Answer:
We have to prove Δ ABO ≅ Δ CDO or, Δ DAO ≅ Δ BCO.
Step-by-step explanation:
Let us assume that ABCD is a parallelogram having diagonals AC and BD.
We have to prove that in a parallelogram the diagonals bisect each other.
Assume that the diagonals of ABCD i.e. AC and BD intersect at point O.
Therefore, to prove that the diagonals AC and BD bisect each other, we have to first prove that Δ ABO and Δ CDO are congruent or Δ DAO and Δ BCO are congruent.
In symbol, we have to prove Δ ABO ≅ Δ CDO or, Δ DAO ≅ Δ BCO. (Answer)
let's say the breakfast price was "x", so that's the 100%, and we know she gave 20% of that and that is 1.80.
so, 1.80 is 20%, and "x" is the 100%, what is "x"?
Answer:
- 6. See solution
- 7. k = 2, k = -6
Step-by-step explanation:
6.
<u>Given equation:</u>
- The sum of the roots is q1 and the product of the roots is q2
Need to show that q1+q2 = 0
<h3>Solution</h3>
<u>Bringing the equation into standard form of ax² + bx + c = 0:</u>
- 2(x + 2)² + p(x + 1) = 0
- 2x² + 8x + 8 + px + p = 0
- 2x² + (p + 8)x + (p + 8) = 0
<u>Sum of the roots: </u>
<u>Product of the roots:</u>
<u>We see that q1 and q2 are opposite numbers, therefore their sum equals zero:</u>
- q1 + q2 = -(p + 8)/2 + (p + 8)/2 = 0
=============================================
7.
<u>Given quadratic equation:</u>
Need to find the possible values of k
<h3>Solution</h3>
<u>When the quadratic equation has equal roots, then its discriminant is equal to zero:</u>
- D = 0
- √b² - 4ac = 0
- √(-k -2)² - 4*1*4 = 0
- √k² + 4k + 4 - 16 = 0
- √k² + 4k - 12 = 0
- k² + 4k - 12 = 0
- k = {-4 ± √4² -4*1*(-12)}/2
- k = (-4 ± √16 + 48)/2
- k = (-4±√64)/2
- k = -2 ± 4
- k = 2, k = -6
Answer:
The distance between the parallel sides is 20cm.
Step-by-step explanation:
Area of a trapezoid:
where a and b are the 2 bases, and h is the height. The value we're trying to find here is the height.
3 of the 4 variables in this equation are already given:
A = 800
a = 48
b = 32
Just plug those in and solve for h:
