solve the equation using elimination

Answer:

3

Step-by-step explanation:

Step 1: Find the factors of 3 and 33.

Step 2: Find the largest common factor they share.

Therefore, the GCF of 3 and 33 is 3.

Use the multinomial theorem to compute some polynomial expansions:

(a + b + c)² = a² + b² + c² + 2 (ab + ac + bc)

(a + b + c)³ = a³ + b³ + c³

… … … … … … + 3 (a²b + a²c + ab² + b²c + ac² + bc²)

… … … … … … + 6 abc

(a + b + c)⁴ = a⁴ + b⁴ + c⁴

… … … … … … + 4 (a³b + a³c + ab³ + b³c + ac³ + bc³)

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 12 (a²bc + ab²c + abc²)

Now, given that

a + b + c = 4

a² + b² + c² = 10

it follows that

ab + ac + bc = (4² - 10)/2 = 3

We use this result to simplify the extra terms in the 3rd-degree expansion.

a²b + a²c + ab² + b²c + ac² + bc²

= a (ab + ac) + b (ab + bc) + c (ac + bc)

= a (ab + ac + bc) + b (ab + ac + bc) + c (ab + ac + bc) - 3abc

… … I underline the terms that are added and subtracted … …

= (a + b + c) (ab + ac + bc) - 3abc

= 4 • 3 - 3abc

= 12 - 3abc

Given that

a³ + b³ + c³ = 22

this tells us that

4³ = 22 + 3 (12 - 3abc) + 6abc

4³ = 58 - 3abc

and so

abc = (4³ - 58)/(-3) = -2

from which it follows that

a²b + a²c + ab² + b²c + ac² + bc² = 12 - 3 • (-2) = 18

Now we similarly simplify the extra terms in the 4th-degree expansion.

a³b + a³c + ab³ + b³c + ac³ + bc³

= a² (ab + ac) + b² (ab + bc) + c² (ac + bc)

= a² (ab + ac + bc) + b² (ab + ac + bc) + c² (ab + ac + bc) - a²bc - ab²c - abc²

= (a² + b² + c²) (ab + ac + bc) - (a²bc + ab²c + abc²)

= 10 • 3 - (a²bc + ab²c + abc²)

which means

4⁴ = a⁴ + b⁴ + c⁴

… … … … … … + 4 (30 - a²bc - ab²c - abc²)

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 12 (a²bc + ab²c + abc²)

reduces to

136 = a⁴ + b⁴ + c⁴

… … … … … … + 6 (a²b² + a²c² + b²c²)

… … … … … … + 8 (a²bc + ab²c + abc²)

Now, we know a + b + c = 4 and abc = -2, so we have

a²bc + ab²c + abc² = abc (a + b + c) = -2 • 4 = -8

and so

136 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²) + 8 • (-8)

200 = a⁴ + b⁴ + c⁴ + 6 (a²b² + a²c² + b²c²)

Finally, we know that ab + ac + bc = 3. Squaring this gives

(ab + ac + bc)² = 3²

a²b² + a²c² + b²c² + 2 (a²bc + ab²c + abc²) = 9

but we also know that a²bc + ab²c + abc² = -8, so

a²b² + a²c² + b²c² + 2 • (-8) = 9

a²b² + a²c² + b²c² = 25

Therefore, we end up with

200 = a⁴ + b⁴ + c⁴ + 6 • 25

⇒   [[[   a⁴ + b⁴ + c⁴ = 50   ]]

Answer: x=14

Step-by-step explanation: have a good day

Answer:

I would have done it the same way. Believing it is correct.

Step-by-step explanation:

Answer: Looks precise

Step-by-step explanation:

Answer:

$54 = 71%, $22 = 29%

Step-by-step explanation:

54+22=76

54/76 = 0.7105

22/76 = 0.2894

Answer:

26V^5+2V^7

Step-by-step explanation:

Answer:

1 month.

Step-by-step explanation:

When reading a graph, the most important thing is knowing what the axes are. Here, the horizontal x-axis is months, and the vertical y-axis is the number of books read. Those are our 2 variables.

Now, a line on a graph shows the relationship between those 2 variables. At any given point on the line, it'll have an output value of y (books read) for whatever input value of x.

The question gives you the value on the y-axis (books read), so all you need to do is find the value of x that corresponds to that point on the line. I marked that point on the line in the attached image. Look directly below that point on the line, and you can see that 1 month corresponds to 4 books read.

Answer:

We can simplify everything to the power of 2:

[tex]8^{x+2} = 2^{3*(x+2)}=2^{3x+6[/tex]

[tex]16^{x+1} = 2^{4*(x+1)}=2^{4x+4[/tex]

As the two equations are equal to each other and they have common bases, their powers must be equal too. We can come up with this equation:

3x+6=4x+4

solve for x

x=2

D (last answer choice)

plug x=2 in and check and you will get 4096=4096

Answer:

Golf balls

Step-by-step explanation:

There is a much higher chance of her picking an even number in the golf ball tank because there are way more golf balls with even numbers. (2, 4, 6, 8, etc.)

