Answer: x = 2
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Explanation:
Refer to the diagram below.
I've added points D,E,F,G. This helps with labeling the segments and angles, and identifying the proper triangles (to see which are congruent pairs).
Triangle GEA is congruent to triangle GFA. We can prove this using the AAS congruence theorem. We have AG = AG as the pair of congruent sides, and the congruent pairs of angles are marked in the diagram (specifically the blue pairs of angles and the gray right angle markers)
Since triangle GEA is congruent to triangle GFA, this means the corresponding pieces segment GF and GE are the same length.
The diagram shows GF = 3x-4, so this means GE = 3x-4 as well.
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Through similar steps, we can show that triangle GEC is congruent to triangle GDC. We also use AAS here as well.
The congruent triangles lead to GD = GE. So GD = 3x-4. The diagram shows that GD = 6x-10
Since GD is equal to both 3x-4 and 6x-10, this must mean the two expressions are equal.
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Now let's solve for x
6x-10 = 3x-4
6x-3x = -4+10
3x = 6
x = 6/3
x = 2
Using the percentage concept, it is found that 75% of the population of Gorgeous Sunset is on Beautiful Sunrise now.
<h3>What is a percentage?</h3>
The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
In this problem, we have that:
- We consider that the population of both Beautiful Sunrise and Gorgeous Sunset islands is of x.
- There is a fiesta at Beautiful Sunrise, and a number a of people from Gorgeous Sunset are coming, hence, there will be x + a people at Beautiful Sunrise and x - a people t Gorgeous Sunset.
The percentage of people from Gorgeous Sunset is on Beautiful Sunrise now is:
Now the number of people on Beautiful Sunrise is seven times the number of people on Gorgeous Sunset, hence:
We can find a <u>as a function of x</u> to find the percentage:
Then, the percentage is:
75% of the population of Gorgeous Sunset is on Beautiful Sunrise now.
You can learn more about the percentage concept at brainly.com/question/10491646
Answer:
positive slope
(0,3)
slope = 2
Step-by-step explanation:
- Slope of the given line is positive
- If the line is sloping upward from left to right, so the slope is positive (+).
or if the angle made by the line to the x axis is < 90 it's slope is positive.
- y-intercept of the line is (0,3)
- The y intercept is the point where the line crosses the y axis. At this point x = 0.
- slope of the line is 2
- slope = (y2 - y1) / (x2 - x1)
lines passing through points (1,5) (0,3)
slope = (3 - 5) / (0 - 1)
= -2 / -1 = 2
Follow the "<em>y = mx + b</em>" formula, in which "m", stands for slope, and "b" stands for y-intercept
m = slope
m is located to the left attached to x.
-2 is in the place of m, therefore, -2 is the slope of the equation given.
-2 is your answer
hope this helps
![\left[\begin{array}{ccc}1&3&7\\1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%263%267%5C%5C1%261%261%5Cend%7Barray%7D%5Cright%5D%20)
multiply 2nd row by -1 and add to first row
![\left[\begin{array}{ccc}0&2&6\\1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%262%266%5C%5C1%261%261%5Cend%7Barray%7D%5Cright%5D%20)
divide the 1st row by 2
![\left[\begin{array}{ccc}0&1&3\\1&1&1\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%263%5C%5C1%261%261%5Cend%7Barray%7D%5Cright%5D%20)
multiply the first row by -1 and add to 2nd row
![\left[\begin{array}{ccc}0&1&3\\1&0&-2\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%263%5C%5C1%260%26-2%5Cend%7Barray%7D%5Cright%5D%20)
now we know
y+3=0
x-2=0
therefor
y=-3
x=2
