Answer:
see explanation
Step-by-step explanation:
To find the y- intercept let x = 0 in the function
g(0) = 0 - 0 - 84 = - 84 ← y- intercept
To find the x- intercepts let y = 0, that is
x² - 5x - 84 = 0
To factor the quadratic
Consider the factors of the constant term (- 84) which sum to give the coefficient of the x- term
The factors are - 12 and + 7, since
- 12 × 7 = - 84 and - 12 + 7 = - 5, thus
(x - 12)(x + 7) = 0
Equate each factor to zero and solve for x
x - 12 = 0 ⇒ x = 12
x + 7 = 0 ⇒ x = - 7
x- intercepts are x = - 7 and x = 12
Answer:
<h2>108 yd²</h2>
Step-by-step explanation:
The formula of an area of a trapezoid:

<em>b₁, b₂</em><em> - bases</em>
<em>h</em><em> - height</em>
From the picture we have

Substitute:

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.
If you would like to transform the following phrase into a math expression, you can do it like this:
8 less than a number is no more than 14 and no less than 5
a number ... n
8 less ... - 8
no more than 14 .... < 14
no less than 5 ... > 5
<span><span><span>Now you just have to put this together: 5 < n - 8 < 14
If 5 and 14 are included: 5 <= n - 8 <= 14
</span></span></span>