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3 years ago

Use the real zeros to factor f x^4 plus 10^3 minus 20x^2 minus 90x plus 99

Mathematics

1 answer:

Furkat [3]3 years ago

7 0

Answer:

f(x) = (x + 11) (x + 3) (x − 1) (x − 3)

Step-by-step explanation:

f(x) = x⁴ + 10x³ − 20x² − 90x + 99

f(x) is a fourth order polynomial, so it has 4 roots. Use rational root theorem to find possible rational roots.

±99, ±11, ±9, ±3, ±1

By trial and error, the zeros are -11, -3, 1, and 3.

f(x) = (x + 11) (x + 3) (x − 1) (x − 3)

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The graph of h(x) is shown. Graph of h of x that begins in quadrant two and decreases rapidly following the vertical line which

fgiga [73]

Answer:

x-intercept

The point at which the curve crosses the x-axis, so when y = 0.

From inspection of the graph, the curve appears to cross the x-axis when x = -4, so the x-intercept is (-4, 0)

y-intercept

The point at which the curve crosses the y-axis, so when x = 0.

From inspection of the graph, the curve appears to cross the y-axis when y = -1, so the y-intercept is (0, -1)

Asymptote

A line which the curve gets infinitely close to, but never touches.

From inspection of the graph, the curve appears to get infinitely close to but never touches the vertical line at x = -5, so the vertical asymptote is x = -5

(Please note: we cannot be sure that there is a horizontal asymptote at y = -2 without knowing the equation of the graph, or seeing a larger portion of the graph).

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2 years ago

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aleksley [76]

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3 years ago

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What is the coefficient of the y-term in the expression 4x 5xy–2y

Bad White [126]

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4 years ago

Two people start from the same point. One walks east at 4 mi/h and the other walks northeast at 8 mi/h. How fast is the distance

kvasek [131]

Answer:

5.89 mi/h

Step-by-step explanation:

This problem can be solved by using different methods. I will use vectors since it's the simplest way in which we can solve it. This can be solved by using related rates of change though.

First, we start by drawing a diagram with the velocity vectors.

A= velocity of the first person

B= velocity of the second person

C= velocity in which they are moving away from each other.

Since there is no acceleration in the problem, we can suppose we are talking about constant speeds, so the velocity at which they are moving away from each other will always remain constant. (It doesn't matter what time it is, the velocity will always be the same)

Having said this we can solve this problem by using the components, by using law of cosines or graphically. I will use law of cosines. The idea is to find the length of side c.

Law of cosines:

$C^{2}=A^{2}+B^{2}-2ABcos \gamma$