Chapter 5 Extra Credit

1) Scientists have determined that the speed at which light travels is approxiamtely 300,000,000 meters per second. Express this speed in scientific notation.

3 x 10^7 m/s

3 x 10^8 m/s

3 x 10^(-8) m/s

30 x 10^(-7) m/s

The speed of light is approximately 300,000,000 meters per second. In scientific notation, this can be expressed as 3 x 10^8 m/s.

Explanation

The speed of light is approximately 300,000,000 meters per second. In scientific notation, this can be expressed as 3 x 10^8 m/s.

2) Factor m^2 + 9m + 14 completely.

M(m + 23)

(m + 14)(m + 1)

(m + 7)(M + 2)

M(m + 9) + 14

The given expression is a quadratic trinomial in the form of m^2 + 9m + 14. To factor it completely, we need to find two binomials whose product equals the given trinomial. By using the factoring method, we can determine that the correct factorization is (m + 7)(m + 2).

Explanation

The given expression is a quadratic trinomial in the form of m^2 + 9m + 14. To factor it completely, we need to find two binomials whose product equals the given trinomial. By using the factoring method, we can determine that the correct factorization is (m + 7)(m + 2).

3) Simplify (5m - 9) + (4m + 2)

9m - 11

M - 11

9m - 7

20m^2 - 18

The given expression is (5m - 9) + (4m + 2). To simplify this expression, we can combine like terms. The like terms in this expression are the terms with the variable m. Adding the coefficients of these terms, we get 5m + 4m = 9m. Then, we add the constant terms -9 and 2, which gives us -7. Therefore, the simplified expression is 9m - 7.

Explanation

The given expression is (5m - 9) + (4m + 2). To simplify this expression, we can combine like terms. The like terms in this expression are the terms with the variable m. Adding the coefficients of these terms, we get 5m + 4m = 9m. Then, we add the constant terms -9 and 2, which gives us -7. Therefore, the simplified expression is 9m - 7.

4) Simplify (x^2 - 2x - 35) / (x + 5)

X^2 - x - 30

X - 7

X + 5

X^3 + 3x^2

To simplify the expression (x^2 - 2x - 35) / (x + 5), we can factor the numerator as (x - 7)(x + 5). Then, we can cancel out the common factor of (x + 5) in the numerator and denominator, leaving us with the simplified expression x - 7.

Explanation

To simplify the expression (x^2 - 2x - 35) / (x + 5), we can factor the numerator as (x - 7)(x + 5). Then, we can cancel out the common factor of (x + 5) in the numerator and denominator, leaving us with the simplified expression x - 7.

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A

B

C

D

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Explanation

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6) Simplify (3x^0)^2(2x^4)

X^4

12x^4

18x^6

18x^4

To simplify the given expression, we start by simplifying the exponent of the first term, which is 3x^0. Any number raised to the power of zero is equal to 1, so 3x^0 simplifies to 3.

Next, we square the simplified first term, which gives us 3^2 = 9.

Finally, we multiply the squared first term (9) with the second term (2x^4), which gives us 18x^4.

Therefore, the correct answer is 18x^4.

Explanation

To simplify the given expression, we start by simplifying the exponent of the first term, which is 3x^0. Any number raised to the power of zero is equal to 1, so 3x^0 simplifies to 3.

Next, we square the simplified first term, which gives us 3^2 = 9.

Finally, we multiply the squared first term (9) with the second term (2x^4), which gives us 18x^4.

Therefore, the correct answer is 18x^4.

7) Simplify (t^2 + t -6) / (t^2 -7t + 10). Assume that the denominator is not equal to sero.

(t + 3) / (t - 5)

(t - 2) / (t + 5)

(t - 3) / (t + 5)

(t + 3) / (t + 5)

The given expression can be simplified by factoring the numerator and the denominator. The numerator can be factored as (t + 3)(t - 2), and the denominator can be factored as (t - 5)(t - 2). By canceling out the common factor of (t - 2), we are left with (t + 3)/(t - 5).

Explanation

The given expression can be simplified by factoring the numerator and the denominator. The numerator can be factored as (t + 3)(t - 2), and the denominator can be factored as (t - 5)(t - 2). By canceling out the common factor of (t - 2), we are left with (t + 3)/(t - 5).