a^3 – 3a^2b + 3ab^2 – b^3
(a – b )(a – b)
If I did not recognize that the numerator was the difference of cubes and that I could factor out (a-b)^2 from numerator and denominator, could this be solved using polynomial division?
Here’s a question from the May 2023 (US) SAT, non-calculator section:
Alice took 60 minutes to complete a task on her first trial. The time it took Alice to complete the task decreased by 10% of the previous time for each additional trial. Approximately how many minutes will it take Alice to complete the task on her fifth trial?
I know we can solve this by subtracting 10% of the current value 5 times, but is there a more direct way to solve, maybe as a function?
The equation ax^2 + 190 x + c has a given factor of px +q. What is the product of ac?
Hi Mike, can you explain #29 Section 4, October 2022 SAT?
For a polynomial p(x), the value of p(3) is -2. Which of the following must be true about p (x) ?
A) x -5 is a factor of p(x).
B) x -2 is a factor of p(x).
C) x +2 is a factor of p(x).
D) The remainder when p(x) is divided by x -3 is -2.
Mike…check the wording on this Q (#37; section4). I lose track of what it’s asking for. Can you break it down? Tks!
The value of r is 20/21 times the value of t, where t>0. The value of t is what percent greater than the value of r?
Hey Mike! Is this a corresponding coefficients question? Can you solve please? Thanks! (#36 Section 4)
-9x + 24qx = 36
In the given equation, q is a constant. The equation has no solution. What is the value of q?
Can you explain this Q #29 from Calculator section of Oct 2022 PSAT:
A quadratic function can be used to model the height, in feet, of an object above the ground in terms of time, in seconds, after the object was launched. According to the model, an object was launched into the air from a height of 0 feet and reached its maximum height of 3136 feet 14 seconds after it was launched. Based on the model, what was the height, in feet, of the object 1 second after it was launched?
So I can’t understand the answer key explanation for the 131st question in the Extra Practice (PWN 5th edition)
Could you explain how to solve this problem?
The distance between the points (2,1) and (x,7) as graphed on the standard (x,y) coordinate plane is 10. What is one possible value for x?
m(t₂)−m(t₁)=15(t₂ − t₁ )
A chemist dissolves sodium acetate in boiling water. As the temperature cools down, the crystals start to grow with increasing mass m(t), in grams (g) t seconds (s) after crystallization. The equation above shows this relationship where t₁ < t₂. Which of the following correctly explains the growth of the crystal mass?
The crystal mass grows linearly by 15g per s
The crystal mass grows exponentially by 1g every 15s
The crystal mass grows linearly by a factor 15 every s
In tennis, a player must win at least 6 games to win a set. If g is the number of games the player won and s is the number of sets the player won, which of the following inequalities must be true?
A. s ≤ 6g
B. s ≥ 6g
C. 6s ≤ g
D. 6s ≥ g
I thought the answer C and D would cancel out since g is games and number of games is 6. So then I chose A but that answer was wrong. Could you explain the reason for that?
x^3 + 7x^2 − 36
The polynomial above has zeros at -6 and 2. If the remaining zero is z, then what is the value of -z?
Mike, can you show best way to solve this insane question!? (#38 with Calculator OCT 1, 2022 SAT)
Two numbers, a and b, are each greater than zero, and 4 times the square root of a is equal to 9 times the cube root of b. If a=2/3, for what value of x is a^x equal to b?
5G + 45R = 380
At a school fair, students can win colored tokens that are worth a different number of points depending on the color. One student won G green tokens and R red tokens worth a total of 380 points. The given equation represents this situation. How many more points is a red token worth than a green token?
Store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. Store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. A certain purchase of raspberries and blackberries would cost $37.00 at Store A or $66.00 at Store B. How many pints of blackberries are in this purchase?