Combine fractions by finding common denominator
Ans: 8x+7y/7x-8y
Answer:
Length of XM is 5.5 units.
Step-by-step explanation:
Given △XYZ where MZ is the angle bisector of ∠YZX . we have to find the length of XM.
A triangle with vertices X, Y, and Z. Side XZ is base. A line segment drawn from Z to M bisects ∠YZX into two parts ∠YZM and ∠XZM.
YZ=7 units, XZ=11 units and YM=3.5 units
By angle bisector theorem which states that an angle bisector of an angle divides the opposite side in two segments that are proportional to the another two sides of the triangle.
Hence,
⇒
⇒ MX=5.5 units.
Hence, length of XM is 5.5 units.
Answer:
- 1) 18 quarters and 30 nickels
- 2) 8 quarters and 12 nickels
Step-by-step explanation:
1) Let quarters be x and nickels be y.
<u>Equations based on given, 48 coins, total of $6 = 600c:</u>
<u>Substitute y in the second equation, y = 48 - x</u>
- 25x + 5(48 - x) = 600
- 25x + 240 - 5x = 600
- 20x = 360
- x = 18
<u>Then value of y is:</u>
2) <u>Similarly to problem 1.</u>
<u>Substitution: y= 20 - x</u>
- 25x + 5(20 - x) = 260
- 25x + 100 - 5x = 260
- 20x = 160
- x = 8
<u>Then finding y:</u>
For part B, you are correct as far as you've gone. There is no algebraic solution to your equation. A graphing calculator or Newton's Method iteration can get you to a solution fairly quickly.
a ≈ 1.114157141
For part C, you need to consider your answer. For a=0, the equation is that of a straight line, so there is no inflection point at x=1. For cos(a)=0, there are an infinite number of possible values of
that will put a point of inflection at x=1. As you have noted, a=π/2 is only one of them in the range 0 < a < 4.
For part D, again you have stopped part way to the answer. Consider what values of
will make
strictly greater than 1. There aren't any. The sine function always crosses zero. This part of the question has no solution.