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3 years ago

Which of the following are ordered pairs for the equation y = -2x - 3?

Mathematics

1 answer:

Alexus [3.1K]3 years ago

5 0

Answer:

b. (0,-3) (1,-5) (-1,-1)

Step-by-step explanation:

we only have to replace the first part of the parenthesis by x and the second part by y, and see if equality is met

y = -2x - 3

(0,-3) (-1,-4) (-1,-5)

y = -2x - 3

-3 = -2(0) -3

-3 = -3

-4 = -2(-1) - 3

-4 = 2 -3

-4 = -1

WRONG OPTION

(0,-3) (1,-5) (-1,-1)

y = -2x - 3

-3 = -2(0) -3

-3 = -3

-5 = -2(1) - 3

-5 = -2 -3

-5 = -5

-1 = -2(-1) -3

-1 = 2 -3

-1 = -1

CORRECT OPTION

(0,-3) (1,4) (-1,-5)

y = -2x - 3

-3 = -2(0) -3

-3 = -3

4 = -2(1) -3

4 = -2 -3

4 = -5

WRONG OPTION

(0,-3) (1,-4) (-1,-5)

y = -2x - 3

-3 = -2(0) -3

-3 = -3

-4 = -2(1) -3

-4 = -2 -3

-4 = -2

WRONG OPTION

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Answer:

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Step-by-step explanation:

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3 years ago

The rate of change of the number of mountain lions N(t) in a population is directly proportional to 725 - N(t), where t is the t

wolverine [178]

Answer:

a) The implied differential equation is $\frac{dN}{725 - N} = kdt$

b) The general equation is $N = 725 - C e^{-kt}$

c) The particular equation is $N = 725 - 325 e^{-0.49t}$

d) The population when t = 5, N(5) = 697 = 700( to the nearest 50)

Step-by-step explanation:

The rate of change of N(t) can be written as dN/dt

According to the question, $\frac{dN}{dt} \alpha (725 - N(t))$

$\frac{dN}{dt} = k (725 - N)\\\frac{dN}{725 - N} = kdt$

Integrating both sides of the equation

$\int {\frac{1 }{725 - N}} \, dN = \int {k} \, dt\\- ln (725 - N) = kt + C\\ ln (725 - N) = -(kt + C)\\725 - N = e^{-(kt + C)} \\725 - N = e^{-kt} * e^{-C} \\725 - N = C e^{-kt}\\N = 725 - C e^{-kt}$

When t = 0, N = 400

$400 = 725 - C e^{-k*0}\\400 = 725 - C\\C = 725 - 400\\C = 325$

When t = 3, N = 650

$650 = 725 - (325 * e^{-3k})\\325 * e^{-3k} = 75\\e^{-3k} = 75/325\\e^{-3k} = 0.23\\-3k = ln 0.23\\-3k = -1.47\\k = 1.47/3\\k = 0.49$

The equation for the population becomes:

$N = 725 - 325 e^{-0.49t}$

At t = 5, the population becomes:

$N = 725 - 325 e^{-0.49*5}\\N = 725 - 325 e^{-2.45}\\N = 696.95\\N(5) = 697$

N(5) = 700 ( to the nearest 50)

6 0

3 years ago

Can someone help me with this

mash [69]

The center of the circle is (h,k) = (-2,-3)

The radius of the circle is r = 2

The standard form of equation of the circle is

${(x + 2)}^{2} + {(y + 3)}^{2} = 4$

<h3>How to find the center, radius and standrad form of the circle?</h3>

The general form of equation of the circle is

${(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}$

Here, (h,k) means centre of the circle.

r means radius of the circle.

given that coordinate points of centre of circle is (-2,-3).

Hence the (h,k) = (-2,-3)

<h3>How to find the radius of the circle?</h3>

Now to find the radius of the circle

The distance from a circle's centre to its circumference is its radius.

The distance from a circle's centre (-2,-3) to its circumference (0,-3) is its radius.

using the formula, distance between the two points to obtain radius.

$d = \sqrt{(x1 - x2) {}^{2} + {(y1 - y2)}^{2} } \\ r = \sqrt{ {( - 2 - 0)}^{2} + {( - 3 - ( - 3))}^{2} } \\ r = \sqrt{ {( - 2)}^{2} + {( - 3 + 3)}^{2} } \\ r = \sqrt{ {4}^{2} + 0 } \\ r = \sqrt{4} \\ r = 2$