Algebra Tek A5A

Consider the following polynomial functions.

f(a) = (2a-7+a²)

g(a) = (5-a)

Which of the following are true?

• The expression that represents the sum of the polynomials is a first-degree polynomial.

• The expression that represents the difference of the polynomials illustrates that polynomials are closed under subtraction.

• The sum of f(a) and g(a) can be represented by the expression a²+a-2

• The different of f(a) and g(a) can be represented by the expression a²+a-12

• The product of f(a) and g(a) can be represented by the expression

  -a³+3a²+17a-35

Which of the following statements about closure is NOT true?

• Polynomials are closed under addition.

• Polynomials are closed under subtraction.

• Polynomials are closed under multiplication.

• Polynomials are closed under division.

Find the zeros of this quadratic.

• b=4/5, b=3
• b=4, b=-3
• b=1/5, b=3
• b=4/5, b=-3

In ideal conditions, 200 colony-forming units (cfu) of E. coli can grow to 400 cfu in 20 minutes, to 800 cfu in 40 minutes, and to 1600 cfu in an hour.

Write the equation that models the function if x represents hours.

• y = 200+200x

• y= 200(2)^x

• y = 1600x

• y = 200(8)^x

• y = 200*2x

A 25,000 gallon swimming pool needs to be completely drained for maintenance purposes. Your pump empties the pool at a rate of 30 gallons/minute.

Write an equation that can be used to determine the number of hours it will take to completely drain the pool.

• 25000-1800h

• 25000 = 1800h

• 30h = 25000

• 25000-30h

A gardener plants two types of trees in a park: Type A is five feet tall and grows at a rate of 12 inches per year. Type B is three feet tall and grows at a rate of 15 inches per year. Algebraically determine how many years it will take for these trees to be the same height.

• 6 years

• 7 years

• 8 years

• 9 years

• 10 years

A parking garage charges an initial fee of $7.00 for up to 2 hours of parking, and an hourly rate for each additional hour. The table below outlines the prices for up to 5 hours of parking. Which of the following linear equation(s) can be used to find x, the hourly parking rate after the initial fee?

• 7.00 + x = 20.50

• 11.50 + 2x = 20.50

• 7 + 4.50x = 16.00

• 3x + 7.00 = 20.50

An ice cream shop was doing research on its sales. The results showed that the relationship between the average daily temperature in Fahrenheit, t, and the daily ice cream profit in dollars, t, could be modeled by the equation c = 17.6t − 721.6. According to the model, which of the following temperatures to the nearest tenth of a degree would make the ice cream shop have a positive profit?

• 17.6^oF

• 35.2^oF

• 41.0^oF

• 72.2^oF

Based on the information provided, which statement explains why his solution is incorrect?

• He forgot to multiply x by 2 in Step 1.

• He added x to both sides of the equation in Step 2 instead of subtracting x.

• He added 1 on both sides of the equation in Step 3 instead of subtracting 1

• He multiplied by the reciprocal of 3 to get x = 2 in Step 4.

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