Answer:
m∠BCE = 28° and m∠ECD = 134°
Step-by-step explanation:
* Lets explain how to solve the problem
- The figure has three angles: ∠BCE , ∠ECD , and ∠BCD
- m∠ECD is six less than five times m∠BCE
- That means when we multiply measure of angle BCE by five and
then subtract six from this product the answer will be the measure
of angle ECD
∴ m∠ECD = 5 m∠BCE - 6 ⇒ (1)
∵ m∠BCD = m∠BCE + m∠ECD
∵ m∠BCD = 162°
∴ m∠BCE + m∠ECD = 162 ⇒ (2)
- Substitute equation (1) in equation (2) to replace angle ECD by
angle BCE
∴ m∠BCE + (5 m∠BCE - 6) = 162
- Add the like terms
∴ 6 m∠BCE - 6 = 162
- Add 6 to both sides
∴ 6 m∠BCE = 168
- Divide both sides by 6
∴ m∠BCE = 28°
- Substitute the measure of angle BCE in equation (1) to find the
measure of angle ECD
∵ m∠ECD = 5 m∠BCE - 6
∵ m∠BCE = 28°
∴ m∠ECD = 5(28) - 6 = 140 - 6 = 134°
* m∠BCE = 28° and m∠ECD = 134°
Answer:
The team can assign field positions to 9 of the 19 players in 181,440 different ways.
Step-by-step explanation:
Since the outfielders (left field, center field, right field) can play any outfield position, the infielders (1st base, 2nd base, 3rd base, short stop) can play any infield position, the pitchers can only pitch, and the catchers can only catch, supposing a certain team has 20 players, of whom 3 are catchers, 4 are outfielders, 6 are infielders, and 7 are pitchers, to determine how many ways can the team assign field positions to 9 of the 19 players, putting each of the 9 selected players in a position he can play, and ensuring that all 9 field positions are filled, the following calculation must be performed:
3 x 7 x 6 x 5 x 4 x 3 x 4 x 3 x 2 = X
21 x 30 x 12 x 24 = X
630 x 12 x 24 = X
181,440 = X
Therefore, the team can assign field positions to 9 of the 19 players in 181,440 different ways.
The graph of the function f(x) = -(x+1)^2 shows that the domain of the function f(x) = -(x+1)² is: -∞ < x < ∞. The range of the function is f(x) ≤ 0.
<h3>What is the graph of a function?</h3>
The graph of a function is the arrangement of all ordered pairs of the function. Typically, they are expressed as points in a cartesian coordinate system. The graph of f is the collection of all ordered pairings (x, f(x)) such that x lies inside the domain of f.
The graph of a function might similarly be defined as the graph of the equation y = f(x). As a result, the graph of a function is a subset of the graph of an equation.
From the given information: the graph of the function f(x) = -(x+1)² can be determined if the domain, the range, and the vertex of the function are known.
- The domain of the function f(x) = -(x+1)² is: -∞ < x < ∞
- The range of the function is f(x) ≤ 0
- The x-intercepts and the y-intercepts are (-1,0) and (0, -1) respectively
- The vertex is maximum at (-1,0)
Since the parabola curve from the graph shows that the graph is facing down, then the function is negative and decreasing.
Learn more about the graph of a function here:
brainly.com/question/24696306
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<u>Question 1 solution:</u>
You have two unknowns here:
Let the Water current speed = W
Let Rita's average speed = R
We are given <em>two </em>situations, where we can form <em>two equations</em>, and therefore solve for the <em>two unknowns, W, R</em>:
Part 1) W→ , R←(against current, upstream)
If Rita is paddling at 2mi/hr against the current, this means that the current is trying to slow her down. If you look at the direction of the water, it is "opposing" Rita, it is "opposite", therefore, our equation must have a negative sign for water<span>:
</span>R–W=2 - equation 1
Part 2) W→ , R<span>→</span>(with current)
Therefore, R+W=3 - equation 2
From equation 1, W=R-2,
Substitute into equation 2.
R+(R–2)=3
2R=5
R=5/2mi/hr
So when W=0 (still), R=5/2mi/hr
Finding the water speed using the same rearranging and substituting process:
1... R=2+W
2... (2+W)+W=3
2W=1
W=1/2mi/hr
