a.
The polynomial w^2+18w+84 cannot be factored
The perfect square trinomial is w^2+18w + 81
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The reason the original can't be factored is that solving w^2+18w+84=0 leads to no real solutions. Use the quadratic formula to see this. The graph of y = x^2+18x+84 shows there are no x intercepts. A solution and an x intercept are basically the same. The x intercept visually represents the solution.
w^2+18w+81 factors to (w+9)^2 which is the same as (w+9)(w+9). We can note that w^2+18w+81 is in the form a^2+2ab+b^2 with a = w and b = 9
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b.
The polynomial y^2-10y+23 cannot be factored
The perfect square trinomial is y^2-10y + 25
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Using the quadratic formula, y^2-10y+23 = 0 has no rational solutions. The two irrational solutions mean that we can't factor over the rationals. Put another way, there are no two whole numbers such that they multiply to 23 and add to -10 at the same time.
If we want to complete the square for y^2-10y, we take half of the -10 to get -5, then square this to get 25. Therefore, y^2-10y+25 is a perfect square and it factors to (y-5)^2 or (y-5)(y-5)
<h3><u>
Answer:</u></h3>
33480783
<h2><u>
Step-by-step explanation:</u></h2>
<u>Finding the Common Ratio:</u>
We know that the formula for the common ratio of a GP is:
r = aₙ / (aₙ₋₁) <em>(Where n is any integer)</em>
<em>replacing the values, taking n=2</em>
r = -21 / 7
r = -3
<u>Solving for the 15th Term:</u>
We know that the Formula for the nth term of a GP:
G(n) = a * r ⁿ⁻¹ <em>(where a is the first term and r is the common ratio)</em>
<em>replacing the values (taking n = 15 since we need the 15th term)</em>
G(15) = 7 * (-3)¹⁴
G(15) = 33480783
Hence, the 15th term of the given GP is 33480783
7.5 divided by 1.5 is 5 so there are 5 lifeguards throughout the day.
Eight and ninety-seven hundredths
Answer:
The coordinates are x = -1 and y = -2.
Step-by-step explanation:
Given:
Equations are 2x-4y=6 and 3x+y=-5.
Now, to find the coordinates.
...........(1)
...........(2)
So, first we solve the equation 1 to get the value of 
.
Subtracting both sides by 
we get:
Dividing both sides by 2 we get:
Now, we put the value of in equation 2 to get 
.
On solving the whole equation we get :
And, now putting the value of in equation (1) we get :
on solving we get:
Therefore, the coordinates are x=-1 and y=-2.
