Brianna's teacher asks her which of these three expressions are equivalent to each other.

Expression A: 9x−3x−4
Expression B: 12x−4
Expression C: 5x+x−4

Brianna says that all three expressions are equivalent because the value of each one is −4 when x=0.
Brianna's thinking is incorrect.

Identify the error in Brianna's thinking.
Determine which of the three expressions are equivalent.
Explain or show your process in determining which expressions are equivalent.

Enter your answers and your explanation or process in the box provided.

Briana's thinking is incorrect because the numbers are different when you substitute x with numbers other than 0.

the two equations that are equivalent to each other are,

5x+x−4 and 9x-3x-4

Step-by-step explanation:

Expression A: 9x−3x−4

Expression B: 12x−4

Expression C: 5x+x−4

First I will substitute x for each of the equations.

9x-3x-4

when x equals: , then y equals:

1                        =        9(1)-3(1)-4= 2

2                       =         9(2)-3(2)-4=8

3                       =      9(3)-3(3)-4= 14

Now for 12x-4

when x equals: , then y equals:

1                        =        12(1)-4=  8

2                    =         12(2)-4= 20

3                       =      12(3)-4=  32

And for the final equation:

5x+x−4

when x equals: , then y equals:

1                        =        5(1)+(1)−4= 2

2                       =         5(2)+(2)−4 = 8

3                       =      5(3)+(3)−4=14

Based on this you can now see that the two equations that are equal are:

5x+x−4 and 9x-3x-4

~CaityConcerto

Expressions A and C are equivalent.

Step-by-step explanation:

Expression A: 9x−3x−4   Combine like terms    6x -4

Expression B: 12x−4   There are no terms to combine  12x-4

Expression C: 5x+x−4  Combine like terms   6x -4

Brianna only looked at one particular value for x.  She must look at all values for x.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

1,918

step-by-step explanation: