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1 year ago

Please explain on how to get the solution for each variable please

Mathematics

1 answer:

Margaret [11]1 year ago

5 0

By algebraic handling we find that the unique solution of the system of linear equations is: (x, y, z) = (- 2, 4, 3). (Correct choice: A)

<h3>What is the nature of a system of linear equations?</h3>

If the system of equations has no solutions, then the determinant of the dependent coefficients of the system of linear equations must be zero. Let see:

$D = \left|\begin{array}{ccc}1&1&1\\4&-1&-8\\-1&-1&7\end{array}\right|$

This determinant can be determined by Sarrus' rule:

D = (1) · (- 1) · (7) + 4 · (- 1) · 1 + (- 1) · 1 · (- 8) - (- 1) · (- 1) · 1 + 4 · 1 · 7 - 1 · (- 1) · (- 8)

D = - 7 - 4 + 8 - 1 + 28 - 8

D = 16

The system of linear equations have at least one solution. This system has only one solution any of the three equations is not a function of the other two. By algebraic handling we find that the unique solution of the system is: (x, y, z) = (- 2, 4, 3).

To learn more on systems of linear equations: brainly.com/question/19549073

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What is −10−f=−6f+10

sammy [17]

-10-f=-6f+10
-f+6f=10+10
5f=20
F=4

4 0

2 years ago

A savings account earns 6% simple interest per year. The principal is $800. What is the balance after 18 months?

Ilia_Sergeevich [38]

Answer:

$872

Step-by-step explanation:

Simple interest = Principle * Rate * Time / 100

= ( 800 * 6 * 18/12 ) / 100

= $ 72

The balance after 18 months = principle + interest

= 800 + 72

= $ 872

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1 year ago

Find the quotient of these Complex Numbers. (5-i) / (3+2i)

JulsSmile [24]

Let the given complex number

z = x + ix = $\dfrac{5-i}{3+2i}$

We have to find the standard form of complex number.

Solution:

∴ x + iy = $\dfrac{5-i}{3+2i}$

Rationalising numerator part of complex number, we get

x + iy = $\dfrac{5-i}{3+2i}\times \dfrac{3-2i}{3-2i}$

⇒ x + iy = $\dfrac{(5-i)(3-2i)}{3^2-(2i)^2}$

Using the algebraic identity:

(a + b)(a - b) = $a^{2}$ - $b^{2}$

⇒ x + iy = $\dfrac{15-10i-3i+2i^2}{9-4i^2}$

⇒ x + iy = $\dfrac{15-13i+2(-1)}{9-4(-1)}$ [ ∵ $i^{2} =-1$ ]

⇒ x + iy = $\dfrac{15-2-13i}{9+4}$

⇒ x + iy = $\dfrac{13-13i}{13}$

⇒ x + iy = $\dfrac{13(1-i)}{13}$

⇒ x + iy = 1 - i

Thus, the given complex number in standard form as "1 - i".

5 0

3 years ago

There are 26 third graders and 32 fourth graders going on a field trip. Each van can carry 10 people

3241004551 [841]

No question was asked buy i'll try to answer anyway.

either im assuming its asking how many vans or how many missing seats.

26+32 58 students total,

You would need 6 vans to carry them, and 2 seats would be missing.

If this isnt what you were looking for please comment a question and i'll try to help

5 0

2 years ago

A sociologist wants to determine if the life expectancy of people in africa is less than the life expectancy of people in asia.

Colt1911 [192]

Answer:

The sample statistics are attached.

First, we need to determine the hypothesis.

The null hypothesis should be: $H_{o} : u_{africa} \geq u_{asia}$ .

The alternative hypothesis should be: $H_{a}: u_{africa}$

The next step is about calculating the t statistics based on the samples. This t test will give the probability value or p-value, which determines if there's enough to reject the null hypothesis. The formula we need to use to find the t-value is: $t=\frac{x_{1}-x_{2} }{\sqrt{\frac{s_{1} ^{2} }{n_{1} } +\frac{s_{2} ^{2} }{n_{2} } } }$

Replacing all the values into the formula, we have:

$t=\frac{52.4-58.1}{\sqrt{\frac{(7.4)^{2} }{45}+\frac{(8.8)^{2} }{35} } } \\t=\frac{-5.7}{\sqrt{1.2+2.2} } =\frac{-5.7}{1.8} =-3.2$

Therefore, the t-value is -3.2.

Now, we using a level of significance of 0.01, and a degree of freedom (df) of 34, we use the t-table to find the p-value for this results. (df = N -1; in this case, we take the smaller sample, which is 35, giving us 34 of df).

Therefore, according to the table attached, the p-value is less than 0.01, which is less than our level of significance. This result means that the null hypothesis is rejected. In other words, there's enough evidence to say that the life expectancy of people in Africa is less than the life of expectancy of people in Asia.

3 0

3 years ago