We can assume that this growth rate can be expressed as y = mx + b as long as the slope is constant, because a quadratic or exponential formula wouldn't make much sense in this situation. If it is growing at least 2 inches a month, the slope (m) will be 2. As x (month) increases by 1 month, y (plant's height) increases by 2 inches. You could make it more, but as long as you plot the points in such a way that the slope for these points are 2 or higher, you will get the answer correct. If you have any other questions or need to clarify more about what you wanted let me know and I'll help.
Answer:
C. 
Step-by-step explanation:
One is asked to find which inequality has (
) in its solution set. Remember that an inequality is another way to represent a set of solutions. In essence, it states that all numbers less than; less than or equal to; greater than; or greater than or equal to, are a part of the solution. One simplifies an inequality in a similar manner to how one simplifies an equation, by using inverse operations and simplification. Just note that when multiplying or dividing the inequality by a negative number, one has to flip the inequality sign to ensure the expression remains true.
Simplify each of the inequalities, then evaluate to see which one has () as a part of its solution set.
A. 
B. 
C.
D. 
As can be seen, option (C ) is the only one that fits this requirement. Since option (C) simplifies down to () or in words, (x) is less than (-2.5). This option is the only one that fits the solution since (-3) is less than (-2.5).
Answer:
2(x - 3)(3x + 2)
Step-by-step explanation:
Given
6x² - 14x - 12 ← factor out 2 from each term
= 2(3x² - 7x - 6) ← factor the quadratic
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × - 6 = - 18 and sum = - 7
The factors are - 9 and + 2
Use these factors to split the x- term
3x² - 9x + 2x - 6 ( factor the first/second and third/fourth terms )
= 3x(x - 3) + 2(x - 3) ← factor out (x - 3) from each term
= (x - 3)(3x + 2)
Thus
3x² - 7x - 6 = (x - 3)(3x + 2) and
6x² - 14x - 12 = 2(x - 3)(3x + 2) ← in factored form
Answer:
8
Step-by-step explanation:
We can start by making the table below to show the given numbers (red) and to assign a variable (x) to <em>the number we want to find: female PhDs</em>.
By subtracting the female numbers from the totals, we can find the corresponding numbers of male PhDs and non-PhDs.
The number of male non-PhDs is twice the number of male PhDs, so we have ...
2(14 -x) = 20 -x
28 -2x = 20 -x . . . . eliminate parentheses
8 = x . . . . . . . . . . . .add 2x-20
The number of female faculty with PhDs is 8.
