Answer: NEITHER
Step-by-step explanation:
From the equation of lines given above, to know if relationships exist between the two lines, we must first determine that from their gradients or slopes.
From first equation
2x - y = 5,
y = 2x - 5
Therefore, m₁ = 2
From the second equation
3x - y = 5
y = 3x - 5
Therefore m₂ = 3
Recall, For the two lines to be parallel, m₁ = m₂ , and for the two line to be perpendicular, m₁m₂ = -1
since none fulfilled the conditions stated above, the answer then is
NEITHER
Answer: sqrt(2)/2 which is choice D
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Explanation
(3pi/4) radians converts to 135 degrees after multiplying by the conversion factor (180/pi).
The angle 135 degrees is in quadrant 2. We subtract the angle 135 from 180 to find the reference angle
180-135 = 45
Then you can use a 45-45-90 triangle to determine that the ratio of opposite over hypotenuse is sqrt(2)/2
sine is positive in quadrant 2
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Alternatively, you can use a unit circle. Refer to the diagram below. In red, I've circled the angle 3pi/4 radians. The terminal point for this angle has a y coordinate of sqrt(2)/2
Recall that y = sin(theta).
Hi there! :)
Answer:
Length = 10.5 m, width = 7 m.
Step-by-step explanation:
Given:
Perimeter, or P = 35 m
Ratio of l to w = 3 : 2
Since the ratio is 3 : 2, let l = 3x, and w = 2x.
We know that the formula for the perimeter of a rectangle is P = 2l + 2w. Therefore:
35 = 2(3x) + 2(2x)
35 = 6x + 4x
35 = 10x
x = 3.5
Plug this value of "x" into each expression to solve for the dimensions:
2(3.5) = w
w = 7 m
3(3.5) = l
l = 10.5 m
Therefore, the dimensions are:
Length = 10.5 m, width = 7 m.
See attachment for math work and answer.
When working with very large or very small numbers, scientists, mathematicians, and engineers use scientific notation to express these quantities. Scientific notation is a mathematical abbreviation, based on the idea that it is easier to read an exponent than to count many zeros in a number. Very large or very small numbers need less space when written in scientific notation because the position values are expressed as powers of 10. Calculations with long numbers are easier to do when using scientific notation
