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Anna [14]
3 years ago
5

Please help me with these two algebra questions. Image attached.

Mathematics
1 answer:
Vera_Pavlovna [14]3 years ago
7 0

1. when x⇒∞, y=∞ and when x⇒-∞, y=-∞

So, we have a odd degree polynomial (x³ or x^5 or even x^9).

The leading coefficient is negative its end behavior matches x³ which has a positive leading coefficient.

2. when x⇒∞, y=∞ and when x⇒-∞, y=∞

So, we have a even degree polynomial (x² or x^4 or even x^{100}).

And because it matches these parent functions listed above (they all have positive leading coefficients), the leading coefficient is again positive.

answers:

1. odd and positive

2. even and positive

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~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{+2}x\stackrel{\stackrel{c}{\downarrow }}{+4}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (2) \pm \sqrt { (2)^2 -4(3)(4)}}{2(3)}\implies x=\cfrac{-2\pm \sqrt{4-48}}{6}

x=\cfrac{-2\pm \sqrt{-44}}{6}\implies x=\cfrac{-2\pm \sqrt{(-1)(2^2)(11)}}{6}\implies x=\cfrac{-2\pm 2~i\sqrt{11}}{6} \\\\\\ x=\cfrac{2(-1\pm i\sqrt{11})}{6}\implies x=\cfrac{-1\pm i \sqrt{11}}{3}

mind you that it has two complex roots, or imaginary values.

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2 years ago
18. The Tennis for Champs company is looking into new ways to package tennis balls. The packaging engineer at the company is exp
9966 [12]

Answer:

Amount of empty space in the cylinder = 395.64 cm³

Step-by-step explanation:

Since the cylinder contains 3 tennis balls each measuring 6 cm in diameter, we can say that the diameter of the cylinder is 6 cm because the balls are on top of each other. Since we have 18 cm is the height of the cylinder,then;

Formula for volume of a cylinder is;

V = πr²h

We are to use π = 3.14

Thus, V_cylinder = 3.14 × (6/2)² × 18

V_cylinder = 508.68 cm³

Volume of a tennis ball is;

V_tennis ball = (4/3)πr³

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V_tennis ball = 37.68 cm³

Thus, volume of 3 tennis balls = 3 × 37.68 = 113.04 cm³

Amount of empty space in the cylinder = V_cylinder - V_3 tennnis ball = 508.68 - 113.04 = 395.64 cm³

8 0
2 years ago
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Sergio [31]

Answer:

x=-3

y=2

Step-by-step explanation:

To solve this problem you can use the elimination method:

- Multiply the second equation by -6:

(-6)5x+y=-13\\-30x-6y=78

- Add both equations:

6x+6y=-6\\-30x-6y=78\\-------\\-24x=72\\x=-3

- Substitute the value of x into one of the original equations and solve for y:

6(-3)+6y=-6\\-18+6y=-6\\6y=12\\y=2

8 0
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Step-by-step explanation:

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HURRY!!
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