Answer:
Step-by-step explanation:
1. 51 degrees
2. 90 degrees
3. 17 degrees
4. 107 degrees
5. 121 degrees
6. 68 degrees
1. Using the exponent rule (a^b)·(a^c) = a^(b+c) ...
![\left(-2x^3y^4\right)\left(5x^9y^{-2}\right)=(-2)(5)\left(x^{(3+9)}y^{(4-2)}\right)\\\\=-10x^{12}y^{2}](https://tex.z-dn.net/?f=%5Cleft%28-2x%5E3y%5E4%5Cright%29%5Cleft%285x%5E9y%5E%7B-2%7D%5Cright%29%3D%28-2%29%285%29%5Cleft%28x%5E%7B%283%2B9%29%7Dy%5E%7B%284-2%29%7D%5Cright%29%5C%5C%5C%5C%3D-10x%5E%7B12%7Dy%5E%7B2%7D)
Simplify. Write in Scientific Notation
2. You know that 256 = 2.56·100 = 2.56·10². After that, we use the same rule for exponents as above.
![8 \left(32\times 10^{11}\right)=(8)(32)\times 10^{11}=256\times 10^{11}=2.56\times 10^{13}](https://tex.z-dn.net/?f=8%20%5Cleft%2832%5Ctimes%2010%5E%7B11%7D%5Cright%29%3D%288%29%2832%29%5Ctimes%2010%5E%7B11%7D%3D256%5Ctimes%2010%5E%7B11%7D%3D2.56%5Ctimes%2010%5E%7B13%7D)
3. The distributive property is useful for this.
(3x – 1)(5x + 4) = (3x)(5x + 4) – 1(5x + 4)
... = 15x² +12x – 5x –4
... = 15x² +7x -4
4. Look for factors of 8·(-3) = -24 that add to give 2, the x-coefficient.
-24 = -1×24 = -2×12 = -3×8 = -4×6
The last pair of factors adds to give 2. Now we can write
... (8x -4)(8x +6)/8 . . . . . where each of the instances of 8 is an instance of the coefficient of x² in the original expression. Factoring 4 from the first factor and 2 from the second factor gives
... (2x -1)(4x +3) . . . . . the factorization you require
Answer:
![x^3-3x^2+2x-\frac{3}{2}](https://tex.z-dn.net/?f=x%5E3-3x%5E2%2B2x-%5Cfrac%7B3%7D%7B2%7D)
Step-by-step explanation:
We can divide polynomials by other polynomials by dividing each term by the denominator. Remember, when we divide a variable by itself, we must change the exponent in our answer according to exponent rules.
![\frac{ (2x^4-6x^3+4x^2-3x)}{2x}=\frac{2x^4}{2x} -\frac{6x^3}{2x} +\frac{4x^2}{2x} -\frac{3x}{2x} =x^3-3x^2+2x-\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%20%282x%5E4-6x%5E3%2B4x%5E2-3x%29%7D%7B2x%7D%3D%5Cfrac%7B2x%5E4%7D%7B2x%7D%20-%5Cfrac%7B6x%5E3%7D%7B2x%7D%20%2B%5Cfrac%7B4x%5E2%7D%7B2x%7D%20-%5Cfrac%7B3x%7D%7B2x%7D%20%3Dx%5E3-3x%5E2%2B2x-%5Cfrac%7B3%7D%7B2%7D)