Li keeps track of the time he spends working out each week. The table shows the
number of cardio workouts and the number of weighted workouts for 3 recent weeks,
The total time in minutes for weeks 1 and 2 are given. Each cardio workout is the same
length of time, and each weighted workout is the same length of time. The system of
equations can be used to represent this situation.
Use the drop-down menus to complete each statement.

The total time Li spent for week 3 was 210 minutes.

Step-by-step explanation:

Step 1; Assume x to be the number of cardio workouts a week and y be the number of weighted workouts a week, so we have

4x + y = 210, take this as equation 1 ,

3x + 2y = 195, take this as equation 2 .

Step 2; We multiply equation 1 with 2 and equation 2 with 1 so we can cancel out the variable x in both equations. By doing this we get

8x + 2y = 420, take this as equation 3,

-18x +4y =32, this is equation 2

If we subtract equation 2 from equation 3, we cancel out the y variable and can calculate the value of x.

5x = 225 , x = 225/5 = 45, x = 45.

Step 3; Substituting this value of x in any of the previous equations we will get x's value. Here this value of x is substituted in equation 1.

4(45) + y = 210, 180 + y = 210 , y = 210 - 180, y = 30.

So we have x = 45 and y = 30.

Step 4; Now we calculate the time spent in the third week by substituting the values of x and y in 2x + 4y,

2x + 4y = 2 (45) + 4 (30) = 90 + 120 = 210 minutes.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.