Transform the equation x-3y=15 to express it in slope-intercept form

The number of degrees does it move is 150 degrees.

The following things should be considered:

• Since there are 12 parts.
• Each one should we 30 degrees i.e.
• Now 8 - 3 = 5
• So, the angle should be = 150 degrees.  

Therefore we can conclude that The number of degrees does it move is 150 degrees.

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Answer:   3/4

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Explanation

The point (p,r) is on the line y = x+b

Plug in x = p and y = r to get r = p+b. Let's solve for b

r = p+b

b = r-p

This will be used later.

The point (2p,5r) is on the line y = 2x+b

Plug in those coordinates:

y = 2x+b

5r = 2*(2p)+b

5r = 4p+b

Next we replace b with r-p. This is valid because b = r-p.

5r = 4p+b

5r = 4p+r-p

5r = 3p+r

5r-r = 3p

4r = 3p

Then we follow the cross multiplication process in reverse.

4r = 3p

4r/4 = 3p/r

r = 3p/4

r/p = (3p/4)*(1/p)

r/p = 3/4  is the final answer

Final answer:

Using the given coordinates and equations, we find that the value of r/p is 3/4 after a process of subtracting and simplifying two equations.

Explanation:

The question is related to the linear equations in the xy-plane. Given two points, (p,r) and (2p,5r) which lie respectively on the equations y = x + b and y = 2x + b.

We have two points on two different lines:

• Point A: (p, r) lies on the line y = x + b.
• Point B: (2p, 5r) lies on the line y = 2x + b.

Substituting the coordinates of the first point into the first equation gives r = p + b. Similarly, substituting the coordinates of the second point into the second equation gives 5r = 2(2p) + b, which simplifies to 5r = 4p + b.

Now, subtract the first equation from the second to eliminate b, resulting in 5r - r = 4p - p, which simplifies to 4r = 3p.

Dividing by 4p gives us r/p = 3/4. So, the value of r/p is 3/4.

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Answer: 3

Step-by-step explanation:

(x + 4i) is a root which means its conjugate (x - 4i) is also a root

(x + 4i)(x - 4i) = x² + 16

Use Long Division for 2x⁵ - 13x⁴ + 22x³ - 187x² - 160x + 336 ÷ x² + 16

            2x³ - 13x² - 10x + 21                              

x² + 16 ) 2x⁵ - 13x⁴ + 22x³ - 187x² - 160x + 336

           - (2x⁵ + 0x⁴ + 32x³)   ↓          ↓         ↓

                       -13x⁴ - 10x³ - 187x²     ↓         ↓

                    - (-13x⁴ +0x³ - 208x²)    ↓         ↓

                                  -10x³ + 21x² - 160x     ↓

                               - (-10x³  + 0x² - 160x)    ↓

                                               21x² + 0x + 336

                                            - (21x² + 0x + 336)

                                                                      0

Use Synthetic Division to divide (x - 7) by the reduced polynomial (2x³ - 13x² - 10x + 21)

7 |  2   -13   -10   21

  |  ↓    14     7   -21        

    2      1     -3     0  ← remainder is 0      

Use grouping to factor the reduced polynomial (2x² + x - 3)  

 2x² - 2x + 3x - 3

= 2x(x - 1) +1(x - 1)

= (2x + 1)(x - 1)  

The factors are: (x - 7) (2x + 1) (x - 1) (x + 4i) (x - 4i)

The first 3 are real roots and the last 2 are complex roots

The zeros of a polynomial function are the factors of the function.

The number of real zeros of f(x) is 3

The function is given as:

Two of the factors are given as:

x - 7 ad x + 4i

The factor x + 4i is a complex factor.

If a polynomial function has a complex factor, then the conjugate of the complex factor is also a factor of the polynomial.

This means that f(x) has 2 complex factors

The degree of the polynomial is 5.

So, the number (r) of real zeros is the difference between the degree of the polynomial and the number of complex factors.

This gives

Hence, the number of real zeros of f(x) is 3

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