Answer:
616/22 = 28
784/28 = 28
Step-by-step explanation:
The answer would be (x+1)(x+3)
Let x=ab=ac, and y=bc, and z=ad.
Since the perimeter of the triangle abc is 36, you have:
Perimeter of abc = 36
ab + ac + bc = 36
x + x + y = 36
(eq. 1) 2x + y = 36
The triangle is isosceles (it has two sides with equal length: ab and ac). The line perpendicular to the third side (bc) from the opposite vertex (a), divides that third side into two equal halves: the point d is the middle point of bc. This is a property of isosceles triangles, which is easily shown by similarity.
Hence, we have that bd = dc = bc/2 = y/2 (remember we called bc = y).
The perimeter of the triangle abd is 30:
Permiter of abd = 30
ab + bd + ad = 30
x + y/2 + z =30
(eq. 2) 2x + y + 2z = 60
So, we have two equations on x, y and z:
(eq.1) 2x + y = 36
(eq.2) 2x + y + 2z = 60
Substitute 2x + y by 36 from (eq.1) in (eq.2):
(eq.2') 36 + 2z = 60
And solve for z:
36 + 2z = 60 => 2z = 60 - 36 => 2z = 24 => z = 12
The measure of ad is 12.
If you prefer a less algebraic reasoning:
- The perimeter of abd is half the perimeter of abc plus the length of ad (since you have "cut" the triangle abc in two halves to obtain the triangle abd).
- Then, ad is the difference between the perimeter of abd and half the perimeter of abc:
ad = 30 - (36/2) = 30 - 18 = 12
Answer:
(4) 0
Step-by-step explanation:
<u>Given:</u>
- cos²27°×cos²34°×...×cos²167 = ?
<u>Looking at the angles measures, they form series of: </u>
This is AP with the first term of 27 and common difference of 7
<u>We can see one of the terms of this AP is 90</u>
Since cos 90° = 0 ⇒ cos²90° = 0 and therefore given series equals to zero as one of the terms of multiplication is zero.
<u>So correct answer choice is</u> Option 4) 0
79% = 0.79= 79/100
(not sure if this is what you meant?)