Answer:

  a[1] = 100

  a[n] = 1.05·a[n -1]

Step-by-step explanation:

The given terms do not have a common difference, but do have a common ratio. Each is 1.05 times the previous. This is expressed in a recursive relation as ...

  a[1] = 100

  a[n] = 1.05·a[n -1]

Answer:

I think it's-12

I am not sure

Please ask to some one else please

The expression that demonstrates the use of the commutative property is

(-1 + 18) + (3i + 5i)

Give two integers A and B, according to the commutative law of addition;

Given the expression (-1+3i) + (18+5i)

The expression that demonstrates the use of the commutative property of addition in the first step of simplifying the expression is given as:

(-1+3i) + (18+5i)

-1 + 3i + 18 + 5i

(-1 + 18) + (3i + 5i)

We can see that the rearrangement does not affect the sum. Hence the expression that demonstrates the use of the commutative property is

(-1 + 18) + (3i + 5i)

Learn more on commutative property here: https://brainly.com/question/778086

Answer:

Step-by-step explanation:

Let the digits be:

Each of them include numbers 1 through 5.

For each digit there are 5 options.

Total number of combinations is:

Answer:20 (p-3)

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

6-2x = 5x-9x+16

leave the x's together: (going over the equal signs changes the sign)

-2x-5x+9x = 16-6

2x = 10

x = 5

Answer:

56% left of the book

Answer:

56 %

Step-by-step explanation: There are two ways to arrive at the answer.

1st Way: 110/250 = 0.44

0.44 * 100 = 44%

44% is the amount he has read and we are looking for the amount that is left to read.

So we know 100% is the maximum percentage.

We then subtract 44 from 100 which is 56, So 56 is the answer.

2nd Way: 250-110 = 140

140/250=0.56

0.56*100= 56%

Hope this helps.

Answer:

No

Step-by-step explanation:

Answer:

1/9

Step-by-step explanation:

There are 3 even numbers. 2,4, and 6. There is a 1/3 chance of rolling one on each dice.

So 1/3*1/3=1/9

Functions are used to represent graphs, and vice versa.

The function represented by the graph is [tex]f(x) =- |x + 4| + 3[/tex]

The graph (see attachment) is an absolute value graph.

An absolute value graph is represented as:

[tex]f(x) =a |x - h| + k[/tex]

Where

[tex]Vertex = (h,k)[/tex]

The vertex is the minimum or the maximum point on the graph.

So, we have:

[tex]Vertex = (-4,3)[/tex]

The function becomes

[tex]f(x) =a |x + 4| + 3[/tex]

The function also passes through the point (-1,0).

So, we have:

[tex]0 =a |-1 + 4| + 3[/tex]

[tex]0 =a |3| + 3[/tex]

Remove the absolute bracket

[tex]0 =3a + 3[/tex]

Subtract 3 from both sides

[tex]3a =- 3[/tex]

Divide both sides by 3

[tex]a =- 1[/tex]

Substitute -1 for (a) in [tex]f(x) =a |x + 4| + 3[/tex]

[tex]f(x) =- |x + 4| + 3[/tex]

Hence, the function represented by the graph is [tex]f(x) =- |x + 4| + 3[/tex]

Read more about absolute value graphs at:

https://brainly.com/question/3381225

Answer:

0.14705882352

Step-by-Step:

Just use a calculator and your answer should pop up.

Answer:

33  1/3%

Step-by-step explanation:

Because there are 3 girls and 9 total animals, you do: 3/9, which is 1/3. You divide to find the percent. 1/3=33.333333..... Because you have a repeating decimal, you do 33 and 1/3, because the repeating decimal is .33333.....

Answer:

Functions: Second Graph

The other two are not. Use the vertical line test. I'm pretty sure but not 100%

Step-by-step explanation:

Answer:

D. Neither table represents a function

Step-by-step explanation:

Functions require a key to go by. In this case, none of the two tables have a key from the start going down.

Answer:WHAT VALUE AND WHAT DIGIT

Step-by-step explanation:

Answer:

C. 4/3

Step-by-step explanation:

2 × ⅓ + ⅔

⅔ + ⅔ = 4/3

Use X as ⅓, and use Y as ⅔.

Answer:

  x = 274 91/107

Step-by-step explanation:

This is called a "two-step linear equation" because it is solved in 2 steps.

Step 1. Identify the constant on the same side of the equation as the variable term, and add its opposite to both sides of the equation.

  2.14x -12.18 +12.18 = 576 +12.18

  2.14x = 588.18

__

Step 2. Identify the coefficient of the variable and multiply both sides of the equation by its reciprocal.

  2.14x(1/2.14) = 588.18(1/2.14)

  x = 274.850467... = 274 91/107 . . . the decimal fraction repeats

The solution to the equation is x = 274 91/107.

Answer:

x = 274 91/107

Step-by-step explanation:

Step-by-step explanation:

This is called a "two-step linear equation" because it is solved in 2 steps.

Step 1. Identify the constant on the same side of the equation as the variable term, and add its opposite to both sides of the equation.

 2.14x -12.18 +12.18 = 576 +12.18

 2.14x = 588.18

__

Step 2. Identify the coefficient of the variable and multiply both sides of the equation by its reciprocal.

 2.14x(1/2.14) = 588.18(1/2.14)

 x = 274.850467... = 274 91/107 . . . the decimal fraction repeats

The solution to the equation is x = 274 91/107.