means and the extremes in the proportion w y x z Means y amp x Extremes w amp z Identify the means and the extremes in the proportion ID: 190033
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Slide1Slide2
Identify the
means
and the extremes in the proportion.
w = y x z
Means:
y
& x
Extremes:
w
&
zSlide3
Identify the
means
and the extremes in the proportion.
9 = 12w 6 + y 5
Means:
6 + y
&
12w
Extremes:
9
&
5Slide4
Identify the
means
and the extremes in the proportion.
q + 3 = 2 5m q
Means:
5m
&
2
Extremes:
q + 3 & qSlide5
Identify the
means
and the extremes in the proportion.
m = T a h
Means:
a
&
T
Extremes:
m & hSlide6
Factor completely.
x
2
– 225
(x + 15)(x – 15)Slide7
Factor completely.
5x
2
– 125y4
5(x
2
– 25y
4
)
5(x + 5y
2
)(x – 5y
2
)Slide8
Factor completely.
12x
13
– 75x
3x(4x
12
– 25)
3x(2x
6
+ 5)(2x
6
– 5)Slide9
Factor completely.
x
2
+ 12x + 32
(x + 4)(x + 8)Slide10
Factor completely.
x
2
– 12x + 32
(x
–
4)(x
–
8)Slide11
Factor completely.
x
2
– 4x + 32
(x
+
4)(x
–
8)Slide12
Factor completely.
x
2
+ 14x + 45
(x
+
9)(x
+ 5
)Slide13
Factor completely.
x
2
+ 15x + 36
(x
+
12)(x
+ 3
)Slide14
Factor completely.
8x
2
+ 2x – 21
8 •-21 = -168
14 & -12
8x
2
+ 14x
–
12x – 21
2x(4x + 7)
–
3(4x + 7)
(4x + 7)(2x – 3) Slide15
Factor completely.
12x
2
+ 53x + 20
12 •20 = 240
48 & 5
12x
2
+ 48x + 5x + 20
12x(x + 4) + 5(x + 4)
(x + 4)(12x + 5) Slide16
Factor completely.
12x
2
– 16x – 11
12 •-11 = -132
-22 & 6
12x
2
–
22x + 6x
–
11
2x(6x
–
11) + 1(6x
–
11)
(2x + 1)(6x
–
11) Slide17
Factor completely.
3
2x
2 – 36x + 9
3
2 • 9 = 288
-24 & -12
3
2x
2
–
24x
–
12x + 9
8x(4x
–
3)
–
3(4x
–
3)
(8x
–
3)(4x
–
3) Slide18
Factor completely.
x
2
– 15x + 36
(x
–
12)(x
–
3
)Slide19
Factor completely.
x
2
+ 4x – 45
(x
–
9)(x
+ 5
)Slide20
Factor completely.
2x
2
– 28x + 90
2(x
2
– 14x + 45)
2(x
–
9)(x
–
5
)Slide21
Factor completely.
3
x
2 – 27x – 108
3
(x
2
– 9x – 36)
3(x
–
12)(x
+ 3
)Slide22
16
x
12
Find the missing side of the triangle.
12
2
+ 16
2
= x
2
144 + 256 = x
2
400 = x
2
20 = xSlide23
3
x
2
Find the missing side of the triangle.
2
2
+ 3
2
= x
2
4 + 9= x
2
13 = x
2
3.6 ≈ xSlide24
10
x
18
Find the missing side of the triangle.
10
2
+ 18
2
= x
2
100 + 324= x
2
424 = x
2
20.6 ≈ xSlide25
12
19
x
Find the missing side of the triangle.
12
2
+ x
2
= 19
2
144 + x
2
= 361
x
2
= 217
14.7 ≈ xSlide26
x
70
30
Find the missing side of the triangle.
30
2
+ x
2
= 70
2
900 + x
2
= 4900
x
2
= 4000
63.2 ≈ xSlide27
x
25
7
Find the missing side of the triangle.
7
2
+ x
2
= 25
2
49 + x
2
= 625
x
2
= 576
24 = xSlide28
Do the following lengths form a
right
triangle?
7
2
+ 24
2
? 25
2
49 + 576
? 625
625
= 625
yes!
7, 24, 25Slide29
Do the following lengths form a
right
triangle?
5
2
+ 12
2
? 13
2
25 + 144 ? 169
169 = 169
yes!
5, 13, 12Slide30
Do the following lengths form a
right
triangle?
9
2
+ 12
2
? 15
2
81 + 144 ? 225
225 = 225
yes!
9, 12, 15Slide31
Do the following lengths form a
right
triangle?
12
2
+ 18
2
? 20
2
144 + 324 ? 400
468
≠
400
no!
12, 20, 18Slide32
Do the following lengths form a
right
triangle?
17
2
+ 18
2
? 19
2
289 + 324 ? 361
613
≠
361
no!
19, 17, 18Slide33
Do the following lengths form a
right
triangle?
2
2
+ 7
2
? 8
2
4 + 49 ? 64
53
≠
64
no!
2, 7, 8Slide34
A
C
B
D
∆ABC ~
∆______
~
∆
_______
DBA DACSlide35
B
Y
U
S
∆YUB
~
∆______
~
∆
_______
YBS BUSSlide36
Q
R
P
M
∆PQR
~
∆______
~
∆
_______
PMQ QMRSlide37
H
J
G
I
∆GHJ
~
∆______
~
∆
_______
GIH HIJSlide38
∆ABC
~
∆DEF. Find the value of x.
B
A
C
3x + 3
4x
D
E
F
21
27
30
4x
=
30
3x + 3 27
90
x + 90 = 108x
90
=
18x
x =
5Slide39
∆GHI
~
∆JKL. Find the value of x.
L
K
J
3x – 20
2x + 5
G
I
H
9
8
10
2x + 5
=
9
3x – 20 8
16x + 40 = 27x – 180
220
=
11x
x =
20Slide40
∆MNO
~
∆PQR. Find the value of x.
N
O
M
5
x – 6
6
x + 1
Q
R
P
28.5
46.5
34.5
6x + 1
=
46.5
5x – 6 28.5
232.5x – 279 = 171x + 28.5
61.5x
=
307.5
x
=
5