Answer:
Line s and Line t are parallel.
Step-by-step explanation:
Now, we know that angles 1 and 2 are congruent, because they have the same angle measures. Now, looking at their positions, we can see that they are alternate exterior angles.
By the converse of the Alternate Exterior Angle, (I do not remember exactly how the theorem went) if two lines are cut by a transversal and have congruent alternate exterior angles, then the lines are parallel. Using this theorem, we can find that lines s and t are parallel, because they are cut by a transversal and their alternate exterior angles are congruent.
I hope you find my answer and explanation to be helpful. Happy studying.
Answer:
Step-by-step explanation:
Given that,
Radius of the cone, r = 5 units
Height of the cone, h = 6 units
We need to find the volume of the cone. The formula for the volume of the cone is given by :
Substitute all the values,
So, the volume of the cone is 
.
Answer:
yes
Step-by-step explanation:
The other factor is (x+5), so the product is ...
(x^4 -1)(x +5) = x^5 +5x^4 -x -5 = P(x)
(x^4 -1) is a factor of P(x).
_____
It is not a <em>primitive</em> factor, because it can be factored as ...
x^4 -1 = (x^2 -1)(x^2 +1) = (x -1)(x +1)(x^2 +1)
The complete factorization of P(x) to real numbers is ...
P(x) = (x -1)(x +1)(x +5)(x^2 +1)
Given :
The original price of the jeans was $56.
The store had marked them down by 25 percent and Seema had a 20 percent off coupon as well.
To Find :
The price of the jeans before tax.
Solution :
Discount offered by store :
Discount = 0.25×56 = $14 .
Selling price = $( 56 - 14 ) = $42 .
Discount offered through coupon on selling price :
Discount = 0.20×42 = $8.4 .
Final price = $( 42 - 8.4 ) = 4= $33.6 .
Therefore, the price of the jeans before tax is $33.6 .
Hence, this is the required solution.
Answer:
The drum capacity is 180 liters.
Step-by-step explanation:
Let the capacity of the drum be c. Then the contents of the drum at the beginning are (3/4)c, and
if 30 liters are drawn out, then the contents are (3/4)c - 30 liters = (7/12)c.
Here the LCD is 12, and so we have (9/12)c - (7/12)c = 30 liters, or
(2/12)c = 30 liters, or c = (12/2)(30 liters) = 180 liters
The drum capacity is 180 liters.
