Answer: 5cm and 8cm
Step-by-step explanation:
Perimeter of a rectangle = 2l + 2w
Area of a rectangle = l × w
where l = length
w = width
Therefore,
2l + 2w = 26 ...... i
l × w = 40 ...... ii
We can reduce equation i to l + w = 13.
l + w = 13 ....... i
l × w = 40 ....... ii
From i, l = 13 - w ...... iii
Put the value of l into equation ii
l × w = 40
(13 - w) × w = 40
13w - w² = 40
13w - w² - 40 = 0
w² - 13w + 40 = 0
w² -8w -5w +40 = 0
w(w - 8) -5(w - 8) = 0
(w - 5) = 0 and (w - 8) = 0
w = 0 +5 and w = 0 + 8
w = 5
l = 8
The dimensions are 5cm and 8cm
16x^2 − 8x + 1 = 0
<span>Part A:
</span>b^2 - 4ac for ax^2 + bx + c
16x^2 − 8x + 1 = 0
so in this case,
a = 16, b = -8, c = 1
b^2 - 4ac
=(-8)^2 - (4 * 16* 1)
= 64 - 64
= 0
because it's equal 0, answer is one solution
Part B:
<span>4x^2 − 8x − 45 = 0
</span><span>solve the equation by factoring </span>
= (2x - 9)(2x + 5)
set (2x - 9)(2x + 5) equal to 0 to solve for x
so
(2x - 9)(2x + 5) = 0
2x - 9 = 0
x = 9/2
x = 4.5
2x + 5 = 0
x = -5/2
x = -2.5
answer
x = -2.5 or x = 4.5
Hope it helps
