Step-by-step answer:
First we need to know the properties of the given figures.
There are many ways to describe a parallelogram. Here we will use the simple description that
"A parallelogram is a convex quadrilateral with opposite sides equal and parallel."
If we take pencil and paper to construct two parallel and equal lines, and join the corresponding points, we can only get a parallelogram (as long as the figure is convex.
Similarly, if we draw four equal lines to draw a parallelogram, we can only get a rhombus. Therefore a rhombus is a parallelogram with all four sides equal.
See the Venn diagram attached.
Note
(in fact, the minimum definition of a rhombus is "a parallelogram with two adjacent sides equal")
The is 42 because that the answer to the question
The cosine function 
meets the y axis at the point 
In fact, you have 
Answer:
k = 1 + sqrt(7/2) or k = 1 - sqrt(7/2)
Step-by-step explanation:
Solve for k over the real numbers:
4 k - 10/k = 8
Bring 4 k - 10/k together using the common denominator k:
(2 (2 k^2 - 5))/k = 8
Multiply both sides by k:
2 (2 k^2 - 5) = 8 k
Expand out terms of the left hand side:
4 k^2 - 10 = 8 k
Subtract 8 k from both sides:
4 k^2 - 8 k - 10 = 0
Divide both sides by 4:
k^2 - 2 k - 5/2 = 0
Add 5/2 to both sides:
k^2 - 2 k = 5/2
Add 1 to both sides:
k^2 - 2 k + 1 = 7/2
Write the left hand side as a square:
(k - 1)^2 = 7/2
Take the square root of both sides:
k - 1 = sqrt(7/2) or k - 1 = -sqrt(7/2)
Add 1 to both sides:
k = 1 + sqrt(7/2) or k - 1 = -sqrt(7/2)
Add 1 to both sides:
Answer: k = 1 + sqrt(7/2) or k = 1 - sqrt(7/2)
Because LP and NP are the same measure, that means that MP is a bisector. It bisects side LN and it also bisects angle LMN. Where MP meets LN creates right angles. What we have then thus far is that angle LMP is congruent to angle NMP and that angle LPM is congruent to angle NPM and of course MP is congruent to itself by the reflexive property. Therefore, triangle LPM is congruent to triangle NMP and side LM is congruent to side NM by CPCTC. Side LM measures 11.
