Answer:
m∠J = 45° , m∠I = 45° and m∠M = 90°
And the ΔJIM is an isosceles right angled triangle.
Step-by-step explanation:
(a). In ΔJIM,
∠J = 2x + 15,
∠I = 5x - 30, and
∠M = 6x
Now, using angle sum property of a triangle that sum of all the angles in a triangle is 180°
⇒ ∠J + ∠I + ∠M = 180°
⇒ 2x + 15 + 5x - 30 + 6x = 180°
⇒ 13x -15 = 180°
⇒ 13x = 195
⇒ x = 15
Therefore, m∠J = 45° , ∠I = 45° and m ∠M = 90°
(b). Now, ΔJIM is a right angled triangle right angled at M.
Also, ∠J = ∠I = 45°
So, JM = IM ( because in a triangle sides opposite to equal angles are equal)
So, ΔJIM is an isosceles triangle because its two sides are equal.
Hence, ΔJIM is a right angled isosceles triangle right angled at M.
Hello,
(u*v)'=u'v+uv'
u=2x²+3 ==> u'=4x
v=sin 5x ==>v'=cos 5x *5
((2x²+3 sin (5x))'=4x* sin (5x) +(2x²+3)*cos (5x) * 5
The easiest way to answer this is to try all choices, plug
in values for the 1st term and 2nd term then check if the
answer matches with 5 and 2. (n = 1 and n = 2)
We know that n starts with 1 because that is our 1st
term, we do not have 0th term, therefore that leaves us with 2
choices.
Choice 1: an = 5 − 2(n − 1); all integers where n ≥ 1
n = 1
a1 = 5 – 2 (1 – 1) = 5 – 2 (0)
a1 = 5
n = 2
a2 = 5 – 2 (2 – 1) = 5 – 2 (1)
<span>a2 = 3 (FALSE!)</span>
Choice 2: an = 5 − 3(n − 1); all integers where n ≥ 1
n = 1
a1 = 5 – 3 (1 – 1) = 5 – 3 (0)
a1 = 5
n = 2
a2 = 5 – 3 (2 – 1) = 5 – 3 (1)
<span>a2 = 2 (TRUE)</span>
Therefore the correct answer is:
<span>an = 5 − 3(n − 1); all integers where n ≥ 1</span>
