We know: The sum of the measures of the angles of a triangle is equal 180°.
We have: m∠A =65°, m∠B = (3x - 10)° and m∠C = (2x)°.
The equation:
65 + (3x - 10) + 2x = 180
(3x + 2x) + (65 - 10) = 180
5x + 55 = 180 <em>subtract 55 from both sides</em>
5x = 125 <em>divide both sides by 5</em>
x = 25
m∠B = (3x - 10)° → m∠B = (3 · 25 - 10)° = (75 - 10)° = 65°
m∠C = (2x)° → m∠C = (2 · 25)° = 50°
<h3>Answer: x = 25, m∠B = 65°, m∠C = 50°</h3>
Answer:
Step-by-step explanation:
Given
5 tuples implies that:
implies that:
Required
How many 5-tuples of integers are there such that
From the question, the order of the integers h, i, j, k and m does not matter. This implies that, we make use of combination to solve this problem.
Also considering that repetition is allowed: This implies that, a number can be repeated in more than 1 location
So, there are n + 4 items to make selection from
The selection becomes:
Expand the numerator
<u><em>Solved</em></u>
Answer:
Step-by-step explanation:
Let the numbers be x,y, where x>y
The geometric mean is
The Arithmetic mean is
The ratio of the geometric mean and arithmetic mean of two numbers is 3:5.
We can write the equation;
or
l
and
or
Make y the subject in equation 2
Put equation 3 in 1
When x=1, y=10-1=9
When x=9, y=10-9=1
Therefore x=9, and y=1
The ratio of the smaller number to the larger number is