Unit 1: Equations
Solve for x: 3x + 8 = 53
x=15
A figure is at A (3, 2), B (3, 4), and C (5, 3) and is then translated three units left and two units up. What are the coordinates of the image?
Image A' (0, 4), B (0, 6), C (2, 5)
A triangle has the angles measures of x, 34, and 92, what is the value of x?
x = 54
Write in slope-intercept form: 3x + 2y = 12
y = - 3/2x + 6
Write and solve the sentence: six less than a number is 12.
n - 6 = 12
n = 18
How many solutions does the equation 4x - 12 = 1/4(16x - 48) have?
Infinite Solutions
A figure is at A (1, -2), B (1, 1), C (2, 1), D (2, -2) and is reflected across the y-axis, what are the coordinates of the image?
A' (-1, -2), B' (-1, 1), C' (-2, 1), D' (-2, -2)
The interior angles of a triangle have measures of 65 and 15, what is the measure of the opposite exterior angle?
80
Write in standard form: y = 3x - 8
-3x + y = -8
A man builds a pen for cows in the shape of a rectangle. The length is 60 meters and the width is 40 meters. He then builds a pen for sheep that is a similar figure with a length of 20 meters, what is the width of the sheep pen?
13 1/3 or 13.3333
Solve for y: 3x - y = 12
y = 3x - 12
A figure is at A (1, 1), B (1, 2) C (2, 2) and is rotated counter-clockwise around the origin 90 degrees, what are the coordinates of the image?
A' (-1, 1), B (-2, 1), C (-2, 2)
What are the two angles relationships regarding measures?
Complementary: pair of angles adding to 90
Supplementary: pair of angles adding to 180
Find the slope of the points (2, 4) and (2, -4). Is the line vertical, horizontal or neither?
vertical line
-4-4 = -8
2-2 = 0
A Milka bar cost 2 euros. Sam buys 3 Milka bars, and Susan buys 4 Milka bars. Draw a graph to show the relationship between the number of Milka bars bought and their total cost. Is the relationship proportional?
(Show Graph)
Yes.
Solve for x: 3(x - 4) = 2x + 1
x = 13
Dilate the figure: A (1, 2), B (2, 4), C (3, -2) by a scale factor of 3. What are the image's coordinates and what type of dilation is this?
A' (3, 6), B' (6, 12), C' (9, -6) - Enlargement
What are the four relationships for congruent angles on a set of parallel lines cut by a transversal?
Corresponding Angles
Vertical Angles
Alternate Interior Angles
Alternate Exterior Angles
Write the equation of the line that passes through (0, 4) and has a slope of 1/3.
y = 1/3x + 4
Two triangles are similar. The first has measures of 65, (x + 10) and (y - 5). The second has angles measures of 90, (x - 15), and 25.
What are the values of x and y?
x = 80, y = 30
Solve for x: 2/3x - 1/3x + 4 = 17
x = 39
Describe the similarity transformation of the given picture.
Option 1: Reduce the large figure by a scale factor of 1/2, then reflect across the x-axis
Option 2: Enlarge the small figure by a scale factor of 2, then reflect across the x-axis
Determine whether the triangles are similar and justify your answer.
Triangle 1: 34, x, 87
Triangle 2: 34, y, 58
No, they are not similar. They do not have two pairs of congruent angles.
Triangle 1: 34, 59, 87
Triangle 2: 34, 88, 58
y-intercept: (0, -9)
x-intercept: (6, 0)
Write and solve: Three times the sum of a number and 2 is the same as 6 times the difference of that number and 3.5. What is the number?
3(n + 2) = 6(n - 3.5)
n = 9