Richard, Henry and Gavin share some sweets in the ratio 3:3:5. Richard gets 15 sweets. How many more sweets does Gavin get over
2 answers:
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Answer:
Step-by-step explanation:
This problem utilizes the Distributive Property, which states
that a(x + y) = ax + ay.
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Answer:
Step-by-step explanation:
Given equation is,
x² + (p + 1)x = 5 - 2p
x² + (p + 1)x - (5 - 2p) = 0
x² + (p + 1)x + (2p - 5) = 0
Properties for the roots of a quadratic equation,
1). Quadratic equation will have two real roots, discriminant will be greater than zero. [(b² - 4ac) > 0]
2). If the equation has exactly one root, discriminant will be zero [(b² - 4ac) = 0]
3). If equation has imaginary roots, discriminant will be less than zero [(b² - 4ac) < 0].
Discriminant of the given equation =
For real roots,
p² + 2p + 1 - 8p + 20 > 0
p² - 6p + 21 > 0
For all real values of 'p', given equation will be greater than zero.
Answer:
A = 5x² + 6x + 1
Step-by-step explanation:
The area (A) of a trapezoid is calculated as
A = h (a + b)
where h is the height and a, b the parallel bases, thus
A = (x + 1)(6x - 5 + 4x + 7)
= (10x + 2)(x + 1)
= (5x + 1)(x + 1) ← distribute using FOIL
= 5x² + 6x + 1