In parallelogram ABCD , diagonals AC⎯⎯⎯⎯⎯ and BD⎯⎯⎯⎯⎯ intersect at point E, AE=x2−16 , and CE=6x .
1 answer:
Answer:
<h3>AC=96 units.</h3>Step-by-step explanation:
We are given a parallelogram ABCD with diagonals AC and BD intersect at point E.
, and CE=6x .
<em>Note: The diagonals of a parallelogram intersects at mid-point.</em>
Therefore, AE = EC.
Plugging expressions for AE and EC, we get
Subtracting 6x from both sides, we get
Factoriong quadratic by product sum rule.
We need to find the factors of -16 that add upto -6.
-16 has factors -8 and +2 that add upto -6.
Therefore, factor of quadratic is (x-8)(x+2)=0
Setting each factor equal to 0 and solve for x.
x-8=0 => x=8
x+2=0 => x=-2.
We can't take x=-2 as it's a negative number.
Therefore, plugging x=8 in EC =6x, we get
EC = 6(8) = 48.
<h3>AC = AE + EC = 48+48 =96 units.</h3>You might be interested in
Answer:
Option A 50-page photo album holds 400 photographs.
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or
step 1
<em>Find the value of k</em>
For the point (3,24)
x=3,y=24
k=y/x
k=24/3=8
The equation is equal to
y=8x
step 2
<em>Verify each statement</em>
case A) 50-page photo album holds 400 photographs.
For x=50
substitute in the equation
y=8(50)=400 -----> is correct
case B) 80-page photo album holds 560 photographs.
For x=80
substitute in the equation
y=8(80)=640 -----> is not correct
case C) 100-page photo album holds 8,000 photographs.
For x=100
substitute in the equation
y=8(100)=800 -----> is not correct
case D) 900-page photo album holds 8,400 photographs.
For x=900
substitute in the equation
y=8(900)=7,200 -----> is not correct