Find m∠1 if m∠2=73°, m∠3=107°, m∠4=92°.
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Answer:
Step-by-step explanation:
This triangle has a small square, which represents a right angle. Therefore, we can use the Pythagorean Theorem.
Where <em>a</em> and <em>b </em> are the legs of the triangle and <em>c</em> is the hypotenuse.
In this triangle, 7 and √15 are the legs, because these sides make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle. So, we know two values:
Substitute these values into the formula.
Solve the exponents.
- (7)²= 7*7=49
- (√15)²=√15*√15=15
Add.
Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.
The third side length is <u>8.</u>
<h3>Answer:</h3>
- C. (9x -1)(x +4) = 9x² +35x -4
- B. 480
- A. P(t) = 4(1.019)^t
Step-by-step explanation:
1. See the attachment for the filled-in diagram. Adding the contents of the figure gives the sum at the bottom, matching selection C.
2. If we let "d" represent the length of the second volyage, then the total length of the two voyages is ...
... (d+43) + d = 1003
... 2d = 960 . . . . . . . subtract 43
... d = 480 . . . . . . . . divide by 2
The second voyage lasted 480 days.
3. 1.9% - 1.9/100 = 0.019. Adding this fraction to the original means the original is multiplied by 1 +0.019 = 1.019. Doing this multiplication each year for t years means the multiplier is (1.019)^t.
Since the starting value (in 1975) is 4 (billion), the population t years after that is ...
... P(t) = 4(1.019)^t