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name: abigailatencia weekly math review - q1:7 date: sep22 monday 22 si…

Question

name: abigailatencia weekly math review - q1:7 date: sep22
monday 22
simplify:
y + z - 2y
if y = 4 and z = 2
bill went to the movies with some of his friends. tickets cost $8.50 each. they spent $18.00 total for food. their total was $52.00. how many friends went to movies, including bill?
solve the equation for y:
25 = 2y - 5
solve the equation for x
4(x - 5) = 5x + 1
solve the equation for y.
y + 7 = \frac{5}{4}(x + 16)
solve each equation for x. how are these equations similar?
w + y = \frac{z}{x}
give the vertices of a triangle that is 3 times as big as △abc if a(0, 0), b(2, 6), and c(6, 4). (centered at the origin)
a 2x2 square is centered at on the origin. it is dilated by a factor of 3. what are coordinates of the vertices of the square?
tuesday 23
simplify using your order of operations:
10(4 + 2)+5·23
solve the equation for x:
\frac{x + 2}{3}=\frac{5}{4}
if it costs $9.50 to buy a movie ticket, what is the most number of tickets someone can buy for $40.00? how much money is left over?
solve the equation for x
2(1.3x + 8) = 20 + 2.4x
solve the equation for y.
23 = 5x - 2y
xw+xy = z
what kind of transformation is depicted in the picture below?
in the problem to the left, what is the ratio of areas from the larger square to the smaller square?

Explanation:

Response
Monday
  1. Simplify \(y + z-2y\) when \(y = 4\) and \(z = 2\):
  • Step1: Combine like - terms
  • \(y+z - 2y=(y - 2y)+z=-y + z\).
  • Step2: Substitute values
  • Substitute \(y = 4\) and \(z = 2\) into \(-y + z\), we get \(-4 + 2=-2\).
  1. Bill's movie - going problem:
  • Let the number of friends (including Bill) be \(n\).
  • Step1: Set up an equation
  • The cost of tickets is \(8.5n\) and the cost of food is \(18\), and the total cost is \(52\). So the equation is \(8.5n+18 = 52\).
  • Step2: Solve for \(n\)
  • Subtract \(18\) from both sides: \(8.5n=52 - 18=34\).
  • Then divide both sides by \(8.5\): \(n=\frac{34}{8.5}=4\).
  1. Solve \(25 = 2y-5\) for \(y\):
  • Step1: Add \(5\) to both sides
  • \(25 + 5=2y-5 + 5\), which simplifies to \(30 = 2y\).
  • Step2: Divide both sides by \(2\)
  • \(y=\frac{30}{2}=15\).
  1. Solve \(4(x - 5)=5x + 1\) for \(x\):
  • Step1: Expand the left - hand side
  • \(4x-20 = 5x + 1\).
  • Step2: Move \(x\) terms to one side
  • Subtract \(4x\) from both sides: \(-20=x + 1\).
  • Then subtract \(1\) from both sides: \(x=-20 - 1=-21\).
  1. Solve \(y + 7=\frac{5}{4}(x + 16)\) for \(y\):
  • Step1: Distribute on the right - hand side
  • \(y + 7=\frac{5}{4}x+20\).
  • Step2: Subtract \(7\) from both sides
  • \(y=\frac{5}{4}x+20 - 7=\frac{5}{4}x + 13\).
  1. Solve \(w + y=\frac{z}{x}\) for \(x\):
  • Step1: Cross - multiply
  • \(x(w + y)=z\).
  • Step2: Solve for \(x\)
  • \(x=\frac{z}{w + y}\), \(w + y

eq0\).

