Acontractor is building a new subdivision on the outside of a city. he has started work on the first street and is planning for the other streets to run in a direction parallel to the first. the second street will pass through (−5, −1). find the equation of the location of the second street in standard form. x − y = −6 2x + y = −11 x + y = −6 2x − y = −9
x + y = -6
The equation of the first street is x+y = 1. The equation of the second street will have the same form, but with a different constant. Since the constant is the sum of the x and y coordinate values, it is easily found to be -5-1 = -6. Then the equation is ...
x + y = -6
The first street is seen from the graph to have a slope of -1 (1 unit down for each 1 unit to the right). Since the y-intercept is +1, the slope-intercept form of its equation is ...
y = -x + 1
In standard form, this is ...
x + y = 1
A parallel line will have the same expression on the left with a different constant on the right.
c. 27 units.
we are told that in circle a, ∠bae ≅ ∠dae.
we can see from our given diagram that in and ;
, as these are radii of our given circle.
therefore, by sas congruence postulate.
hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:
now let us substitute x=17 in the expression for the length of be.
therefore, length of be will be 27 units and option c is the correct choice.