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Fantom [35]
3 years ago
5

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

ct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. 25a 2 - 30a + 9
Mathematics
1 answer:
lilavasa [31]3 years ago
3 0

Answer:

(5a−3)^2

Step-by-step explanation:

25a^2 - 30a + 9

Factor the expression by grouping. First, the expression needs to be rewritten as 25a^2+pa+qa+9. To find p and q, set up a system to be solved.

p+q=−30

pq=25×9=225

Since pq is positive, p and q have the same sign. Since p+q is negative, p and q are both negative. List all such integer pairs that give product 225.

−1,−225

−3,−75

−5,−45

−9,−25

−15,−15

Calculate the sum for each pair.

−1−225=−226

−3−75=−78

−5−45=−50

−9−25=−34

−15−15=−30

The solution is the pair that gives sum −30.

p=−15

q=−15

Rewrite 25a^2 - 30a + 9 as (25a^2−15a)+(−15a+9).

(25a^2−15a)+(−15a+9)

Factor out 5a in the first and −3 in the second group.

5a(5a−3)−3(5a−3)

Factor out common term 5a−3 by using distributive property.

(5a−3)(5a−3)

Rewrite as a binomial square.

(5a−3)^2

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What is the solution of the system?
Kryger [21]
Greetings!

Solve the System, using Elimination:
\left \{ {{4x+2y=18} \atop {2x+3y=15}} \right.

Multiply Equation #2 by 2:
\left \{ {{4x+2y=18} \atop {2(2x+3y)=2(15)}} \right.

\left \{ {{4x+2y=18} \atop {4x+6y=30}} \right.

Eliminate variable x:
-\frac{ \left \{ {{4x+2y=18} \atop {4x+6y=30}} \right.}{0x-4y=-12}

4y=-12

Divide both sides by 4:
\frac{4y}{4}= \frac{12}{4}

y=3

Input this value into one of the Equations: 
4x+2y=18

4x+2(3)=18

Simplify:
4x+6=18

(4x+6)+(-6)=(18)+(-6)

4x=12

Divide both sides by 4.
\frac{4x}{4}= \frac{12}{4}

x=3

The Solution to this System (The Point of Intersection):
\boxed{(3,3)}

I hope this helped!
-Benjamin
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3 years ago
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