mrs. rivas international studies charter school. worksheet practice 7-1 to 7-5section 7-1 algebra...

Mrs. Rivas

International Studies Charter

School.

HomeworkWorksheet Practice 7-1 to 7-5

Section 7-1Algebra Solve each proportion.

1.

𝟏𝟔 (𝟐 𝒙+𝟏)=𝟒𝟎𝒙𝟑𝟐𝒙+𝟏𝟔=𝟒𝟎𝒙

𝟏𝟔=𝟖 𝒙𝒙=𝟐

Mrs. Rivas


School.

HomeworkSection 7-1

Algebra Solve each proportion.

2.

𝟕(𝒃+𝟏)=𝟐(𝟓𝟔)𝟕𝒃+𝟕=𝟏𝟏𝟐

𝟕𝒃=𝟏𝟎𝟓𝒃=𝟏𝟓

Mrs. Rivas


School.

HomeworkSection 7-2

List the pairs of congruent angles and determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain.

3.

Mrs. Rivas


School.

HomeworkSection 7-2

List the pairs of congruent angles and determine whether the polygons are similar. If so, write a similarity statement and give the scale factor. If not, explain.

4.

Mrs. Rivas


School.

HomeworkSection 7-2

Algebra Find the value of y. Give the scale factor of the polygons.

5. ABCD ~ TSVU 𝟑𝒚 −𝟑 .𝟓𝟑 𝒚+𝟔

=𝟏𝟕𝟐𝟓 .𝟓

𝟐𝟓 .𝟓(𝟑 𝒚 −𝟑 .𝟓)=𝟏𝟕(𝟑𝒚+𝟔)

𝟕𝟔 .𝟓 𝒚−𝟖𝟗 .𝟐𝟓=𝟓𝟏 𝒚+𝟏𝟎𝟐

𝟐𝟓 .𝟓 𝒚−𝟖𝟗 .𝟐𝟓=𝟏𝟎𝟐

𝟐𝟓 .𝟓 𝒚=𝟏𝟗𝟏 .𝟐𝟓

𝒚=𝟕 .𝟓

Scale Factor

Mrs. Rivas


School.

HomeworkSection 7-2

In the diagram below, PRQ ~ DEF. Find each of the following.

6. the scale factor of PRQ to DEF

Scale Factor

Mrs. Rivas


School.

HomeworkSection 7-2


7.

𝟑𝟓°

𝟖𝟗°

𝟓𝟔° 𝟓𝟔°

Mrs. Rivas


School.

HomeworkSection 7-2

In the diagram below, PRQ ~ DEF. Find each of the following.8.

𝟑𝟓°

𝟖𝟗°

𝟓𝟔° 𝟓𝟔°

Mrs. Rivas


School.

HomeworkSection 7-2


𝟑𝟓°

𝟖𝟗°

𝟓𝟔° 𝟓𝟔°

Mrs. Rivas


School.

HomeworkSection 7-2


10.

𝟒𝟎𝒙

=𝟐𝟎𝟐𝟒

𝒙

𝟐𝟎𝒙=𝟒𝟎 ∙𝟐𝟒

𝟐𝟎𝒙=𝟗𝟔𝟎𝒙=𝟒𝟖

Mrs. Rivas


School.

HomeworkSection 7-2


𝟑𝟔𝒙

=𝟐𝟎𝟐𝟒

𝒙

𝟐𝟎𝒙=𝟑𝟔 ∙𝟐𝟒

𝟐𝟎𝒙=𝟖𝟔𝟒𝒙=𝟒𝟑 .𝟐

Mrs. Rivas


School.

HomeworkSection 7-3

Determine whether the triangles are similar. If so, write a similarity statement and name the postulate or theorem you used. If not, explain.12.

Mrs. Rivas


School.

HomeworkSection 7-3


Mrs. Rivas


School.

HomeworkSection 7-3

16. A stick 2 m long is placed vertically at point B. The top of the stick is in line with the top of a tree as seen from point A, which is 3 m from the stick and 30 m from the tree. How tall is the tree?

F: G:

Height of the tree.

Height of stick 2 mBase of stick’s 3 mBase of Tree’s 30 m

H: StickH: Tree = B: Stick

B: Tree2 mTree = 3 m

30 m 2 × 30 ÷ 3 = 20 m

Mrs. Rivas


School.

