28 minutes late. 15 minutes until 9 from the start of his shift. 13 minutes after 9 add those two numbers = 28 minutes
Answer:
0.009 units in the positive y direction.
Step-by-step explanation:
Vertical shift is simply the value of the constant.
In this case, if you expand the formula by multiplying 0.9 into the parentheses,
y = 0.9 sin [(π/3) - x] + (0.9)(0.01)
y = 0.9 sin [(π/3) - x] + 0.009
Here the value of the constant is 0.009 and it is positive, hence the vertical shift is 0.009 units in the positive y direction.
A linear pair is a pair of adjacent, supplementary angles which sum is equal 180
So
5x + 5 + 11x - 65 = 180
16x - 60 = 180
16x = 240
x = 15
<PQR = 5(15) + 15 = 75 + 5 = 80
Answer
80°
Let the first number of the five we are looking for equal n.
Because the numbers are consecutive, the next four can be expressed as (n+1), (n+2), (n+3) and (n+4).
Our series of 5 numbers is therefore n,(n+1),(n+2),(n+3),(n+4).
We are told the sum of the squares of the first 3 is equal to the sum of the squares of the last 2 therefore:
n² + (n+1)² + (n+2)² = (n+3)² + (n+4)²
expand all the brackets to give
n² + n² + 2n + 1 + n² + 4n + 4 = n² + 6n + 9 + n² + 8n + 16
3n²+6n+5 = 2n²+14n+25
n²-8n-20=0
factorising this gives us
(n+2)(n-10) = 0 so the solutions are n=10 and n=-2
That means that n,(n+1),(n+2),(n+3),(n+4) could be [-2, -1, 0, 1 and 2] or [10, 11, 12, 13 and 14].
Since the question asks for whole numbers, and negative numbers are not classed as whole numbers, the numbers we want must be 10, 11, 12, 13 and 14.
You can check this on a calculator by doing 10² + 11² + 12² (=365) and 13² + 14² (=365).
Answer:
Please check the explanation.
Step-by-step explanation:
Given the expression
Apply exponent rule:
∵
Factor out common term 2y
We know that the Binomial is an expression that consists of two terms. Thus,
(4x²y²- 9) represents the binomial factor of
We can further simplify by Factoring 4x²y² - 9: (2xy + 3) (2xy - 3)
Here:
(2xy + 3) and (2xy -3) are the binomial factors of as each of them consists of two terms.