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2 years ago

P(x) = -2x – 2; Find p(-3)

Mathematics

2 answers:

irinina [24]2 years ago

5 0

P(-3)= -2(-3) -2
p(-3)= 6-2
p(-3)= 4

svetlana [45]2 years ago

4 0

The answer is p(3)=4

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What is 412,639 rounded to the nearest thousand

MariettaO [177]

Answer:

413,000

Step-by-step explanation:

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3 years ago

How can I calculate the angle of elevation from point A to B?

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If I remember correctly I’m pretty sure you need to subtract

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3 years ago

Each week, Alfonso earns $85 for every shift he works at the theater and $15 for every dog-walking job. He uses the expression 8

xeze [42]

The coefficients are 15 and 85.
the variables are x and y.

85 represents 85 dollars for each x, which is the number of shifts.
15 represents 15 dollars for each y, which is the number of dog walking jobs.

7 0

3 years ago

The graph of the quadratic function y=-x^2-2x+3 is shown below

Karolina [17]

Answer:

The axis of symmetry is at $x=-1$

The graph has an x-intercept at $(1,0)$

The graph has a vertex at $(-1,4)$

Step-by-step explanation:

we have

$y=-x^{2}-2x+3$

Statements

case 1) The graph has root at $3$ and $1$

The statement is False

Because, the roots of the quadratic equation are the values of x when the value of y is equal to zero (x-intercepts)

Observing the graph, the roots are at $-3$ and $1$

case 2) The axis of symmetry is at $x=-1$

The statement is True

Observing the graph, the vertex is the point $(-1,4)$

The axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex

the equation of the axis of symmetry is $x=-1$

case 3) The graph has an x-intercept at $(1,0)$

The statement is True

see procedure case 1)

case 4) The graph has an y-intercept at $(-3,0)$

The statement is False

Because, the y-intercept is the value of y when the value of x is equal to zero

Observing the graph, the y-intercept is the point $(0,3)$

case 5) The graph has a relative minimum at $(-1,4)$

The statement is False

Because, is a vertical parabola open downward, therefore the vertex is a maximum

The point $(-1,4)$ represent the vertex of the parabola, so is a maximum

case 6) The graph has a vertex at $(-1,4)$

The statement is True

see the procedure case 5)

see the attached figure to better understand the problem

6 0

3 years ago

Read 2 more answers

A. Do some research and find a city that has experienced population growth.

horrorfan [7]

A. The city we will use is Orlando, Florida, and we are going to examine its population growth from 2000 to 2010. According to the census the population of Orlando was 192,157 in 2000 and 238,300 in 2010. To examine this population growth period, we will use the standard population growth equation $N_{t} =N _{0}e^{rt}$
where:
$N(t)$ is the population after $t$ years
$N_{0}$ is the initial population
$t$ is the time in years
$r$ is the growth rate in decimal form
$e$ is the Euler's constant
We now for our investigation that $N(t)=238300$ , $N_{0} =192157$ , and $t=10$ ; lets replace those values in our equation to find $r$ :
$238300=192157e^{10r}$
$e^{10r} = \frac{238300}{192157}$
$ln(e^{10r} )=ln( \frac{238300}{192157} )$
$r= \frac{ln( \frac{238300}{192157}) }{10}$
$r=0.022$
Now lets multiply $r$ by 100% to obtain our growth rate as a percentage:
$(0.022)(100)$ =2.2%
We just show that Orlando's population has been growing at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

B. Here we will examine the population decline of Detroit, Michigan over a period of ten years: 2000 to 2010.
Population in 2000: 951,307
Population in 2010: 713,777
We know from our investigation that $N(t)=713777$ , $N_{0} =951307$ , and $t=10$ . Just like before, lets replace those values into our equation to find $r$ :
$713777=951307e^{10r}$
$e^{10r} = \frac{713777}{951307}$
$ln(e^{10r} )=ln( \frac{713777}{951307} )$
$r= \frac{ln( \frac{713777}{951307}) }{10}$
$r=-0.029$
$(-0.029)(100)$ = -2.9%.
We just show that Detroit's population has been declining at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

C. Final equation from point A: $N(t)=192157e^{0.022t}$ .
Final equation from point B: $N(t)=951307e^{-0.029t}$
Similarities: Both have an initial population and use the same Euler's constant.
Differences: In the equation from point A the exponent is positive, which means that the function is growing; whereas, in equation from point B the exponent is negative, which means that the functions is decaying.

D. To find the year in which the population of Orlando will exceed the population of Detroit, we are going equate both equations $N(t)=192157e^{0.022t}$ and $N(t)=951307e^{-0.029t}$ and solve for t:
$192157e^{0.022t} =951307e^{-0.029t}$
$\frac{192157e^{0.022t} }{951307e^{-0.029t} } =1$
$e^{0.051t} = \frac{951307}{192157}$
$ln(e^{0.051t})=ln( \frac{951307}{192157})$
$t= \frac{ln( \frac{951307}{192157}) }{0.051}$
$t=31.36$
We can conclude that if Orlando's population keeps growing at the same rate and Detroit's keeps declining at the same rate, after 31.36 years in May of 2031 Orlando's population will surpass Detroit's population.

E. Since we know that the population of Detroit as 2000 is 951307, twice that population will be $2(951307)=1902614$ . Now we can rewrite our equation as: $N(t)=1902614e^{-0.029t}$ . The last thing we need to do is equate our Orlando's population growth equation with this new one and solve for t:
$192157e^{0.022t} =1902614e^{-0.029t}$
$\frac{192157e^{0.022t} }{1902614e^{-0.029t} } =1$
$e^{0.051t} = \frac{1902614}{192157}$
$ln(e^{0.051t} )=ln( \frac{1902614}{192157} )$
$t= \frac{ln( \frac{1902614}{192157}) }{0.051}$
$t=44.95$
We can conclude that after 45 years in 2045 the population of Orlando will exceed twice the population of Detroit.

8 0

3 years ago