HomeworkSection 7-4

Use the figure at the right to complete each proportion.

17. 18.

19. 20.

21. 22.

Mrs. Rivas


School.

HomeworkSection 7-4

Algebra Solve for the value of the variables in each right triangle.

23.

aGM

=b

GM

𝟏𝒙

=𝒙

𝟏+𝟗

𝒙𝟐=𝟏𝟎

𝒙=√𝟏𝟎

Mrs. Rivas


School.

HomeworkSection 7-4


23.

aGM

=b

GM

𝟗𝒚

=𝒚

𝟗+𝟏

𝒙𝟐=𝟗𝟎

𝒙=√𝟗𝟎 ¿√𝟑 ∙𝟑 ∙𝟐 ∙𝟓 𝒙=𝟑√𝟏𝟎

Mrs. Rivas


School.

HomeworkSection 7-4


aGM

=b

GM

24.

𝟔𝒙

=𝒙

𝟔+𝟐

𝒙𝟐=𝟒𝟖𝒙=√𝟒𝟖 ¿√𝟐 ∙𝟑 ∙𝟐 ∙𝟐 ∙𝟐𝒙=𝟒 √𝟑

Mrs. Rivas


School.

HomeworkSection 7-4


aGM

=b

GM24.

𝟔𝒙

=𝒙

𝟔+𝟐

𝒙𝟐=𝟒𝟖𝒙=√𝟒𝟖 𝒙=𝟒 √𝟑

𝟐𝒚

=𝒚𝟔

𝒚𝟐=𝟏𝟐𝒚=√𝟏𝟐 𝒚=𝟐√𝟑

¿√𝟐 ∙𝟐 ∙𝟑

Mrs. Rivas


School.

HomeworkSection 7-4


aGM

=b

GM25.

𝟒𝟏𝟎

=𝟏𝟎𝒙

𝟒 𝒙=𝟏𝟎𝟎

𝒙=𝟐𝟓

Mrs. Rivas


School.

HomeworkSection 7-4


aGM

=b

GM

26.

𝟔𝒙

=𝒙

𝟔+𝟏𝟒

𝒙𝟐=𝟏𝟐𝟎𝒙=√𝟏𝟐𝟎 𝒙=𝟐√𝟑𝟎

¿√𝟐 ∙𝟐 ∙𝟑 ∙𝟐 ∙𝟓

Mrs. Rivas


School.

HomeworkSection 7-4


aGM

=b

GM

26.

𝟔𝒙

=𝒙

𝟔+𝟏𝟒

𝒙𝟐=𝟏𝟐𝟎𝒙=√𝟏𝟐𝟎 𝒙=𝟐√𝟑𝟎

𝟔𝒚

=𝒚𝟏𝟒

𝒚𝟐=𝟖𝟒𝒚=√𝟖𝟒 𝒚=𝟐√𝟐𝟏

¿√𝟐 ∙𝟐 ∙𝟑 ∙𝟕

Mrs. Rivas


School.

HomeworkSection 7-4


aGM

=b

GM

27.

𝟏𝟐𝒙

=𝒙

𝟏𝟐+𝟑

𝒙𝟐=𝟏𝟖𝟎𝒙=√𝟏𝟖𝟎 𝒙=𝟔√𝟓

¿√𝟐 ∙𝟐 ∙𝟑 ∙𝟑 ∙𝟓

Mrs. Rivas


School.

HomeworkSection 7-4


aGM

=b

GM27.

𝟏𝟐𝒙

=𝒙

𝟏𝟐+𝟑

𝒙𝟐=𝟏𝟖𝟎𝒙=√𝟏𝟖𝟎 𝒙=𝟔√𝟓

𝟑𝒚

=𝒚

𝟑+𝟏𝟐𝒚𝟐=𝟒𝟓

𝒚=√𝟒𝟓 𝒚=𝟑√𝟓

¿√𝟑 ∙𝟑 ∙𝟓

Mrs. Rivas


School.

HomeworkSection 7-4


aGM

=b

GM

27.

𝟏𝟐𝒙

=𝒙

𝟏𝟐+𝟑

𝒙𝟐=𝟏𝟖𝟎𝒙=√𝟏𝟖𝟎 𝒙=𝟔√𝟓

𝟑𝒚

=𝒚

𝟑+𝟏𝟐𝒚𝟐=𝟒𝟓

𝒚=√𝟒𝟓 𝒚=𝟑√𝟓

𝟑𝒛

=𝒛𝟏𝟐

𝒛𝟐=𝟑𝟔𝒛=√𝟑𝟔 𝒙=𝟔

Mrs. Rivas


School.

