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4 years ago

Consider the following system of equations:

Mathematics

2 answers:

Temka [501]4 years ago

7 0

Answer:

Step-by-step explanation:

Using substitution method of simultaneous equation,

2x + 3y = 45 ___________(1)

x + y = 10 ___________(2)

From equation 2 solve for x to produce equation 3

x = 10 - y ______________(3)

Now put equation 3 or rather substitute for x in equation 1

2( 10 - y )+ 3y = 45

Solve the equation now

2x10 -2 X y + 3y =45

20 -2y +3y = 45

y = 45 - 20

y = 25

To get x, substitute for y in equation 3

x = 10 - 25

x = -15

Therefore,

x = -15.

,To check.

Put x=-15 and y = 25 in equation

x +y = 10

-15 +25 = 10.

Therefore, x = -15.

Kobotan [32]4 years ago

5 0

Answer:

x=-15, y=25. (-15, 25).

Step-by-step explanation:

2x+3y=45

x+y=10

--------------

x=10-y

2(10-y)+3y=45

20-2y+3y=45

20+y=45

y=45-20

y=25

x+25=10

x=10-25

x=-15

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What are the orders of 3,7,9,11,13,17 and 19(mod20)?does 20 have primitive roots?

bezimeni [28]

$3\equiv3\mod{20}$
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$3^4\equiv3\cdot3^3\equiv3\cdot7\equiv21\equiv1\mod{20}$

$7\equiv7\mod{20}$
$7^2\equiv49\equiv9\mod{20}$
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$9\equiv9\mod{20}$
$9^2\equiv3^4\equiv1\mod{20}$

$11\equiv11\mod{20}$
$11^2\equiv121\equiv1\mod{20}$

$13\equiv-7\equiv13\mod{20}$
$13^2\equiv169\equiv9\mod{20}$
$13^3\equiv13\cdot13^2\equiv(-7)9\equiv-63\equiv-3\mod{20}$
$13^4\equiv13\cdot13^3\equiv(-7)(-3)\equiv21\equiv1\mod{20}$

$17\equiv-3\equiv17\mod{20}$
$17^2\equiv(-3)^2\equiv9\mod{20}$
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Generally speaking, a number $x$ coprime to $n$ will be a primitive root of $n$ if we have $x^n\equiv x\mod{n}$ , or $x^{n-1}\equiv1\mod{n}$ . In other words, if $x$ is of order $n-1$ modulo $n$ , then $x$ is a primitive root of $n$ .

Since none of these numbers has order 19, it follows that 20 does not have any primitive roots.

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4 years ago

ILL GIVE BRAINLIEST<br> 1 x/3 - 3/4= 5/12<br> solve for x

mel-nik [20]

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2 years ago

The graph of f(x) = 1/3

Illusion [34]

The transformed function is defined by:

g(x) = -f(x/5 - 2) - 6

Where f(x) is the given function.

<h3 /><h3>How to get the equation of the transformed function?</h3>

Here we start with the function:

f(x) = (1/3)*x

(I don't know if this is the actual function, but that does not matter, I will solve it in a general way).

If first, we reflect it vertically, then the new function is:

g(x) = -f(x).

If now we compress it horizontally by a factor of 5, then we get:

g(x) = - f(x/5)

Now we shift it 2 units to the right, then:

g(x) = -f(x/5 - 2)

Finally, we shift it down 6 units, then we get:

g(x) = -f(x/5 - 2) - 6

That is the general form of the function g(x).

Replacing f(x) by what is defined above, we get:

g(x) = -(1/3)*(x/5 - 2) - 6

If you want to learn about transformations:

brainly.com/question/4289712

#SPJ1

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2 years ago