Answer:
m∠1 = 112°
Consider x and 68° only. They are considered supplementary angles (angles that add up to 180°)
So,
m∠1 + 68 = 180
m∠1 = 180 - 68
m∠1 = 112°
m∠3 = 68°
Do the same thing as m∠1. Consider the two angles that would add up to 180, m∠1 and m∠3.
Since we know m∠1, we can easily solve m∠3.
So,
m∠3 + m∠1 = 180
m∠3 + 112 = 180
m∠3 = 180 - 112
m∠3 = 68
By now, you have noticed, why is the same as the other angle next to m∠1? This is because they are vertical angles. This is called vertical angle congruence theory.
m∠4 = 22
This is almost the same as solving for m∠3 and m∠1. The only difference is we conclude two angles that are <em>complement to each other (angles that add up to </em><em>90</em><em>°)</em>
So,
m∠3 + m∠4 = 90
68° + m∠4 = 90
m∠4 = 90 - 68
m∠4 = 22
m∠5 = 90° (correct)
C.
Find the value of "x"
Just like we solved for the questions above, we arrange them to add up to <em>180°.</em>
So,
(2x + 11) + (6x - 7) = <em>180</em>
2x + 11 + 6x - 7 = 180
2x + 6x + 11 - 7 = 180
8x + 4 = 180
8x = 180 - 4
8x = 176
x = 176 ÷ 8
x = 22°
Check:
2x + 11 + 6x - 7 = 180
2(22) + 11 + 6(22) - 7 = 180
44 + 11 + 132 - 7 = 180
55 + 125 = 180
180 = 180 (correct)
<em>Good luck sleeping </em>
Since we can't use a zero at the start and end, then we have 810 different ways.
If we can't have a leading digit of zero, then we still have 9 available digits to choose from (9P1)
Now, the second term can be of any number, so we will have 10 different digits to choose 1 (10P1)
Now, the final term cannot be a zero, so we will have 9 available digits to choose from (9P1)
Hence, our final number of ways is: 9 × 10 × 9 = 810 ways.
Step-by-step explanation:
Look for keywords
when you see "per" that means theres a rate (something happens every unit of time)
To write a rate you divide whatever happens by whatever unit of time youre useing
In this example our rate is 15$ <em>per</em> hour which can be written as:
15$/1 hour (but we usually dont write it if theres a 1)
You can think of this as a regular fraction
Here the hour will cancel and youre left with $
<u>Given</u>:
The given geometric series is
We need to determine the value of r and a₁
<u>Value of a₁:</u>
The term a₁ denotes the first term of the geometric series.
Hence, from the given series, the first term of the series is 2.
Thus, a₁ = 2.
Therefore, the value of a₁ is 2.
<u>Value of r:</u>
The term r denotes the common ratio between the terms in the geometric series.
The value of r is given by
Thus, the value of r is 1.5
In a right triangle the sum of the squares of the lengths of two shorter sides is equal to the square of the length of the longest side.
a.
b.
c.
The answer is A and C.