Answer:
The expression for the length of the rectangle is 2x + 4
Step-by-step explanation:
The formula for determining the area of a rectangle is expressed as
Area = length × width
The area of a rectangle is expressed as (14x + 28) square feet. If the width of the rectangle is 7 feet, then the expression for the length of the rectangle would be
Length = Area/ width
= (14x + 28)/7
The numerator has a common factor of 7. Therefore, if we factorize 7 out, it becomes
7(2x + 4)/7
Length = 2x + 4
Answer:
The coordinates of the point Q is (4, 1)
Step-by-step explanation:
The given parameters are;
The directed line segment extends from R(-2, 4), to S(18, -6)
The ratio in which the point Q partitions the directed line segment = 3:7
Therefore, the proportions of the R to Q = 3/(3 + 7) = 3/10 the length of RS
Which gives;
(-2 + (18-(-2))×3/10, 4 +(-6 -4)×3/10) which is (4, 1)
The coordinates of the point Q = (4, 1)
We check the length from R to S is given by the relation for length as follows
Where;
R(-2, 4) = (x₁, y₁)
S(18, -6) = (x₂, y₂)
Length of segment RS = 22.36
length from R to Q = 6.7086
We check RQ/RS = 6.7082/22.36 = 0.3
Also QS/RS = (22.36 - 6.7082)/22.36 = 0.6999≈ 0.7
The coordinates of the point Q = (4, 1).