Answer:
m₁×m₂ = -1
m₁ = 3 and m₂ = -1/3
3×-1/3 = -1
-1 = -1
Hence proved, the given two lines are perpendicular.
Step-by-step explanation:
You can prove that the two lines are perpendicular if the following condition holds true.
m₁×m₂ = -1
Where m₁ is the slope of line 1 and m₂ is slope of line 2
So first you have to find out the slope of each line.
You are given 2 equations
y = 3x + 5 eq. 1
6y + 2x = 1 eq. 2
You have to write these equations in slope-intercept form to find out their slopes.
The slope-intercept form is given by
y = mx + b
Comparing the general form with eq. 1
y = 3x + 5
We notice that the slope is m₁ = 3
Now convert the eq. 2 into slope-intercept form
6y + 2x = 1 eq. 2
6y = -2x + 1
y = (-2x + 1)/6
y = -1/3x + 1/6 eq. 2
Comparing the general form with eq. 2
y = -1/3x + 1/6
We notice that the slope is m₂ = -1/3
Now we have slopes of both lines so let us test whether they are perpendicular or not
m₁×m₂ = -1
m₁ = 3 and m₂ = -1/3
3×-1/3 = -1
-1 = -1
Hence proved, the given two lines are perpendicular.
Answer:
1st integer = 5
2nd integer = 6
3rd integer = 7
Step-by-step explanation:
Let:
1st integer = x
2nd integer = x + 1
3rd integer = x + 2
Now according to given conditions:
x + x + 1 = 4+ x +2
Adding like terms
2x +1 = 6 + x
Taking terms with x on left side and others on right
2x - x = 6 -1
x = 5
Proof:
x + x + 1 = 4+ x +2
Putting x = 5
5 + 5 + 1 = 4 +5 +2
11 = 11
Hence proved!
So,
1st integer = 5
2nd integer = 5 + 1 = 6
3rd integer = 5+ 2 = 7
I hope it will help you!
Answer:
140 markers
Step-by-step explanation:
From the question;
- The teacher bought 5 boxes of markers
- Markers in 1 box = 28 markers
We are required to determine the total number of markers she bought
- Number of markers = Number of boxes × number of markers per box
Therefore;
Number of markers bought = 5 boxes × 28 markers/box
= 140 markers
Thus, the teacher bought 140 markers
Cos(x)/(1+sin(x) + (1+sin(x))/cos(x)=
cos²(x)/cos(x)(1+sin(x)) + (1+sin(x))²/cos(x)(1+sin(x))=
cos²(x)+1+2sin(x)+sin²(x) /cos(x)(1+sin(x))=
2+2sin(x) / cos(x)(1+sin(x))=
2(1+sin(x)) / cos(x)(1+sin(x))=
2/cos(x)=
2*sec(x)
Answer:
[0,2]
Step-by-step explanation: