Algebra Class: Distance, Lines, and Sequences

Play an AI-generated podcast conversation about this lesson

What is the distance between the points A(4, 3) and B(-2, 7)?

$6$

$rac{10}{ ext{√2}}$

$8$

$ ext{√( ext{68})}$ (correct)

What is the equation of the line that passes through the points (-3, 5) and (2, -1)?

$y = rac{6}{5}x + 3$

$y = -rac{2}{5}x - 1$

$y = rac{2}{5}x + 3$

$y = -rac{6}{5}x - 1$ (correct)

What is the gradient of the line described by the equation 4x + y = 9?

$-rac{1}{4}$ (correct)

$rac{1}{4}$

$-4$

$4$

What are the coordinates of the point where the line y = 3x − 4 crosses the y-axis?

(0, -4) (C) Signup and view all the answers

What is the value of $x$ in Problem 6, where the equations are $3x + 2y = 14$ and $x - y = 1$?

2 (B) Signup and view all the answers

Which method is primarily suggested for solving the simultaneous equations in the provided problems?

10 (A) Signup and view all the answers

After solving Problem 7, what is the value of $y$ if the equations are $4x - 3y = 7$ and $2x + 5y = 11$?

4 (C) Signup and view all the answers

In Problem 8, which equation is derived by substituting to isolate $x$ or $y$?

8 (B) Signup and view all the answers

What is the next term in the sequence 3, 8, 15, 24, 35?

46 (C) Signup and view all the answers

In Problem 6, which value of $y$ corresponds to the solution of $x = 2$?

4 (D) Signup and view all the answers

What is the nth term of the sequence 7, 12, 17, 22, 27?

4n + 3 (C) Signup and view all the answers

If the rule of a sequence is $T_n = 2n^2 + 3n$, what is the second term?

10 (D) Signup and view all the answers

What is the 12th term in an arithmetic sequence where the first term is 9 and the common difference is 4?

57 (C) Signup and view all the answers

In a geometric sequence with a first term of 5 and common ratio of 2, what is the 6th term?

320 (A) Signup and view all the answers

What is the classification of a triangle with vertices at (0, 0), (4, 0), and (4, 3)?

Right-angled (D) Signup and view all the answers

Which option describes a quadrilateral formed by points (0, 0), (2, 2), (0, 2), and (2, 0)?

Parallelogram (B) Signup and view all the answers

What is the equation of a circle with a center at (2, -3) and a radius of 5?

(x - 2)^2 + (y + 3)^2 = 25 (A) Signup and view all the answers

What method is primarily used to solve systems of linear equations in this context?

Elimination method (C) Signup and view all the answers

In a system of equations, what is the purpose of multiplying one or more equations?

To facilitate elimination of a variable (B) Signup and view all the answers

Which of the following represents an example of solving a system of equations by elimination?

{ 2x + 3y = 13, 3x + 2y = 17 } (D) Signup and view all the answers

For the equations { 2x + 5y = 1, x - 7y = 2 }, what is the result when both sides of the first equation are multiplied by 3?

6x + 15y = 3 (A) Signup and view all the answers

What is a key step involved when using the elimination method?

Making coefficients of one variable opposite for cancellation (D) Signup and view all the answers

In Problem 8, what is the value of y after substituting the second equation into the first equation?

y = 5 (D) Signup and view all the answers

In Problem 9, what is the value of x after eliminating y?

x = 2 (D) Signup and view all the answers

What is the value of y in the solution to Problem 8?

y = 7 (A) Signup and view all the answers

In Problem 10, what is the value of x after solving the system of equations?

x = 7 (D) Signup and view all the answers

If we were to solve Problem 10 by substitution, which equation would be easiest to solve for one variable in terms of the other?

4x + 3y = 50 (D) Signup and view all the answers