Answer:
300 girls were there in the gym.
Step-by-step explanation:
Given:
The ratio of the number of boys to the number of girls was 4:3, after 160 boys left the gym, the ratio became 4:5.
Now, to find the number of girls in the gym.
The girls in the gym does not left, their quantity is same before and after.
So, we multiply the both ratios to make the girls ratio same:
4:3 × 5 = 20:15
4:5 × 3 = 12:15
Now, <em>we find the units of the ratio</em>.
<em>The ratio of boys dropped down by 160</em>:
20 - 12 = 8 units.
160 = 8 units
Now, dividing both sides by 8 we get:
20 = 1 unit
So, 1 unit = 20.
Now, girls = 15 units
So, 15 × 20 = 300.
Therefore, 300 girls were there in the gym.
<u>Answer:</u>
Angle A = 39°
<u>Step-by-step explanation:</u>
We are given that there is a triangle ABC where a = 9, c = 5 and angle B = 120° and we are to find the measure of angle A.
But first we need to find the side b using the law of cosine:
Now finding angle A using law of cosine:
Therefore, the measure of angle A = 39°.
The answer is <span>c. 16x2 + 24xy + 9y2.
Since we need trinomial (three term expression) choices a and b are incorrect because they have only two terms.
So, our square trinomial is a</span>² + 2ab + b² or a² - 2ab + b²
a² + 2ab + b² = (a + b)²
a² - 2ab + b² = (a - b)²
Let's check choices c and d:
c) 16x² + 24xy + 9y²
a² = 16x²
a² = (4x)²
a = 4x
b² = 9y²
b² = (3y)²
b = 3y
a² + 2ab + b² = (4x)² + 2 * 4x * 3y + (3y)² = 16x² + 24xy + 9y²
CORRECT
d) 49x² - 70xy + 10y²
a² = 49x²
a² = (7x)²
a = 7x
b² = 10y²
b² = (y√10)²
b = y√10
a² + 2ab + b² = (7x)² + 2 * 7x * y√10 + (y√10)² = 49x² + 14xy√10 + 10y²
INCORRECT
So, c) is correct answer
