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KatRina [158]
3 years ago
5

Find the solution to the following system of equations using substitution:

Mathematics
2 answers:
galina1969 [7]3 years ago
6 0

Answer:

x = 5 and y = 1

Step-by-step explanation:

x - 3y = 2 then x = 2 + 3y

Substituting x in: 2x + 5y = 15

2*(2 + 3y) + 5y = 15

4 + 6y + 5y = 15

11y = 15 - 4

11y = 11

y = 11/11

y = 1

Then

x = 2 + 3y

x = 2 + (3*1)

x = 2 + 3

x = 5

I hope it's clear

vichka [17]3 years ago
5 0

Answer:

x = 5

y =1

Step-by-step explanation:

following image will help you understand this:

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bazaltina [42]

the probability that a positive integer less than 100 picked at random has all distinct digits is 90.

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The integers that do not have all distinct digits have the same digit twice.

11, 22, 33, 44, 55, 66, 77, 88, 99

There are 9 integers that do not have distinct digits, therefore there are 99-9 integers that do.

Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.

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8 0
2 years ago
What two numbers add to be 6 and multiply to be 15
yarga [219]
   
\displaystyle \bf \\
x_1+x_2=6\\\\
x_1\cdot x_2=15\\\\
\Longrightarrow~~x^2-6x+15=0\\\\
x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{6\pm\sqrt{36-60}}{2}=\\\\
=\frac{6\pm\sqrt{-24}}{2}=\frac{6\pm2\sqrt{-6} }{2}=3\pm i\sqrt{6}\\\\
x_1=\boxed{3-i\sqrt{6}}\\\\
x_2=\boxed{3+i\sqrt{6}}\\\\
\texttt{Verify:}\\\\
x_1+x_2=3-\underline{i\sqrt{6}}+3+\underline{i\sqrt{6}}=3+3=6~~correct\\\\
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4 0
3 years ago
5) Your stock investments went from $450 in 2013 to $350 ir
Hatshy [7]

The most appropriate choice for percentage will be given by Percentage decrease in the investment is 22.22%

<h3>What Does Percent Mean?</h3>

Using a percentage of 100, we may express a ratio as a %.

Stock investments in this case decreased from $450 in 2013 to $350 in 2014.

Decrease in stock equals $100 ($450 - $355)

Decrease in percentage: 100/450 100 = 22.22%

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The definition of percentage is "out of 100." In mathematics, percentages are used to represent parts of a whole, much as fractions and decimals. A total is considered to be made up of 100 equal parts when expressed as a percentage. The symbol % or, less commonly, the abbreviation 'pct' can be used to represent a percentage.

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3 0
1 year ago
Can I see how long division works on these? pls no sketchy links
alexandr1967 [171]

Answer:

Step-by-step explanation:

11) First write in decreasing exponential terms and fill in blanks with zeros.

Our goal is to eliminate all term in the dividend by subtraction

          ________________

2v - 2 |  2v³ - 16v² + 0v + 13

we see that 2v needs to be multiplied by 1v² to eliminate the first term

          <u>              v²                </u>

2v - 2 |  2v³ - 16v² + 0v + 13

         <u>- (2v³ - 2v²)</u>

              0  - 14v²

multiply your estimate by your divisor and subtract from the dividend.

bring down the next term and repeat.

          <u>              v²    -7v       </u>

2v - 2 |  2v³ - 16v² + 0v + 13

         <u>- (2v³ - 2v²)</u>

              0  - 14v² + 0v

                 <u>-(-14v² + 14v)</u>

                             - 14v

repeat again

<u />

          <u>              v²  -  7v  -  7 </u>

2v - 2 |  2v³ - 16v² + 0v + 13

         <u>- (2v³ - 2v²)</u>

              0  - 14v² + 0v

                 <u>-(-14v² + 14v)</u>

                             - 14v + 13

                            <u>-(-14v + 14)</u>

                                          -1

and remainder gets put over the divisor and appended

v²  -  7v  -  7 - 1/(2v - 2)

13) Same process

          <u>                                      </u>

5a + 1 |  40a³ - 12a² - 39a - 5

          <u>              8a²                 </u>

5a + 1 |  40a³ - 12a² - 39a - 5

          <u>-(40a³ + 8a²)</u>

                     -20a² - 39a

          <u>              8a² -    4a     </u>

5a + 1 |  40a³ - 12a² - 39a - 5

          <u>-(40a³ + 8a²)</u>

                     -20a² - 39a

                   -(-<u>20a² -   4a)</u>

                                -35a - 5

          <u>              8a² -    4a  - 7  </u>

5a + 1 |  40a³ - 12a² - 39a - 5

          <u>-(40a³ + 8a²)</u>

                     -20a² - 39a

                    -(<u>20a² -   4a)</u>

                                -35a - 5

                              -<u>(-35a - 7)</u>

                                           2

8a² - 4a - 7 + 2/(5a + 1)

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