Three times the sum of a number and 7 is equivalent to 57.
2 answers:
Equivalent expressions are expressions that have the same values.
The expression is and the number is 12
Represent the number with x.
So, the sum of a number (x) and 7 would be represented as: x + 7
Three times the sum would be represented as: 3(x + 7)
This expression is equivalent to 57.
So, we have:
Divide both sides of the equation by 57
Subtract 7 from both sides of the equation
Hence, the number is 12
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Answer:
The product of the slopes of lines is -1.
i.e. m₁ × m₂ = -1
Thus, the lines are perpendicular.
Step-by-step explanation:
The slope-intercept form of the line equation
where
- m is the slope
- b is the y-intercept
Given the lines
y = 2/3 x -3 --- Line 1
y = -3/2x +2 --- Line 2
<u>The slope of line 1</u>
y = 2/3 x -3 --- Line 1
By comparing with the slope-intercept form of the line equation
The slope of line 1 is: m₁ = 2/3
<u>The slope of line 2</u>
y = -3/2x +2 --- Line 2
By comparing with the slope-intercept y = mx+b form of the line equation
The slope of line 2 is: m₂ = -3/2
We know that when two lines are perpendicular, the product of their slopes is -1.
Let us check the product of two slopes m₁ and m₂
m₁ × m₂ = (2/3)(-3/2 )
m₁ × m₂ = -1
Thus, the product of the slopes of lines is -1.
i.e. m₁ × m₂ = -1
Thus, the lines are perpendicular.
Answer:
The system has infinitely solutions
Step-by-step explanation:
we have
Multiply by 3 both sides
----> equation A
The equation A is a circle centered at origin with radius
and
Divide by 5 both sides
----> equation B
The equation B is a circle centered at origin with radius
Equation A and Equation B are the same
Therefore
The system has infinitely solutions