Can someone please help me do the following problems? I don't care for the answers, I just wanna know how to do this stuff. I am always forgetting how to do certain things in math.
1)ABCD is a rhombus with diagonals intersecting at E. If m<ABC= 4m<BAD, find m<EBC.
2)The length of the median of trapezoid EFGH is 17 centimeters. If the bases have lengths 2x+4 and 8x-50, find x.
3) If the slope AB is 1/2, the slope of BC is -4, and the slope of CD is 1/2, find the slope of DA so that ABCD is a parallelogram.
This are the ones I still can't figure out how to do.
Oh, nevermine about #3...it's easy. I already figured out by reading it again. Sorry. It's just the other two I don't know how to solve
2. Median of trapezoid = Sum of bases divided by 2
2x+4+8x-50/2=17
10x-46/2=17
5x-23=17
5x=17+23
5x=40
------> x=8
Checking:
2(8)+4 + 8(8)-50 =17
16+4 + 64-50 = 17
20+14 = 17
34/2= 17
17=17
Certainly! I would be happy to help you with these math problems and explain how to solve them.
1) To find the measure of angle EBC, we first need to understand some properties of a rhombus. In a rhombus, opposite angles are congruent, and the diagonals bisect each other. Let's call m<ABC as 'x'.
Since m<ABC = 4m<BAD, we can write x = 4x. Simplifying, we get 4x - x = 0. Solving for x, we find that x = 0.
Now, we know that m<ABC = 0 and m<BAD = 4(0) = 0. Since opposite angles in a rhombus are congruent, we can determine that m<BCD = 0 as well.
Since the diagonals of a rhombus bisect each other, we can conclude that m<EBC = m<BCD / 2.
Therefore, m<EBC = 0 / 2 = 0.
2) In a trapezoid, the median is the segment that connects the midpoints of the two bases. Let's call the length of the median as '17'.
The formula to find the length of the median in a trapezoid is given by: median = (base1 + base2) / 2.
Substituting the given lengths, we have:
17 = (2x + 4 + 8x - 50) / 2.
To remove the fraction, we can multiply both sides of the equation by 2:
2 * 17 = 2 * [(2x + 4 + 8x - 50) / 2].
Simplifying, we get:
34 = 2x + 4 + 8x - 50.
Combining like terms, we have:
34 = 10x - 46.
Next, we can isolate the variable by moving the constant term to the other side of the equation:
34 + 46 = 10x - 46 + 46.
Simplifying further, we get:
80 = 10x.
Finally, divide both sides of the equation by 10 to solve for x:
x = 8.
Therefore, the value of x is 8.
3) In order for ABCD to be a parallelogram, opposite sides must be parallel. Moreover, parallel lines have equal slopes.
Given that the slope of AB is 1/2, the slope of BC is -4, and the slope of CD is 1/2, we can conclude that the slope of DA should be equal to the slope of BC to form parallel lines.
Therefore, the slope of DA is -4.
I hope these explanations help you understand how to solve these math problems! Let me know if you have any further questions.