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2 years ago

Divide using synthetic division (3x^2 + 4x - 5) +(x+4)

Mathematics

1 answer:

Mashcka [7]2 years ago

5 0

Answer:

Factor the numerator and denominator and cancel the common factors.

Step-by-step explanation:

3x² + 5x - 1

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Pleasantburg has a population growth model of P(t)=at2+bt+P0 where P0 is the initial population. Suppose that the future populat

yulyashka [42]

Answer:

The population will reach 34,200 in February of 2146.

Step-by-step explanation:

Population in t years after 2012 is given by:

$P(t) = 0.8t^{2} + 6t + 19000$

In what month and year will the population reach 34,200?

We have to find t for which P(t) = 34200. So

$P(t) = 0.8t^{2} + 6t + 19000$

$0.8t^{2} + 6t + 19000 = 34200$

$0.8t^{2} + 6t - 15200 = 0$

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$0.8t^{2} + 6t - 15200 = 0$

So $a = 0.8, b = 6, c = -15200$

Then

$\bigtriangleup = 6^{2} - 4*0.8*(-15100) = 48356$

$t_{1} = \frac{-6 + \sqrt{48356}}{2*0.8} = 134.14$

$t_{2} = \frac{-6 - \sqrt{48356}}{2*0.8} = -141.64$

We only take the positive value.

134 years after 2012.

.14 of an year is 0.14*365 = 51.1. The 51st day of a year happens in February.

So the population will reach 34,200 in February of 2146.

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2 years ago

4. In the accompanying diagram, AABC – ADEF, DE = x + 2, DF = x+8, AB = x-3, and AC = x. Determine, algebraically, the value of

alexira [117]

Danggg that is sooo longgg I feel bad for you

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2 years ago

A sphere and a cylinder have the same radius and height. The volume of the cylinder have the same height and radius. The volume

USPshnik [31]

Step-by-step explanation:

radius of sphere, rs

radius of cylinder, rc

height of cylinder, h

given: h = rs = rc =r..eq1

volume of cylinder, vc = 27pi ft...eq2

volume of cylinder, vc = pi × rc^2 × h...eq3

volume of sphere, vs = 4/3(pi×rs^3)...eq4

subst for h & rs from eqn 1 in eqn 3...

vc = pi x r^2 x r= pi x r^3...eqn 5

subst for vc from eqn 2 in eqn 5...

=> 27 pi ft = pi x r^3

=> 27 = r^3

=> r = 3ft...eqn 6

subst for rs from eqn 1 in eqn 4

vs = 4/3 (pi x r^3)...eqn7

subst for pi x r^3 from eqn 5 in eqn 7

vs = 4/3 vc = 4/3 (27pi ft) = 36 pi ft

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3 years ago

Polygon Y is a scaled copy of Polygon X using a scale factor of 1/3. Polygon Y’s area isn’t what fraction of Polygon X’s area?

loris [4]

Answer:

1/9th.

Step-by-step explanation:

Because the area is measured in units squared, then you have to square 1/3 which is 19th.

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2 years ago

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