Section 9.2.1
a.
Are the two triangles at right similar?
How do you know?
x cm
30°
9 cm
b. Find x. Show your strategy.
c.
30°
24 cm
big
What is the scale factor ( small
)?
d. Find the area of each triangle.
9-57.
Jenna is working with three squares. Their areas are 16 cm2, 9 cm2, and 36
cm2. She thinks they will make an obtuse triangle. Do you agree? Explain
your reasoning.
An obtuse triangle’s side lengths must follow the inequality
+
<
and
+
therefore, Jenna is correct.
9-58.
Copy and complete the following table.
x
y
a.
5
–17
What is the rule?
b. What is the slope?
4
–5
–2
–2
4
3
–11
16 cm
9-56.
Section 9.2.1
9-59.
Write an equation to represent the situation below, and then answer the
question.
Ella is trying to determine the side lengths of a triangle. She knows that the
longest side is three times longer than the shortest side. The medium side is
ten more than twice the shortest side. If the perimeter is 142 cm, how long is
each side?
Let
x
= shortest side
2x + 10 = medium side
3x
= longest side
Check
22
2(22) + 10
3(22)
Equals 22 + 54 + 66 = 142 checks
Topic Sentence
Perimeter
142
142
132
22
= short side + medium side + longest side
= x + 2x + 10
+ 3x
= 6x + 10
= 6x
=x
9-60.
Cisco was looking at a table of values for the rule y = x 2 . She said, “This table
contains (0, 0) , so I think it shows a proportional relationship.” Is Cisco
correct? Why or why not?
9-61.
Solve these equations for x. Check your answers.
a.
2(x + 4.5) = 32
2x + 9 = 32
2x = 23
x = 11.5
b.
6 + 2.5x = 21
2.5x = 15
x =6
c.
x
9
= 165
16x = 45
x = 45/16
Section 9.2.1
9-62.
What kind of triangle will the
edges of the squares at right
form? What will the side lengths
be?
36
625
400
Determine by inspection whether the lines in each system below intersect,
coincide, or are parallel. Do not actually solve the systems. Justify your
reasons.
a.
y = 2x + 3
y=
1
2
x−2
Intersect, slopes are different
c.
b.
y = 13 x + 2
Parallel, slopes are the same
d.
y = 13 x − 2
Parallel, slopes are equal
9-64.
2x + 3y = 6
2x + 3y = 9
x − 2y = 4
−2x + 4y = −8
Coincide, equations are equivalent
Use the graph below to answer the following questions.
a.
What kind of growth does this graph show?
How do you know?
b. What is this graph describing? Write an
appropriate title for the graph.
c.
How far from home is the person when the
graph starts?
Distance From Home (miles)
9-63.
d. How fast is the person traveling? Explain how
you can use the graph to determine the rate of travel.
e.
Write an equation to represent the line on the graph.
Time (hours)
Section 9.2.1
9-65.
Eric set up this ratio for two similar
triangles:
=
x
12
5
12
5
9
He solved the problem and found
x ≈ 6.67 . What was his mistake?
9
x
He wrote his proportion incorrectly. He did
not order his corresponding parts correctly.
9-66.
If one atom of carbon weighs 1.99 ×10 −22 g and one atom of hydrogen weighs
1.67 ×10 −27 g, which element weighs more? Explain your choice.
9-67.
Andrea wants to have $9500 to travel to France when she is 22. She currently
has $5976 in a savings account earning 5% annual compound interest. Andrea
is 14 now.
a.
If she does not take out or deposit any money, how much money will
Andrea have when she is 18?
A=P
+
A = 5976
where A is the total amount after n years @ rate r
+.
A=7263.87
b. Will Andrea have enough money for her trip when she is 22?
A = 8829.27