Question 1

Determine whether the equation is a quadratic equation.
-x + 5 = 0

Accepted Answer

A quadratic equation is an equation where the highest power of the variable is 2. In this equation, the highest power of x is 1, therefore it is not a quadratic equation. A quadratic equation is an equation with a degree of two which means it has a variable raised to the second power. The given equation, x + 5 = 0, only has a variable raised to the first power which means it is a linear equation not a quadratic equation.

Question 2

Solve.
-(y - 7)(3y + 14) = 0

Accepted Answer

Using the zero product property, we know that one of the factors must be equal to zero. Therefore, either y - 7 = 0 or 3y + 14 = 0. Solving for y in each equation, we get y = 7 or y = -14/3. Therefore, the solutions to the equation are y = 7 and y = -14/3. These values correspond to the factors (y - 7) and (3y + 14), respectively. Therefore, the equation can be written as (y - 7)(3y + 14) = 0. Thus, choice B is the correct answer, as it contains the correct factors that multiply to zero.

Question 3

Solve.
-x(6x + 30) = 0

Accepted Answer

The answer of Solve.
-x(6x + 30) = 0
...

Question 4

Determine whether the quadratic equation is in standard form.
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Accepted Answer

The given quadratic equation is not in standard form because the term containing the first degree of the variable is missing. The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a is not equal to 0. The given equation is missing the term containing x or any other variable. The quadratic equation in standard form is written as ax² + bx + c = 0, but the given equation contains symbols and format that does not match this form. Therefore, the quadratic equation is not in standard form.

Question 5

Solve.
-x(x + 12) = 0

Accepted Answer

The equation can be solved by setting each factor equal to zero: x = 0 and x + 12 = 0, which simplifies to x = -12.

Question 6

Determine whether the equation is a quadratic equation.
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Accepted Answer

The answer of Determine whether the equation is a quadratic...

Question 7

Solve.
-(x - 5)(x + 8) = 0

Accepted Answer

The equation (x - 5)(x + 8) = 0 is solved by setting each factor equal to zero: x - 5 = 0 gives x = 5, and x + 8 = 0 gives x = -8.

Question 8

Factor completely.
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Accepted Answer

The answer of Factor completely.
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Question 9

Determine whether the equation is a quadratic equation.
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Accepted Answer

The equation given is not a quadratic equation because it contains variables with exponents greater than two. It is not in the standard form of a quadratic equation, which is ax² + bx + c = 0. This is not a quadratic equation as there is no exponent of 2 on any variable terms.

Question 10

Solve.
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Accepted Answer

The given string of characters and numbers seems to be a random code with no information about its purpose. Therefore, we cannot use any mathematical techniques to solve this or derive any logical meaning from it. Thus, the only feasible option is to consider this as a random string and not choose any of the given choices.

Question 11

Solve.
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Accepted Answer

The answer of Solve.
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Question 12

Factor completely.
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Accepted Answer

The given expression does not seem to have any common factors or be able to be factored using any common techniques. Therefore, it is likely prime. However, none of the answer choices reflect a prime expression. So, the only answer choice left is C, which is a completely different expression entirely, so it cannot be factored any further into the original expression. The given expression follows the form of a difference of squares: (a^2 - b^2) = (a+b)(a-b). So, we can rewrite the expression as (z+6)(z-6), which is fully factored.

Question 13

Factor completely.
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Accepted Answer

The expression can be factored by grouping: 
11ebb63d_1b79_336a_b851_970b28182036 = (5a)^2 - 2^2 = (5a + 2)(5a - 2)
Therefore, the overall factorization is a(5a + 2)(5a - 2) The given expression is a quadratic trinomial with leading coefficient 11ebb63d_1b79_336a_b851_970b28182036_TB8475_11. Factoring out an 'a' from the expression gives us a(11ebb63d_1b79_336a_b851_970b28182036_TB8475_11a^2 + 5a - 2), which can then be factored further into a(5a + 2)(11ebb63d_1b79_336a_b851_970b28182036_TB8475_11a - 1). Therefore, the correct factorization is option C.

Question 14

Solve.
-25x2 = 4

Accepted Answer

The answer of Solve.
-25x2 = 4
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Question 15

Factor completely.
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Accepted Answer

The expression can be factored using the difference of squares formula to get (3y(2x+7)(2x-7)). This is not prime, so the answer is C. The expression can be factored using the difference of squares pattern:
(11ebb63d_1b79_5a7d_b851_451912edb895_TB8475_11) = 3y(2x + 7)(2x - 7)

Question 16

Determine whether the quadratic equation is in standard form.
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Accepted Answer

The answer of Determine whether the quadratic equation is in...

Question 17

Factor completely.
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Accepted Answer

The given expression can be factored into (11ebb63d_1b79_8192_b851_67b66d1c8e9e)(TB8475)(11), where the first factor cannot be simplified any further. It is also not a prime because it can be written as a product of two factors. Therefore, choice C is the correct answer.

Question 18

Solve.
--x(x + 17) = 0

Accepted Answer

To solve this equation, we use the Zero Product Property, which states that if ab=0, then either a=0 or b=0 (or both). Therefore, we set each factor equal to 0:
-x = 0 or x + 17 = 0
Solving for x, we get x = 0 or x = -17. Therefore, the solution set is {0, -17}.
The only choice that includes both 0 and -17 is C.

Question 19

Solve.
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Accepted Answer

The given expression can be simplified by breaking it down into simpler parts: 
- 11ebb63d_1b7a_1ce3_b851_eb5729e15562 represents some arbitrary number
- TB8475_11 can be rewritten as 11_TB8475
Thus, the simplified expression is: 
some number - 11_TB8475
To solve for this expression, we need to know the value of TB8475. Unfortunately, there is not enough information to determine the value of TB8475 from the given expression. Therefore, the best choice is option C, which acknowledges that we cannot solve for a specific value and instead provides a range of possible answers (-2 and 2). This is likely a hexadecimal equation. Converting the first part to decimal, we get -4661466858425907428. 
Converting the second part to decimal, we get 8212. 
Taking the absolute value of the first part and subtracting the second part from it, we get 4661466858425695216. 
Taking the square root of that, we get 68273113.72736, which rounds to 68273114. 
Therefore, the answer is the factors of the last value: -2 and 2.

Question 20

Factor completely.
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Accepted Answer

The answer of Factor completely.
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Quiz 6: Factoring

Determine whether the equation is a quadratic equation. -x + 5 = 0

Solve. -(y - 7) (3y + 14) = 0

Solve. -x(6x + 30) = 0

Determine whether the quadratic equation is in standard form. -

Solve. -x(x + 12) = 0

Determine whether the equation is a quadratic equation. -

Solve. -(x - 5) (x + 8) = 0

Factor completely. -

Determine whether the equation is a quadratic equation. -

Solve. -

Solve. -

Factor completely. -

Factor completely. -

Solve. -25x2 = 4

Factor completely. -

Determine whether the quadratic equation is in standard form. -

Factor completely. -

Solve. --x(x + 17) = 0

Solve. --

Factor completely. -