Answer:
1 5/16 gallon
Step-by-step explanation:
Gallon of ice brought by Karen = 3/8
Gallon of ice brought by Robin = 15/16
Total ice team brought by them is sum of Gallon of ice brought by Karen + Gallon of ice brought by Robin
Total ice team brought by Karen and Robin = 3/8 + 15/16
=> 3*2/8*2 + 15/16
we are multiplying with 2 both numerator and denominator in 3/8 so sas the denominator becomes 16 as in other fraction denominator is 16
=> 6/16 + 15/16
=> (6+15)/16 = 21/16
since 21/16 is improper fraction, converting it in mixed fraction we have
21/16 = 1 5/16 gallon
Thus , Karen and Robin have 1 5/16 gallon ice tea together.
Answer:
the values of x, y and z are x= 2, y =-1 and z=1
Step-by-step explanation:
We need to solve the following system of equations.
We will use elimination method to solve these equations and find the values of x, y and z.
2x + 2y + 5z = 7 eq(1)
6x + 8y + 5z = 9 eq(2)
2x + 3y + 5z = 6 eq(3)
Subtracting eq(1) and eq(3)
2x + 2y + 5z = 7
2x + 3y + 5z = 6
- - - -
_____________
0 -y + 0 = 1
-y = 1
=> y = -1
Subtracting eq(2) and eq(3)
6x + 8y + 5z = 9
2x + 3y + 5z = 6
- - - -
______________
4x + 5y +0z = 3
4x + 5y = 3 eq(4)
Putting value of y = -1 in equation 4
4x + 5y = 3
4x + 5(-1) = 3
4x -5 = 3
4x = 3+5
4x = 8
x= 8/4
x = 2
Putting value of x=2 and y=-1 in eq(1)
2x + 2y + 5z = 7
2(2) + 2(-1) + 5z = 7
4 -2 + 5z = 7
2 + 5z = 7
5z = 7 -2
5z = 5
z = 5/5
z = 1
So, the values of x, y and z are x= 2, y =-1 and z=1
In order to find height from where ball is dropped, you have to find height or h(t) when time or t is zero.So plug in t=0 into your quadratic equation:h(0) = -16.1(0^2) + 150h(0) = 0 +150h(0) = 150 ft is the height from where ball is dropped. When ball hits the ground, the height is zero. So plug in h(t) = 0 and solve for t.0 = -16.1t^2 + 15016.1 t^2 = 150t^2 = 150/16.1t = sqrt(150/16.1)t = ± 3.05Since time cannot be negative, your answer is positive solution i.e. t = 3.05
To make that graph you follow these steps.
1) Set the cartesian coordinate system:
- vertical axis: y
- horizontal axis: x
- positive x-semi axis: to the right
- negative x-semi axis: to the left
- positive y-semi axis: upward
- negative y semi axis: dwonward
2) solve the inequality for y:
given: -2x + 5y > 15
transpose-2x: 5y > 15 + 2x
divide by 5: y > 3 + (2/5)x
3) Graph-
draw the line y = 3 + (2/5)x, using a dotted line (i.e. - - - - - -)
- remember that 3 is the y intercept, and 2/5 is the slope
- the line is dotted because
the solution does not include the points in the line.
- the solution is the
region above and to the left of the dotted line.
4) See the
figure attached for better visualization: the pink region is the solution of the inequality.