A rectangle measures 2 2 /3 inches by 1 5/ 9 inches. What is its area?
1 answer:
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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.
For this case we propose a system of equations. We have to:
x: Let the variable that represents the number of dimes
y: Let the variable that represents the number of quaters
We know that:
One dime equals 10 cents, $0.10
A quater equals 0.25 cents, $0.25
According to the statement we have:
We multiply the first equation by -0.10:
We have the following equivalent system:
We add the equations:
Approximately 3 quater coins
And two dimes
Answer:
3 quater
2 dimes
Answer:
see explanation
Step-by-step explanation:
sinΘ is only valid for values in the interval
- 1 ≤ Θ ≤ 1
sinΘ = is outwith this interval and is not valid