Vocabulary
A figure that results from a transformation or sequence of transformations.
Image
Two figures are *this* if there is a sequence of rigid transformations and/or dilations that maps one figure onto the second.
Similar
A dolphin swims at constant speed for 5 seconds and travels 55 meters. The relationship between time and distance of the dolphin's trip is proportional. How far does the dolphin swim in 2 seconds?
22 meters in 2 seconds (unit rate: 11/1)
x = y + 4
15x + 12y = 195
Solve for x and y
x = 9
y = 5
A transformation that makes a scale copy of a figure. This is a proportional shrinking or enlargement of a figure.
Dilation
If my original vertex is at (2,5), and is translated 2 units to the right, this is my new vertex.
(4,5)
Kyle signs up for a membership at a rock climbing gym. He pays a $100 membership fee and then will pay a $25 monthly fee. Represent this situation in slope-intercept form with y equaling the total cost of the gym membership for x months.
y = 25x + 100
Solve for the amount of solutions to the following system of equations.
4x - 2y = 12
2x + 2y = 24
One solution, x = 6, y = 6
In a linear relationship between x and y, it tells how much y changes when x changes by 1.
If a figure is rotated 90 degrees counterclockwise, this sequence of transformations occurs.
The coordinates flip (x,y) --> (y,x) and the y-coordinate changes signs.
Evelyne knits hats and scarves for charity. It takes her 5 hours to knit a hat and 15 hours to knit a scarf. She uses 110 yards of yarn to knit all the hats and 150 yards to knit all the scarves. Overall, it took her 180 hours to knit all the items and she used a total of 2,520 yards of material. How many hats and scarves did she make each?
12 hats and 8 scarves.
Tell how many solutions for each
A) 3x - 2y = - 1
-6x + 4y = 2
B) 12x - 15y = 24
-8x - 10y = -36
A) infinitely many solutions
B) no solution
A group of related linear equations in which a solution makes all the equations true at the same time. It can have zero, one or infinitely many solutions.
System of linear equations
Angles A and B are supplementary linear angles. If angle A is (2x + 30) and angle B is (x + 60), what is the value of x?
x = 30
Adam walks from school to the library. He walks at a pace of 4 miles per hour. After he is already .2 miles away from school, Cameron leaves school. Cameron jogs at a pace of 6 miles per hour. How long will it take Cameron to catch up to Adam?
0.1 hour or 6 minutes.
Antonio is a set designer. He is gluing ribbon on 4 square and 2 triangular posters to be used as stage props in upcoming play. Use the system of equations to find s, the amount of ribbon needed for a square poster, and t, the amount of ribbon needed for a triangular poster.
s = t + 5
4s + 2t = 110
t = 15
s =20
This process involves multiplying each term in a sum or difference by a common factor, which does not change the value of the expression.
Distributive property
x = 18
Alyssa is mixing solutions in chemistry class. Solution A is 10% acid and Solution B is 40% acid. She uses both toe make 10 liters of mixture, Solution C, which is 16% acid and solve for how many liters of Solution A and Solution B each make up Solution C.
Solution A - 8 liters, Solution B - 2 liters
Lines a and b are a graph of a system of equations. Line a passes through the points (0,4) and (8,6). Line b passes through the points (0,-2) and (8,1). Where do the lines intersect?
(48, 16)