Answer:
We know that:
Sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)
Then if we use this property in our expression:
sin(a-30)-sin(a+30)
We get:
sin(a)*cos(-30°) + sin(-30°)*cos(a) - sin(a)*cos(30°) - sin(30°)*cos(a)
Now remember that:
sin(-x) = -sin(x)
and
cos(-x) = cos(x)
Then we can rewrite our expression as:
sin(a)*cos(30°) - sin(30°)*cos(a) - sin(a)*cos(30°) - sin(30°)*cos(a)
= -2*sin(30°)*cos(a)
and sin(30°) = 0.5
Then:
-2*sin(30°)*cos(a) = -2*0.5*cos(a) = -cos(a)
So we get:
sin(a-30)-sin(a+30)= - cos(a)
Answer:
Step-by-step explanation:
The ladder forms a right angle triangle with the wall and the ground. The height of the ladder represents the hypotenuse of the right angle triangle.
Let x represent the distance from the top of the ladder to the bottom of wall. This forms the opposite side of the triangle.
The distance from the top of the ladder to the bottom of wall is 7ft more than the distance from the bottom of the ladder to the wall. This means that the distance from the bottom of the ladder to the wall is x - 7. It represents the adjacent side of the triangle.
To find the distance from the bottom of the ladder to the wall, we would apply Pythagorean theorem.
Hypotenuse² = opposite² + adjacent²
13² = x² + (x - 7)²
169 = x² + x² - 14x + 49
169 = 2x² - 14x + 49
2x² - 14x + 49 - 169 = 0
2x² - 14x - 120 = 0
Dividing through by 2, it becomes
x² - 7x - 60 = 0
x² + 5x - 12x - 60 = 0
x(x + 5) - 12(x + 5) = 0
(x - 12)(x + 5) = 0
x = 12 or x = - 5
the distance cannot be negative, so x = 12
the distance from the bottom of the ladder to the wall is
x - 7 = 12 - 7 = 5 feet
Answer:
For the boys box, the answer is 8.
For the Girls top box the answer is 18.
Step-by-step explanation:
81/ 72=1.125
9/ 8=1.125
18/16=1.125
Hope this helps! :)
The answer in simplify is (5b)(-3a)= -15ab