Answer:
<u>x = 6, length = 8 cm and width = 7 cm</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Area of a rectangle = 56 cm²
Length of the rectangle = x + 2
Width of the rectangle= 2x - 5
2. Solve for x. Round to the nearest whole number.
Area of a rectangle = Length * Width
(x + 2) (2x - 5) = 56
2x² + 4x - 5x -10 = 56
2x² - x - 66 = 0
Factoring, we have:
(2x + 11) * (x - 6) = 0
x₁ = 2x + 11 = 0 ⇒ 2x = -11; x₁ = - 5.5
x₂ = x - 6 = 0 ⇒ x₂ = 6
We picked x₂ because x₁ will give us negative values for length and width.
Length = 6 + 2 = 8 cm
Width = 2 * 6 - 5 = 12 - 5 = 7 cm
Answer:

Step-by-step explanation:
By definition, two lines are perpendicular if and only if their slopes are negative reciprocals of each other:
, or equivalently,
.
Given our linear equation 3x + y = 3 (or y = -3x + 3):
We can find the equation of the line (with a y-intercept of 5) that is perpendicular to y = -3x + 3 by determining the negative reciprocal of its slope, -3, which is
.
To test whether this is correct, we can take first slope,
, and multiply it with the negative reciprocal slope
:


Therefore, we came up with the correct slope for the other line, which is
.
Finally, the y-intercept is given by (0, 5). Therefore, the equation of the line that is perpendicular to 3x + y = 3 is:

Answer:
Step-by-step explanation :
N = number of nickels
D = number of dimes
Q = number of quarters
`
252 = N + D + Q <---- Equation 1
D = 3(N+Q) <---- Equation 2
24.85 = 0.05N + 0.10D + 0.25Q <---- Equation 3
We a have set of three linear equations to solve for three unknowns N, D, and Q.
Rearranging the equations we have :
N + D + Q = 252
3N - D + 3Q = 0
0.05N + 0.10 D + 0.25Q = 24.85
Solving the set of linear equations, we end up with :
N = 49
D = 189
Q = 14
(see the attached images for the entire solution)
Answer:
F. -5s = -47.5
Step-by-step explanation:
F. -5s = -47.5
s = -47.5 / -5
s = 9.5
This is the correct option
G. -3 + s = 12.5
s = 12.5 + 3
s = 15.5 (Incorrect option)
J. –1 + s = 10.5
s = 10.5 + 1
s = 11.5 (Incorrect option)