It's B.) The student’s answer is not reasonable. Estimation: 170 + 90 = 260
Answer:
= −11.2
Step-by-step explanation:
64.8=6(m+22)
We move all terms to the left:
64.8-(6(m+22))=0
We calculate terms in parentheses: -(6(m+22)), so:
6(m+22)
We multiply parentheses
6m+132
Back to the equation:
-(6m+132)
We get rid of parentheses
-6m-132+64.8=0
We add all the numbers together, and all the variables
-6m-67.2=0
We move all terms containing m to the left, all other terms to the right
-6m=67.2
Answer:
(−1.5,1)
Step-by-step explanation:
Finding the distance, midpoint, slope, equation and the x y-intercepts of a line passing between the two points p1 (6,7) and p2 (-9,-5)
The distance (d) between two points (x1,y1) and (x2,y2) is given by the formula
d = √ ((X2-X1)2+(Y2-Y1)2)
d = √ (-9-6)2+(-5-7)2
d = √ ((-15)2+(-12)2)
d = √ (225+144)
d = √ 369
The distance between the points is 19.2093727122985
The midpoint of two points is given by the formula
Midpoint= ((X1+X2)/2,(Y1+Y2)/2)
Find the x value of the midpoint
Xm=(X1+X2)/2
Xm=(6+-9)/2=-1.5
Find the Y value of the midpoint
Ym=(Y1+Y2)/2
Ym=(7+-5)/2=1
The midpoint is: (-1.5,1)
The equation is derived from the conservation of energy, specifically from potential energy stored at a given height in a gravitational field.
When potential energy is completely converted to kinetic energy you have:
(mv^2)/2=mgh divide both sides by the mass m
v^2/2=gh multiply both sides by 2
v^2=2gh take the square root of both sides
v=√(2gh) and working with imperial units for acceleration due to gravity, g=-32ft/s^2
v=√(-64h) but the change of h as it falls is negative h so
v=-√(64h) so if an object falls from a height of 88ft we have:
v=-√(64*84)
v=-√5376
v≈-73.32 ft/sec (to the nearest hundredth of a foot per second)
Note that this is the velocity, it is negative 73.32 ft/sec.
The question inadvertently asked for velocity and provided answers for SPEED. Velocity is a vector and has both magnitude and direction, whereas speed just has magnitude.
So its final speed is 73.32 ft/sec
So if they actually wanted velocity none of their answers is correct :P
Let x and y be the two unknown numbers. If one number, say x,is 5 more than 3 times another, say y, the equation would be
x = 5 + 3y
When their difference is 35, x-y = 35, since x is the much larger number here. We substitute x to solve for the smaller number, y.
x - y = 35
(5 + 3y) -y = 35
5 +2y = 35
2y = 35-5
2y = 30
y = 15
The larger number x would be
x = 5 + 3(15)
x = 50
The answer is 50.
