Which expression is equivalent to 2x^5 + 4x^4 - 5x^5 - (3x^4 - 8x^5)

Mathematics

1 answer:

Naddika [18.5K]3 years ago

6 0

One that could be close is Letter B?

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What is the order, from narrowest to widest graph, of the quadratic functions f (x) = -10x2, f (x) = 2x2, and f (x) = 0.5x2?

Varvara68 [4.7K]

The <em>correct answer</em> is:

f(x) = -10x², f(x) = 2x², and f(x) = 0.5x²

Explanation:

For a quadratic in standard form, f(x) = ax²+bx+c, the value of a describes the width and direction of the parabola. If a is positive, the parabola is open upward. If a is negative, the parabola is open downward.

If a < 1, a fraction or decimal, the graph is wider than the parent function f(x)=x². If a > 1, the graph is narrower than the parent function f(x)=x². The larger the value of a is (a > 1), the narrower the graph is. This makes the function with the decimal value of a the widest; the remaining graphs are in order of the value of a, least to greatest.

3 0

3 years ago

Read 2 more answers

Find the distance between the points with polar coordinates (4, π/3) and (8, 2π/3).

musickatia [10]

A suitable vector calculator can perform this arithmetic directly, as can many graphing or scientific calculators that are capable of handling complex numbers. Mine says
(8, 2π/3) - (4, π/3) = (4√3, 5π/6)
The distance is 4√3 ≈ 6.9282.

If you cannot use your calculator for this purpose, you can use the Law of Cosines. You have two sides of the triangle (4 and 8) and the angle between them (2π/3 - π/3), so you have all the information needed.
c² = a² + b² -2ab·cos(C)
c² = 4² + 8² - 2·4·8·cos(π/3)
c² = 16 + 64 - 32 = 48
c = √48 = 4√3

Or, you can simply recognize that the two vectors have the ratio 1:2 and the angle between them is 60°. That is, they are one leg and the hypotenuse of a 30°-60°-90° triangle, so the other leg is 4√3.