Answer:
y = - 3x² - 24x - 60
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (- 4, - 12 ), thus
y = a(x + 4)² - 12
To calculate a substitute (- 7, - 39) into the equation
- 39 = a(- 7 + 4)² - 12 ( add 12 to both sides )
- 27 = 9a ( divide both sides by 9 )
- 3 = a
y = - 3(x + 4)² - 12 ← in vertex form
Expand (x + 4)²
y = - 3(x² + 8x + 16) - 12
= - 3x² - 24x - 48 - 12
y = - 3x² - 24x - 60 ← in standard form
= - 3(x²
Answer:
Inequality = 6 + x ≤ 10
x(Number of hours more of television Sarah can still watch this week) = 4 hours
Step-by-step explanation:
Define a variable, set up an inequality and solve that inequality to determine how many more hours of television Sarah can watch this week.
We are told in the question that:
Sarah is allowed to watch no more than 10 hours of television each week.
This means :
Sarah can watch tv for less than or equal to 10 hours in a week. Sarah has already watched 6 hours of television.
Hence:
The number of hours left that Sarah can watch television in a week is represented as x
Our Inequality Equation =
6hours + x hours ≤ 10 hours
6 + x ≤ 10
Solving the inequality
x ≤ 10 - 6
x ≤ 4 hours
This means Sarah still has no more than (less than or equal to) 4 hours or television left to watch in this week
Answer:
(x^2 + 3)(x + 1).
Step-by-step explanation:
x^3 + x^2 + 3x + 3
= x^2(x + 1) + 3(x + 1)
= (x^2 + 3)(x + 1).
Answer:
12 and 28
Step-by-step explanation:
Represent the numbers using x and y. Then y - x = 16. (y is the larger one.)
Then 3y = 7x, and y = (7/3)x.
Substituting (7/3)x for y in y - x = 16, we get:
(7/3)x - x = 16.
Eliminate the fraction by multiplying all three terms by 3:
7x - 3x = 48, or 4x = 48, yielding x = 12. Then y = (7/3)(12) = 28.
Answer:
<u>$239.68</u>
Step-by-step explanation:
<u>Given</u>
- Cost = $224
- Sales Tax = 7%
<u>Solving</u>
- Cost w/ Tax = Cost (1 + Tax)
- Cost w/ Tax = 224 (1 + 0.07)
- Cost w/ Tax = 224 * 1.07
- Cost w/ Tax = <u>$239.68</u>
