10 Algebra 2 Questions!

Question

 

12

Solve the following system of equations.

2x - 3y + z = -1
2x - 2y - 2z = -8
x + 5y - 3z = 2
Choose one answer.
A. (1, 1, 0)
B. (-1, 2, 8)
C. (1, 2, 3)
D. (1, 5, -3)

 

Question 13

A bus has traveled 210 miles, and continues at a rate of 50 miles per hour. A van has driven 170 miles, and continues at a rate of 60 miles per hour. In how many hours will the two vehicles have traveled the same distance?
Choose one answer.
A. 3
B. 4
C. 5
D. 6

 

Question 14

Which point is a solution to the following system of inequalities?

4x + 3y < 12
2x - 5y > 10
Choose one answer.
A. (2, 5)
B. (1, -3)
C. (-2, 5)
D. (-1, 2)

 

Question 15

Which system of inequalities is graphed below?

A graph shows two lines that intersect in the first quadrant. Shading below a solid line that passes through (2, 0) and (-2, -10). Shading above a solid line that passes through (0, -3) and (two-thirds, 0).</div>


<div class= Choose one answer.
A. 5x - 2y < 10
2x - y > 3
B. 5x - 2y less than or greater to 10
2x - y greater than or equal to 3
C. 5x - 2y > 10
2x - y < 3
D. 5x - 2y greater than or equal to 10
2x - y less than or greater to 3

 

Question 16

What is the degree of the polynomial 2h5 + 3h4 + h2 - 3?
Choose one answer.
A. 2
B. 3
C. 4
D. 5

 

Question 17

Simplify (7a2 - 11a - 9) + (13a2 + 21a - 3)
Choose one answer.
A. 20a2 - 32a - 12
B. 20a2 + 10a - 12
C. 20a2 - 32a - 6
D. 20a2 + 10a - 6

 

Question 18

Simplify 2c3(3c3 - 4c2 - 5c + 1)
Choose one answer.
A. 5c3 - 2c2 - 3c + 3
B. 5c6 - 2c5 - 3c4 + 3c3
C. 6c3 - 8c - 10c + 2
D. 6c6 - 8c5 - 10c4 + 2c3

 

Question 19

Simplify. (x - 4)(x2 + 3x - 1)
Choose one answer.
A. x3 - x2 + 11x + 4
B. x3 - x2 - 13x + 4
C. x3 + 7x2 + 11x + 4
D. x3 + 7x2 - 13x + 4

 

Question 20

Factor completely. 9x2 - 4
Choose one answer.
A. (2x - 3)(2x - 3)
B. (2x - 3)(2x + 3)
C. (3x - 2)(3x - 2)
D. (3x - 2)(3x + 2)

 

Question 21

Which expression is a factor of 3ab - 6a + 4b - 8?
Choose one answer.
A. 4b - 2
B. 3a + 4
C. 3b - 4b
D. 3ab - 2

Answer 1

12)

 

2x - 3y + z = -1               eq1
2x - 2y - 2z = -8               eq2
x + 5y - 3z = 2                  eq3

 

We have 3 equations with three variables.  We need to use a combination of substation method and elimination. Let's substitute one equation into 2 other equations to reduce the number equations and variables.

 

Substitute eq1 into eq2 and eq3.

 

From eq1,

 

z = -2x + 3y - 1

 

2x - 2y - 2(-2x + 3y - 1) = -8

2x - 2y + 4x - 6y + 2 = -8

6x - 8y = -10               new eq2

 

 

x + 5y - 3(-2x + 3y - 1) = 2

x + 5y + 6x - 9y + 3 = 2

7x - 4y = -1                  new eq3

 

 

These are the new equations we will work with.

 

6x - 8y = -10          new eq2

7x - 4y = -1            new eq3

 

 

Multiply new eq3 by 2.  Keep new eq2.

 

6x - 8y = -10           new eq2

14 - 8y = -2             new eq3

 

Subtract new eq3 from new eq2 to eliminate the y terms.

 

-8x = -8

 

   x = 1

 

 

Substitute this value of x into new eq2 to solve for y.

 

6(1) - 8y = -10

    6 - 8y = -10

       -8y = -16

          y = 2

 

We can solve for z, but that is not necessary.  If we look at our answer choices, each solution set in written in the form (x y, z).

 

So far, our solution is (1, 2, z).  The only answer choice that matches this pair is choice (C).

 

 

13)

 

We can write a system of equations to represent the situation.

 

Let x = time in hours

Let y = distance

 

For the bus

 

y = 50x + 210             eq1

 

 

For the van

 

y = 60x + 170           eq2

 

 

Since both vehicles need to be at the same distance, we equate both of them.

 

50x + 210 = 60x + 170

 

Solve for x.

 

 

Subtract 50x on both sides of the equation.

 

210 = 10x + 170

 

 

Subtract 170 on both sides of the equation.

 

40 = 10x

 

 

Divide 10 on both sides of the equation.

 

4 = x

 

 

Your answer is (B).

 

 

14)

 

Solve for y in each equality.

 

 

4x + 3y < 12    ----->   3y < -4x + 12    ----->   y < (-3/4)x + 4 

2x - 5y > 10     ----->    -5y > -2x + 10    ----->    y > (2/5)x - 2

 

 

Now we just look for the point that lies below the line    y=(-3/4)x + 4 ,  and at the same time  above the line  y=(2/5)x - 2.

 

 

15) This is same as the previous question.  Draw a coordinate system and draw lines on that coordinate system based on the restrictions.

 

Pick the answer that satisfies all of those restrictions.

 

 

16)

 

The degree of a polynomial is the highest value of the exponent in the polynomial.  The highest exponent is 5 because of the term 2h⁵.

 

The degree is 5.

 

 

17)

 

(7a² - 11a - 9) + (13a² + 21a - 3)

 

 

Distribute the terms to get rid of parentheses.

 

7a² - 11a - 9 + 13a² + 21a - 3

 

 

Combine like terms and get your answer.

 

 

18)

 

The fastest way to do this is to multiply the term outside the parenthesis by the first term inside the parenthesis.

 

(2c³)(3c³) = 6c⁶

 

 

This is the first term in the polynomial.  The answer choice that has this first term is  choice (D).

 

 

19)

 

(x - 4)(x² + 3x - 1)

 

 

Use (x² + 3x - 1) as the GCF.

 

x(x² + 3x - 1) - 4(x² + 3x - 1)

 

 

Now distribute and combine like terms to get your answer.

 

 

20)

 

 9x² - 4

 

This is difference of perfect squares.  This is because 3² is 9, x*x is x², and 2² is 4.

 

(3x + 2)(3x - 2)

 

 

 

21)

 

3ab - 6a + 4b - 8

 

 

To factor, we group each part.

 

3a(b - 2) + 4(b - 2)

 

 

Notice that (b - 2) is the GCF here.

 

(b - 2)(3a + 4)

 

 

Since the question only asks for a single factor, pick the one from the answer choice that match the work done here.

 

 

 

And we are done here!   :)