Answer:
150
Step-by-step explanation:
First you have to find what number 80 is 2/5 of, to do this do the reciprocal of 2/5 which would be 5/2. Multiply 80 by 5/2 and you'll get 200, then find what 3/4 of 200. Multiply 200 by 3, then divide by 4 to get the answer of 150.
Answer:
The correct answer to the following question will be "70.56".
Step-by-step explanation:
The given values are:
Loan requires, PV = $100,000
Years = 20
Number of months, n = 240
Rate interest = 4.90000%
Monthly rate, r = 0.408333%
Monthly rental payment = $725
As we know,
![PV=PMT\times (\frac{1}{r})\times [1-[\frac{1}{(1+r)^n}]]](https://tex.z-dn.net/?f=PV%3DPMT%5Ctimes%20%28%5Cfrac%7B1%7D%7Br%7D%29%5Ctimes%20%5B1-%5B%5Cfrac%7B1%7D%7B%281%2Br%29%5En%7D%5D%5D)
On putting the values in the above formula, we get
⇒ ![100000=PMT\times (\frac{1}{0.004083333})\times [1-(\frac{1}{(1+0.004083333^{240})})]](https://tex.z-dn.net/?f=100000%3DPMT%5Ctimes%20%28%5Cfrac%7B1%7D%7B0.004083333%7D%29%5Ctimes%20%5B1-%28%5Cfrac%7B1%7D%7B%281%2B0.004083333%5E%7B240%7D%29%7D%29%5D)
⇒ 
⇒ 
⇒ 
Now,

On putting the values, we get
⇒ 
⇒ 
To enable the completion of the proof that line <em>l</em> is parallel to line <em>m</em>, a
diagram showing the lines and their common transversal is attached.
The completed two column proof is presented as follows;
Statement
Reason
1. ∠1 and ∠2 are supplementary angles
1. Given
2. m∠1 + m∠2 = 180°
2. <u>Definition of supplementary ∠s</u>
3. ∠1 and ∠3 are supplementary angles
3. Exterior sides in opposite rays
4. <u>m∠1 + m∠3 = 180° </u>
4. <u>Definition of supplementary ∠s</u>
5. m∠1 + m∠2 = m∠1 + m∠3
5. <u>Transitive property of equality</u>
6. <u>m∠2 = m∠3 </u>
6. <u>Subtraction property of equality</u>
7. l ║ m
7. <u>Converse of alternate interior </u>
<u>angles postulate</u>
Reasons:
- Reason for statement 2: Supplementary angles are defined as two angles that sum up to 180°
- Reason for statement 3: Two angles are supplementary if the exterior sides that form each angle are opposite rays (rays that are drawn out infinitely in opposite direction but have the same endpoint)
- Statement 4: Mathematical expression of the sum of ∠1 and ∠3; Reason for statement 4 is the definition of supplementary angles
- Reason for statement 5: Transitive property of equality describes the property that if a number <em>x</em> = <em>y</em>, and <em>z </em>= <em>y</em>, then <em>x</em> = <em>z</em>.
- Statement 6: Subtracting m∠1 from both sides of the equation in statement 5. gives; m∠1 + m∠2 - m∠1 = m∠1 + m∠3 - m∠1 ⇒ m∠2 = m∠3. Reason for statement 6 is the subtraction property of equality
- Reason for statement 7: The converse of the alternate interior angles postulate states that if the alternate interior angles formed between two lines and a common transversal are congruent, the two lines are parallel.
Learn more here:
brainly.com/question/25178453
Let the two sides of a right triangle be equal to one, which means that the hypotenuse is √2
Since cosa=adjacent side / hypotenuse
cos45=1/√2
We can rationalize the denominator by multiplying numerator and denominator by √2
√(2)/2
or if you prefer: √(1/2)