Robin

In the “Proving Grounds” Quiz 1 #5 explanation, you state: “…We know that, as a general rule, the remainder when a polynomial f(x) is divided by x – a is f(a).” Can you explain this further?

Posted:

In the “Proving Grounds” Quiz 1 #5, this question is given:

p(x) = ax^2 + bx + c
q(x) = ax^2 + bx + d

The functions p(x) and q(x) are defined above, and a, b, c, and d are constants. If x – 3 is a factor of p(x) and d is 8 greater than c, what is the remainder when q(x) is divided by x – 3?

In your answer explanation, you state:
“…We know that, as a general rule, the remainder when a polynomial f(x) is divided by x – a is f(a).”

Can you explain this further?

Robin

In the system of equations above, a and b represent the distance, in meters, two marathon runners are…

Posted:

a = 4800 – 6t
b = 5400 – 8t

In the system of equations above, a and b represent the distance, in meters, two marathon runners are from the finish line after running for four hours and t seconds. How far will runner a be from the finish line when runner b passes her?

A. 300 meters
B. 500 meters
C. 100 meters
D. 3000 meters

Robin

A rideshare app charges $2 per trip plus $0.4 per mile…

Posted:

A rideshare app charges $2 per trip plus $0.4 per mile. A competitor charges $1 for the first 6 miles plus $0.5 per mile for every additional mile. For what length trip would the two services charge the same amount?

A. 10 miles
B. 18 miles
C. 20 miles
D. 40 miles

Can you craft an algebraic equation to solve this directly – or is plugging in the answers the way to go?

Robin

This may be a little advanced for the SAT…

Posted:

This may be a little advanced for the SAT, but complex numbers sometimes show up –as do cubic polynomials– so hopefully you can address this for me! TIA!

Which of the following could be the full set of complex roots of a cubic polynomial with real coefficients?

A. { 0, 1, i}
B. {1, i, 2i}
C. {2, i}
D. {3, 2 + i, 2 – i}

Robin

A question about composite functions

Posted:

A question about composite functions:
If f(x) = √x and g(x) = x^2, and you are solving for f(g(x)), ordinarily you solve for g(x) and then plug that value into f(x) to solve for f(g(x)). But what if x is a negative number? When you square it, you’ll get a positive value and then when you take the square root of that to solve for g(f(x)), the final answer will be positive only. Is that correct?

Robin

A logarathim question

Posted:

A logarathim question:

pH = – log h

The pH of a solution is dependent on the concentration of hydronium ions, h, and can be calculated by the equation above. If the concentration of hydronium in solution A is 100 times the concentration of the hydronium in solution B, what is the absolute value of the difference in their pH values?

A. –2
B. 2
C. 3
D. 10
E. 100

Robin

One gallon of honey weighs approximately 12 lbs. If one gallon of honey is mixed with 5 gallons of water to make tea, how many ounces of honey will be in each 8 fluid ounce cup of tea?

Posted:

One gallon of honey weighs approximately 12 lbs. If one gallon of honey is mixed with 5 gallons of water to make tea, how many ounces of honey will be in each 8 fluid ounce cup of tea?
Choices are 1, 2, 3 or 4. (Answer= 2) given: 16 oz = 1 lb, 128 fl oz = 1 gallon

Robin

PWN the SAT Parabolas drill explanation p. 325 #10

Posted:

PWN the SAT Parabolas drill explanation p. 325 #10: The final way to solve: If we are seeking x=y, since the point is (a,a), why can you set f(x) = 0? You start out with the original equation in vertex form, making y=a and x=a, but halfway through you change to y=0 (while x is still = a). How can we be solving the equation when we no longer have a for both x and y?