$\frac{9-r^2}{r^2-2r-3}\cdot\frac{4-4r^2}{r^2+4r+3}=\frac {4\left(r-1\right)}{r+1}$9− r 2 r 2−2 r −3 ·4−4 r 2 r 2+4 r +3 =4( r −1) r +1. Steps.
Answer/Step-by-step explanation:
5. ✔️Exterior angle = angle outside the triangle = W
✔️Remote interior angle of the triangle to the exterior angle W = opposite angles to angle W which are X and Y
✔️m<X + m<Y = m<W (exterior angle theorem of a triangle)
✔️m<W + m<Z = 180° (linear pair/angles on a straight line)
6. m<6 = 115°
m<5 = 120°
✔️m<2 = 180° - m<5° (linear pair/angles on a straight line)
m<2 = 180° - 120°
m<2 = 60°
✔️m<3 = 180° - m<6° (linear pair/angles on a straight line)
m<3 = 180° - 115°
m<3 = 65°
✔️m<1 = 180° - (m<2 + m<3) (sum of triangle theorem)
m<1 = 180° - (60° + 65°)
m<1 = 55°
✔️m<4 = 180° - m<1 (linear pair/angles on a straight line)
m<4 = 180° - 55°
m<4 = 125°
The value of c that makes the given trinomial a perfect square is 9.
The given expression is:
<h3>What is a perfect square trinomial? </h3>
A polynomial is called a perfect square trinomial if it can be written in terms of the square of another polynomial.
Let us write the given expression in (a+b)² form
.....(1)
We know ......(2)
To make (1) like we need to put c=9
Hence, the value of c that makes the given trinomial a perfect square is 9.
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Answer:
t = 1.5 seconds
Step-by-step explanation:
Given that d = −4t^2 + 2t + 6,
where d = distance above the water and
t = seconds.
Let assume that it's a perfect parabola
At the symmetry
t = -b/2a
Where a = -4, b = 2
t = -2/2(-4)
t = 1/4
To determine how long it will take a diver to reach the water’s surface
d = −4t^2 + 2t + 6
At water surface d =0
4t^2 - 2t - 6 = 0
Factorizing the above equation leads to
4t^2 + 4t - 6t - 6 = 0
4t(t + 1) -6(t + 1) = 0
4t - 6 =0
4t = 6
t = 6/4= 3/2 = 1.5 seconds
Since t can't be negative so we ignore the second factor.