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KonstantinChe [14]
3 years ago
11

-5/4-(-1/6) help please

Mathematics
1 answer:
tiny-mole [99]3 years ago
3 0
A way to add fractions that always works is to multiply each numerator by the denominator of the other, then express the sum of products over the product of the denominators.
\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{a}{b}\cdot\dfrac{d}{d}+\dfrac{c}{d}\cdot\dfrac{b}{b}\\\\=\dfrac{ad+bc}{bd}

Here, you have
\dfrac{-5}{4}-\dfrac{-1}{6}=\dfrac{-5\cdot6-(-1)\cdot4}{4\cdot6}=\dfrac{-26}{24}\\\\=\dfrac{-13}{12}=-1\frac{1}{12}

The sum is -1 1/12
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Need help with this
Alecsey [184]

\frac{x {}^{3}  - 3x {}^{2} - 10x {}^{2} + 30x + 4x - 12  }{x - 3 }  \\  \frac{x {}^{2} \times (x - 3) - 10x \times (x - 3) + 4 \times (x - 3) }{x - 3}  \\  \frac{(x - 3)(x  {}^{2}  - 10x + 4 )}{x - 3}  \\ x {}^{2}  - 10x + 4
8 0
3 years ago
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
Find the value of x.
dmitriy555 [2]

Answer:

x = 57°

Step-by-step explanation:

The angle not 76° or x° is 180-133 which is 47°. A triangles angles always sum up to 180° so:

76°+47°+x°=180°

123°+x°=180°

x°=57°

6 0
3 years ago
Type the correct answer in each box.
Vikki [24]

Answer:

Cos<42 sin<16 :)

Step-by-step explanation:

3 0
3 years ago
1) What is 5/7 x 3/5? A)2/3 B)2/9 C)3/7 D)5/4
Yuliya22 [10]

Answer: 3/7

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
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