Answer:
3
Step-by-step explanation:
these are 2 similar triangles (all 3 pairs of corresponding angles are equal in their pair, and the lengths of corresponding sides have the same ratio in every pair of corresponding sides and other lengths).
and they are also right-angled triangles.
so, what else do we know about them ?
PQ = 18
RT = 6
ST = QT + 9
therefore
QT = ST - 9
and
QR = QT + RT = ST - 9 + 6 = ST - 3
due to the principles of cumulative triangles
PQ/ST = QR/RT = 18/ST = (ST - 3)/6
108/ST = (ST - 3)
108 = (ST - 3)ST = ST² - 3ST
ST² - 3ST - 108 = 0
we can the write
x² - 3x - 108 = 0
and the solution for such a squared equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = -3
c = -108
x = (3 ± sqrt(9 - 4×1×-108))/2 = (3 ± sqrt(441))/2 =
= (3 ± 21)/2
x1 = (3+21)/2 = 24/2 = 12
x2 = (3-21)/2 = -18/2 = -9
a negative solution for real lengths is not valid, so we know
x = ST = 12
so,
QR = ST - 3 = 12 - 3 = 9
and then
QT = QR - RT = 9 - 6 = 3
Answer:
i thought the answer was -80
〒▽〒
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
We are finding the discriminant of the function
It needs to be written in the form ax^2 +bx+c =0
2x^2 +3x = -1
Add 1 to each side
2x^2 +3x+1 = -1+1
2x^2 +3x+1 = -0
b^2 -4ac
a=2 b=3 and c = 1
3^2 - 4(2)(1)
9 - 8
1
Step-by-step explanation:
(x^3 - 9x) divided by (x^3 + x^2 - 6x)
= x(x^2 - 9) divided by x(x^2 + x - 6)
= x(x + 3)(x - 3) divided by x(x - 2)(x + 3)
= (x - 3)/(x - 2).
Answer:
The answer is "
"
Step-by-step explanation:
Given:
