Answer:
The answer to (A) is -9.
The answer to (B) is 61.
The answer to (C) is [tex]-\frac{5}{24}[/tex] in fraction form or -0.208 in decimal form.
Step-by-step explanation:
For problem (A), which is [tex]a+b-c[/tex], in order to solve for this problem, plug in the information given from the question. The problem will look like [tex](-2)+(-3)-(4)[/tex]. Solve the problem by first adding (-2) + (-3), which equals (-5), and then, solve for (-5) -(4), which equals -9. The final answer for problem (A) will be -9.
For problem (B), which is [tex]b+c^{3}[/tex], start by plugging in the information given from the question. The problem will look like [tex](-3)+(4)^{3}[/tex]. Solve the problem by cubing 4, which equals 64, and then, solve for (-3)+(64), which equals 61. The final answer for problem (B) will be 61.
For problem (C), which is [tex]\frac{3b^{2}-c^{2}+a^{2} }{-3abc}[/tex], start by plugging in the information given from the question. The problem will look like [tex]\frac{3(-3)^{2}-(4)^{2}+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. Solve the problem by first simplifying the numerator.
To simplify the numerator, raise -3 to the power of 2, which will equal 9, and multiplying 3 by 9, which will look like [tex]\frac{27-(4)^{2}+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. Next, raise 4 to the power of 2, which equals 16, and multiply -1 by 16, which will look like [tex]\frac{27-16+(-2)^{2} }{-3(-2)(-3)(4)}[/tex]. The next step is to raise -2 to the power of 2, which will look like [tex]\frac{27-16+4 }{-3(-2)(-3)(4)}[/tex]. Then, subtract 16 from 27, which equals 11, and add (11) + (4), which equals 15. The numerator equals 15.
Next, simplify the denominator. First, multiply -3 by -2, which equals 6, and the problem will look like [tex]\frac{27-16+4 }{6(-3)(4)}[/tex]. Then, multiply 6 by -3, which equals -18, and the problem will look like [tex]\frac{27-16+4 }{-18(4)}[/tex]. The next step is to multiply -18 by 4, which equals -72, and the denominator will equal -72.
Then, reduce the expression by cancelling the common factor, and the common factor is 3. The final answer will be [tex]-\frac{5}{24}[/tex] in fraction form or -0.208 in decimal form.
