ARE THESE ANSWERS RIGHT ?

Express as a trinomial:
(2x-3)(x+7)
IS THE ASNWER 2x^2 + 11x - 21

WHAT IS THE VALUE OF 2 times 5^-2
IS THE ANSWER 2/25

DIVIDE:
x/x^2-49 divide by 5x^3/x^2 + 9x + 14

IS THE ANSWER x+2/5x^2(x-7)

PLEASE CHECK THESE ANSWERS

1. Correct.

2. Correct.

3. Correct! Good job!!

thanks

x/(x^2-49) divided by 5x^3/(x^2 + 9x + 14)

= [x/(x^2-49])*[(x^2 + 9x + 14)/5x^3]
= x/[(x+7)(x-7)]*[(x+7)(x+2)/5x^2]
= (x+2)/[5x^2*(x-7)]

Yes, #3 is correct. Your #2 requires parentheses. One of the ambiguous versions is correct.

Let's go through each question and explain how to get the correct answer:

1. Express as a trinomial: (2x-3)(x+7)
To multiply these binomials, you can use the FOIL method, which is multiplying the First terms, the Outer terms, the Inner terms, and finally the Last terms. So, let's do the multiplication step by step:
First terms: 2x * x = 2x^2
Outer terms: 2x * 7 = 14x
Inner terms: -3 * x = -3x
Last terms: -3 * 7 = -21
Now, combine all of these results together:
2x^2 + 14x - 3x - 21
Simplify by combining like terms:
2x^2 + 11x - 21
So, the correct answer is 2x^2 + 11x - 21.

2. What is the value of 2 times 5^-2?
To evaluate this expression, we can make use of the exponent rule which states that when you have a negative exponent, it is equivalent to its reciprocal with the positive exponent. So, let's apply this rule:
5^-2 is the same as 1/5^2
Simplify 1/5^2:
1/25
Now, multiply 1/25 by 2:
2/25
Thus, the correct answer is 2/25.

3. Divide: (x/x^2-49) ÷ (5x^3/x^2 + 9x + 14)
To divide two fractions, you need to invert the divisor (the second fraction) and multiply it by the dividend (the first fraction). So, let's calculate this step by step:
Invert the second fraction:
(x/x^2-49) * (x^2 + 9x + 14)/(5x^3)
Now, simplify the expressions:
(x/(x+7)(x-7)) * (x^2 + 9x + 14)/(5x^3)
Cancel out common factors:
(x/(x+7)(x-7)) * (x^2 + 9x + 14)/(5x^3)
Multiply the numerators and denominators:
x(x^2 + 9x + 14) / (5x^3(x+7)(x-7))
Expand the numerator:
(x^3 + 9x^2 + 14x) / (5x^3(x+7)(x-7))
Simplify to get the final answer:
x(x^2 + 9x + 14) / (5x^3(x+7)(x-7))
Thus, the correct answer is x(x^2 + 9x + 14) / (5x^3(x+7)(x-7)) or simplified as x^3 + 9x^2 + 14x) / (5x^3(x+7)(x-7)).