Answer:
3x - y = 0; 2x - y = -5
Step-by-step explanation:
Let x be the present age of Hans and y be the present age of Grace,
Since, in present Grace is three times as old as Hans,
⇒ y = 3x
⇒ 3x - y = 0
Now, after 5 years,
The age of Hans = x + 5,
And, the age of Grace = y + 5
Also, in 5 years Grace will be twice as old as Hans is then,
⇒ y + 5 = 2 ( x + 5 )
⇒ y + 5 = 2x + 10
⇒ 2x - y = -5
Hence, the required system of linear equations is,
3x - y = 0; 2x - y = -5
Answer:
Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.
Step-by-step explanation:
Answer: Angle ABC = 60, angle CBD = 120 and angle GFH = 60
Step-by-step explanation: Line ABD is parallel to line EFG. Line line CFH is a straight line that cuts across both parallel lines. Therefore, angle FBD and angle HFG are corresponding angles. That means angle FBD equals 3x. Also 3x plus 6X equals 180. That is,
3x + 6x = 180 {Sum of angles on a straight line equals 180}
9x = 180
Divide both sides of the equation by 9
x = 20.
That means angle 6x measures 6(20) and that is 120 degrees.
Also angle 3x measures 3(20) and that is 60 degrees.
Angle ABC + Angle CBD = 180 {Sum of angles on a straight line equals 180}
Angle ABC + 120 = 180
Angle ABC = 180 - 120
Angle ABC = 60
Also angle CBD equals 6x, and x = 20. Therefore angle CBD = 6 x 20
Angle CBD = 120.
And then, angle GFH = 3x, and x equals 20. Hence angle GFH = 60.
Therefore angle ABC = 60, angle CBD = 120 and angle GFH = 60.
