Answer:
It take 37.5 hours to fill the tank
Step-by-step explanation:
Given:
Time Taken to fill the tank = 15 hours
Time Taken to empty the tank = 25 hours
To Find:
Time taken to fill the tank when both the inlet and outlet is opened at the same time = ?
Solution:
Let the time to fill the tank be x
In 15 hours the tap fills the tank
Rate at which the tank is filled =
In 25 hours the tap empties the tank
Rate at which the tank is drained =
The net gain per minute on the total filling rate is
=> Rate at which the tank is filled - Rate at which the tank is drained
=>
=>
=>
=> 10x = 375
=>
=>x = 37.5
9514 1404 393
Answer:
C) ΔDCE ≅ ΔDQR
Step-by-step explanation:
Corresponding vertices can be identified by the number of arcs signifying congruence.
1 mark: angles D and D
2 marks: angles C and Q
3 marks: angles E and R
Corresponding angles are listed in the same order in the congruence statement:
ΔDCE ≅ ΔDQR
Binomial when added to polynomial
gives polynomial that does not contain the variable y .
A mathematical expression consisting of two terms connected by a plus sign or minus sign .
Example: x + 2 is a binomial, where x and 2 are two separate terms.
<h3>What is polynomial?</h3>A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer
According to the question
polynomial
when added with
= (as
got cancelled )
that does not contain the variable y
Hence, Binomial when added to polynomial
gives that does not contain the variable y .
To know more about Binomial and polynomial here :
# SPJ2
So firstly, to factor this we need to first find the potential roots of this polynomial. To find it, the equation is , with p = the factors of the constant and q = the factors of the leading coefficient. In this case:
Next, plug in the potential roots into x of the equation until one of them ends with a result of 0:
Since we know that 3 is a root, this means that one of the factors is (x - 3). Now that we know one of the roots, we are going to use synthetic division to divide the polynomial. To set it up, place the root of the divisor, in this case 3 from x - 3, on the left side and the coefficients of the original polynomial on the right side as such:
Firstly, drop the 1:
Next, multiply 3 and 1, then add the product with -10:
Next, multiply 3 and -7, then add the product with 25:
Next, multiply 3 and 4, then add the product with -40:
Lastly, multiply -28 and 3, then add the product with 84:
Now our synthetic division is complete. Now since the degree of the original polynomial is 4, this means our quotient has a degree of 3 and follows the format . In this case, our quotient is
.
So right now, our equation looks like this:
However, our second factor can be further simplified. For the second factor, I will be factoring by grouping. So factor x³ - 7x² and 4x - 28 separately. Make sure that they have the same quantity inside the parentheses:
Now it can be rewritten as:
Since the polynomial cannot be further simplified, your answer is: