15)$ or $(-4,-15)$
  4. Graph: Line through $(5,0)$ and $(0,-2)$
  5. Factor pairs of 54: $(1,54), (2,27), (3,18), (6,9), (-1,-54), (-2,-27), (-3,-18), (-6,-9)$
  6. Pair with largest perfect square: $(6,9)$ or $(-6,-9)$

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