The choices are missing but we can find the right equation from the given information
The equation that models this situation is 6 g + 10 m = 162
Step-by-step explanation:
The given is:
- Max earned a total of $162 working at two jobs
- He worked 6 hours at his grandfather's store
- He worked 10 hours at the local movie theater
- g represents the hourly rate paid by Max's grandfather, and m represents the hourly rate paid by the movie theater
We need to write an equation models this situation
∵ g represents the hourly rate paid by Max's grandfather
∵ He worked 6 hours at his grandfather's store
∴ He earned from his grandfather = 6 × g = 6 g dollars
∵ m represents the hourly rate paid by the movie theater
∵ He worked 10 hours at the local movie theater
∴ He earned from the local movie theater = 10 × m = 10 m dollars
Add 6 g and 10 m to find his total earning
∵ His total earning = 6 g + 10 m
∵ Max earned a total of $162
- Equate his total earning by 162
∴ 6 g + 10 m = 162
The equation that models this situation is 6 g + 10 m = 162
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Answer:
Step-by-step explanation:
A box plot is the diagrammatic representation of the five number summary. It includes 5 items:
The minimum.
Q1 = the first quartile or the 25% mark.
The median.
Q3 = the third quartile or the 75% mark.
The maximum.
Rearranging the data in ascending order, it becomes
169, 163, 153, 166, 149, 148, 146, 145, 152, 163
145, 146, 148, 149, 152, 153, 163, 163, 166, 169
Minimum = 145
Maximum = 169
Median = (152 + 153)/2 = 152.5
The median divides the data into two equal halves. The middle of the lower halve is Q1 while the middle of the upper halve is Q3
Q1 = 148
Q3 = 163
The diagram of the box plot is shown in the attached photo
Answer:
4.31 units
Step-by-step explanation:
A pentagon is a polygon with five straight sides.
The formula to apply here will be finding area from side length, assuming that this is a regular pentagon with five sides of equal length.
Lets take each side length to be x units
Divide the pentagon into five triangles by joining a line from the center to any vertex of the pentagon.
Now you have five equal triangle.Take the base triangle and divide it into two(take a line from center of pentagon to hit the base at 90°)
This will divide the base triangle of length x unit into two equal triangles with base length x/2 units.
The angle at the pentagon center for the small formed triangle will be 36°. Here you have a triangle with base x/2 units and angle 36° at top center.
To get the height of the triangle you apply formula for tangent of an angle;
height, h=0.5x /tan 36°
Find area of the small triangle;
Area=1/2 *b*h
where b is base length=0.5x and h is height = 0.5x/tan 36°
Area=1/2*0.5x * (0.5x /tan 36°) Area for one small triangle.
However, you notice that you will have 10 small triangles for the whole pentagon, hence multiply this area by 10 which should be equal to the area of the pentagon given 32.
32=1/2 * 0.5x *(0.5x /tan 36°) *10
32=1.25x² /tan 36°
32*0.7265=1.25x²
18.60=x²
√18.60=x
4.31=x
Measurement of one side is 4.31 units
Answer:
Step-by-step explanation:
The equations given are:
For the equations to generate the same independent value, then
This implies that:
Group similar terms to get:
Simplify to get:
