Answer:
1) 7 2) (-1,0) 3) m=-4 4) y=3x-4 5) y=x+6 6)
g(x)=-1/3x+10 7) y= $0.36
Step-by-step explanation:
These questions are all about Cartesian Geometry.
1) The Distance from point (7,-6) to vertical axis (0,-6) is measured with a straight line, between point (7,-6) and nearer point (0,-6)
d=|7-0|=7
2) To determine the value of k, let's determine the function with the two known points: (0, −1), (10, −11).
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\Rightarrow m=\frac{-11+1}{10-0}\Rightarrow m=-1\\-11=-1*(10)+b\therefore b=-1\Rightarrow f(x)=-x-1\\f(k)=-k-1\\0=-k-1\therefore k=-1[/tex]
So (k,0)=(-1,0)
3) To find the slope of the line, we must apply that formula used above.
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\Rightarrow m=\frac{7+9}{1-5}\Rightarrow m=\frac{16}{4}=-4[/tex]
4) To find the equation of the line which the midpoint (2,2) since Midpoint is given by
[tex]Midpoint=(\frac{x_{1}+x_{2}}{2}+\frac{y_{1}+y_{2}}{2})\\[/tex]
And the slope is 3, then m=3. Notice the formula is the same to calculate the slope, but we will only pick one point. Since (2,2) ∈ to the function let's use this point, as initial value (x0,y,0)
[tex]m(x-x_{0})=y-y_{0}\\3(x-2)=y-2\\3x-6=y-2\Rightarrow 3x-y=6-2\Rightarrow -y=4-3x\Rightarrow y=3x-4[/tex]
5) Similarly to the previous one:
[tex]m(x-x_{0})=y-y_{0}\\(x-0)=y-6\\x=y-6\Rightarrow -y=-x-6\Rightarrow y=x+6[/tex]
6) A ball being twirled. The center of the rotation is the origin of Coordinate System (0,0) when the string breaks at point (3,9)
If the line was straight from the origin to point (3,9)[tex]m=\frac{9-0}{3-0}\Rightarrow m=3\therefore 9=3(3)+b\Rightarrow b=0\Rightarrow f(x)=3x[/tex]
But the point (3,9) ∈ to a tangent line to the circumference described by the twirling.
Since it is perpendicular instead of m=3 it is -1/m i.e. -1/3, also the circumference intercepts the y-axis in ≈10
g(x)=-1/3x+10
7) In this case, we must also find the function.
x=units of electricity, y=units of gas |
500x+100y=331
400x+250y=326
The cost per unit of gas is y. Finding out the unit value for y
[tex]100y=331-500x\rightarrow y=\frac{331-500x}{100}\\500x=331-100y\\x=\frac{331-100y}{500}\\400(\frac{331-100y}{500})+250y=326\\52.96-80y+250y=326\Rightarrow y=\frac{9}{25} \,and \,x=\frac{59}{100}[/tex]
