Let`s assume that points M, N and P are the touching points of those 3 circles:Then:Y M + M Z = 14,Z N + N X = 20X P + P Y = 18And also: M Z = ZN, Y M = P Y and N X = X P.Now we have a system of 3 equations ( Y M, M Z and X P are the radii of each circle ):Y M + M Z = 14M Z + X P = 20X P + Y M = 18 Y M - M Z = - 14+X P + Y M = 18 X P - M Z = 4Y M - M Z = - 14+M Z + X P = 20 X P - Y M = 6 /* ( - 1 )X P - M Z = 4 X P + Y M = - 6 X P - M Z = 4 Y M - M Z = - 2 Y M + M Z = 14 2 Y M = 12 => Y M = 6M Z - 6 = 2 => M Z = 8X P + 6 = 18
X P = 12
Radii of the circles are: 12, 8 and 6.
Answer:
y = x-4
Step-by-step explanation:
y = -x-5
Slope of line is -1.
Slope of perpendicular to line is 1.
Point-slope equation for line of slope 1 that passes through (6,2):
y-2 = 1(x-6)
Rearrange equation to slope-intercept form:
y = 1(x-6) + 2
y = x-4
<h3>Given Equation:</h3>
x = 7 + 3y
or, x - 3y - 7 = 0 ........ (i)
5x + 6y = 14
or, 5x + 6y - 14 = 0 .........(ii)
<h3>To Find:</h3>
The value of x and y.
<h3>Solution:</h3>
By dividing eq. ii by 2, we get
5/2x + 3y - 7 = 0 ........ (iii)
By adding eq. i and eq. iii, we get
15/2x = 0
or, <u>x = 0</u> ........(iv)
By putting eq.(iv) in eq. (i), we get
0 - 3y - 7 = 0
or, -3y = 7
or, <u>y = </u><u>-</u><u>7/</u><u>3</u>
<h2>Answer: ( 0, -7/3 )</h2>
The value of x and y is 0 and -7/3 respectively.
Answer:
Step-by-step explanation:
first we are told that side and ae and a f are the same
so that means one side of each triangle is the same
next we are told that that the lines coming off of those sides are both right angles. so we know these are both right triangles
and b/c both of those angle are right angles... the sides ab and ac have to also be the same length.. or the angle could not be a right angle
therefore since two sides are the same length then all 3 must be the same lengths
and b/c all three are the same these two triangles are the same .. congruent
