Answer:
The length is 8 inches and the width is 3 inches
Step-by-step explanation:
Let w represent the width.
The length can be represented by 2w + 2
Use the area formula, A = lw, and plug in the area and the expressions for the length and width:
A = lw
24 = (2w + 2)(w)
Simplify and solve for w:
24 = 2w² + 2w
2w² + 2w - 24
Divide everything by 2:
w² + w - 12
Factor:
(w + 4)(w - 3)
Set equal to 0 and solve for each factor:
w + 4 = 0
w = -4
w - 3 = 0
w = 3
Since the width cannot be negative, the width has to be 3.
Next, find the length by plugging in 3 as w:
2w + 2
2(3) + 2
= 8
So, the length is 8 inches and the width is 3 inches
Answer:
x = -1, y = 2 and z = 1
Step-by-step explanation:
The given system of equations are :
2x - y + 3z= -1 ....(1)
x + 2y - 4z = -1 ......(2)
y – 2z = 0 .....(3)
Equation (3) can be written as :
y = 2z
Use y = 2z in equation (2)
x + 2(2z) - 4z = -1
x + 4z - 4z = -1
x = -1
Put the value of x in equation (1) :
-2 -y +3z = -1
-y+3z = 1 ....(4)
Adding equation (3) and (4)
y-2z+(-y+3z)=1
z = 1
Now put z = 1 in equation (4)
-y+3=1
-y = -2
y = 2
Hence, the values of x,y and z are -1, 2 and 1 respectively.
Noelle goes east at N mph.
Karina travels west at N + 9
then their velocity between them is (N + N + 9)
After 8 hours they travel 8(2N + 9) = 232
(2N + 9) = 29
2N = 20
N = 10 mph for Noelle
N+9=19 mph for Karina
Answer:
Step-by-step explanation:
Start on the x-axis, the horizontal one Start at (0,0), where the two lines meet. Then go over to the right 2 tic marks. Then go up the y-axis, the vertical one, 5 tic marks.
