Practice:A) (2x – 9)(3x + 1) =
2 answers:
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Answer:
The number of beads used must be at least 40 to make a decorated rope of at least 20 feet length. The inequality is:
Step-by-step explanation:
Let the number of beads used be 'n'.
Now, length of 1 bead = 6 in
∴ Length of 'n' beads =
Now, minimum length of rope is 20 ft. Converting feet to inches, we get:
Now, beads are inserted in the rope. So, the length of rope is same as the length of all the beads joined together.
As per question, length must be at least 20 ft or 240 in.
Therefore, the length of all beads joined together must be at least 240 inches. This gives,
Therefore, the number of beads used must be at least 40 to make a decorated rope of at least 20 feet length.
Answer:
B. x < -4 and x > 3
Step-by-step explanation:
Factor and set = to 0
= 0
x = - 4 or x = 3 I call these critical values
The two numbers would divide a number line into 3 intervals. Pick a value in one of the intervals and put it in the original expression. If it makes the function positive, then all the values in that interval make the function positive. If the value you picked makes the function negative, then the values in the other intervals will make the function negative. Let's pick the value of 0 and substitute it into the function
We get + 0 - 12 = -12 which is not positive. Therefore, all the values between -4 and 3 will make the function negative. So, the values less than -4 or greater than 3 will make the function positive. Therefore, B is the correct answer.
Another way to do this problem is to graph the function and see where the graph is above the x-axis. But, sometimes it is not easy to graph the function.