Basically, you have to find the line through (-3, 1) that is perpendicular to the line 6x + y = 9 and then find where the two lines intersect. Dropping a perpendicular from the point to the line is the shortest distance from the point to the line.
6x + y = 9
y = -6x + 9
slope is -6
perpendicular would have slope 1/6
(y - 1) = (1/6) (x + 3)
y - 1 = (1/6) x + (1/2)
multiplying both sides by 6
6y - 6 = x + 3
x - 6y = -9
Where do these two lines intersect?
From above we know given equation is y = -6x + 9
Plugging into other equation
x - 6(-6x + 9) = -9
x + 36x - 54 = -9
37 x = 45
x = 45/37
y = -6(45/37) + 9
y = -270/37 + (333/37)
y = 63/37
point is (45/37, 63/37)
Answer:
diagonal of a polygon is a line from a vertex to a non-adjacent vertex. So a triangle, the simplest polygon, has no diagonals. You cannot draw a line from one interior angle to any other interior angle that is not also a side of the triangle.
Step-by-step explanation:
To find the length of the diagonal (or hypotenuse) of a right triangle, substitute the lengths of the two perpendicular sides into the formula a2 + b2 = c2, where a and b are the lengths of the perpendicular sides and c is the length of the hypotenuse. Then solve for c
Answer:
The answer would be (x+7)(x-7).
Step-by-step explanation:
(49 is a perfect square, which would be 7)
Answer:
<em>y = 5x + 100</em>
Step-by-step explanation:
Using the x and corresponding y values from the given table.
Let's use the coordinate (0, 100) and (1, 105)
The equation in slope intercept form is expressed as y = mx+c
m is the slope
c is the y-intercept
Slope m = y2-y1/x2-x1
m = 105-100/1-0
m = 5/1
m =5
Get the y intercept
Substitute the slope m = 5 and any point say (0, 100) into the equation
y = mx+c
100 = 5(0) + c
100 = c
c = 100
Get the required equation;
y = mx+c
y = 5x + 100
<em>Hence the equation in slope-intercept form that represents the data is expressed as y = 5x + 100</em>
Answer:
y = 4
Step-by-step explanation:
2[2y-1]+5=19 (by PEDMAS, distribute parentheses first)
(2)(2y) - (2)(1) + 5 = 19
4y - 2 + 5 = 19
4y +3 = 19 (subtract 3 from both sides)
4y = 19 - 3
4y = 16 (divide both sides by 4)
y = 16/4
y = 4
