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3 years ago

Which system of linear equations can be solved using the information below?

Mathematics

2 answers:

Murljashka [212]3 years ago

3 0

Answer:

2x-3y=20

12x+8y=-192

Solution

In the determinant of the matrix to find the variable "x" [Ax], we replace the coefficients of "x" (2 and 12) by the independent terms (20 and -192 respectively).

In the determinant of the matrix to find the variable "y" [Ay], we replace the coefficients of "y" (-3 and 8) by the independent terms (20 and -192 respectively).

SVEN [57.7K]3 years ago

3 0

Answer:

Step-by-step explanation:

Edge2020

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Answer:

Step-by-step explanation:

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

Find the value of 4^2 + 6^2

seraphim [82]

Answer:

Step-by-step explanation:

4^2=4×4=16

6^2=6×6=36

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3 years ago

Orlando wants to borrow $3,000 for the purchase of a used car. he has to pay back the loan after 4 years. the two loan options a

gtnhenbr [62]

The amount in simple interest is $3624 and in compound interest is $3674 the difference is of $50. So he should choose Simple interest.

<h3>What is compound and simple interest?</h3>

Simple interest is based on the principal amount of a loan or deposit. In contrast, compound interest is based on the principal amount and the interest that accumulates on it in every period.

Here we have the principle is $3000 for 4 years at the rate of interest of 5.2%. Now we will calculate the total amount by simple interest and compounded annually.

By using Simple interest:-

$\rm SI=\dfrac{P\times T\times R}{100}=\dfrac{3000\times 4\times 5.2}{100}=624$

So the total amount will be =3000+624=$3624

By using the Compound interest formula:

$A=P(1+\dfrac{r}{n})^{nt}$

$A=3000(1+\dfrac{5.2}{1})^{4}$

$A=\$3674$

The difference between the two amounts will be =3764-3624=$50

Hence amount in simple interest is $3624 and in compound interest is $3674 the difference is of $50. So he should choose Simple interest.

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1 year ago

How is the series 5+11+17…+251 represented in summation notation?

NISA [10]

Answer:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

Step-by-step explanation:

Given:

Series 5+11+17+...+251

To find:

Summation notation of the given series

Summation Notation:

$\displaystyle \large{\sum_{k=1}^n a_k}$

Where n is the number of terms and $\displaystyle \large{a_k}$ is general term.

First, determine what kind of series it is, there are two main series that everyone should know:

Arithmetic Series

A series that has common difference.

Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

11-5 = 6
17-11 = 6

Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:

<u>Arithmetic Sequence</u>

$\displaystyle \large{a_n=a_1+(n-1)d}$

Where $\displaystyle \large{a_n}$ is the nth term, $\displaystyle \large{a_1}$ is the first term and $\displaystyle \large{d}$ is the common difference:

So for our general term:

$\displaystyle \large{a_n=5+(n-1)6}\\\displaystyle \large{a_n=5+6n-6}\\\displaystyle \large{a_n=6n-1}$

And for number of terms, substitute $\displaystyle \large{a_n}$ = 251 and solve for n:

$\displaystyle \large{251=6n-1}\\\displaystyle \large{252=6n}\\\displaystyle \large{n=42}$

Now we can convert the series to summation notation as given the formula above, substitute as we get:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

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2 years ago