All you have to do is substitute the values in for y to see if they are true.
0: 9 ≤ 6 - 0 = 9 ≤ 6 (FALSE)
3: 9 ≤ 6 - 3 = 9 ≤ 3 (FALSE)
-3: 9 ≤ 6 - -3 = 9 ≤ 9 (TRUE)
-1: 9 ≤ 6 - -1 = 9 ≤ 7 (FALSE)
-6: 9 ≤ 6 - -6 = 9 ≤ 12 (TRUE)
6: 9 ≤ 6 - 6 = 9 ≤ 0 (FALSE)
-4: 9 ≤ 6 - -4 = 9 ≤ 10 (TRUE)
So, the values that belong to 9 ≤ 6 - y are -3, -4, and -6.
The answer is 80 square meters.
The square area is expressed as:
A = a²,
where A is the area of the square, and a is the side of the square.
The rectangle area is expressed as:
A₁ = a₁ · b₁,
where A₁ is the area of the rectangle, and a₁ and b₁ are the sides of the rectangle.
After renovations, square garden becomes rectangular.
One side is doubled in length:
a₁ = 2a
The other side is decreased by three meters.
b₁ = a - 3
The new area is 25% than the original square garden:
A₁ = A + 25%A =
= A + 25/100·A
= A + 1/25·A
= a² + 1/25·a²
= <span>a² + 0.25·a²
</span> = 1.25·a²
If the starting equation is:
A₁ = a₁ · b₁
Thus, the equation is:
1.25a² = 2a·(<span>a - 3)
</span>1.25a² = 2a · a - 2a · 3
1.25a² = 2a² - 6a
<span>Therefore, the equation that could be used to determine the length of a side of the original square garden is:
</span><u>2a² - 6a = </u><span><u>1.25a²</u></span>
Now, we will solve the equation:
2a² - 6a = 1.25a²
2a² - 1.25a² - 6a = 0
0.75a² - 6a = 0
⇒ a(0.75a - 6) = 0
From here, one of the multiplier must be zero - either a or (0.75a - 6). Since a could not be zero, (0.75a - 6) is:
0.75a - 6 = 0
0.75a = 6
a = 6 ÷ 0.75
a = 8
If the side of the square is 8, then the area of the rectangle is
A₁ = 1.25 · a²
A₁ = 1.25 ·8²
A₁ = 1.25 · 64
A₁ = 80
Therefore, the area of the new rectangle garden is 80 square meters.
Answer: OPTION A
Step-by-step explanation:
It is important to remember the "Angle Addition Postulate" in order to solve this exercise.
You have this larger angle:
According to the "Angle Addition Postulate", if the point "C" is in the interior of , then the measure of this angle can be obtained by adding the angle 
and the angle 
.
You can observe in the figure that:
Then you get that:
Therefore, the correct answer is Option A.
Because it does not specify that she has to choose one or two from each category all pieces of jewelry can be treated as choices in a combination set.
the formula for a combination is
where n is a total number of choices ( 11 )
and r is number chosen out of those choices (4)
so
C(11,4)= \frac{11!}{4!(11-4)!}
She has 330 possible choices to come home with 4 pieces of jewelry
The total number of mattresses that are sold in a year = 1,330
Percentage of King size mattresses sold = 30% = 30/100 = 0.3
Next, we have to calculate the actual number sold by using the formula given below:
Number of king size mattresses sold = Total mattresses sold in a year * percentage of king size mattresses sold
Number of King Size mattresses sold = 1,330*0.3 = 399
Number of king size mattresses sold = 399
