27.5
put the numbers in order
find median (134.5)
find lower quartile (121)
upper quartile (148.5)
subtract upper from lower to get 27.5
Answer:
We want to prove the relation:
cosec(a)^2 - cot(a)^2 = 1
where:
cosec(a) = 1/sin(a)
cot(a) = 1/tg(a) = cos(a)/sin(a)
We can start with the relationship:
cos(a)^2 + sin(a)^2 = 1
Now, let's divide by sin(a)^2 in both sides:
(cos(a)^2 + sin(a)^2)/sin(a)^2 = 1/sin(a)^2
cos(a)^2/sin(a)^2 + sin(a)^2/sin(a)^2 = (1/sin(a))^2
(cos(a)/sin(a))^2 + 1 = (1/sin(a))^2
and remember that:
cosec(a) = 1/sin(a)
cot(a) = 1/tg(a) = cos(a)/sin(a)
Then we can write:
(cos(a)/sin(a))^2 + 1 = (1/sin(a))^2
as:
cot(a)^2 + 1 = cosec(a)^2
1 = cosec(a)^2 - cot(a)^2
And this is the relation we wanted to prove.
Length: 2(x + 6); Width: 3.5x
A rectangle has 4 sides. 2 sides are lengths and 2 sides are widths.
The perimeter is the sum of the measures of all 4 sides.
perimeter = length + length + width + width
perimeter = 2(x + 6) + 2(x + 6) + 3.5x + 3.5x
Use the distributive property on 2(x + 6).
perimeter = 2x + 12 + 2x + 12 + 3.5x + 3.5x
Now let's group all terms with x first, then all the numbers.
perimeter = 2x + 2x + 3.5x + 3.5x + 12 + 12
Now we add like terms. Like terms have exactly the same variables and the same exponents. All terms with x are like terms and can be added together. All terms with no variable are like terms and can be added together.
perimeter = 11x + 24
11x and 24 are not like terms since 11x contains the variable x and 24 has no variable. Since 11x and 24 are not like terms, they cannot be added together. No more simplification can be done, and 11x + 24 is the answer.
Answer: 11x + 24
As diameter is twice of the radius , so diameter= 2multiplied by 5.5 that is 11.0 cm
To answer, we set the expression inside the absolute value symbol (II) equal to 0. That is,
x + 2 = 0
Then, we solve for the value of x.
x + 2 - 2 = 0 - 2
Hence, the value of x from the equation above is equal to -2.
Then, substitute the value of x to the equation and drop the absolute value symbol.
y = 4(x + 2) + 7
Substituting,
y = 4(-2 + 2) + 7
y = 4(0) + 7
y = 7
Thus, the vertex of the absolute value equation is equal to (-2,7). The answer is the last choice.
