Answer:
n=178/19
Step-by-step explanation:
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Answer:
The dimensions of the rectangle are length = 7cm and width = 6cm.
Step-by-step explanation:
In order to solve for the dimensions, you will need to set up two equations in order to solve for the missing variable. Given the information that the length is 5 cm less then twice it's width, using 'L' for length and 'w' for width we get the following equation: L = 2w - 5. Perimeter is the sum of all the sides, or in the case of a rectangle P = 2w + 2L. We can then use our expression for 'L' in our perimeter formula: 26 = 2w + 2(2w - 5). First, using the distributive property we get: 26 = 2w + 4w - 10. Next, we combine like terms: 26 = 6w - 10. Then, we use inverse operations to isolate the variable: 26 + 10 = 6w - 10 + 10 to get 36 = 6w, divide both sides by 6 to get w = 6. Lastly, plug in the value of 'w' to 'L': L = 2(6) - 5 or L = 7.
Using the midpoint formula, the coordinates of the intersection of the diagonals of the parallelogram is: (1, 2.5).
<h3>What are Diagonals of a Parallelogram?</h3>
The diagonals of a parallelogram bisect each other, therefore, the coordinates of their intersection can be determined using the midpoint formula, which is: .
A diagonal is XZ.
X(2, 5) = (x1, y1)
Z(0, 0) = (x2, y2)
Plug in the values
= (1, 2.5).
Learn more about the diagonals of a parallelogram on:
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Answer:
x³ - 8x² - 11x + 148
Step-by-step explanation:
Given that x = 6 + i is a root then x = 6 - i is also a root
Complex roots occur as conjugate pairs.
The factors are therefore (x - (6 + i)) and(x - (6 - i))
Given x = - 4 is a root then (x + 4) is a factor
The polynomial is the product of the factors, that is
p(x) = (x + 4)(x - (6 + i))(x - (6 - i))
= (x + 4)(x - 6 - i)(x - 6 + i)
= (x + 4)((x - 6)² - i²)
= (x + 4)(x² - 12x + 36 + 1)
= (x + 4)(x² - 12x + 37) ← distribute
= x³ + 4x² - 12x² - 48x + 37x + 148
= x³ - 8x² - 11x + 148