Answer:
x = -3
Step-by-step explanation:
36(x + 4) = 36
Divide both sides by 36
x + 4 = 1
Subtraact 4 from both sides
x = -3
Distance traveled in the first hour = 50 miles
Distance traveled in the second hour = 72 miles
Distance traveled in the third hour = 46 miles
Total distance = 50 + 72 + 46 = 168 miles
23 miles = 1 gallon
168 ÷ 23 = 7.30 gallons (nearest hundredth)
Answer: 7.30 gallons
Answer:
B)Create a circle with the origin as its center and a radius of the origin and point A, then locate a point on the circle that is 90 clockwise
Step-by-step explanation:
This is because, to locate a point rotated by 90° from point A, we first draw a circle with the origin as its center and a radius of the origin and point A. We then locate a point on the line that is 90° clockwise from point A. For a 90° clockwise rotation, for a given pair of coordinates, (x,y), the resulting pair of coordinates is (y,-x). So, for the coordinates (1,4), the resulting coordinates we are looking for is (4, -1), which is the point rotated 90° clockwise from point A. The point is thus (4,-1).
Answer:
See explanation
Step-by-step explanation:
a) To prove that DEFG is a rhombus, it is sufficient to prove that:
- All the sides of the rhombus are congruent:

- The diagonals are perpendicular
Using the distance formula; 








Using the slope formula; 
The slope of EG is 

The slope of EG is undefined hence it is a vertical line.
The slope of DF is 

The slope of DF is zero, hence it is a horizontal line.
A horizontal line meets a vertical line at 90 degrees.
Conclusion:
Since
and
, DEFG is a rhombus
b) Using the slope formula:
The slope of DE is 

The slope of FG is 
