ANSWER
(3,-1)
EXPLANATION
The given system of equations is :
5x+y=14
2x-y=7
For the first equation when x=0,
5(0)+y=14
y=14
The y-intercept is (0,14).
When y=0, 5x+0=14
The x-intercept is (2.8,0).
We plot the intercepts and draw a straight line through them to obtain the graph of 5x+y=14 as shown in the attachment.
We repeat the same process for the second equation 2x-y=7.
The intercepts are (0,-7) and (3.5,0)
The solution to the system is the point of intersection of the two straight lines.
The two straight lines intersected at
(3,-1)
Hence x=2, y=-1
Answer:
137.25 inch ²
Area of triangle = 1/2× base × height
= 1/2×15.25×18
= 15.25×9
=137.25 inch²
Answer:
y=-1/4x-6
Step-by-step explanation:
The problem wants the form y=mx+b where m is the slope and b is the y-intercept.
The y-intercept in this case is -6 (where the line intercepts the y-axis).
We can use points (0,-6) and (4,-7) to calculate the slope. We just divide the difference in y-values by the difference in x-values.
-6-(-7)/0-4=-6+7/-4=1/-4=-1/4
So the equation of the line is y=-1/4x-6
I'm assuming no air friction here, first use conservation of energy to find velocity, so initially all the energy is from the spring, (1/2)kx^2, then it is converted to kinetic energy, (1/2)mv^2. so .5kx^2=.5mv^2. the .5s cancel, kx^2=mv^2. solve for v, v=sqrt(kx^2/m) plug in your values for the variables and find v. then use vf^2=vi^2+2ax in the u direction and solve for vf, vf=sqrt(vi^2+2ax). use that velocity in vf=vi+at and solve for t. vi=0 and a=g=9.81, so vf/a=t. plug in the values from the previous equation and the acceleration due to gravity to find the time it takes to hit the ground vertically. Now use v=x/t and solve for x. x=vt, plug in the velocity of the ball horizontally, which we found with the conservation of energy part, and y which we found with the previous equation, and you get your x, the distance it will take for the ball to hit the ground.
I am answering this for points, so don’t know for sure but I think you might find 6.9