Answer: See below
Step-by-step explanation:
(f+g)(x) is another way for saying f(x)+g(x). Since we know f(x) and g(x), we can add them together.
-5x-4+(-3x-2) [distribute the 1 to (-3x-2)]
-5x-4-3x-2 [combine like terms]
-8x-6
(f+g)(x) is -8x-6. You can also factor this.
1. Factoring
-2(4x+3)
- Quadratic Formula:
, with a = x^2 coefficient, b = x coefficient, and c = constant.
Firstly, starting with the y-intercept. To find the y-intercept, set the x variable to zero and solve as such:

<u>Your y-intercept is (0,-51).</u>
Next, using our equation plug the appropriate values into the quadratic formula:

Next, solve the multiplications and exponent:

Next, solve the addition:

Now, simplify the radical using the product rule of radicals as such:
- Product Rule of Radicals: √ab = √a × √b
√1224 = √12 × √102 = √2 × √6 × √6 × √17 = 6 × √2 × √17 = 6√34

Next, divide:

<u>The exact values of your x-intercepts are (-4 + √34, 0) and (-4 - √34, 0).</u>
Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:

<u>The approximate values of your x-intercepts (rounded to the hundredths) are (1.83,0) and (-9.83,0).</u>
5:8 and 20:32 would be a proportion.
Easy way to find this:
Set up the proportion as a fraction.
Use the cross product property. Multiply the diagonals and if the products of the diagonals are the same, then they are proportional.
Answer:
The coordinates are 3,1
Step-by-step explanation:
i did the assignment and it js correct
Answer:



Step-by-step explanation:
<u>Optimizing With Derivatives
</u>
The procedure to optimize a function (find its maximum or minimum) consists in
:
- Produce a function which depends on only one variable
- Compute the first derivative and set it equal to 0
- Find the values for the variable, called critical points
- Compute the second derivative
- Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum
We know a cylinder has a volume of 4
. The volume of a cylinder is given by

Equating it to 4

Let's solve for h

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

Replacing the formula of h

Simplifying

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

Rearranging

Solving for r

![\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%7D%7B%5Cpi%20%7D%7D%5Capprox%201.084%5C%20feet)
Computing h

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.
The minimum area is

