The range of the given relation is D. R = {-1, 3, 5, 8}.
Step-by-step explanation:
Step 1:
The range of a relation is the second set of values while the domain constitutes the first set of values.
There are 4 given relations with two sets of values so there would be 4 domain values and 4 range values.
Step 2:
The range of (1, -1) = -1,
The range of (2, 3) = 3,
The range of (3, 5) = 5,
The range of (4, 8) = 8.
Combining these values we get the range as {-1, 3, 5, 8} which is option D.
Option B:
Solution:
In the given figure 
.
If two triangles are similar, then their corresponding sides and angles are equal.
By CPCTC, in 
,
– – – – (1)
– – – – (2)
– – – – (3)
– – – – (4)
– – – – (5)
– – – – (6)
Option A: 
By CPCTC proved in equation (2) .
Therefore 
. Option A is false.
Option B:
By CPCTC proved in equation (1) .
Therefore Option B is true.
Option C: 
By CPCTC proved in equation (4) .
Therefore 
. Option C is false.
Option D: 
By CPCTC proved in equation (5) .
Therefore 
. Option D is false.
Hence Option B is the correct answer.
Answer:
a= 2/5
b= 30
c= 18
d= 3:2
e= No, because the fraction or ratio is the same, all you need to do is simplify it!
Answer:
x = 2.5 or -0.8
Step-by-step explanation:
Here, we are to use completing the square method to solve for the values of x
Firstly, we divide through by 4
= x^2 -7/4x -2 = 0
Now, we move the two term to the right hand side
x^2 -7/4x = 2
Now, we divide the coefficient of x by 2 and square it;
That would be;
(-7/4 * 1/2)^2 = 49/64
we now add this value to both sides of the equation
x^2 -7/4x + 49/64 = 2 + 49/64
The right hand side can be rewritten as;
(x-7/8)^2 = 177/64
taking the square root of both sides
x-7/8 = √(177/64)
x = 7/8 ± √(177/64)
x = 7/8 + √(177/74) or 7/8 - √(177/64)
= x = 2.53802 or -0.788017
Which to the nearest tenth is
x = 2.5 or -0.8
