Answer:
1. Callum = 2; Eilidh = 17; Caitlin's =22.
2. Ewan = 44; tree = 308.
Explanation:
Q1. Callum, Eilidh, and Caitlin
Let x = Callum's age
y = Eilidh's age
z = Caitlin's age
We have three conditions.
(1) x = y - 5
(2) z = y + 15
(3) x + y + z = 31
Step 1. Eliminate one of the variables in two of the equations
Subtract (1) from (2): z - x = 20
Rearrange: (4) -x + z = 20
Solve (2) for y: (5) y = z - 15
Substitute into (3): x + z - 15 + z = 31
(6) x + 2z = 46
Step 2. Set up two new equations in two variables
(5) -x + z = 20
(6) x + 2z = 46
Add (5) and (6): 3z = 66
Divide each side by 2: z = 22
Step 3. Substitute z into (5)
-x + 22 = 20
x = 2
Step 4. Substitute x into (1)
2 = y - 5
Add 5 to each side y = 7
Callum's age is 2; Eilidh's age is 7; Caitlin's age is 22.
Q2. Ewan and the tree
Let x = Ewan's age
y = tree's age
We have two conditions.
(1) y = 7x
(2) x + y = 352
Rearrange (1) (3) -7x + y = 0
(2) x + y = 352
Subtract (3) from (2) 8x = 352
Divide each side by 8 x = 44
Substitute y into (1) y = 7 × 44
y = 308
Ewan's age is 44; the tree's age is 308.
Answer:
8:1
Step-by-step explanation:
Don reads 8 pages a minute. Therefore the amount of pages he could read is 8 and the amount of time it takes is a minute
14.
Angles 4 and 6 are supplementary, because they are on the same line. Supplementary angles add up to 180 degrees, and a line must be 180 degrees.
15.
Angles 1 and 8 are congruent, because they are alternate exterior angles
16.
m = y2 - y1 / x2 - x1
m = 7 - 2 / 4 - 5
m = 5 / -1
m = -5
17.
m = 3 - 3 / 7 - (-5)
m = 0 / 12
m = 0
18.
m = 1 - (-2) / 5 - (-4)
m = 3 / 9
m = 1/3
19.
A = (0, 3) - B = (3,0)
m = 0 - 3 / 3 - 0
m = -3 / 3
<em>m = -1</em>
C = (0, -2) - D = (4, 2)
m = 2 - (-2) / 4 - 0
m = 4 / 4
<em>m = 1</em>
Perpendicular, because the slopes are opposite reciprocals.
20.
E = (1, 2) - F = (0, 0)
m = 0 - 2 / 0 - 1
m = -2 / -1
<em>m = 2</em>
G = (1, -3) - H = (3, 0)
m = 0 - (-3) / 3 - 1
<em>m = 3 / 2</em>
Neither, because the slopes are different.
21.
I = (0, 1) - J = (2, -4)
m = -4 - 1 / 2 - 0
<em>m = -5/2</em>
K = (-1, -2) - L = (4, 0)
m = 0 - (-2) / 4 - (-1)
<em>m = 2/5</em>
Perpendicular, because the slopes are opposite reciprocals.
22.
M = (-2, 2) - N = (2, 2)
Horizontal line
<em>m = 0</em>
O = (3, 0) - P = (-3, 0)
Horizontal line
<em>m = 0
</em>Parallel, because the slopes are the same.
<em>
</em>23.
Angle 2 is congruent to angle 1 because of the alternate exterior angle theorem.
Angle 1 is congruent to angle 3 because of the vertical angle theorem.
Angle 2 is congruent to angle 3 because of substitution.
Line l is parallel to line m because the corresponding angles are congruent.
Get the x variable on one side and the numbers another side.
9/10(x + 2/3) = 4 1/2
Distribute the 9/10 across the x and 2/3.
(9/10)x + 18/30 = 4 1/2
Simplify 18/30 to make our life easier.
(9/10)x + 3/5 = 4 1/2
Subtract 3/5 from each side of the equation.
(9/10)x = 3 9/10
Divide both sides by 9/10.
x = 4 1/3
