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dsp73
3 years ago
15

Which graph shows the solution to the following system of linear inequalities?

Mathematics
1 answer:
bonufazy [111]3 years ago
8 0

Answer:

The fourth graph will be the solution.

Step-by-step explanation:

The system of linear inequalities are  

- 3x - 3y < - 3, ⇒ x + y > 1

And y ≤ -x + 1, ⇒ x + y ≤ 1

There is no solution for those two inequalities because there are no values of x and y that can satisfy both the equations.

Now, the fourth graph will be the solution as there is no shaded region for the solution in the graph and also the line x + y = 1 is plotted as a dotted line that means the solution does not include the line also. (Answer)

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3. Jessica is awake 2/3 of the day. She spends 5/8 of this time at home
ruslelena [56]

Answer:  a. 5/12     b. 10 hours

Step-by-step explanation:

5/8 x 2/3 = 10/24 = 5/12

she spends 5/12 of the day awake at home

if a day has 24 hours then 5/12 of that is 5/12 x 24 = 10

so she spends 10 hours awake at home

7 0
3 years ago
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
Gnoma [55]

There would be 12 people at the party!

In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.

Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.

This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.

Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.

Hope this helps!

3 0
3 years ago
Read 2 more answers
You deposit $7550 in an account that pays 7.25% interest, compounded continuously. How long to the
Afina-wow [57]

~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$\stackrel{tripled}{(7550)3}\\ P=\textit{original amount deposited}\dotfill & \$7550\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ t=years \end{cases}

3(7550)=7550e^{0.0725\cdot t}\implies \cfrac{3(7550)}{7550}=e^{0.0725t}\implies 3=e^{0.0725t} \\\\\\ \log_e(3)=\log_e\left( e^{0.0725t} \right)\implies \ln(3)=0.0725t \\\\\\ \cfrac{\ln(3)}{0.0725}=t\implies 15.15327\approx t\implies 15\approx t

7 0
3 years ago
What is the shape name<br>please do fast.​
vivado [14]

Answer:

\boxed{\sf Parallelogram}

Step-by-step explanation:

A parallelogram has opposite parallel sides and it is a quadrilateral.

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3 years ago
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The number of lines that can be drawn perpendicular to a given line at a given point on that line in a plane is
Neko [114]
Only one.
it has a long proof.
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3 years ago
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