Answer:
The side length of the original square was 6 inches
Step-by-step explanation:
we know that
The area of a square is
where
b is the length side of the square
Let
x ---> the length of the original square
The area of the original square is
The length of the smaller square is
The area of the smaller square is
The area of the smaller square is 1/4 the area of the original square
so
solve for x
Multiply by 4 both sides
Solve the quadratic equation by graphing
using a graphing tool
x=2, x=6
see the attached figure
The solution is x=6 in
Remember that the solution must be greater than 3 inches (because Stacey cuts 3 inches off of the length of the square and 3 inches off of the width)
therefore
The side length of the original square was 6 inches
Each square unit is one unit. Each triangle is half a unit.
Shape 1 has 6 units and 4 half units.
6 + 4/2 =
6 + 2 =8
Shape 1 has 8 units.
Shape 2 is almost like shape 1 but it has an extra bit which would make it larger than shape 1.
So shape 2 is larger than shape 1.
Answer:
<u>CF = 7</u>
Step-by-step explanation:
Given: Δ ABC
Altitudes ⇒ AD = 12 , BE = 14 and CF = ?
The area of the triangle = 0.5 AD * BC ⇒ (1)
OR area = 0.5 BE * AC ⇒ (2)
OR area = 0.5 CF * AB ⇒ (3)
By equating (1) and (3)
∴ 0.5 CF * AB = 0.5 AD * BC
∴ 
⇒ (4)
By equating (1) and (2)
0.5 BE * AC = 0.5 AD * BC
∴ 
(5)
We should know that about the relation between the sides of the triangle:
The sum of two sides will be greater than the third side
So, AB < BC + AC ⇒ divide both sides by BC
∴ 
By substitution from (5) with AC/BC
∴ 
∴ 
∴ 
⇒ (6)
By substitution from (6) at (4)
∴ CF > 12 * 7/13
CF > 6.46
But CF is a positive integer
<u>∴ CF = 7</u>
(6,-3)(-4,-9)
slope(m) = (-9 -(- 3) / (-4 - 6) = (-9 + 3) / -10 = -6/-10 = 3/5
y - y1 = m(x - x1)
slope(m) = 3/5
(6,-3)....x1 = 6 and y1 = -3
now we sub
y - (-3) = 3/5(x - 6) =
y + 3 = 3/5(x - 6) <==
