Let the numbers be a and b and b>a
2a=3b and 3(b-a)=2(b-a)+13
Solving the first for a:
2a=3b
a=3b/2, now using this value of a in the second equation gives you:
3(b-3b/2)=2(b-3b/2)+13 upon performing indicated operations.
3b-9b/2=2b-6b/2+13 making all terms have a common denominator of 2
(6b-9b)/2=(4b-6b+26)/2 multiplying the whole equation by 2
6b-9b=4b-6b+26 combining like terms
-3b=-2b+26 adding 2b to both sides
-b=26 dividing both sides by -1
b=-26, since a=3b/2
a=3(-26)/2
a=-39
So the numbers are -39 and -26
check...
2a=3b becomes:
2(-39)=3(-26)
-78=-78
3(b-a)=2(b-a)+13 becomes:
3(-26--39)=2(-26--39)+13
3(13)=2(13)+13
39=26+13
39=39
correct :P
9514 1404 393
Answer:
BC = 6
Step-by-step explanation:
Tangents from the same point are congruent, so ...
2x = x+3
x = 3 . . . . . . . subtract x
BC = x+3 = 3+3 = 6 . . . . . . substitute for x
The length of BC is 6.
Answer:
slope = 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = 
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 1) ← 2 points on the line
m = 
= 1
Answer:
60 units
Step-by-step explanation:
Ratio of the perimeter = ratio of sides
Sides are in the ratio:
6 : 24
1 : 4
Perimeter of the first triangle:
4+5+6 = 15
Perimeter of the second triangle:
4(15) = 60
Answer:
Step-by-step explanation:
1. Given WX>XY.
2. Then angle 3 has larger measure than angle 4, because angle opposite longer side is larger angle. This means that
3. Consider exterior angle 1. By the exterior angle theorem, the measure of the exterior angle is equal to the sum of the measures of remote interior angles. Then
4. Note that angle 2 has positive measure and then
5. Since 
and 
by the transitive property,
