Answer:
Parallel line:
Perpendicular line:
Step-by-step explanation:
we are given equation 4x+5y=19
Firstly, we will solve for y
we can change it into y=mx+b form
so,
Parallel line:
we know that slope of two parallel lines are always same
so,
Let's assume parallel line passes through (1,1)
now, we can find equation of line
we can plug values
now, we can solve for y
Perpendicular line:
we know that slope of perpendicular line is -1/m
so, we get slope as
Let's assume perpendicular line passes through (2,2)
now, we can find equation of line
we can plug values
now, we can solve for y
Answer:
12 boys
Step-by-step explanation:
From the above question:
Number of boys = 3
Number of girls = 2
Boys: Girls
3:2
Let :
a = boys
b = girls
Hence, a : b = 3 : 2
a/b = 3/2
Cross Multiply
2a = 3b .......... Equation 1
a = 3b/2
If four more girls join the class, there will be the same number of boys and girls
Hence,
a: b + 4 = 3 : 3
a/b + 4 = 3/3
Cross Multiply
3a = 3(b + 4)
3a = 3b + 12 ........ Equation (2)
From Equation 1: a = 3b/2
Substitute 3b/2 for a in Equation 2 we have:
3a = 3b + 12 .........Equation 2
3(3b/2) = 3b + 12
9b/2 = 3b + 12
Cross Multiply
9b = 2(3b + 12)
9b= 6b + 24
9b - 6b = 24
3b = 24
b = 8
Substitute 8 for b in Equation 1
a = 3b/2
a = 3 × 8/2
a = 24/2
a = 12
Therefore, the number of boys in the class is 12
Answer:
[-1, infinity)
Step-by-step explanation:
I must assume that you meant y = √(x - 5) - 1.
The range of the square root function is [0, infinity.
If 1 is subtracted from the square root function, the range of the resulting function is [-1, infinity).
Given that the First term of the Arithmetic sequence = -3
⇒ a = -3
We know that nth term of a Arithmetic sequence is : Tn = a + (n - 1)d
where a is the first term and d is the common difference
Given that 10th term is 15
⇒ T₁₀ = -3 + (10 - 1)d
⇒ -3 + (10 - 1)d = 15
⇒ 9d = 18
⇒ d = 2
⇒ Common difference of given Arithmetic Sequence is 2