  1. Vertices of a triangle dilation:
  • If a triangle with vertices \(A(0,0)\), \(B(2,6)\), and \(C(6,4)\) is dilated by a factor of \(3\) centered at the origin, we multiply the coordinates of each vertex by \(3\).
  • \(A'(0\times3,0\times3)=(0,0)\), \(B'(2\times3,6\times3)=(6,18)\), \(C'(6\times3,4\times3)=(18,12)\).
  1. Vertices of a square dilation:
  • A \(2\times2\) square centered at the origin with vertices \((1,1)\), \((1, - 1)\), \((-1,1)\), \((-1,-1)\) dilated by a factor of \(3\) has vertices \((1\times3,1\times3)=(3,3)\), \((1\times3,-1\times3)=(3,-3)\), \((-1\times3,1\times3)=(-3,3)\), \((-1\times3,-1\times3)=(-3,-3)\).
Tuesday
  1. Simplify \(10(4 + 2)+5\times23\):
  • Step1: Solve inside the parentheses
  • \(4 + 2 = 6\).
  • Step2: Multiply
  • \(10\times6=60\) and \(5\times23 = 115\).
  • Step3: Add
  • \(60+115 = 175\).
  1. Solve \(\frac{x + 2}{3}=\frac{5}{4}\) for \(x\):
  • Step1: Cross - multiply
  • \(4(x + 2)=3\times5\).
  • Step2: Expand the left - hand side
  • \(4x+8 = 15\).
  • Step3: Solve for \(x\)
  • Subtract \(8\) from both sides: \(4x=15 - 8 = 7\).
  • Then \(x=\frac{7}{4}=1.75\).
  1. Movie ticket - buying problem:
  • Let the number of tickets be \(n\). We have the inequality \(9.5n\leq40\).
  • Step1: Solve for \(n\)
  • \(n\leq\frac{40}{9.5}\approx4.21\). Since \(n\) is the number of tickets (a whole number), \(n = 4\).
  • Step2: Calculate the leftover money
  • The cost of \(4\) tickets is \(4\times9.5 = 38\). The leftover money is \(40-38 = 2\).
  1. Solve \(2(1.3x + 8)=20 + 2.4x\) for \(x\):
  • Step1: Distribute on the left - hand side
  • \(2.6x+16 = 20 + 2.4x\).
  • Step2: Move \(x\) terms to one side
  • Subtract \(2.4x\) from both sides: \(0.2x+16 = 20\).
  • Subtract \(16\) from both sides: \(0.2x=4\).
  • Then \(x=\frac{4}{0.2}=20\).
  1. Solve \(23 = 5x-2y\) for \(y\):
  • **Step1: Move \(5x\) to the…

Answer:

  • Monday:
  • \(y + z-2y\) simplified with \(y = 4,z = 2\) is \(-2\).
  • Number of friends (including Bill) is \(4\).
  • \(y\) in \(25 = 2y-5\) is \(15\).
  • \(x\) in \(4(x - 5)=5x + 1\) is \(-21\).
  • \(y\) in \(y + 7=\frac{5}{4}(x + 16)\) is \(y=\frac{5}{4}x + 13\).
  • \(x\) in \(w + y=\frac{z}{x}\) is \(x=\frac{z}{w + y}(w + y

eq0)\).

  • Vertices of dilated triangle: \(A'(0,0)\), \(B'(6,18)\), \(C'(18,12)\).
  • Vertices of dilated square: \((3,3)\), \((3,-3)\), \((-3,3)\), \((-3,-3)\).
  • Tuesday:
  • \(10(4 + 2)+5\times23\) simplifies to \(175\).
  • \(x\) in \(\frac{x + 2}{3}=\frac{5}{4}\) is \(x = 1.75\).
  • Number of tickets is \(4\) and leftover money is \(2\).
  • \(x\) in \(2(1.3x + 8)=20 + 2.4x\) is \(20\).
  • \(y\) in \(23 = 5x-2y\) is \(y=\frac{5x - 23}{2}\).
  • \(x\) in \(xw+xy = z\) is \(x=\frac{z}{w + y}(w + y

eq0)\).

  • Ratio of areas of squares is \(9\).