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2 years ago

A city determines that a planned community must have at least 4 acres of developed and open space, and the difference

Mathematics

1 answer:

FinnZ [79.3K]2 years ago

3 0

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x -----> the number of open acres

y ----> the number of developed acres

we know that

$x+y \geq 4$ -----> inequality A

$x\leq 1$ ----> inequality B

Remember that

if the number of open acres, x, can be no more than 1. then the number of open acres, x must be less than or equal to 1

Solve the system of equations by graphing

The solution is the shaded area (Note The number of acres cannot be a negative number)

The graph in the attached figure

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A rectangle that had the perimeter of 70 and the area of 250 has enlarged; its sides became twice as long. what is the new area

aliya0001 [1]

The perimeter of the original rectangle is:
P = 2w + 2l = 70
The area of the original rectangle is:
A = w * l = 250
Then, by modifying the length of its sides we have:
Perimeter:
P '= 2 (2w) +2 (2l)
Rewriting:
P '= 2 (2w + 2l)
P '= 2P
P '= 2 (70)
P '= 140
Area:
A '= (2w) * (2l)
Rewriting:
A '= (2) * (2) (w) * (l)
A '= 4 * w * l
A '= 4 * A
A '= 4 * 250
A '= 1000
Answer:
the new area and the new perimeter are:
P '= 140
A '= 1000

3 0

2 years ago

Solve the system of equations – 5x + y = 56 and x + y = -4 by combining the<br> equations.

anygoal [31]

Answer:

Your solution is (-10, 6).

Step-by-step explanation:

Combining the equations is also known as substitution. This is done when you substitute one variable into another equation.

-5x + y = 56

x + y = -4

Let's change the second equation into one with one variable on each side.

y = -x - 4

Now, plug this into your first equation.

-5x + (-x - 4) = 56

Distribute the + sign.

-5x - x - 4 = 56

Combine the like terms.

-6x - 4 = 56

-6x = 60

Isolate x by dividing both sides by -6.

x = -10

Now plug this back into either equation.

-10 + y = -4

Add 10 to both sides to find y.

y = 6

Your solution is (-10, 6).

Check this by plugging in these values into the equation you have not checked yet.

-5(-10) + (6) = 56

50 + 6 = 56

56 = 56

Your solution is correct.

Hope this helps!

5 0

1 year ago

Read 2 more answers

The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ≤ t ≤ 8. (a) When is the position function decreas

iren [92.7K]

For the last part, you have to find where $f'(t)$ attains its maximum over $0\le t\le8$ . We have

$f'(t)=-6\sin3t+6\cos2t$

so that

$f''(t)=-18\cos3t-12\sin2t$

with critical points at $t$ such that

$-18\cos3t-12\sin2t=0$

$3\cos3t+2\sin2t=0$

$3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0$

$\cos t(3\cos^2t-9\sin^2t+4\sin t)=0$

$\cos t(12\sin^2t-4\sin t-3)=0$

So either

$\cos t=0\implies t=\dfrac{(2n+1)\pi}2$

$12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi$

where $n$ is any integer. We get 8 solutions over the given interval with $n=0,1,2$ from the first set of solutions, $n=0,1$ from the set of solutions where $\sin t=\dfrac{1+\sqrt{10}}6$ , and $n=1$ from the set of solutions where $\sin t=\dfrac{1-\sqrt{10}}6$ . They are approximately

$\dfrac\pi2\approx2$

$\dfrac{3\pi}2\approx5$

$\dfrac{5\pi}2\approx8$

$\sin^{-1}\dfrac{1+\sqrt{10}}6\approx1$

$2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7$

$2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6$

4 0

2 years ago

The following table shows the annual income, in dollars, and amount spent on vacation, in dollars, for a sample of 8 families.

marishachu [46]

Answer:

a. Scatterplot is attached.

b. Positive Correlation

c. Correlation coefficient=0.9219

Step-by-step explanation:

The following procedure will be used to obtain the scatter plot

Open an Google Sheets file online or excel sheet on your computer.
In column B and C, enter the Income and Vacation data as provided above.
Select the data > click on insert CHART.
Chose Scatter Chart option

Click OK.

A scatter plot visualizing your data should be displayed as attached.

On your computer, open a spreadsheet in Google Sheets.
Double-click on your scatter plot.
At the right, click on Customize tab and then Series.
Scroll down and check the Trend line box

-From the trend line, your notice that your variables have a positive correlation.

-As the income increases, so does vacation expenditure.

c. The correlation coefficient can be calculated as follows.

Click on any empty cell in the sheet and enter the formula
"=CORREL((y-axis range),(x-axis range))"
ENTER

-From our Google Sheets calculation our variables have a positive correlation and the correlation coefficient is 0.9219

-The correlation coefficient,r can also be calculated manually:

-let x be income, and y be vacation and divide all the values by 100 to make the smaller and easier to manipulate:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2-(\sum x)^2][n\sum y^2-(\sum y)^2}}\\\\\\\sum xy=153914\\\sum x=4485\\\sum y=246\\\sum x^2=2878447\\(\sum x)^2=4485^2=20115225\\(\sum y)^2=246^2=60516\\\sum y^2=8392\\n=8\\\\\#substitute \ and \ solve \ for \ r\\\\=\frac{8\times153914-4485\times 246}{\sqrt{[8\times 2878447-4485^2][8\times 8392-246^2]}}\\\\=0.92186\\\\\approx 0.9219$

4 0

2 years ago

Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 year

Mamont248 [21]

Answer: equations 1,3,4 and 5 stated has solutions.

Step-by-step explanation:

From the question, (x + 5) + 5 = (x + 5) + 5

The equations that represent the situation are:

1. x + 5 = (5 − x) − 5 :which has one solution

2. x + 5 = (x + 5) − 5 : many solutions

3. x + 5 = (x + 5) − 5: no solution

4. x + 5 = (5 − x) − 5 : many solutions

5. (x + 5) + 5 = (x + 5) + 5: many solutions

Equation 2 has no solution. While the other equations have one and more than one solutions.

6 0

2 years ago