How many solutions exist for the given equation? StartFraction one-half left-parenthesis x plus 12 right-parenthesis equals 4 x
2 answers:
Answer:
Only one solution.
Step-by-step explanation:
We have to solve for x from a linear single variable equation of x.
We have to determine the number of the solution of the given equation.
The equation is
⇒ x + 12 = 8x - 2
⇒ 7x = 14
⇒ x = 2
So, there is only one solution of the given equation of x. (Answer)
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The question is incomplete so I am writing the complete question below and attaching the scatter plot as well.
The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown
How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?
Answer:
4 people have an actual height that differs by more than 3 cm from the height predicted by the line of best fit.
Step-by-step explanation:
The question is asking us to identify which people have a height that is more than 3 cm greater or more than 3 cm less then the height predicted by the line of best fit. Hence, we need to look at the outliers of the line if best fit i.e. the points which do not lie on the line. We need to select the points that differ by 3 or more cm.
So, we can see that the first person (4 cm) has an actual height of 157 cm but the line of best fit shows the height is 161.5. So, there is a difference of more than 3 cm (161.5 - 157 = 4.5).
The second outlier at 4.3 has an actual height of 175 cm but the line of best fit shows a height of 167 cm. There is a difference of 8 cm hence this person also has an actual height which differs by more than 3 cm from the line of best fit.
At 4.8 cm metacarpal bone height, the person's actual height is 172 cm but the graph shows a height of 176 cm hence this person also has an actual height which differs by more than 3 cm from the line of best fit.
At 4.9 cm on the x-axis, the person has an actual height of 183 cm but the line of best fit shows 178 cm so this person also has an actual height which differs by more than 3 cm from the line of best fit.
So, in total there are 4 people out of 9 whose heights differ by more than 3 cm from the line of best fit.
