Answer:
B) All the real numbers except 4.
Step-by-step explanation:
The given rational expression f(x) = 
To find the domain of the rational function, first we have to find the restricted domain.
To find the restricted domain set the denominator equal to zero.
4 - x = 0
x = 4
The restricted domain is at x = 4.
Which means the function does not exist when x = 4. When we plug in x =4 in the rational function, we get the denominator is 0.
Therefore, the function does not exist at x =- 4.
This means except 4 all the real numbers are the domain.
Hope this will help you to understand the concept.
Answer: B) All the real numbers except 4.
Thank you.
Answer:
7/15
Step-by-step explanation:
So basically, you need to count the numbers (3,5,7,9,11,13,15) those are 7 numbers in total, so that's 7/15, if you want a percentage its 47% (rounded)
Answer:
87.92 mm³
Step-by-step explanation:
The area of the base of the cylinder and cones is the same for all, the area of a circle of radius 2 mm:
B = π·r² = 3.14·(2 mm)² = 12.56 mm²
If we call the heights of the lower cone, cylinder, and upper cone h1, h2, and h3, respectively, then the total volume is ...
V = (1/3)Bh1 + Bh2 + (1/3)Bh3
Here is is convenient to factor out B and also 1/3, so we have ...
V = B(h2 + (1/3)(h1 +h3))
V = (12.56 cm²)·((5 +(2+4)/3) cm) = 7·12.56 cm³
V = 87.92 cm³
Answer:
$8 per yard of fabric
1 yard is equal to 3 feet
8 divided by 3 = 2.67(rounded)
$2.67 per foot of fabric
1 foot is equal to 12 inches
2.67 divided by 12 =0.22(rounded)
1 inch of fabric cost $0.22
First off, I think the equation should have a negative 9 in it originally and then you move it to the other side and it becomes positive.
You'll basically complete the square for two equations at the same time. Set it up like this:
(16x^2 + 96x) + (9y^2 - 18y) = 9
Divide everything by 16 to get the x^2 by itself, then divide everything by 9 to get y^2 by itself. You should end up with this.
(x^2 + 6x) + (y^2 - 2y) = 9/144
then complete the square by taking the second term of each polynomial, dividing by two, and squaring it.
For instance the first one will be 6/2 = 3^2 = 9
The next one will be 2/2 =1^2 = 1
Add these to numbers to the polynomials as well as to the other side of the equation to keep it equal. You should end up with this.
(x^2 + 6x+9) + (y^2 - 2y+1) = (9/144)+9+1
Then find a common denominator on the right side of the equals sign and add them all together to get:
(x^2 + 6x+9) + (y^2 - 2y+1) = 1449/144
Factor out the two polynomials
(x+3)^2 + (y-1)^2 = 1449/144
the center of the circle is (-3,1) according to the factored out polynomials and the radius will be the square root of the number on the right side of the equals sign = sqrt(1449/144) = 3.17
