Answer:
x = 14
Step-by-step explanation:
Extend line AB so that it intersects ray CE at point G. Then angles BGC and BAD are "alternate interior angles", hence congruent.
The angle at B is exterior to triangle BCG, and is equal to the sum of the interior angles at C and G:
138 = (376 -23x) +(x^2 -8x)
Subtracting 138 and collecting terms we have ...
x^2 -31x +238 = 0
For your calculator, a=1, b=-31, c=238.
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<em>Additional comment</em>
You will find that the solutions to this are x = {14, 17}. You will also find that angle BCE will have corresponding values of 54° and -15°. That is, the solution x=17 is "extraneous." It is a solution to the equation, but not to the problem.
For x=14, the marked angles are A = 84°, C = 54°.
Answer: B
Step-by-step explanation: The question is asking for the point greatly different from all the rest, the outlier. Point B is far away from the grouping of all the other points, making it the outlier.
Since both of the angles are supplementary, you'd set the expressions up into an equation equal to 180(degrees).
So, your equation should look like:
22x + 4 + 35x + 5 = 180.
Next, you combine your like terms so that your next move will look like:
57x + 9 = 180.
Then you'd follow the subtraction and division property, so your next moves will look as the following:
57x + 9 - 9 = 180 - 9 equals 171
57x / 57 = 171 / 57 equals 3
So, finally, your answer is: x = 3.
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▹ Answer
<em>1/18 of a gallon of juice in each cup.</em>
▹ Step-by-Step Explanation
Since we have 4/9 of a gallon of juice for 8 cups, we will divide to find the amount of juice in each cup.
Since this operation is division, we have to change 8 to it's reciprocal which is 1/8:
Our final answer will be 1/18 of a gallon of juice in each cup.
Hope this helps!
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a.84
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