Length - l
Width - w
Given,
Perimeter = 60
2(l +w) = 60
l + w = 30
l = 30 - w
Given,
l = 3w
30 - w = 3w
4w = 30
--- w = 7.5
--- l = 3w = 3 * 7.5 = 29.5
Hence, the length of the rectangle is 29.5 and the width is 7.5
Answer:
Step-by-step explanation:
4a² b³ * (9a⁴b² - 4a² + 3) = 4a²b³ * 9a⁴b² - 4a²b³*4a² + 4a²b³*3
= 36a²⁺⁴ b³⁺² -16a²⁺²b³ + 12a²b³
= 36a⁶b⁵ - 16a⁴b³ + 12a²b³
Answer:
Step-by-step explanation:
Given that:
for 
That means, angle 
is in the 3rd quadrant.
To find:
Value of cot(t)
Solution:
First of all, let us recall what trigonometric ratios are positive and what trigonometric ratios are negative in 3rd quadrant.
In 3rd quadrant, tangent and cotangent are positive.
All other trigonometric ratios are negative.
Let us have a look at the following identity:
here, 
So, 
But, angle is in 3rd quadrant, so value of
Answer:
The expression 35 - m is used to determine the number of gallons left in the tank after m minutes.Solution:Given that a tank containing 35 gallons of water is leaking at a rate of gallon per minute. Let "m" represent the number of minutes spent Number of gallons left in the tank = initial amount of water present – leaked amount of water
Number of gallons of water left = 35 gallons – number of minutes spent rate of leakage.
Number of gallons of water left = 35 gallons – m minutes 1 gallons per minute Hence, the required expression is 35 – m
Answer: Option C
Step-by-step explanation:
If the graph of the function 
represents the transformations made to the graph of 
then, by definition:
If 
the graph moves vertically upwards.
If 
the graph moves vertically down
In this problem we have the function 
and our parent function is 
therefore it is true that 
Therefore the graph of 
is moves vertically upwards by a factor of 5 units.
The answer is the Option C: "The graph of g(x) is the graph of f(x) shifted up 5 units"
