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4 years ago

What is the solution to the following system of linear equations x+y=5 x-y=1

Mathematics

2 answers:

nevsk [136]4 years ago

8 0

Answer: The required solution of the given system is

x = 3 and y = 2.

Step-by-step explanation: We are given to find the solution to the following system of linear equations :

$x+y=5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x-y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

We will be using the method of Elimination to solve the given system as follows :

Adding equations (i) and (ii), we get

$(x+y)+(x-y)=5+1\\\\\Rightarrow 2x=6\\\\\Rightarrow x=\dfrac{6}{2}\\\\\Rightarrow x=3.$

Substituting the value of x in equation (i), we get

$x+y=5\\\\\Rightarrow 3+y=5\\\\\Rightarrow y=5-3\\\\\Rightarrow y=2.$

Thus, the required solution of the given system is

x = 3 and y = 2.

agasfer [191]4 years ago

7 0

$\underline{+\left\{\begin{array}{ccc}x+y=5\\x-y=1\end{array}\right}\ \ \ |\text{add both sides of the equations}\\.\ \ \ \ \ \ \ 2x=6\ \ \ \ |:2\\.\ \ \ \ \ \ \ \ \ x=3\\\\\text{substitute the value of x to the first equation}\\\\3+y=5\ \ \ \ |-3\\y=2\\\\\text{Answer:}\ \ \ \boxed{x=3;\ y=2}\to(3;\ 2)$

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Value rent a car rents a luxury car at a daily rate of $37.49 plus 20 cents per mile. A business person is allotted $130 for car

alex41 [277]

Answer:

In the allocated budget of $130 , the business person can travel 462.55 miles a day.

Step-by-step explanation:

The daily rate of car service = $37.49

Cost per mile of the car = 20 cents = $ 0.20

Total allocated budget for each day = $130

Now, out of the total budget :

The actual travelling budget = Total Budget - Daily car rate

= $130 - $37.49

= $92.51

So, the actual travelling budget each day = $92.41

Now, $\textrm{Number of total miles traveled } = \frac{\textrm{Actual traveling budget}}{\textrm{Rate per mile }}$

= $\frac{92.51}{0.20} = 462.55$

or, the number of miles traveled = 462.55 miles

Hence, in the allocated budget of $130 , the business person can travel 462.55 miles a day.

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4 years ago

How to represent lengths in line plot math

Radda [10]

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3 years ago

If BC = 6.5, CD = 7.8, and AD = 12.2, find AB to the nearest tenth.

Sladkaya [172]

This can be solved using the angle bisector theorem. Note that line segment AD is the angle bisector of triangle DAB from angle DAB. Therefore, we know that the ratios $\frac{\text{AD}}{\text{CD}}$ and $\frac{\text{AB}}{\text{CB}}$ are equal. Solving, we get $\frac{\text{12.2}}{\text{7.8}}=\frac{\text{AB}}{\text{6.5}}$ . Cross multiplying, we get $79.3 = 7.8x$ , and solving this equation we get $x = 10.1666... \approx 10.2$ . 10.2 is your answer.

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4 years ago

An Austrian study was completed to determine if untrained sea lions and sea lionesses could follow various experimenter-given cu

Sholpan [36]

Using the z-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.

<h3>What are the hypothesis?</h3>

At the null hypothesis, it is tested if Zwerg cannot correctly follow this type of direction by an experimenter more than 50% of the time, that is:

$H_0: p \leq 0.5$

At the alternative hypothesis, it is tested if Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time, that is:

$H_1: p > 0.5$

<h3>Test statistic</h3>

The <em>test statistic</em> is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

In which:

$\overline{p}$ is the sample proportion.

p is the proportion tested at the null hypothesis.

n is the sample size.

For this problem, the parameters are:

$n = 48, \overline{p} = \frac{37}{48} = 0.7708, p = 0.5$

The value of the <em>test statistic</em> is:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

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Considering a <u>right-tailed test</u>, as we are testing if the proportion is greater than a value, with a <u>significance level of 0.05</u>, the critical value for the z-distribution is $z^{\ast} = 1.645$ .

Since the test statistic is greater than the critical value for the right-tailed test, this result shows that Zwerg can correctly follow this type of direction by an experimenter more than 50% of the time.

To learn more about the z-distribution, you can take a look at brainly.com/question/16313918

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2 years ago

(Area of triangle).

pochemuha

Your answer is B for this one

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3 years ago

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