By definition, we have to:
In plane geometry, a rectangle is a parallelogram whose four sides are at right angles to each other. Opposite sides have the same length.
There is a proof that a quadrilateral is a rectangle:
1) Its parallel sides are the same.
2) Its two diagonals are the same, and they bisect each other at the common midpoint
3) Any rectangle can be inscribed in a circle, two of whose diameters coincide with the diagonals of the rectangle.
4) If all the angles of a quadrilateral are right angles, then it is a rectangle
Answer:
2(x+6)(x-3)
Step-by-step explanation:
Factor the GCF out of the trinomial on the left side of the equation.
Greatest common factor of 2, 6, 18 is 2
so GCF is 2
divide each term when we take out GCF 2
so 
now factor the trinomial
product is -18 and sum is +3
6 times -3 is -18 and 6-3=3
Answer:
D)2
Step-by-step explanation:
ƒ(x) = x²/4 - 5; 3 ≤ x ≤ 5
Calculate the values of f(3) and f(5)
f(3) = 3²/4 - 5 = 9/4 - 5 = -2.75
f(5) = 5²/4 - 6 = 25/4 - 5 = 1.25
Calculate the average rate of change
Rate of change = (y₂ - y₁)/(x₂-x₁) = [1.25 -(-2.75)]/(5 - 3) = 4.00/2
= 2.00
The average rate of change is 2.00.
In the figure below, the red curve represents the function ƒ(x), while the black dashed line represents the average rate of change over the interval (3, 5).
The value of ƒ(x) increases by two units for every unit that x increases.
Answer:
A' = (5,7)
Step-by-step explanation:
So, we start with the original point A at (3,1), that means x = 3 and y = 1.
We move it 2 units to the right... so we're moving along the X-axis... and we're moving to the right.. so we're increasing the value of x. That means starting with x = 3, we go 2 more units... we then get to x = 5.
In the same way, we move 6 units up... so we move along the Y-axis. We go up, so we also increase the value of y. Starting with y = 1, we move up by 6 units... so we are now at y = 7.
A' point is then at (5,7).
Answer:
<h3>D. -1, 1</h3>
Step-by-step explanation:
If x-1 is a factor of x⁴ + 2x³ - 2x - 1, then x-1 =0 is a factor
if x-1 = 0
x = 1
To get other factors we will divide the polynomial by x-1
Find the division in the attachment
x⁴ + 2x³ - 2x - 1,/x-1 = x³ +3x²+ 3x + 1,
let x = -1 be a factor of the resulting expression
f(-1) = (-1)³ +3(-1)²+ 3(-1) + 1
f(-1) = -1 +3(1)-3 + 1
f(-1) =-1+1-3+3
f(-1) = 0
Since f(-1) =0, hence x+1 is a factor of the resulting polynomial'
Dividing x³ +3x²+ 3x + 1, by x+1 to reduce the power of the polynomial
x³ +3x²+ 3x + 1/x+1 = x²+2x+1
Factorizing x²+2x+1
= x²+2x+1
=x²+x+x+1
= x(x+1)+1(x+1)
= (x+1)(x+1)
if the function is equal to zero
x+1 = 0 and x+1 = 0
x = -1 twice
Hence the solutions to the polynomial are 1 and -1(three times)
