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Answer:
6
Step-by-step explanation:
2y/3 + 1/3 = y/2 + 1/6
We want to eliminate the fractions
The least common multiple of 3,2 and 6 is 6
Multiply each side by 6 to get rid of the fractions
6(2y/3 + 1/3) = 6(y/2 + 1/6)
4y +2 = 3y +1
The bisector of the angle at A (call it AQ) divides the segment BC into segments BQ:QC having the ratio AB:AC. Use this fact to find x.
.. 9:15 = (2x -1):3x
.. 15(2x -1) = 9*3x . . . . . the product of the means equals the product of extremes
.. 30x -15 = 27x
.. 3x = 15
.. x = 5
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According to the value of x, the bisector AQ divides the triangle into two isosceles triangles: ABQ, ACQ.
Let's take l and w as the length and the width of the rectangle.
According to the given information the length is 3 less than twice the width:
And the area, which is the product of the length times the width is 14. Using the equation above, we can re write the formula for the area, this way:
Now, we have to solve the quadratic equation using the quadratic formula:
w has 2 values, but for this context, the logic value is 7/2. It means that the width of the rectangle is 7/2.
Now, we can use this value and the first equation to find the length:
The length of the rectangle is 4 and the width is 7/2.
Answer: OPTION B.
Step-by-step explanation:
The missing figure is attached.
For this exercise you need to use the Pythagorean Theorem. This is:
Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.
In this case you can identify in the figure the triangle PRS, so the diagonal PR is the hypotenuse of the triangle PRS.
Then you can say that:
Therefore, knowing these values, you can substitute them into :
Finally you must solve for PR in order to find its value. This is: