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Nat2105 [25]
3 years ago
9

Numbers like 10,100,1000 and so on are called

Mathematics
1 answer:
nevsk [136]3 years ago
5 0
They are called integers.
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1. Make sure your answers and work is SHOWN please and steps are in order.
JulijaS [17]

Been a while since I've done synthetic division.

1a. Let's assume that's supposed to be an equals sign

p(x) = 2x⁴ - 3x³ - 6x² + 5x + 6

possible rational roots have factors of 6 in the numerator and of 2 in the denominator.  We'll only worry about negative numerators.

Factors of six: 1,2,3,6, and we don't forget -1,-2,-3,-6

Factors of 2: 1,2

Possible rational roots:

(dividing by 1:) 1,-1,2,-2,3,-3,6,-6

(dividing by 2:) 1/2, -1/2  (2/2=1 is a duplicate, don't have to repeat it), 3/2, -3/2

Possible rational roots: 1,-1,2,-2,3,-3,6,-6, 1/2, -1/2, 3/2, -3/2

Synthetic division, trying x=1,

   1 | 2  -3  -6  5  6

             2  -1  -7  -2

       2    -1  -7  -2  4

Got a remainder of 4, so 1 isn't a root;

Trying x=-1  

-1 | 2  -3  -6  5  6

         -2   5  1  -6

     2  -5  -1  6  0

Zero remainder, found a root, x=-1.  This division says

(2x⁴ - 3x³ - 6x² + 5x + 6) / (x + 1) = 2x³ - 5x² - x + 6

Same set of rational roots on the cubic, we continue with x=2

2 | 2 -5 -1 6

         4 -2 -6

    2  -1 -3 0

Another zero remainder, x=2 is a root.  We're left with 2x² - x - 3 = 0, which factors as

(2x - 3)(x + 1) = 0

That's a second factor of x+1.  Our final factorization is

2x⁴ - 3x³ - 6x² + 5x + 6 = (x + 1)²(x-2)(2x - 3)

Fourth degree with a positive leading coefficient so goes to +infinity at both ends.  Double zero at x=-1, so it's tangent there, just touching the x axis, then down through x=3/2 and up through x=2.  

I'll leave the actually sketching and the other two polynomials to you -- that took some time.

4 0
3 years ago
GIVEN: f(x)=3x-7, g(x)=2x^(2)-3x+1, h(x)=4x+1, k(x)=-x^(2)+3
tekilochka [14]

Answer:

32x^2+4x

3x-7, g(x)=2x^(2)-3x+1, h(x)=4x+1, k(x)

3 0
3 years ago
Write the equation of the line that passes through (3, 4) and (2, –1) in slope-intercept form.
matrenka [14]
1) slope is 6 and y-intercept is ( 0,5)    y = mx + b, m = 6, b = 5    y = 6x + 5 2)line passes through the points ( 3,6) and ( 6,3 )   First find the slope:  m = (3-6)/(6-3) = -3/3 = -1   y = -x + b   Plug in one of the given points (x,y) and find b   6 = -3 + b   9 = b  <span> y = -x + 9</span> a horizontal line that passes through the point ( -1,7)Horizontal lines have a constant y-value and formaty = c  where c is a constant number. y = 7 y=-3x+3x intercept:  set y = 0 and solve for x0 = -3x + 33x = 3x = 1x-intercept: (1, 0) y-intercept:  set x = 0 and solve for yy = -3(0) + 3y = 3y-intercept: (0,3) y=0,5x-1Is this two equations? The line y=0 has y-intercept at (0,0)The x-intercept is the entire x-axis y=5x-1x -intercept:  Set y = 0 and solve for x y-intercept: Set x = 0 and solve for y 
5 0
3 years ago
Need help on this math problem
Lyrx [107]

Answer:

the expression would be 20h+25

Step-by-step explanation:


3 0
3 years ago
Ivan packed 56 apples and 72 pears into boxes. he packed both apples and pears into each box. he put the same number of apples i
Gekata [30.6K]
To find how much money Ivan can earn selling fruit you will find what the greatest number of boxes of fruit he can make by finding the greatest common factor of 56 and 72.

Do the by listing the factors of each and find the greatest way they can divide.

56 - 1, 2, 4, 7, 8, 14, 28, 56
72 - 1, 2, 3,4, 6,8, 9,12, 18,36,72

8 is the biggest way to divide them, so

8 x $19.95 = $159.60

Ivan can earn $159.60.
3 0
3 years ago
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