Answer:
The correct options are;
1) Write tan(x + y) as sin(x + y) over cos(x + y)
2) Use the sum identity for sine to rewrite the numerator
3) Use the sum identity for cosine to rewrite the denominator
4) Divide both the numerator and denominator by cos(x)·cos(y)
5) Simplify fractions by dividing out common factors or using the tangent quotient identity
Step-by-step explanation:
Given that the required identity is Tangent (x + y) = (tangent (x) + tangent (y))/(1 - tangent(x) × tangent (y)), we have;
tan(x + y) = sin(x + y)/(cos(x + y))
sin(x + y)/(cos(x + y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y))
(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y))
(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y)) = (tan(x) + tan(y))(1 - tan(x)·tan(y)
∴ tan(x + y) = (tan(x) + tan(y))(1 - tan(x)·tan(y)
Step-by-step explanation:
a rectangular prism (like this brick) has the same basic structure as a cube (like a die) : it has 6 sides.
while a die has 6 equal sides, a rectangular prism has 3 pairs of equal sides :
top and bottom
left and right
front and back
all we have to do is calculate the areas of the 6 rectangles and add them up. that's it.
your remember, the area of a rectangle is
length × width
in our case we have
top and bottom : 2.5×11.5 × 2 = 28.75×2 = 57.5 in²
left and right : 2.5×5 × 2 = 12.5×2 = 25 in²
front and back : 11.5×5 × 2 = 57.5×2 = 115 in²
so, the total surface area of the whole block is
57.5 + 25 + 115 = 197.5 in²
Answer:
see explanation
Step-by-step explanation:
Given A = 3x² + 2y + 2 and B = 6x² - 8y + 1 , then
A + B
= 3x² + 2y + 2 + 6x² - 8y + 1 ← collect like terms
= 9x² - 6y + 3
-------------------------------
A - B
= 3x² + 2y + 2 - (6x² - 8y + 1) ← distribute parenthesis by - 1
= 3x² + 2y + 2 - 6x² + 8y - 1 ← collect like terms
= - 3x² + 10y + 1
Answer:
x = -5
y = 2
Step-by-step explanation:
x = – 2y – 1
= -x - 2y - 1
-x - 2y = 1
x = – 5y + 5
= -x - 5y + 5
-x - 5y = -5
-x - 2y = 1
-x - 5y = -5
___________--
3y = 6
y = 6/3
<u>y = 2</u>
-x - 2y = 1
-x - 2(2) = 1
-x - 4 = 1
-x = 1 + 4
-x = 5
<u>x = -5</u>
Answer:
56
Step-by-step explanation:
The mean is the average number of a data set.
To find the mean:
First, add all the numbers in the data set:
30 + 45 + 45 + 70 + 90 = 280
Next, divide the sum (280) by 5 (amount of values):
280 / 5 = 56
56 represents the mean of your data set.