HomeworkSection 7-4


aGM

=b

GM

28.

𝟖𝟏𝟐

=𝟏𝟐𝟖+𝒙

𝟖 (𝟖+𝒙 )=𝟏𝟒𝟒𝟔𝟒+𝟖 𝒙=𝟏𝟒𝟒

𝟖 𝒙=𝟖𝟎𝒙=𝟖

Mrs. Rivas


School.

HomeworkSection 7-4


aGM

=b

GM= 10

28.

𝟖𝟏𝟐

=𝟏𝟐𝟖+𝒙

𝟖 (𝟖+𝒙 )=𝟏𝟒𝟒𝟔𝟒+𝟖 𝒙=𝟏𝟒𝟒

𝟖 𝒙=𝟖𝟎𝒙=𝟖

𝟖𝒚

=𝒚𝟏𝟎

𝒚𝟐=𝟖𝟎𝒚=√𝟖𝟎 𝒚=𝟒√𝟓

¿√𝟐 ∙𝟐 ∙𝟐 ∙𝟐 ∙𝟓

Mrs. Rivas


School.

HomeworkSection 7-4


aGM

=b

GM= 10

28.

𝟖𝟏𝟐

=𝟏𝟐𝟖+𝒙

𝟖 (𝟖+𝒙 )=𝟏𝟒𝟒𝟔𝟒+𝟖 𝒙=𝟏𝟒𝟒

𝟖 𝒙=𝟖𝟎𝒙=𝟖

𝟖𝒚

=𝒚𝟏𝟎

𝒚𝟐=𝟖𝟎𝒚=√𝟖𝟎 𝒚=𝟒√𝟓

𝟏𝟎𝒛

=𝒛𝟏𝟖

𝒚𝟐=𝟏𝟖𝟎𝒚=√𝟏𝟖𝟎 𝒚=𝟔√𝟓

¿√𝟐 ∙𝟐 ∙𝟑 ∙𝟑 ∙𝟓

Mrs. Rivas


School.

HomeworkSection 7-5

Algebra Solve for x.

12 – x

x + 3 = 6

4

4(12 – x) = 6(x + 3)

48 – 4x = 6x + 18 30 – 4x = 6x

30 = 10x3 = x

29.

Mrs. Rivas


School.

HomeworkSection 7-5


12

3 = 2x –

3 x – 5

3(2x – 3) = 12(x - 5)

6x – 9 = 12x - 60

6x = 12x - 51

-6x = -51

8.5 = x

30.

Mrs. Rivas


School.

HomeworkSection 7-5


x + 4

4x + 1

= 8

20

20(x + 4) = 8(4x + 1) 20x + 80 = 32x + 8 20x + 72 = 32x

72 = 12x6 = x

31.

Mrs. Rivas


School.

HomeworkSection 7-5


20

4=16

x

4(16) = 20(x)

3.2 = x

64 = 20x

32.

Mrs. Rivas


School.

HomeworkSection 7-5


20

8=35 - x

x

20x = 8(35 – x)

10 = x

20x = 280 – 8x

28x = 280

33.

35 - x

Mrs. Rivas


School.

HomeworkSection 7-5


12

20= x

40 – x

20x = 12(40 – x)

15 = x

20x = 480 – 12x

32x = 480

34.

40 - x

Mrs. Rivas


School.

HomeworkSection 7-5


21

x= 15

12

21(12) = 15(x)

16.8 = x

252 = 15x

35.

Mrs. Rivas


School.

HomeworkSection 7-5


xx + 4

= 3x + 2

3(x + 4) = x(x + 2)

3x + 12 = x² + 2x 12 = x² - x

0 = x² - x - 12

X = 4

(x + 3)(x – 4) = 0x + 3 = 0 x – 4 = 0

x = -3

36.

Mrs. Rivas


School.

HomeworkSection 7-5


1510

= 18 - xx

10(18 - x) = 15(x)

7.2 = x

180 – 10x = 15x 180 =

25x

37.

mrs. rivas international studies charter school. worksheet practice 7-1 to 7-5section 7-1 algebra...

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