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3 years ago

3x+2y=-19 -3x-5y=25 solve for x and y

2 answers:

5 0

X= -5
y= -2
I didn't double check the answers by inputting them back into the equations, but if you want to then you can. Yet I am 99% positive my answer is correct.

aksik [14]3 years ago

3 0

Add both equations;
3x+2y=-19
-3x-5y=25
o-3y=6
so, y=6÷(-3)=-2
and for x 3x+2(-2) =-19⇒ 3x-4=-19⇒3x=-15⇒x=-5
hope so it will help

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A population of bees is decreasing. The population in a particular region this year is 1,250. After 1 year, it is estimated tha

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To model this situation, we are going to use the decay formula: $A=Pe^{rt}$
where
$A$ is the final pupolation
$P$ is the initial population
$e$ is the Euler's constant
$r$ is the decay rate
$t$ is the time in years

A. We know for our problem that the initial population is 1,250, so $P=1250$ ; we also know that after a year the population is 1000, so $A=1000$ and $t=1$ . Lets replace those values in our formula to find $r$ :
$A=Pe^{rt}$
$1000=1250e^{r}$
$e^{r}= \frac{1000}{1250}$
$e^{r}= \frac{4}{5}$
$ln(e^{r})=ln( \frac{4}{5} )$
$r=ln( \frac{4}{5} )$
$r=-02231$

Now that we have $r$ , we can write a function to model this scenario:
$A(t)=1250e^{-0.2231t}$ .

B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.

C.
- The function is decreasing
- The function doe snot have a x-intercept
- The function has a y-intercept at (0,1250)
- Since the function is decaying, it will have a maximum at t=0:
$A(0)=1250e^{(-0.2231)(0)$
$A_{0}=1250e^{0}$
$A_{0}=1250$
- Over the interval [0,10], the function will have a minimum at t=10:
$A(10)=1250e^{(-0.2231)(10)$
$A_{10}=134.28$

D. To find the rate of change of the function over the interval [0,10], we are going to use the formula: $m= \frac{A(0)-A(10)}{10-0}$
where
$m$ is the rate of change
$A(10)$ is the function evaluated at 10
$A(0)$ is the function evaluated at 0
We know from previous calculations that $A(10)=134.28$ and $A(0)=1250$ , so lets replace those values in our formula to find $m$ :
$m= \frac{134.28-1250}{10-0}$
$m= \frac{-1115.72}{10}$
$m=-111.572$
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.

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3 years ago

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Answer:

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3 years ago

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Answer:

186 beats per minute

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r = 220 - 34

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Hence, the maximum heart rate is 186 beats per minute.

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3 years ago

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<u></u><u>The correct answer is 47.5%, or 0.475.</u>

Explanation:
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The mean is 500 and the standard deviation is 100. This means that 700 is 2 standard deviations away from the mean:

(700-500)/100=200/100=2.

We know that 95% of data will fall within 2 standard deviations from the mean. However, included in the 95% is data less than the mean and greater than the mean. Since we are only concerned with the scores from 500 to 700, we only want the half that is greater than the mean:

95/2 = 47.5%, or 0.475.

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4 years ago