The balloon assumes the shape of a sphere with a formula of the volume equal to V = 4/3 pi r^3 where r is the radius of the balloon. In this case, we are given with volume of 288 pi in^3. We just substitute the given volume such that the resulting radius that answers the problem is 6 inches.
Our matrix C is the encoder. Let X be our secret message and let B be our encoded message. Therefore the relationship between the 3 can be represented as:
CX = B
So we want to solve for X (our secret message). So using matrix algebra:
X = C^-1*B
where C^-1 is the inverse of C.
C^-1 = | 3 -2 |
|4 -3 |
So we take C^-1 and multiply it by matrix B to get X. Matrix B is already given to us. So just multiply those two. I used a calculator to get:
X = | 20 8 5 3 15 12 15 |
| 18 9 19 2 12 21 5 |
And since A = 1, B = 2, C = 3, etc....
We decode our message and it says:
X = | T H E C O L O |
| R I S B L U E |
So the answer is: The color is blue (D)
Answer:

Step-by-step explanation:
Use the <u>Slope Formula</u> to help you determine the slope of the following two points:

(Where
is the first point and
is the second point)
-Apply both points onto that formula:



-Solve:



The answer is d because if you sketch it out it'll show d to have the vertical angle
Answer:
x = -3±i sqrt(2)
Step-by-step explanation:
x^2+6x + 11 =0
Subtract 11 from each side
x^2+6x + 11-11 =0-11
x^2+6x =-11
Take the coefficient of the x terms
6
Divide by 2
6/2 =3
Square it
3^2 =9
Add it to each side
x^2+6x + 9 =-11+9
x^2 + 6x+9 = -2
The left hand side becomes (x+ (6/2) )^2
(x+3)^2 = -2
Take the square root of each side
sqrt((x+3)^2) = ±sqrt(-2)
x+3 = ±sqrt(-2)
x+3= ±i sqrt(2)
Subtract 3 from each side
x+3-3 = -3±i sqrt(2)
x = -3±i sqrt(2)