Answer:
B
Step-by-step explanation:
When finding the area of a circle you have to use the formula
Area= Pie x radius^2
Radius=8.5
So you have to plug that into the equation.
8.5x8.5=72.25
72.25x3.14=226.87
So Area is 226.87
So your answer is B
Estimate 3458092=3500000~; 57=60~.
3500000*60=210000000.
The answer is 210000000
Answer: -2.85
Step-by-step explanation:
To convert 22/20 into a decimal, we must multiply it by 5 to get a denominator of 100.
5(22/20)= 110/100= 1.10
So now lets solve the equation.
-1.75-1.10 = -2.85
Answer:
x-intercepts = 1,2, and 4, y-intercept = -8
Step-by-step explanation:
x^3 - 7x^2 - 14x - 8 in factored form is equal to (x-1)(x-2)(x-4).
Solving for x-intercepts:
- We are actually able to solve for all x-intercepts without the given factor. But since we are given one of the factors, our job becomes much easier.
- Using synthetic division, or long division, we factor out the x-intercept 4. Which leaves us with the polynomial x^2 - 3x + 2.
- From here we can separate the polynomial into two binomials.
- x^2 - 3x + 2 = (x-1)(x-2). Giving us all 3 x-intercepts.
- Using Descartes' rules we can identify before even starting the problem how many real x-intercepts there are (Not needed for this problem).
Solving for y-intercept:
- The y-intercept is always the coefficient that does not have any assigned x-variables.
- The coefficient is -8, thus the y-intercept.
- If unsure of the y-intercept, you can always plug in x = 0. Solving for the y-intercept will give you the value of f(0).
- If there is no coefficient, the y-intercept is equal to zero.
Answer:
Thus, the answer is:
Step-by-step explanation:
Considering the system of equations
Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)
![\left \{ {{x+y+z=2} \atop {4x+y+z=14}} \ \atop {x-y+4z=-14}} \right\}\rightarrow \left[\begin{array}{ccc}1&1&1:2\\4&1&1:14\\1&-1&4:-14\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%2By%2Bz%3D2%7D%20%5Catop%20%7B4x%2By%2Bz%3D14%7D%7D%20%5C%20%20%5Catop%20%7Bx-y%2B4z%3D-14%7D%7D%20%5Cright%5C%7D%5Crightarrow%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%3A2%5C%5C4%261%261%3A14%5C%5C1%26-1%264%3A-14%5Cend%7Barray%7D%5Cright%5D)
R2 - 4 R1 → R2 (multiply 1 row by 4 and subtract it from 2 row); R3 - 1 R1 → R3 (multiply 1 row by 1 and subtract it from 3 row)
![\left[\begin{array}{ccc}1&1&1:2\\0&-3&-3:6\\0&-2&3:-16\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%3A2%5C%5C0%26-3%26-3%3A6%5C%5C0%26-2%263%3A-16%5Cend%7Barray%7D%5Cright%5D)
R2 / -3 → R2 (divide the 2 row by -3)
![\left[\begin{array}{ccc}1&1&1:2\\0&1&1:-2\\0&-2&3:-16\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%261%3A2%5C%5C0%261%261%3A-2%5C%5C0%26-2%263%3A-16%5Cend%7Barray%7D%5Cright%5D)
R1 - 1 R2 → R1 (multiply 2 row by 1 and subtract it from 1 row); R3 + 2 R2 → R3 (multiply 2 row by 2 and add it to 3 row)
![\left[\begin{array}{ccc}1&0&0:4\\0&1&1:-2\\0&0&5:-20\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%3A4%5C%5C0%261%261%3A-2%5C%5C0%260%265%3A-20%5Cend%7Barray%7D%5Cright%5D)
R3 / 5 → R3 (divide the 3 row by 5)
![\left[\begin{array}{ccc}1&0&0:4\\0&1&1:-2\\0&0&1:-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%3A4%5C%5C0%261%261%3A-2%5C%5C0%260%261%3A-4%5Cend%7Barray%7D%5Cright%5D)
R2 - 1 R3 → R2 (multiply 3 row by 1 and subtract it from 2 row)
![\left[\begin{array}{ccc}1&0&0:4\\0&1&0:2\\0&0&1:-4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%3A4%5C%5C0%261%260%3A2%5C%5C0%260%261%3A-4%5Cend%7Barray%7D%5Cright%5D)
Thus, the answer is:
Make a check:
4 + 2 + (-4) = 4 + 2 - 4 = 2
4·4 + 2 + (-4) = 16 + 2 - 4 = 14
4 - 2 + 4·(-4) = 4 - 2 - 16 = -14
Check completed successfully.
