Answer:
Option (B)
Step-by-step explanation:
CDEF is a quadrilateral having vertex C(2, 3), D(1, 2), E(4, 1), F(5, 3).
To prove that the given quadrilateral has a right angle, we will use the property of perpendicular lines.
where 
and 
are the slopes of the consecutive sides of the quadrilateral.
Since CD and DE are the consecutive sides of the quadrilateral, Carla is on the right track by finding the slopes of CD and DE.
Since Jonah is finding the slopes of opposite sides so he will not be able to use the property of perpendicular lines.
Option (B) will be the answer.
The answer is C. x=4
Explanation) 49 - 7 (4) = 21
7 (4) = 28
49 - 28 = 21
Answer:
15 years old
Step-by-step explanation:
Start by defining the variables that we are going to use throughout our working:
Let the current age of Wei Ling and Wei Xuan be L and X years old respectively.
Next, form equations using the given information.
<u>5 years </u><u>ago</u>
Wei Ling: (L -5) years old
Wei Xuan: (X -5) years old
Given that the ratio of Wei Ling's age to that of Wei Xuan's is 2: 5,
Cross multiply:
2(X -5)= 5(L -5)
Expand:
2X -10= 5L -25
2X= 5L -25 +10
2X= 5L -15 -----(1)
<u>9 years time</u>
Wei Ling: (L +9) years old
Wei Xuan: (X +9) years old
Given that the ratio of Wei Ling's age to that of Wei Xuan is 3: 4,
Cross multiply:
3(X +9)= 4(L +9)
Expand:
3X +27= 4L +36
3X= 4L +36 -27
3X= 4L +9 -----(2)
Let's solve using the elimination method.
(1) ×3:
6X= 15L -45 -----(3)
(2) ×2:
6X= 8L +18 -----(4)
(3) -(4):
6X -6X= 15L -45 -(8L +18)
0= 15L -45 -8L -18
0= 7L -63
7L= 63
L= 63 ÷7
L= 9
Substitute L= 9 into (1):
2X= 5(9) -15
2X= 45 -15
2X= 30
X= 30 ÷2
X= 15
Thus, Wei Xuan is 15 years old now.
1) 6x-7y=-11
2) x=-2
3) y=-4x+1
4) y-5=3(x-1)
