In the system of equations above, a and b represent the cost, in dollars, of buying x buffalo wings at two different restaurants. What amount of money will get you the same number of buffalo wings at both restaurants?
1/2 x = a
x + y = 5a
In the system of equations above, a is a constant such that 0 <a <1/3. If (x,y) is a solution to the system of equations, what is one possible value of y?
(Answer: 0 < x < 1)
Thank you, Mike, for your ever-awesome explanations! Here’s a question from April 2017 SAT:
A question from the May 2018 SAT (Section 4 #18)
kx + y = 1
y = -x² + k
In the system of equations above, k is a constant. When the equations are graphed in the xy-plane, the graphs intersect at exactly two points. Which of the following CANNOT be the value of k?
A. 3
B. 2
C. 1
D. 0
If f and g are functions, where f(x) = x^3 -10x^2 +27x – 18 and g(x) = x^3 – x^2 – 6x, which of the following gives a relationship between f and g?
A) g(x) = 3 f(x)
B) g(x) = f(x) – 3
C) g(x) = f(x) + 3
D) g(x) = f(x – 3)
E) g(x) = f(x + 3)
Can you solve w/o graphing?
Here are a couple questions from the old official SAT Subject Test Math I practice exam:
The function f is defined by f(x) is x^4 – 4x^2 + x + 1 for -5 ≤ x ≤ 5. In which of the following intervals does the minimum value of f occur?
A) -5 ≤ x ≤ -3
B) -3 ≤ x ≤ -1
C) -1 ≤ x ≤ 1
D) 1 ≤ x ≤ 3
E) 3 ≤ x ≤ 5
Can you solve w/o graphing?
In PWN p. 159 (p. 157 later printing) #8
In the xy-plane, where a and b are constants, the graphs …
The question does not specify that a and b are positive values. If one or both were negative, wouldn’t that change the answer?
PWN p. 151 #8 question
In PWN the SAT Math Guide (4th Ed, first printing p. 151), Polynomials chapter question #8, you explain the answer by graphing on calculator. Could you explain the answer to this question without graphing, in particular, why A, C and D are true and why B is false? Many thanks!
PWN the SAT Math Guide p. 122 (p. 120 in newer printing) #9
h = -4.9^2 + t + 1.5
The equation … After how many seconds will the coin land on the ground?
When the coin lands, y=0, so we just need to solve the quadratic. Using the quadratic formula, however, I get a messy repeating decimal, not .664, .665. Could you solve this for me using the quadratic formula?
Also, I tried to search the Q&A here to see if you had already answered this question. Could you make an index for PWN the SAT Math Gu
PWN the SAT Math Guide p. 112 (p. 110 in later printing) #3:
Question relating to the exponent in the answer: It is a little unclear to me that the Value column indicates the value at the END of each year. The text states that the values represent “the value of his account in each of the next three years.” Must we presume that “in each” means at the END of each of those years, at which point the interest would have been accrued for that full year?
College Board Test 4 Section 3 #9:
____
√x-a = x-4
If a=2 what is the solution set of the preceding equation?
A. {3, 6}
B. {2}
C. {3}
D. {6}
Is there another way to solve this quickly besides plugging in the answer choices?
Functions f and g intersect at the points (–3,5), (2,8) and (11,–17). Which of the following could define the function h(x) = f(x) – g(x)?
A) h(x) = (x + 3)(x – 2)(x –11)
B) h(x) = (x – 5)(x – 8)(x + 17)
C) h(x) = (x + 5)(x – 6)(x + 6)
D) h(x) = (x – 3)(x + 2)(x + 11)
f(x) = x^3 – cx^2 + 4x – 4c
In the function f above, c is a constant. How many x-intercepts does the function have?
Can you show how to solve this through logic/algebra? TIA!!
The graph of a linear function f has a positive slope with intercepts (a,0) and (0,b), where a and b are non-zero integers. Which of the following statements about a and b could be true?
A) a + b = 0
B) a – 2b = 0
C) a = b
D) 0 <a < b
(I only know that Choice C is out because that would be true only if the slope=1 and the line passed through the origin, but since a and b are non-zero integers, there can be no point (0,0), so that one answer choice is out. )
y = x^2 + a
y = -x^2 + b
In the system of equations above, a and b are constants. Which of the following must be true if th esystem of equations has two solutions?
A) a is less than b.
B) a is greater than b.
C) a is equal to b.
D) a and b are both equal to zero.