X=5 if that's what you were asking for
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:
Ok! When given points, to find the slope, you would use this equation: y2-y1/x2-x1. Let me demonstrate. In this set to find the slope with the coordinates (10,8) and (14,20), the y2 value is 20, and the y1 value is 8, and the x2 value is 14, and the y1 value is 10. So, your equation would look like this: (20-8)/(14-10), which simplifies to 12/4, or 3! So the slope is three, and that's how you do that when using an equation. OR, you could graph them, but that isn't too reliable so I do not recommend trying it, since you may not create the right slope.
Answer:
Rule: If working with an inequality and you either mult. or div. by a negative number, you must reverse the direction of the inequality symbol.
Step-by-step explanation:
Your job here is to simplify 9t-4>32, in which the variable (t) is already positive. Here you do NOT switch signs or reverse the direction of the inequality symbol. Adding 4 to both sides, we get 9t > 36, or t > 4.
If, however, you had -9t-4>32 to work with, the situation would be different because t in this inequality is negative. Adding 4 to both sides results in:
-9t > 36. To solve for t, we must divide both sides by -9 AND reverse the direction of the inequality symbol:
t < -4.
Rule: If working with an inequality and you either mult. or div. by a negative number, you must reverse the direction of the inequality symbol.
Answer:
B
Step-by-step explanation:
Because all of the other ones are decimals and integers are WHOLE number positive or negative, and B is equal to -5
Hope This Helps
