Answer:
x=10, y=25
Step-by-step explanation:
First, in a trapezoid, the two angles on the same leg (the legs are the opposite sides that are not parallel) add up to 180 degrees. Therefore, 4y as well as (2y+3x) are supplementary. We can write this out as
4y + (2y+3x) = 180
6y+3x = 180
Next, the angles of a triangle add up to 180 degrees. Therefore, as the angles 2y, 4y, and (5x-20) make up a triangle, they add up to 180 degrees. We can write this as
4y + 2y + (5x-20) = 180
6y + 5x -20 =180
Our two equations are thus
6y + 5x - 20 = 180
6y + 3x = 180
If we subtract 6y from both sides in each equation, we can say
5x - 20 = 180-6y
3x = 180-6y
Therefore, we can write
5x-20 = 180-5y = 3x
5x-20=3x
subtract 3x from both sides to make all x variables on the same side
2x-20 = 0
add 20 to both sides to isolate the x and its coefficient
2x = 20
divide both sides by 2 to isolate x
x = 10
Therefore,
x = 10
6y + 3x = 180
6y + 30 = 180
subtract 30 from both sides to isolate the y and its coefficient
6y = 150
y = 25
3.75 miles because 3/4 is .75 in money and the 3 is howm many miles
Answer:
Answer:
(B)
Step-by-step explanation:
We have to construct two equilateral triangles that is one with the side length of 2 inches and the another triangle with side length of 3 inches.
Now, both the triangles are equilateral triangles, thus they have same shape.
Also, both triangles have different side lengths, one having 2 inches and another having 3 inches, thus they have different size.
Hence, the true statement about the two triangles is:
The two triangles are the same shape but not the same size.
Therefore, option B is correct.
Step-by-step explanation:
Answer:
0.625
Step-by-step explanation:
Given the points :
(0, 4) and (-8, -1)
x1 = 0 ; y1 = 4
x2 = - 8 ; y2 = - 1
Slope, m = rise / run
Rise = y2 - y1 = - 1 - 4 = - 5
Rise = x2 - x1 = - 8 - 0 = - 8
The slope, m = - 5 / - 8
Slope, m = 0.625
Answer:
correct option is C) 2.8
Step-by-step explanation:
given data
string vibrates form = 8 loops
in water loop formed = 10 loops
solution
we consider mass of stone = m
string length = l
frequency of tuning = f
volume = v
density of stone =
case (1)
when 8 loop form with 2 adjacent node is
so here
..............1

and we know velocity is express as
velocity = frequency × wavelength .....................2
= f ×
here tension = mg
so
= f ×
..........................3
and
case (2)
when 8 loop form with 2 adjacent node is
..............4

when block is immersed
equilibrium eq will be
Tenion + force of buoyancy = mg
T + v ×
× g = mg
and
T = v ×
- v ×
× g
from equation 2
f ×
= f ×
.......................5
now we divide eq 5 by the eq 3

solve irt we get

so
relative density 
relative density = 2.78 ≈ 2.8
so correct option is C) 2.8