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
Hello there I hope you are having a great day :)
Your Question, -4(2x + 4) > 8x + 64 Solve for X
1) Expand -8x-16>8x+64
2) Add 16 to both sides -8x-16+16>8x+64+16
3) Simplify -8x>8x+80
4) Subtract 8x from both sides -8x-8x>8x+80-8x
5) Simplify -16x>80
6) Multiply both sides -1 (Reverse the inequality) (-16x) (-1) >80 (-1)
7) Simplify 16x<-80
8) divide both sides by 16 16x/16 < -80/16
9) Simplify x < -5
This should be your answer x < -5
Hopefully that helps you :)
Answer:
x=-6
Step-by-step explanation:
Let x be the number
3x = x^2 -54
Subtract 3x
3x-3x = x^2 -3x-54
0 = x^2 -3x-54
Factor
What 2 numbers multiply to -54 and add to -3
-9*6 = -54
-9+6 = -3
0=(x-9) (x+6)
Using the zero product property
x-9=0 x+6=0
x=9 x=-6
The questions asks for the negative solution
x=-6
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Answer:
for a single pizza 1/10 a cup
for 12 pizzas 1 1/5 a cup
you can make 56 pizzas with 5 2/3 cups.
Step-by-step explanation:
for 5 pizzas you need 1/2 cup of flour, so to find out how much you'll need for a single pizza you'll need to divide it with 5. 1/2÷5=1/10
for a dozen pizzas you'll need to multiply that with 12. 1/10x12=12/10=1 1/5
Then to find out how many can we make with 5 2/3 cups we'll divide it with that 1/10
56/10÷1/10= 56 pizzas
