Marissa has taken four 100-point tests in math this semester. Her mean score is 89%. How many points has she scored altogether o
n the four tests?
1 answer:
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The given ratios expresses the number of time a value is larger or smaller
than another value.
The correct responses are;
- 3. <u>(B) 12 and 24</u>
- 4. <u>(D) 6, 9, 21</u>
- 5.
- 6.
- 7. (B)
=<u> 6</u>,
= <u>9·√5</u>
- 8. <u>(C) The values are equal</u>
- 9. <u>(A) The value in column A is greater</u>
Reasons:
3. Given that the perimeter of the rectangle = 72
The ratio of the lengths of the sides = 1:2
Let <em>a</em> and <em>b</em> represent the sides, we have;
2·a + 2·b = 72
Which gives;
2·a = b
2·a + 2·(2·a) = 72
6·a = 72
a = 72 ÷ 6 = 12
b = 2·a = 2 × 12 = 24
The lengths of the sides are; <u>(B) 12 and 24</u>
4. Extended ratio = 2:3:7
The perimeter = 36
The lengths of the sides are;
The lengths are; <u>(D) 6, 9, 21</u>
5. The given equation is presented as follows;
5 × (x + 2) = 3 × (x + 7)
5·x + 10 = 3·x + 21
5·x - 3·x = 21 - 10
2·x = 11
The correct option is;
6. The width to length ratio is
The simplified ratio is therefore;
The correct option is (E)
7. The given ratio of the lengths is 3:1
Therefore;
:
= 3:1
Which gives;
= 18
Therefore;
18 × 1 = 3 ×
= 6
By Pythagorean theorem, we have;
² =
² +
²
Which gives;
² = 3² + 6² = 45
= √(45) = 3·√5
Using the given ratio, we have;
= 3 ×
Which gives;
= 3 × 3·√5 = 9·√5
= 9·√5
The correct option is; (B) =<u> 6</u>,
= <u>9·√5</u>
8. EF = 1, AB = 2
CD = 2, CE = 4
Therefore;
Which gives;
<u>(C) The values are equal</u>
9. AC = 6, BE = 8
DF = 3, BD = 6
Column A
Column B
Therefore;
Column A is greater than column B
<u>(A) The value in column A is greater</u>
Learn more about ratios here:
