Diagonals must be congruent in a rectangle.
Answer: Largest exterior angle is 85.44 degrees
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Explanation
Rule: The exterior angles of any polygon always add to 360 degrees
Based on that rule, we simply add up the 8 expressions given to us and set that sum equal to 360. Then we solve for x
(x+12)+(2x-3)+(3x+10)+(3x+15)+(2x-19)+(4x-1)+(4x-10)+(6x) = 360
(x+2x+3x+3x+2x+4x+4x+6x)+(12-3+10+15-19-1-10) = 360
25x+4 = 360
25x = 360-4
25x = 356
x = 356/25
x = 14.24
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Once you determine the value of x, you plug that into each of the 8 exterior angle expressions
- x+12 = 14.24+12 = 26.24
- 2x-3 = 2(14.24)-3 = 25.48
- 3x+10 = 3(14.24)+10 = 52.72
- 3x+15 = 3(14.24)+15 = 57.72
- 2x-19 = 2(14.24)-19 = 9.48
- 4x-1 = 4(14.24)-1 = 55.96
- 4x-10 = 4(14.24)-10 = 46.96
- 6x = 6*(14.24) = 85.44
In short we have these 8 exterior angles
- x+12 = 26.24
- 2x-3 = 25.48
- 3x+10 = 52.72
- 3x+15 = 57.72
- 2x-19 = 9.48
- 4x-1 = 55.96
- 4x-10 = 46.96
- 6x = 85.44
We see that 85.44 degrees is the largest exterior angle (which is the angle that corresponds to the 6x). This makes sense because the 6 is the largest x coefficient compared to something like 2x-3 or 3x+10 which have x coefficients of 2 and 3 respectively.
Well, anything that's rotated (turned), reflected (flipped), or translated (moved) is still the same shape of the same size, so the new figures would be congruent with the originals. Dilation, however, is when the shape stays the same but the size changes, so when a figure is dilated, it's not congruent, just similar. 2 out of the 4 are dilated, so those ones would be the answer.
The question is incomplete, here is the complete question:
You and your friend are selling magazine subscriptions. You sell 8 fewer magazine subscriptions than your friend. Together you sell 42 magazine subscriptions. Write a system of linear equations that represents this situation.
The system of linear equations that represents this situation is:
x + y = 42
x - y = 8
Step-by-step explanation:
To solve the problem assume that
- x represent the number of magazine subscriptions that your friend sell
- y represents the number of magazine subscriptions that you sell
∵ Your friend sells x magazine subscriptions
∵ You sell y magazine subscriptions
∵ Together you sell 42 magazine subscriptions
∴ x + y = 42 ⇒ (1)
∵ You sell 8 fewer magazine subscriptions than your friend
∵ Your friend sells x magazine subscriptions
∵ You sell y magazine subscriptions
- That means y = x - 8
∴ y = x - 8
- Add 8 for both sides
∴ 8 + y = x
- Subtract y from both sides
∴ 8 = x - y
- Switch the two sides
∴ x - y = 8 ⇒ (2)
The system of linear equations that represents this situation is:
x + y = 42
x - y = 8
Learn more:
You can learn more about the system of linear equations in brainly.com/question/6075514
#LearnwithBrainly
(f∘g)(x) is equivalent to f(g(x)). We solve this problem just as we solve f(x). But since it asks us to find out f(g(x)), in f(x), each time we encounter x, we replace it with g(x).
In the above problem, f(x)=x+3.
Therefore, f(g(x))=g(x)+3.
⇒(f∘g)(x)=2x−7+3
⇒(f∘g)(x)=2x−4
Basically, write the g(x) equation where you see the x in the f(x) equation.
f∘g(x)=(g(x))+3 Replace g(x) with the equation
f∘g(x)=(2x−7)+3
f∘g(x)=2x−7+3 we just took away the parentheses
f∘g(x)=2x−4 Because the −7+3=4
This is it
g∘f(x) would be the other way around
g∘f(x)=2(x+3)−7
now you have to multiply what is inside parentheses by 2 because thats whats directly in front of them.
g∘f(x)=2x+6−7
Next, +6−7=−1
g∘f(x)=2x−1
Its a lts easier than you think!
Hope this helped