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Mashutka [201]
2 years ago
7

Write a system of linear inequalities so the points (1, 2) and (4, −3) are solutions of the system, but the point (−2, 8) is not

a solution of the system. PLEASE SOMEONE HELP AND SOLVE IT AS A SYSTEM OF LINEAR EQUATIONS
Mathematics
2 answers:
dalvyx [7]2 years ago
7 0
I can’t see it where is it it’s blurry
Travka [436]2 years ago
4 0

Answer:

<u>The sample system is given below:</u>

  • y < 5
  • y > x - 8

<em>see the attached for the graph</em>

The points (1, 2) and (4, -3) are in the intersected region but the point (-2, 8) is outside

  • <em>The easy way to get the inequalities to plot the points and add lines to divide the regions where desired point are inside and not required point is outside. </em>
  • <em>I put y = 5 and y = x - 8 lines and shaded the region below y = 5 line and above the other line.</em>

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a motor boat traveled 18 miles down a river in 2 hours but took 4.5 hours to return upstream. Find the rate of the motor boat in
tangare [24]

Answer:

  • rate of the boat in still water = 6.5 miles / hour

  • rate of the current = 2.5 miles / hour.

Explanation:

<u>1) Name the two variables:</u>

  • c: rate of the current
  • b: rate of the boat in still water:

With that, the net rates of the boat down the river and upstrean are:

  • down the river: b + c
  • upstream: b - c

<u>2) Now set the equations for the distance as a function of the times and the rates:</u>

  • distance = rate × time

  • downstream: 18 miles = (b + c) × 2 hours
  • upstream: 18 miles = (b - c) × 4.5 hours

<u>3) Set the system of equations:</u>

  • 18 = 2(b + c) ⇒ 9 = b + c . .  . Equation (1)
  • 18 = 4.5 (b - c) ⇒ 4 = b - c . . . Equation (2)

<u>4) Solve the system by </u><u>elimination</u><u>:</u>

  • Add equations (1) and (2): 9 + 4 = 2b
  • Divide both sides by 2: 13/2 = b
  • Simplify: b = 6.5

  • Replace b with 6.5 in equation (2) and solve:

       4 = 6.5 - c ⇒ c = 6.5 - 4 = 2.5

<u>5) Results:</u>

  • b = rate of the boat in still water = 6.5 miles / hour

  • c = rate of the current = 2.5 miles / hour.

   

3 0
2 years ago
Read 2 more answers
Li Na made 144 fliers for her new business. Five of her friends are helping her distribute the fliers. If they divide the fliers
AleksAgata [21]
The Answer Is 24 fliers each
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Consider the following random sample from a normal population: 14, 10, 13, 16, 12, 18, 15, and 11. What is the 95% confidence in
seraphim [82]

Answer:

13.625-2.365\frac{2.669}{\sqrt{8}}=11.393  

13.625+2.365\frac{2.669}{\sqrt{8}}=15.857  

So on this case the 95% confidence interval would be given by (11.393;15.857)  

Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Data: 14, 10, 13, 16, 12, 18, 15, 11

We can calculate the sample mean and deviation with the following formulas:

\bar X = \frac{\sum_{i=1}^n X_i}{n}

s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}

\bar X=13.625 represent the sample mean  

\mu population mean (variable of interest)  

s=2.669 represent the sample standard deviation  

n=8 represent the sample size  

Calculate the confidence interval

The confidence interval for the mean is given by the following formula:  

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}} (1)  

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:  

df=n-1=8-1=7  

Since the confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,7)".And we see that t_{\alpha/2}=2.365

Now we have everything in order to replace into formula (1):  

13.625-2.365\frac{2.669}{\sqrt{8}}=11.393  

13.625+2.365\frac{2.669}{\sqrt{8}}=15.857  

So on this case the 95% confidence interval would be given by (11.393;15.857)  

3 0
2 years ago
A recipe states that 5 servings of peanuts have 1,250calories. How many calories is 2 servings of peanuts? *
MrMuchimi

Answer:

500 calories

Step-by-step explanation:

divide the 1250 calories by the initial five servings and you get 250 then multiply that by the 2 servings they are asking for and you get 500 calories

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2 years ago
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The track team is trying to reduce their time for a relay race. First they reduce their time by 2.1 minutes. Then they are able
klemol [59]
Answer: 15.7 minutes

Step-by-step explanation:

Let x be the time in the beginning (in minutes).

Given: The track team is trying to reduce their time for a relay race.

First they reduce their time by 2.1 minutes.

Then they are able to reduce that time by 10

If their final time is 3.96 minutes, then

x-t1-t2= 3.6
x= 3.6+ t1+ t2
x= 3.6+ 2.1+ 10
x= 15.7

Hence, their beginning time was 15.7 minutes.
3 0
2 years ago
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