<u>Solution-</u>
Given that,
In the parallelogram PQRS has PQ=RS=8 cm and diagonal QS= 10 cm.
Then considering ΔPQT and ΔSTF,
1- ∠FTS ≅ ∠PTQ ( ∵ These two are vertical angles)
2- ∠TFS ≅ ∠TPQ ( ∵ These two are alternate interior angles)
3- ∠TSF ≅ ∠TQP ( ∵ These two are also alternate interior angles)
<em>If the corresponding angles of two triangles are congruent, then they are said to be similar and the corresponding sides are in proportion.</em>
∴ ΔFTS ∼ ΔPTQ, so corresponding side lengths are in proportion.
As QS = TQ + TS = 10 (given)
If TS is x, then TQ will be 10-x. Then putting these values in the equation
∴ So TS = 3.85 cm and TQ is 10-3.85 = 6.15 cm
We know that
if the y terms is squared so it opens left or right
Is a Horizontal Parabola, the equation is of the form
(y-k)²=4(p)(x-h)
vertex is (h,k)
and
p is distance from focus to vertex, also distance from vertex to directrix
if p>0, then it opens to the right and directrix is to the left of vertex
if p<0, then it opens to the left and directrix is to the right of vertex
so
(y-1)²=4(4)(x-(-3))
vertex is (-3,1)
4>0 so directrix is to left of vertex
left is in x direction
-3-4=-7
directrix is x=-7
the answer isx=-7
see the attached figure
The LCM is the lowest number that is a multiple of all three numbers.
First, list the multiples of each number
8: 8, 16, 24, 32,40 48, 56, 64, 72, 80, 88, 96, 104, 112, 120
10: 10, 20, 30 40, 50, 60, 70, 80, 90, 100, 110, 120
12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
The LCM is 120 because there is no lower number that is a multiple of all three numbers.
Hope this helped!
Answer:
2,8
Step-by-step explanation:
