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3 years ago

Solve the system of equations by using substitution. y = 2x +3 y = -x + 6

Mathematics

1 answer:

padilas [110]3 years ago

4 0

Answer:

x =3, y =3

Step-by-step explanation:

From the second equation( y= -x+6) we can get x alone.

Subtracting 6 from both sides we get, y-6 = -x

And then dividing both sides by -1, -y+6 = x

Then we can substitute this value of x into the first equation.

y = 2(-y+6) +3

Simplifying,

y = -2y + 12+ 3

3y = 15

y = 3

Substituting this back into second equation we get 3 = -x + 6

and -x = -3

Dividing both sides by -1,

we get x =3

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Write an equation of the line passing through the given points.

ANEK [815]

Answer:

The equation of the line passing through the given points.

(1,-5) and (-4,5) is

$y=-2x-3$

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( 1 ,-5)

point B( x₂ , y₂ )≡ (-4 , 5)

To Find:

Equation of Line AB =?

Solution:

Equation of a line passing through a points A( x₁ , y₁) and point B( x₂ , y₂ ) is given by the formula Two -Point Form,

$(y-y_{1})=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\times (x-x_{1})$

Now on substituting the slope and point A( x₁ , y₁) ≡ ( 1 ,-5) and B( x₂ , y₂ )≡ (-4 , 5) we get

$y-(-5)=\frac{5--5}{-4-1}\times (x-1)\\ \\y+5=\frac{10}{-5}(x-1)\\ \\y+5=-2(x-1)\\y+5=-2x+2 ......Applying\ Distributive\ property\\\\y=-2x+2-5\\\\y=-2x-3....Which\ is\ required$

The equation of the line passing through the given points.

(1,-5) and (-4,5) is

$y=-2x-3$

3 0

3 years ago

A con is tossed n times. How many difference sequences of head and tails can you get?

ryzh [129]

Answer:

2^n

Step-by-step explanation:

So whenever you flip a coin, you can see it as 2 nodes branching off of each existing node. so for example when you flip a coin once you're going to have 2 sequences initially H and T, now when you flip a coin again for each of those 2 sequences 2 are going to branch off of that, making the total sequences 4, and the next flip 2 sequences are going to branch off each of the 4 sequences and so on. this can generally be described as: 2^n

I attached an image describing this a bit better but the bottom line is that for each 'end node'/sequence you're going to have 2 branch off of it, thus for each coin flip the number of sequences multiplies by 2

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2 years ago

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The recursive formula An+1 = 2∙An number of people with a virus in a school each week. If there are 96 people infected with the

Alex777 [14]

Each week the number infected doubles. the formula would be 2(2(2(96))). the sum is equal to 768.

768.

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3 years ago

Estimate. what is 0.4% of 520

Snezhnost [94]

0.4% of 510 is 2.04
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chose each. subset of the real number system that can be used to classify the number 5.33 rational irrational number integer who

tresset_1 [31]

The subset of real number that can be used to classify the number 5.33 is irrational number.

<h3 /><h3>Classifying the number</h3>

We know that 5.33 = 5 + 0.33 contains a decimal part which is 0.33 and 5 which is a whole number part.

Since 0.33 is the irrational or decimal part which makes 5 + 0.33 = 5.33 irrational since a rational number + an irrational number = irrational number.

Since an irrational number is a number which cannot be expressed as a ratio of two integers.

<h3 /><h3>Conclusion</h3>

So, 5.33 is an irrational number.

So, the subset of real number that can be used to classify the number 5.33 is irrational number.

Learn more about irrational number here:

brainly.com/question/5342576

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