Which expression is equivalent to 9x − 2x + 3 and why?
2 answers:
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Answer: 5y + 4x = - 10
Step-by-step explanation:
Two lines are said to be perpendicular if the product of their gradients = -1.
If the gradient of the first line is and the gradient of the second line is
, if the lines are perpendicular, them
x
= -1 , that is
=
The equation of the line given is 5x - 4y = -3 , we need to write this equation in slope - intercept form in order to find the slope.
The equation in slope -intercept form is given as :
y =mx + c , where m is the slope and c is the y - intercept.
Writing the equation in this form , we have
5x - 4y = + 3
4y = 5x -+3
y = 5x/4 + 3/4
comparing with the equation y = mx + c , then = 5/4
Which means that = -4/5 and the line passes through the point ( -5 , 2 ).
Using the equation of line in slope - point form to find the equation of the line;
y - = m ( x -
)
y - 2 = -4/5 ( x +5)
5(y - 2 ) = -4 ( x + 5 )
5y - 10 = -4x - 20
5y + 4x = - 10
The area of the frame not covered by the painting is 192 square inches
<em><u>Solution:</u></em>
Given that, A rectangular painting is 24 inches wide and 20 inches tall without the frame
The area of rectangle is given as:
<em><u>Find the area of painting without frame:</u></em>
Length = 20 inches
Width = 24 inches
Thus area of painting without frame is 480 square inches
With the frame, it is 28 inches wide and 24 inches tall
<em><u>Find the area of painting with frame:</u></em>
Length = 24 inches
Width = 28 inches
Thus area of painting with frame is 672 square inches
<em><u>What is the area of the frame not covered by the painting</u></em>
Area of the frame not covered by the painting = Area with farme - Area without frame
Area of the frame not covered by the painting = 672 - 480 = 192
Thus the area of the frame not covered by the painting is 192 square inches