Vertical angles are always equal. Given that one angle is 2x and the other is 80°, we set up the equation:
2x = 80°
Solving for x:
x = 80° / 2 = 40°
A sphere has one continuous curved surface with no edges or vertices.
Examples include a ball or a globe.
To solve 2(b - 3) + 5 = 3(b - 1):
First, distribute the numbers outside the parentheses:
2b - 6 + 5 = 3b - 3
Combine like terms:
2b - 1 = 3b - 3
Now, isolate b:
2b - 3b = -3 + 1
-b = -2
Multiply both sides by -1:
b = 2
To find the price without GST:
Let the original price be x.
The GST amount is 16.5% of x:
GST = 0.165x
The sales price (including GST) is:
4248 = x + 0.165x
4248 = 1.165x
Now, divide by 1.165:
x = 4248 / 1.165
x ≈ 3646.35
Set Difference (B A) means the elements in B that are not in A.
Given:
A = {2, 4, 5, 7}
B = {3, 4, 7}
Elements of B are {3, 4, 7}.
4 and 7 are also in A, so they are removed.
3 is not in A, so it remains.
Therefore, B A = {3}
Given y varies directly with x, so y = kx.
Given y = 99 and x = 11,
99 = k × 11
k = 9
Now, y = 9x
When x = 3,
y = 9 × 3
y = 27
A reflex angle is any angle greater than 180° but less than 360°.
215° fits this definition.
The absolute value of a number is its distance from 0 on the number line, always positive.
So, |−13| = 13.
The sequence of plants planted each year is an arithmetic sequence with:
First term (a) = 6000
Common difference (d) = 2200
To find the number of plants in the 7th year, we need to find the 7th term:
a₇ = a + (n - 1)d
= 6000 + (7 - 1) × 2200
= 6000 + 6 × 2200
= 6000 + 13200
= 19200