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Find x :
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Sum of adjacent angles on a straight line is 180.
∠ABY + ∠YBC = 180
x + 25 + 2x + 50 = 180
3x + 75 = 180
3x = 105
x = 35
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Check if AC is parallel to DF :
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If AC is parallel to DF,
∠YBC = ∠BEF (Corresponding angles)
∠YBC = 2x + 50 = 2(35) + 50 = 120
∠BEF = 5x - 55 = 5(35) - 55 = 120
Since ∠YBC = ∠BEF, AC and DF are parallel.
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Answer: Since ∠YBC = ∠BEF, AC and DF are parallel.
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9514 1404 393
Answer:
i = 2
Step-by-step explanation:
The outside factor multiplies each term in parentheses.
5(2i +4) -i = 38
10i +20 -i = 38 . . . . eliminate parentheses
9i +20 = 38 . . . . . . collect terms
9i = 18 . . . . . . . . . . subtract 20
i = 2 . . . . . . . . . . . . divide by 9
Answer:
7
Step-by-step explanation:
English:
Which digit should go in the box to
make the next number divisible
between 2, 3 and 9? 8 ,? 48
Let x be the number, then the number will look like this:
8x48
This number is already divisible by 2, because it ends with an even number.
Now we need to check for divsibility by 3.
For this to be divisible by 3, the sum of the digit should be a multiple of 3.
We know if a number is divsible by 9, it is also divsible by 3.
So
The least positive solution is
Therefore 8748 is divsible by 2,3, and 9.
Answer:
The desired equation is y = 4x - 34
Step-by-step explanation:
Start with the general slope-intercept form y = mx + b.
The new line is parallel to y = 4x - 5, and so the slope of the new line is the same as that of the old one: 4. Then we have:
y = 4x + b
Find b. Do this by substituting 6 for x and -10 for y:
-10 = 4(6) + b. Then -10 - 24 = b, and b = -34.
The desired equation is y = 4x - 34
