According to HL theorem if one leg and hypotenuse of one right triangle are equal to one leg and hypotenuse of other right triangle, then the triangles are congruent.
By using this theorem we can set up the system of equations as follows:
x=y+1 ...(1)
2x+3= 3y + 3 ..(2)
By using equation (1) next step is to plug in y+1 for x in equation (2). So,
2 ( y + 1) + 3 = 3y + 3
2y + 2 + 3 = 3y + 3 By using distribution property.
2y + 5 = 3y + 3
2y + 5 - 5 = 3y + 3 - 5 Subtract 5 from each side.
2y = 3y - 2
2y - 3y = -2 Subtract 3y from each sides.
-y = -2
So, y=2
Next step is to plug in y=2 in equation (1) to get the value of x. Hence,
x= 2+1
=3
So, x=3 and y=2 make these triangles congruent.
So, the correct choice is 3. x = 3, y = 2.
What it is basically asking is if Y = -4, find the value of x in the equation 6x + 7y = 4x + 4y
To solve this you just need to plug in -4 for y and solve for x
6x + 7(-4) = 4x + 4(-4)
6x - 28 = 4x - 16
Now isolate x by adding 28 to both sides
6x - 28 + 28 = 4x - 16 + 28
6x = 4x + 8
and subtract 4x from both sides
6x - 4x = 4x - 4x + 8
2x = 8
divide both sides by 2
2/2x = 8/2
x = 4
x = 4, y = -2
Answer: (4, - 2)
Hope it helps :)
Bransliest would be appreciated
Answer: 100
set up equation: GHE+EHI=GHI
(x+38)+(x+104)=134
calculate
you get x= -4
put -4 into EHI
(-4)+104= 100
Answer:
the angle of elevation is 12.56°
Step-by-step explanation:
the height of the ramp represents the opposite side and the length of the ramp the hypotenuse
we see that it has (angle, hypotenuse, opposite)
well to start we have to know the relationship between angles, legs and the hypotenuse
a: adjacent
o: opposite
h: hypotenuse
sin α = o/h
cos α= a/h
tan α = o/a
we choose the one with opposite and hypotenuse
sin α = o/h
sin α = 5ft / 23ft
sin α = 5/23
α = sin^-1 ( 5/23)
α = 12.56°
the angle of elevation is 12.56°
