Answer:
1)
2)
Step-by-step explanation:
1)
The two triangles are similar by AA similarity.
That means .
We can add to both sides to get .
We can then subtract from both sides to get .
We know that the because they both lie on a straight line.
We can plug in for to get .
We can divide both sides of the equation by to get .
We then add to both sides to get .
So, and we're done!
2)
Because the two bases of a trapezoid are parallel, meaning adjacent top and bottom angles sum to , we have that .
We can subtract a and an from both sides to get .
We then divide both sides of the equation by to get .
We do the same thing for . On the other side of the trapezoid, we have that .
We combine like terms on the left side to get .
We subtract a from both sides to get .
We divide both sides of the equation to get .
So, and we're done!
Answer:
Step-by-step explanation:
Question 1
System of equations is,
y = -6x -------(1)
y = -4x - 2 ---------(2)
Substitute the value of y from equation (1) to equation (2)
-6x = -4x - 2
-6x + 4x = -2
-2x = -2
x = 1
From equation (1)
y = -6(1)
y = -6
Question (2)
System of equations is,
-y = x --------(1)
3x + 5y = 20 ---------(2)
Substitute the value of x from equation (1) to equation (2)
3(-y) + 5y = 20
-3y + 5y = 20
2y = 20
y = 10
From equation (1)
-y = x
x = -10
Question (3)
System of the equations is,
y = -2x - 7 --------(1)
9x - 10y = 12 ----------(2)
Substitute the value of y from equation (1) to equation (2)
9x - 10(-2x - 7) = 12
9x + 20x + 70 = 12
29x = 12 - 70
29x = -58
x = -2
From equation (1)
y = -2(-2) - 7
y = 4 - 7
y = -3
Answer:
Step-by-step explanation:
EK = ½ER
x+5 = ½(4x+2)
x+5 = 2x+1
x=4
First, let's convert 1 km 125 m into metres.
1 km = 1000 m
1.125 km - 1,125 m
On Tuesday, Eric biked 375 metres fewer than on Monday.
1125 - 375 = 750 m
Eric biked 750 m on Tuesday.
On both days he biked 1125 + 750 = 1,875 m or
1 kilometre and 875 metres