1.Solve the inequality (x-2)(x+1) ≥ 0 .
1 answer:
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Answer:
()***********************
<--------------------(-2)-------(0)------(2)--------------------------->
Step-by-step explanation:
Subtract on both sides:
Simplify both sides:
Divide both sides by 2:
So this means we want values of greater than 2, not including 2.
()***********************
<--------------------(-2)-------(0)------(2)--------------------------->
G = number of girls taking the martial arts classes
and
B = number of boys taking the martial arts classes
We know that for every girl, there are 3 boys. Therefore, the proportion of girls to boys is:
= 
When you simplify this ratio by cross-multiplying you get:
3G = B
When you think about this, it makes sense because you know that there are 3 times as many boys as there are girls. Therefore you would need to multiply the number of girls by 3 to equal the number of boys in the class.
We know that there are 236 total people in the class, Therefore we know that:
G + B = 236
You can replace the B in the equation above with your simplified ratio to solve, since both contain the variable B:
G + B = 236
is the same as
G + 3G = 236 ->
4G = 236 ->
G = 59
So there are 59 girls in the class, but you need to figure out the number of boys, not girls. Therefore, subtract 59 from 236 to get to the final answer:
G + B = 236
59 + B = 236
59 + B - 59 = 236 - 59
B = 177
and
B = number of boys taking the martial arts classes
We know that for every girl, there are 3 boys. Therefore, the proportion of girls to boys is:
When you simplify this ratio by cross-multiplying you get:
3G = B
When you think about this, it makes sense because you know that there are 3 times as many boys as there are girls. Therefore you would need to multiply the number of girls by 3 to equal the number of boys in the class.
We know that there are 236 total people in the class, Therefore we know that:
G + B = 236
You can replace the B in the equation above with your simplified ratio to solve, since both contain the variable B:
G + B = 236
is the same as
G + 3G = 236 ->
4G = 236 ->
G = 59
So there are 59 girls in the class, but you need to figure out the number of boys, not girls. Therefore, subtract 59 from 236 to get to the final answer:
G + B = 236
59 + B = 236
59 + B - 59 = 236 - 59
B = 177