Question

Cw 7.1 7.2 homework help

Answer 1

QUESTION 1

The given ratio is


`40:15`


Let us write the ratio in terms of prime factors to obtain,



`= {2}^(3) * 5:3 * 5`



We cancel out the common factor of

5 to get



`= {2}^(3):3`

We simplify to get,


`= 8:3`


`\therefore 40:15 =8:3`


QUESTION 2

The given ratio is

`49 : 7`

We factor each term in the ratio, it will now be


`= 7 * 7: 7`


If we cancel out the common factor of 7, the ratio will now be


`= 7 : 1`


QUESTION 3



We want to simplify 80 inches over 10 days, which is,


`(80 \: inches)/(10 \: days)`

We convert this into ratio to get,





`80 \:inches:10 \: days`


We factor the terms in the ratio to obtain,


`8 * 10\:inches:10 \: days`

We cancel out common factors to obtain,



`8 \:inches:1\: days`


QUESTION 4


3 ounces costs $2.70.

We can write this as,



`(3)/( 2.7 )`

We change the denominator to fraction,



`= (3)/( (27)/(10) )`



We change the first bar to a normal division sign to get,


`= 3 / (27)/(10)`



We now multiply by the reciprocal to get,


`= 3 * (10)/(27)`



`= (10)/(9)`



We convert this back to ratio to get,


`3ounce: 2.7 \: dollars= 10 \: ounce: 9 \: dollars`


QUESTION 5


`10 \: ounce: 3.9 \: dollars`


We multiply each term in the ratio by 10, to get,



`10 * 10 \: ounce: 3.9 * 10 \: dollars`



`100\: ounce: 39 \: dollars`


QUESTION 6


`12 \: boxes: 96 \: books`

If we factor each term, the ratio


`= 12 \: boxes: 12 * 8 \: books`

We cancel out the common factors and the ratio will be


`= 1 \: box: 8 \: books`



QUESTION 7

The ratio of the sides of the triangle is


`3:4:6`


The total ratio is

`= 3 + 4 + 6 = 13`



The shortest sides corresponds to the least ratio which is 3,


The shortest side is

`= (3)/(13) * 104`

`= 24 \: units`


The length of the medium side is




`= (4)/(13) * 104`


`= 32 \: units`


The length of the longest side,


`= (6)/(13) * 104`


`= 48 \: units`



QUESTION 8.



The ratio of the sides of the triangle is



`7 : 9: 12`



The total ratio is


`7 + 9 + 12 = 28`

The shortest sides of the triangle corresponds to the least ratio which is 7,



The shortest side

`= (7)/(28) * 84`

`= 21 \: units`


The length of the medium side is


`= (9)/(28) * 84`


`= 27 \: units`


The length of the longest side is


`= (12)/(28) * 84`

`= 36 \: units`



QUESTION 9.


The given ratio is


`6:7:9`


The total ratio is


`= 6 + 7 + 9 = 22`

The length of the shortest side is,



`= (6)/(22) * 77`



`21 \: units`


The length of the medium side is


`= (7)/(22) * 77`


`= 24.5 \: units`



The length of the shortest side is


`= (9)/(22) * 77`


`= 31.5 \: units`


QUESTION 4

The given ratio is


`4:5:6`


The total ratio is

`= 4 + 5 + 6 = 15`
The sum of the interior angles of the triangle is 180°.


The measure of the smallest angle is

`= (4)/(15) * 180 \degree`



`= 48 \degree`
The measure of the medium angle is,


`= (5)/(15) * 180 \degree`


`= 60 \degree`


The measure of the biggest angle is


`= (6)/(15) * 180 \degree`



`= 72 \degree`



We could have also gotten this angle by subtracting the measure of the sum of smallest and the medium angle from 180°,


`= 180 - (48 + 60)`



`= 180 -108`




`= 72 \degree`


QUESTION 11

The given ratio is


`5:7:8`


The sum of the total ratio is


`= 5 + 7 + 8 = 20`

The measure of the biggest angle corresponds to the biggest ratio which is 8.


The biggest angle is



`= (8)/(20) * 180 \degree`



`= 72 \degree`



The measure of the smallest angle corresponds to 5,



`= (5)/(20) * 180 \degree`



`= 45 \degree`

The measure of the third angle is

`= (7)/(20) * 180 \degree`



`= 63 \degree`