A line is parallel to y = 3x + 5 and intersects the point (-2 , 6). What is the equation of this parallel line?
2 answers:
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Answer:
StartFraction 50 miles Over 1 hour EndFraction = StartFraction 200 miles Over question mark hours EndFraction
Step-by-step explanation:
For constant speed, miles and hours are proportional. One possible equation is ...
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<em>Comment on the solution</em>
I personally like to put the unknown in the numerator, so the equation can be solved in one step. The equation above requires two steps: one to cross-multiply, and one to divide by 50.
I might write the equation as ...
(? hours)/(200 mi) = (1 hour)/(50 mi) . . . . multiply by 200 mi to solve
Another way to write the equation is matching the ratios of times to corresponding miles:
(? hours)/(1 hour) = (200 mi)/(50 mi)
This only requires simplification to solve it: ? = 4.
Answer:
The length of the base is 11 meters.
Step-by-step explanation:
The diagram of the triangle is not shown; However, the given details are enough to solve this question.
Given
<em>Shape: Triangle</em>
<em>Represent the height with h and the base with b</em>
Required
Find the length of the base
The area of a triangle is calculated as thus;
Substitute 22 for Area and 3 + 2h for b
The formula becomes
Multiply both sides by 2
Open the bracket
Subtract 44 from both sides
Rearrange
At this point, we have a quadratic equation; which is solved as follows:
Split the above
Solve the above linear equations separately
Add 4 to both sides
---- <em>First value of h</em>
Subtract 11 from both sides
Divide both sides by 2
<em> ------ Second value of h</em>
Since height can be negative, we'll discard
Hence, the usable value of height is
Recall that
Substitute 4 for h
Hence, the length of the base is 11 meters