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 correct 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

(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

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

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