How do you factor 64-x^2 completely?

Answer:

B, C

Step-by-step explanation:

Amy should have flip the numerator and the denominator of the second fraction before multiplying. She also used addition instead of multiplication for the numerators.

Answer:

B C

Step-by-step explanation:

A. The number of different colors on the page.

D. Half the speed of the car.

These statements contain variables representing unknown quantities or values.

Variables in mathematics and science are symbols that represent unknown values or quantities. Let's analyze each statement to identify the ones containing variables:

A. "The number of different colors on the page."

This statement contains a variable because it represents an unknown quantity, the number of colors.

B. "They scored 27 points."

This statement does not contain a variable as it explicitly states a specific value (27 points).

C. "Eighty miles per hour."

This statement does not contain a variable as it provides a specific constant value (80 miles per hour).

D. "Half the speed of the car."

This statement contains a variable because it represents an unknown value, which would depend on the actual speed of the car.

In summary, the statements containing variables are:

A. The number of different colors on the page.

D. Half the speed of the car.

These statements represent quantities that can vary, making them suitable for mathematical or scientific analysis where variables are used to express relationships and solve equations.

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Answer :

All values of \( c \), specifically \( c = 49, 100, 144, \) and \( 169 \), can make a polynomial a perfect square trinomial depending on the other terms of the polynomial.

Step-by-step explanation :

1. Understanding Perfect Square Trinomials :

A perfect square trinomial is one that can be written in the form:

\[ (ax + b)^2 = a^2x^2 + 2abx + b^2 \]

From this formula, the value \( c \) would be equivalent to \( b^2 \), and the coefficient of the linear term (the term with \( x \)) would be \( 2ab \).

2. Analyzing Given Options :

  - Option 1 : c = 49

    For \( c = 49 \), \( b^2 = 49 \) which implies \( b = \pm 7 \). The middle term would then be \( 2a(7) = 14a \).

  - Option 2 : c = 100  

    For \( c = 100 \), \( b^2 = 100 \) which means \( b = \pm 10 \). The middle term would then be \( 2a(10) = 20a \).

  - Option 3 : c = 144  

    For \( c = 144 \), \( b^2 = 144 \) which translates to \( b = \pm 12 \). This makes the middle term \( 2a(12) = 24a \).

  - Option 4 : c = 169  

    For \( c = 169 \), \( b^2 = 169 \) which gives \( b = \pm 13 \). Consequently, the middle term would be \( 2a(13) = 26a \).

3. Conclusion :

Without specific details on the polynomial or its middle term, we can deduce that any of the provided options for \( c \) can result in a perfect square trinomial if the linear term of the polynomial matches the \( 2ab \) value corresponding to that \( c \).