Answer:
number 1 is a real number and 2 and 3 and 4 and 5 and 6 and 7 and 8 and 9
Step-by-step explanation:
a real number is a value of a continuous quantity that can represent a distance along a line.
21x - 19 = 3x + 17 |add 19 to both sides
21x = 3x + 36 |substract 3x from both sides
18x = 36 |divide both sides by 18
x = 2
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:
1:13
Step-by-step explanation:
A standard deck has 52 cards not including the joker. each suit has one 10. there are total four "10" in a deck of playing cards. 4/52 = 1/13 or 1:13
Answer:
A.) 2x - 9x - 30 = -6
Step-by-step explanation:
hello !
to solve this system of equations, first, we substitute the equation 
to the <em>y </em>variable in the equation 
. Therefore, we get:
now, we simplify by multiplying -3 to the variables inside the parenthesis, which, in short, is also called the distributive property. thus, we get:
