It is not factorable. Factors of 21 are. 21 and 1
7 and 3. None of those add up to 12
This should be easy because we just have to use substitution method. Substitute the value of x from the second equation into the x of the first equation.
-4(2y) + 11y = 15
-8y + 11y = 15
3y = 15 ; y = 5
Substitute this value of y to either the first or second equation.
x = 2(5) = 10
The ordered pair is therefore (10,5).
Answer:

Step-by-step explanation:
Let
, we proceed to transform the expression into an equivalent form of sines and cosines by means of the following trigonometrical identity:
(1)
(2)
Now we perform the operations: 



(3)
By the quadratic formula, we find the following solutions:
and 
Since sine is a bounded function between -1 and 1, the only solution that is mathematically reasonable is:

By means of inverse trigonometrical function, we get the value associate of the function in sexagesimal degrees:

Then, the values of the cosine associated with that angle is:

Now, we have that
, we proceed to transform the expression into an equivalent form with sines and cosines. The following trignometrical identities are used:
(4)
(5)




If we know that
and
, then the value of the function is:


Recall the logarithm rules :
a^y = x is the same as log_a x = y
In this case,
a = 18
y = r - 10
x = 93
So,
18^ (r-10) = 93
is the same as
log_18 93 = r - 10
Solve for r to get :
10 + log_18 93 = r
Answer:
The common ratio is 1.2.
After 12 weeks the plant will be 4.46 meters long.
After one year the plant will be 6,552.32 meters long.
Step-by-step explanation:
Given that a marrow plants 0.5 m long and every week it grows by 20%, to find the value of the common ratio, calculate how long the plant is after 12 weeks and comment on the predicted length of the marrow after one year must be performed the following calculations:
0.50 x 1.2 ^ X = Y
Therefore, the common ratio is 1.2.
0.50 x 1.2 ^ 12 = Y
0.50 x 8.916 = Y
4.4580 = Y
Therefore, after 12 weeks the plant will be 4.46 meters long.
0.50 x 1.2 ^ 52 = Y
0.50 x 13,104.63 = Y
6,552.32 = Y
Therefore, after one year the plant will be 6,552.32 meters long.