A quadrilateral is a kite if the diagonals are:
i) perpendicular
ii) bisect each other
iii) not equal ( together with conditions i and ii this would make the quadrilateral a square)
Another definition of the kite is :
a quadrilateral with 2 pairs of equal adjacent sides.
Let's check the choices one by one:
A. <span>∠M is a right angle and MK bisects ∠LMJ.
according to these, ML and MJ may well be not equal...
</span><span>B. LM = JM = 3 and JK = LK = √17.
</span>
this makes the quadrilateral a kite.
<span>C. MK intersects LJ at its midpoint
</span>
if they are not perpendicular, the quadrilateral is not a kite.
<span>D. The slope of MK is –1 and the slope of LJ is 1.
this only means that MK and LJ are perpendicular, but not whether they bisect each other,
Answer: only B</span>
Answer:
1.20, 10.8
Step-by-step explanation:
d = n^2 - 12n + 43
d = 30
30 = n^2 - 12n + 43
0 = n^2 - 12n + 13
now solve for n using quadratic formula:
a=1, b=-12, c=13
n = (-b +- sqrt( b^2 -4ac))/2a
two answers ( one for + the square root, one for - the square root)
n = 1.20, n = 10.8
First we are going to group the terms that contains the common factor
in one parenthesis, and the other ones in another parenthesis:
Notice that our the terms in our first parenthesis have a common factor
, and the terms in our second one have the common factor
. Lets factor those out:
Now we have a common factor
in both terms, so we can factor those out as well:
We can conclude that the completely factored expression ordered alphabetically is
.
Answer:
98 degrees.
Step-by-step explanation:
The opposite angles of a cyclic quadrilateral add up to 180 degrees.
So m <A + 82 = 180
m<A = 180 - 82 = 98 degrees.
Answer:
14
Step-by-step explanation:
In an equation our aim is to find the value of what we are looking for as well as keeping the equation balanced. For example if we took away 16 only from one side then the equation would change so it's an important rule to bare in mind when solving equations, that you need to keep both sides of the equation the same.
4 ( d + 4 ) = 72
→ Expand the brackets
4d + 16 = 72
→ Minus 16 from both sides to isolate 4d
4d = 56
→ Divide both sides by 4 to isolate d
d = 14
