Answer to Question #266090 in Algebra for Israel

Question #266090


  1. Given a flow diagram, Calculate the values of the output: 2,5,4,3,9.
  2. If A=2 and B=5, Determine the values of a^2+ab+b^2.
  3. Expand and calculate: 2^2 x 3^2.
  4. Calculate: 5x (-5) + 6x (-8) -16.
  5. Simplify: a) 4x (x + 2); b) (3x + 5)(2x + 3); c) 27x y^3 /3x^3 y^2.

6. Solve for x: a) 10x - 6= 5x - 4; b) 4x (2x - 1) = 2(3 - x).

7. Given a triangle KLM with an unknown angle, calculate the value of x if K= 12, L= 23, and M= x.



1
Expert's answer
2022-02-08T00:16:25-0500
  1. There is no the diagram
  2. a^2 + ab + b^2 =a2+ab+b2=22+52+52=22+52+55=4+10+25=14+25=39a^2 + ab + b^2 = 2^2 + 5 \cdot 2 + 5^2 = 2\cdot2 + 5\cdot2 + 5\cdot5 = 4 + 10 + 25 = 14 + 25 = 39
  3. 2232=(22)(33)=49=362^2 \cdot 3^2 = (2\cdot2) \cdot (3\cdot3) = 4 \cdot 9 = 36
  4. 5(5)+6(8)16=25+(48)16=254816=7316=895\cdot(-5) + 6\cdot(-8) - 16 = -25 + (-48) - 16 = -25 - 48 - 16 = -73 - 16 = -89
  5. a) if 4x (x + 2) is 4(x+2)4\cdot(x+2), then 4(x+2)=4x+424\cdot(x+2) = 4\cdot x + 4\cdot2 (by distributivity property) =4x+8=4x + 8

if 4x (x + 2) is 4x(x+2)4x\cdot(x+2) , then 4x(x+2)=4xx+4x2=4x2+8x4x\cdot(x+2) = 4x\cdot x + 4x\cdot2 = 4x^2 + 8x (4x2=42x4x\cdot2 = 4\cdot2\cdot x by associativity property)

b) (3x+5)(2x+3)=3x(2x+3)+5(2x+3)=3x2x+3x3+52x+53=6x2+9x+10x+15=6x2+19x+15(3x + 5)(2x + 3) = 3x\cdot(2x + 3) + 5\cdot(2x + 3) = 3x\cdot2x + 3x\cdot3 + 5\cdot2x + 5\cdot3 = 6x^2 + 9x + 10x + 15 = 6x^2 + 19x + 15

c) if 27x y^3 /3x^3 y^2 is 27y33x3y2\frac{27\cdot y^3} {3x^3 y^2} then 27y33x3y2=/y3y2=y/=27y3x3=/273=9/=9yx3\frac{27\cdot y^3} {3x^3 y^2} = /\frac{y^3}{y^2} = y/ = \frac{27\cdot y} {3x^3} = /\frac{27}{3} = 9/ = \frac{9\cdot y} {x^3}

if 27x y^3 /3x^3 y^2 is 27xy33x3y2\frac{27x\cdot y^3} {3x^3 y^2} then 27xy33x3y2=27xy3x3=9xyx3=9yx2\frac{27x\cdot y^3} {3x^3 y^2} = \frac{27x\cdot y}{3x^3} = \frac{9x\cdot y}{x^3} = \frac{9y}{x^2}


6. a)


10x6=5x410x5x=4+65x=2x=25=0.410x - 6= 5x - 4 \\ 10x - 5x = -4 + 6 \\ 5x = 2 \\ x = \frac{2}{5} = 0.4

b) if 4x (2x - 1) is 4x(2x1)4x (2x - 1) then:


4x(2x1)=2(3x)4x2x4x=232x8x24x=62x8x24x+2x6=08x22x6=0:24x2x3=0D=(1)244(3)=1+48=49=72x1=(1)+724=1+78=88=1x2=(1)724=178=68=34=0.754x (2x - 1) = 2(3 - x) \\ 4x \cdot 2x - 4x = 2 \cdot 3 - 2\cdot x \\ 8x^2 - 4x = 6 - 2x \\ 8x^2 - 4x + 2x - 6 = 0 \\ 8x^2 - 2x - 6 = 0 |:2 \\ 4x^2 - x - 3 = 0 \\ D = (-1)^2 - 4\cdot4\cdot(-3) = 1 + 48 = 49 = 7^2 \\ x_1 = \frac{-(-1) + 7}{2\cdot4} = \frac{1 + 7}{8} = \frac{8}{8} = 1 \\ x_2 = \frac{-(-1) - 7}{2\cdot4} = \frac{1 - 7}{8} = \frac{-6}{8} = \frac{-3}{4} = -0.75

if 4x (2x - 1) is 4(2x1)4\cdot (2x - 1) then:


4(2x1)=2(3x)42x41=232x8x4=62x8x+2x=6+410x=10x=10:10=14\cdot (2x - 1) = 2(3 - x) \\ 4\cdot2x - 4 \cdot 1 = 2 \cdot 3 - 2 \cdot x \\ 8x - 4 = 6 - 2x \\ 8x + 2x = 6 + 4 \\ 10x = 10 \\ x = 10 : 10 = 1

7. Sum of triangle's angles is 180°180\degree. Then


K+L+M=180°12°+23°+x=180°35°+x=180°x=180°35°=145°\angle K + \angle L + \angle M = 180\degree \\ 12\degree + 23\degree + x = 180\degree \\ 35\degree + x = 180\degree \\ x = 180\degree - 35\degree = 145\degree

Answers:

  1. -
  2. 39
  3. 36
  4. -89
  5. a) 4x+84x + 8 OR a) 4x2+8x4x^2 + 8x -- depends on the condition

b) 6x2+19x+156x^2 + 19x + 15

c) 9yx3\frac{9\cdot y} {x^3} OR c) 9yx2\frac{9y}{x^2} -- depends on the condition

6. a) x = 2/5 = 0,4

b) x1 = 1, x2 = -0,75 OR b) x = 1 -- depends on the condition

7. 145


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