Answer:
x = 35 degrees
Step-by-step explanation:
the little box on the left side of the ttriangle means that is a 90 degrees angle.
So you add 55 + 90 = 145
Then subtract 180 - 145
which gives you 35
Y=(x-h)^2+k where (h,k) is the vertex
So, equation of new parabola is:
y=(x+1)^2+7
14. 36x^2 - 16
4(9x^2 - 4) =
4(3x + 2)(3x - 2) <==
15. 3x^2 + 10x - 8
(3x - 2)(x + 4) <==
16. 5x^2 - 16x + 15 = 4x - 5
5x^2 - 16x - 4x + 15 + 5 = 0
5x^2 - 20x + 20 = 0
5(x^2 - 4x + 4)
5(x - 2)(x - 2)
x - 2 = 0....x = 2
Recall the formula for finding the area of a rectangle:
Area = Length × Width
Recall the formula for finding the perimeter of a rectangle:
Perimeter = 2 ( Length + Width )
Given in your problem:
Area = 40 sq. units
Perimeter = 26 units
Required to solve for:
Length (L) and width (W)
• First, substitute the given to the formula:
Area = Length x Width
40 = L × W ⇒ equation number 1
Perimeter = 2 ( Length + Width )
26 = 2 ( L + W ) ⇒ equation number 2
• Simplifying equation number 2,
13 = L + W
• Rearranging the equation,
L = 13 - W ⇒ equation 3
Substituting equation 3 from equation 1:
( equation 1 ) 40 = (L)(W)
( equation 3 ) L = 13 - W
40 = (13 - W) (W)
40 = 13W - W²
( regrouping ) W² - 13W + 40 = 0
( factoring ) (W - 8) (W - 5) = 0
W - 8 = 0 ; W - 5 = 0
W = 8 ; W = 5
Therefore, there are 2 possible values for the width of the rectangle. It can be 8 units or 5 units.
• Now to solve for the length of the rectangle, substitute the two values of width to equation 3.
(equation 3) L = 13 - W
for W = 8 ⇒ L = 13 - 8
L = 5 units
for W = 5 ⇒ L = 13 - 5
L = 8 units
1 multiplied by 0.50 or multiplied by any number between .05 and 0.75
