# 4, 7, 3, 4,….In the sequence above, the first term is 4, the second term is 7, and each term after the second term is the nonnegative difference…

4, 7, 3, 4,….
In the sequence above, the first term is 4, the second term is 7, and each term after the second term is the nonnegative difference between the previous two terms. If the nth term is the first term of the sequence that is equal to zero, what is the value of n?

Okay I know this number can be solved through first principles(finding each number in the sequence manually) but I can’t help but wonder if there’s a certain algebraic formula or method one can utilize to solve it.

# On page 28, question 8, when I looked at the solutions, the number 1 was plugged in to solve the problem…

On page 28, question 8, when I looked at the solutions, the number 1 was plugged in to solve the problem. However, on the beginning of the book the author said to never plug 0 and 1…Anyhow, my question is, if never plugging 1 is suggested, how did you know that plugging 1 in would work in your favor for the question(btw I got it right but I didn’t plug 1 in, I thought of other numbers but it did take me longer to figure out the numbers that’d add up to 11)

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

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

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

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?

# This may be a little advanced for the SAT…

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}

# Do you have the techniques and concepts for each question as your book only goes to Test #6?

Hi Mike! Your SAT book is amazing. Thank you. My daughter is prepping and is on Test #7 of the official tests. Do you have the techniques and concepts for each question as your book only goes to Test #6. I remember reading you had supplement, but now can’t find the link. Please let me know. Thank you!

Lisa

# 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?

# Can you help me with Question #29 in Practice Test 3, Section 4?

Can you help me with Question #29 in Practice Test 3, Section 4? I found the answer by subtracting multiples of 9 from 122 to find one that was divisible by 5. Is there a better way?

# How do you solve number 2 on page 28 with the plugging in method?

How do you solve number 2 on page 28 with the plugging in method?

# Test 4, section 4, question #27. Why is the answer D instead of C? Please explain this.

Test 4, section 4, question #27. Why is the answer D instead of C? Please explain this.

# The following expression represents the concentration, in microbubbles per milliliter…

The following expression represents the concentration, in microbubbles per milliliter, of the microbubble suspension remaining in a client t seconds after the technician has begun the ultrasound process.

100,000,000 ⋅ 0.5^(t/120)

Which expression shows the multiple of the concentration remaining each minute as a constant or coefficient?

# Thomas is making a sign in the shape of a regular hexagon with 4-inch sides…

Thomas is making a sign in the shape of a regular hexagon with 4-inch sides, which he will cut out from a rectangular sheet of metal. What is the sum of the areas of the four triangles that will be removed from the rectangle?

# After doing some practice problems on Rational Equations on Khan Academy, I was wondering…

After doing some practice problems on Rational Equations on Khan Academy, I was wondering would the equation be undefined if after factoring the equation we obtain cancellable factors on the denominator and the numerator? For ex: ( (2x-1) (x+4) ) / (x+4) would -4 be a plausible argument? I see the x+4 factor can be cancelled together with the one in the numerator.

# There are five houses on each side of a street…

There are five houses on each side of a street, as shown in the figure above. No two houses next to each other on the same side of the street and no two houses directly across from each other on opposite sides of the street can be painted the same color. If the houses labeled G are painted gray, how many of the seven remaining houses cannot be painted gray?

# A marine aquarium has a small tank and a large tank, each containing only red and blue fish…

Here’s a problem from Khan Academy’s SAT practice section. Please explain this one for me.

A marine aquarium has a small tank and a large tank, each containing only red and blue fish. In each tank, the ratio of red fish to blue fish is 3 to 4. The ratio of fish in the large tank to fish in the small tank is 46 to 5. What is the ratio of blue fish in the small tank to red fish in the large tank?