Answer:
195 pages
Step-by-step explanation:
Given:
195 = (35)5
This equation basically means that if you need to make 5 books and each book has 35 pages, you will need 195 pages to make all 5 books.
The question is asking you to identify the different parts of the equation and locate what information each number corresponds to.
So, 195 pages would be in 5 books.
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The answer, in short, is that the short leg equals 15 mm, the long leg equals 20 mm, and the hypotenuse equals 25mm. but if you'd like to see how I solved it, here are the steps.
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The Pythagorean theorem (also known as Pythagoras's Theorem) can be used to solve this. This theorem states that one leg or a right triangle squared plus the other side of that same triangle squared equals the hypotenuse of that triangle squared. To put it in equation form, L² + L² = H².
Let's call the longer leg B, the shorter leg A, and the hypotenuse H.
From the question, we know that A = B - 5, and H = B + 5.
So if we put those values into an equation, we have (B - 5)² + B² = (B + 5)²
Now, to solve. Let's square the two terms in parentheses first:
(B² - 5B - 5B + 25) + B² = B² + 5B + 5B + 25
Now combine like terms:
2B² -10B + 25 = B² + 10B + 25
And now we simplify. Subtract 25 from each side:
2B² - 10B = B² + 10B
Subtract B² from each side:
B² - 10B = 10B
Add 10B to each side:
B² = 20B
And finally, divide each side by B:
B = 20
So that's the length of B. Now to find out A and H.
A = B - 5, so A = 15.
H = B + 5, so H = 25.
And your final answer is A = 15mm, B = 20mm, and H = 25mm
It would be helpful if a figure is drawn as you can see clearly the situation of the problem. We would see that a right triangle is made where the angle between the elevation of the airplane with respect to the ground is 7 degrees and the horizontal distance is the base of the triangle. We use trigonemetric functions.
tan 7 = opposite side / adjacent = height / 3729
height = 458 meters
Express x from the secondequation: x=3+y.
Then substitude it in first equation:
4(3+y)+2y=12,
4·3+4y+2y=12,
12+6y=12,
6y=12-12,
6y=0,
y=0 and x=3+0=3
Answer: (3,0)
