1,260 possible arrangements of "balloon" using 7!/[2!*2}
Answer:
$15 < $4n + $5
Step-by-step explanation:
We know that Billy needs to make more than $15 between his allowance and the lawns that he mows. This means our inequality should include $15<. Also, since Billy will make $4 per lawn, that means we need to multiply $4 by the number of lawns he needs to mow, n: $4n. So far we have the following: $15<$4n. Next, we know that he makes $5 each week, on top of what he makes mowing each law. This means we need to add the $5 to the $4n. When we put all of these pieces together, we will get the following inequality: $15<$4n+$5
Answer:
π
Step-by-step explanation:
The *period* of a function is the length it takes before it repeats. Usually, the period of the sine function is 2π; it takes a full rotation around the unit circle for it to repeat. When we replace the input x with -2x, this does a few things:
- Changes the rotation direction
- Makes the rotation go twice as fast
If we rotate around the unit circle twice as fast, it’ll take us half of 2π, or just π to complete a cycle.
Start by finding x. Look at the second parallel line; you have a straight line that is made up of a 90 degree angle, 2x, and x.
Since a straight line is 180 degrees, and you know a part of it is already 90 degrees, you can make 2x and x add up to 90 degrees.
2x + x = 90, combine like terms.
3x = 90, divide both sides by 3.
x = 30
Find y next. 2y and x are on opposite sides of the transversal and make a Z shape, so they must be alternate interior angles. The alternate interior angle theorem states that these types of angles are congruent.
We know what x is, 30 degrees, so make 2y and x equal to each other.
2y = 30, divide both sides by 2.
y = 15
Find z. Same thing as the bottom parallel line; 2y and z make up the straight line so they must add up to 180 degrees. We found y was 15, so multiply y by 2. y = 30, so make 30 + z add up to 180 degrees.
30 + z = 180, subtract 30 from both sides.
x = 150
