<em>The polynomial product has the distributive property.</em>
<em>Step 1:</em><em> We have to distribute each term of the first polynomial to every term of the second polynomial.</em>
(2x + y) * (5x - y +3) = 2x(5x - y + 3) + y(5x - y + 3) =
= 10x² - 2<u>xy</u> + 6x + 5<u>xy</u> - y² + 3y =
<em>Step 2: </em><em>Combine like terms.</em>
= 10x² - y² + 3xy + 6x + 3y
Answer : 10x² - y² + 3xy + 6x + 3y
Answer:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Step-by-step explanation:
The area for a rectangle is given by the formula:
Where <em>w</em> is the width and <em>l</em> is the length.
We are given that the length of the rectangle is increasing at a rate of 6 cm/s and that the width is increasing at a rate of 5 cm/s. In other words, dl/dt = 6 and dw/dt = 5.
First, differentiate the equation with respect to <em>t</em>, where <em>w</em> and <em>l</em> are both functions of <em>t: </em>
By the Product Rule:
Since we know that dl/dt = 6 and that dw/dt = 5:
We want to find the rate at which the area is increasing when the length is 12 cm and the width is 4 cm. Substitute:
The area of the rectangle is increasing at a rate of 84 square centimeters per second.
Answer:
Explanation:
Follow PEMDAS in reverse to undo what's happening to x.
We first add 1 to both sides, then divide both sides by 5 to fully isolate x.
Refer to the steps below to see what I mean.
The inequality sign stays the same the entire time. The only time it flips is when you divide both sides by a negative number.
The solution set for x is anything -3 or larger.
If x was an integer, then we could say the solution set is {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, ...}