Factorize 5n - mp - 5n + pn in a an algebra expression
1 answer:
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Answer:
2/3
Step-by-step explanation:
Let x be the number of books that Millicent has. So the number of books that Harold has is x/2. And the number of book that Harold is bringing to the new home is (x/2)/3 = x/6.
The home has enough room for another half of Millicent's books, which is x/2. So the total books capacity of the new home is
Since x is also the number of books in Millicent's old library capacity, we can conclude that the fraction of Millicent's old library capacity to the new home's library capacity is 2/3, or 2 thirds
Answer:
Part 4)
Part 5)
Part 6)
Step-by-step explanation:
Part 4) Find ER
we know that
In the right triangle ERF
Applying the Pythagorean Theorem
substitute the given values
solve for ER
Part 5) Find DF
we know that
In the right triangle DRF
Applying the Pythagorean Theorem
substitute the given values
simplify
Part 6) Find DE
we know that
----> by segment addition postulate
we have
substitute
Answer:
Compare the given equation of the circle (x - 1)² + (y -2)² = 2²
with standard form of circle: (x - h)² + (y - k)² = r²
Here, (h, k) is the center of the circle
and r is the radius of the circle.
Thus, The center of the circle is: (1, 2)
Also, for finding the point of intersections of (x - 1)² + (y -2)² = 2² and y = 2x + 2,
Substitute the value of y from equation of line in the equation of circle.
(x - 1)² + (2x + 2 - 2)² = 2²
⇒ (x - 1)² + (2x)² = 2²
⇒ x² + 1 - 2x + 4x² = 4
⇒ 5x² - 2x - 3 = 0
Applying Middle term splitting method
5x² - 5x + 3x - 3 = 0
⇒ 5x(x - 1) + 3(x - 1) = 0
⇒ (5x + 3)(x - 1) = 0
⇒ x = and x = 1
Thus, we get coordinates: and (1, 4)