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3 years ago

13

Why in the world did I have nearly 800 points worth of questions deleted? Every single one of them were right! What do I do now?

1 answer:

vekshin13 years ago

5 0

Answer:

read your username :)

Step-by-step explanation:

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Which of the following sequences of transformation is used to obtain figure A’B’C’D’ from ABCD?

weeeeeb [17]

Answer:

Most likely (B)

Step-by-step explanation:

Points of ABCD:

A (3,1)

B (3,4)

C (5,5)

D (5,2)

The algebraic rule for reflecting across the y axis:

(x,y) ---> (-x, y)

Points of ABCD after being reflected: (shown by figure 2)

A (-3, 1)

B (-3, 4)

C (-5, 5)

D (-5, 2)

Then, the figure got translated two units to the left, resulting in figure F in the picture, and A’B’C’D’ in the question.

Points of ABCD after being translated by (x-2, y) : (shown by figure F)

A (-5, 1)

B (-5, 4)

C (-7, 5)

D (-7, 2)

This should be the coordinates of A’B’C’D’.

7 0

3 years ago

During optimal conditions, the rate of change of the population of a certain organism is proportional to the population at time

Lana71 [14]

Answer:

The population is of 500 after 10.22 hours.

Step-by-step explanation:

The rate of change of the population of a certain organism is proportional to the population at time t, in hours.

This means that the population can be modeled by the following differential equation:

$\frac{dP}{dt} = Pr$

In which r is the growth rate.

Solving by separation of variables, then integrating both sides, we have that:

$\frac{dP}{P} = r dt$

$\int \frac{dP}{P} = \int r dt$

$\ln{P} = rt + K$

Applying the exponential to both sides:

$P(t) = Ke^{rt}$

In which K is the initial population.

At time t = 0 hours, the population is 300.

This means that K = 300. So

$P(t) = 300e^{rt}$

At time t = 24 hours, the population is 1000.

This means that P(24) = 1000. We use this to find the growth rate. So

$P(t) = 300e^{rt}$

$1000 = 300e^{24r}$

$e^{24r} = \frac{1000}{300}$

$e^{24r} = \frac{10}{3}$

$\ln{e^{24r}} = \ln{\frac{10}{3}}$

$24r = \ln{\frac{10}{3}}$

$r = \frac{\ln{\frac{10}{3}}}{24}$

$r = 0.05$

So

$P(t) = 300e^{0.05t}$

At what time t is the population 500?

This is t for which P(t) = 500. So

$P(t) = 300e^{0.05t}$

$500 = 300e^{0.05t}$

$e^{0.05t} = \frac{500}{300}$

$e^{0.05t} = \frac{5}{3}$

$\ln{e^{0.05t}} = \ln{\frac{5}{3}}$

$0.05t = \ln{\frac{5}{3}}$

$t = \frac{\ln{\frac{5}{3}}}{0.05}$

$t = 10.22$

The population is of 500 after 10.22 hours.

7 0

2 years ago

The table shows the values of a function f(x).

QveST [7]

Answer:

The average rate of change is $=-4$

Step-by-step explanation:

The average rate of change from x=a to x=b of f(x) is given by;

$=\frac{f(b)-f(a)}{b-a}$

We want to find the average rate of change of the function represented in the table from x=-2 to x=2.

$=\frac{f(2)-f(-2)}{2--2}$

From the table f(-2)=25 and f(2)=9

The average rate of change from x=-2 to x=2 is

$=\frac{9-25}{2--2}$

$=\frac{-16}{4}$

$=-4$

3 0

3 years ago

A line passes through the points (0, 9) and (9, 19). What is its equation in slope-intercept form?

STatiana [176]

Answer:

y = 10/9x + 9

Step-by-step explanation:

To write the equation in its slope-intercept form, y = mx + b, we need to find the slope (m) of the line and its y-intercept (b).

Given the points (0, 9) and (9, 19), we can solve for the slope of the line using the following formula:

$m = \frac{y2 - y1}{x2 - x1}$

Let (x1, y1) = (0, 9)

and (x2, y2) = (9, 19)

Substitute these values on the formula:

$m = \frac{y2 - y1}{x2 - x1} = \frac{19 - 9}{9 - 0} = \frac{10}{9}$

Therefore, the slope (<em>m </em>) = 10/9.

Next, the <u>y-intercept</u> is the point on the graph where it crosses the y-axis, and has the coordinates, (0, <em>b </em>). It is also the value of the y when x = 0.

One of the given points is the y-intercept of the line, given by (0, 9). The y-coordinate, 9, is the value of b.

Therefore, the linear equation in slope-intercept form is: y = 10/9x + 9

3 0

2 years ago

K+(-5)=-4 solve each equation

Otrada [13]

Answer:

1

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers