Answer:
You can make 27 different 3 digit numbers
Step-by-step explanation:
Since we can use 3 different numbers this means that each of the 3 digits can be one of the 3 numbers (4,2,9). This means that there are 3 different values for the first digit, 3 different values for the second digit, and 3 different values for the third digit, which mean that we can make 3 x 3 x 3 different 3 digit numbers (we took the number of possible values for each digit and multiplied them together.
3 x 3 x 3 = 27
Answer:
4.167(10²)
Step-by-step explanation:
Step 1: Put number into proper decimal form
416.7 = 4.167
Step 2: Figure out exponent
Since we are moving the decimal places 2 places to the right, our exponent is 2
9514 1404 393
Answer:
- y-intercept: (0, -6)
- x-intercepts: (-3, 0), (-1, 0), (1, 0)
Step-by-step explanation:
We notice the first pair of coefficients is the same as the last pair (with the sign changed). This means we can factor by grouping.
f(x) = (2x^3 +6x^2) -(2x +6)
f(x) = 2x^2(x +3) -2(x +3)
f(x) = 2(x^2 -1)(x +3) = 2(x -1)(x +1)(x +3)
The factors are made to be zero when x is 1, -1, or -3.
The x-intercepts are (1, 0), (-1, 0), (-3, 0).
The y-intercept is the constant, -6.
The minimum distance is the perpendicular distance. So establish the distance from the origin to the line using the distance formula.
The distance here is: <span><span>d2</span>=(x−0<span>)^2</span>+(y−0<span>)^2
</span> =<span>x^2</span>+<span>y^2
</span></span>
To minimize this function d^2 subject to the constraint, <span>2x+y−10=0
</span>If we substitute, the y-values the distance function can take will be related to the x-values by the line:<span>y=10−2x
</span>You can substitute this in for y in the distance function and take the derivative:
<span>d=sqrt [<span><span><span>x2</span>+(10−2x<span>)^2]
</span></span></span></span>
d′=1/2 (5x2−40x+100)^(−1/2) (10x−40)<span>
</span>Setting the derivative to zero to find optimal x,
<span><span>d′</span>=0→10x−40=0→x=4
</span>
This will be the x-value on the line such that the distance between the origin and line will be EITHER a maximum or minimum (technically, it should be checked afterward).
For x = 4, the corresponding y-value is found from the equation of the line (since we need the corresponding y-value on the line for this x-value).
Then y = 10 - 2(4) = 2.
So the point, P, is (4,2).
Answer:
10
Step-by-step explanation:
20-(5×2)
5×2=10
20-10=10
