Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.
-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3
The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.
y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b
The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.
We know that,
diameter is twice the radius, I.e d = 2r
Now d = 2(8)ft = 16 feet
Answer:
the volume of the larger cube is 512
Step-by-step explanation:
we plug in the value of the side into the equation
so we get
8 x 8 x 8= 512
hope this helps <3
Answer: 11 sqrt2 inches
Step-by-step explanation:
have a good night :)
Answer:
AC = 5 cm
BD = 12.5 cm (3 sf) [or 2 × root 39]
BE = 6.93 cm (3 sf) [or 4 × root 3]
Step-by-step explanation:
CE = 8cm [CE is radius of circle]
AC + 3 = 8
<u>A</u><u>C</u><u> </u><u>=</u><u> </u><u>5</u><u> </u><u>c</u><u>m</u>
BC = 8cm [BC is a radius of circle]
(AC)^2 + (AB)^2 = (BC)^2 [Pythagoras theorem]
25 + (AB)^2 = 64
AB = 6.2450 cm (5 sf) [or root 39]
BD = 2(BA)
= 2(6.2450)
<u>B</u><u>D</u><u> </u><u>=</u><u> </u><u>1</u><u>2</u><u>.</u><u>5</u><u> </u><u>c</u><u>m</u><u> </u><u>(</u><u>3</u><u> </u><u>s</u><u>f</u><u>)</u><u> </u><u>[</u><u>o</u><u>r</u><u> </u><u>2</u><u> </u><u>×</u><u> </u><u>r</u><u>o</u><u>o</u><u>t</u><u> </u><u>3</u><u>9</u><u>]</u>
(BA)^2 + (AE)^2 = (BE)^2 [Pythagoras theorem]
39 + 9 = (BE)^2
<u>B</u><u>E</u><u> </u><u>=</u><u> </u><u>6</u><u>.</u><u>9</u><u>3</u><u> </u><u>c</u><u>m</u><u> </u><u>(</u><u>3</u><u> </u><u>s</u><u>f</u><u>)</u><u> </u><u>[</u><u>o</u><u>r</u><u> </u><u>4</u><u> </u><u>×</u><u> </u><u>r</u><u>o</u><u>o</u><u>t</u><u> </u><u>3</u><u>]</u>