Answer:
x = 0, x = 1
Step-by-step explanation:
Both graphs correctly plot f(x).
Only the bottom graph correctly plots g(x).
The points of intersection of f(x) and g(x) are (0, -4) and (1, -2). The x-value of these points are x = 0 and x = 1. These are the values of x for which f(x) = g(x).
Answer:
297.84 miles
Step-by-step explanation:
176 miles in 13 hours is 13.5 miles per hour
13.5 * 22 = 297.84
Answer:
approximately 26.7 million
Step-by-step explanation:
Let x be the number of cruise passengers in 2017.
6.7% increase of x gives us 28.5 m cruise passengers in 2018.
Thus, 106.7 % of x = 28.5
![\frac{106.7}{100} * x = 28.5](https://tex.z-dn.net/?f=%20%5Cfrac%7B106.7%7D%7B100%7D%20%2A%20x%20%3D%2028.5%20)
![\frac{106.7x}{100} = 28.5](https://tex.z-dn.net/?f=%20%5Cfrac%7B106.7x%7D%7B100%7D%20%3D%2028.5%20)
Multiply both sides by 100
![\frac{106.7x}{100} * 100 = 28.5*100](https://tex.z-dn.net/?f=%20%5Cfrac%7B106.7x%7D%7B100%7D%20%2A%20100%20%3D%2028.5%2A100%20)
![106.7x = 2850](https://tex.z-dn.net/?f=%20106.7x%20%3D%202850%20)
Divide both sides by 106.7
![\frac{106.7x}{106.7} = \frac{2850}{106.7}](https://tex.z-dn.net/?f=%20%5Cfrac%7B106.7x%7D%7B106.7%7D%20%3D%20%5Cfrac%7B2850%7D%7B106.7%7D%20)
(approximated)
Number of passengers in 2017 must have been approximately 26.7 million
Answer:
340 degrees
Step-by-step explanation:
So the key thing here is to notice that we are given the circumference which will allow us to find a value for the radius of the circle and hence the angle subtended by the arc (the central angle).
So the circumference of a circle = 2pi(r)
This means:
6 = 2pi(r)
Which means that
r = 6/2pi or r = 3/pi
Now we can use this value of r to find our angle in conjunction with the value of the arc length. So:
Arc length is defined by: length = θr
Where θ is our angle value.
So lets plug in:
![\frac{17}{3} = (angle)\frac{3}{\pi }](https://tex.z-dn.net/?f=%5Cfrac%7B17%7D%7B3%7D%20%3D%20%28angle%29%5Cfrac%7B3%7D%7B%5Cpi%20%7D)
Multiply by pi to get:
![\frac{17\pi }{3} = 3(angle)](https://tex.z-dn.net/?f=%5Cfrac%7B17%5Cpi%20%7D%7B3%7D%20%3D%203%28angle%29)
Divide by 3 to get that:
θ = 17pi/9
So if we convert that from radians to degrees we get 340 degrees.
Answer:
II, III, and IV
Step-by-step explanation:
Define:
Similar polygons:
- Corresponding angles are equal
- Corresponding sides are in a constant proportion
Congruent polygons:
- Corresponding angles are equal
- Corresponding sides are equal
Let's break each statement down one-by-one:
<u>I. Corresponding sides of similar figures are the same.</u>
False - Corresponding sides of similar figures are in a constant proportion, but not necessarily the same. <em>Congruent</em> figures have equal corresponding sides, but similar figures only have their corresponding sides in a constant proportion.
<u>II. Corresponding sides of congruent figures are the same.</u>
True - By definition, corresponding figures have equal sides and angles. Therefore, this statement is true.
<u>III. Corresponding angles of congruent figures are the same.</u>
True - By definition, corresponding figures have equal sides and angles. Therefore, this statement is true.
<u>
</u>
<u>IV. Corresponding angles of similar figures are the same.</u>
True - While corresponding sides of similar figures may not be the same, their angles are. This is what gives them the similar characteristic. All similar polygons have equal angles, therefore this statement is true.