The shown bellow question answer
1 answer:
Answer:
The area of the shape can be divided into the area of the rectangle, and the area of the semi-circle.
The area of the rectangle can be found by
The area of a semi-circle can be found with the formula where r is the radius.
Since we know the diameter of the semi-circle is 4,
the radius will be 4 ÷ 2 = 2.
Therefore, the area of the semi-circle is
Therefore, the area of the shape is or
(3 decimal places)
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<u>Note: this answer assumes the equation of the line can be put in slope-intercept form. </u>
Answer:
Step-by-step explanation:
1) First, find the slope of y + 7 = -2 (x - 6). We can see that it's already in point-slope form, or format. Remember that the number in place of the
is the slope. Therefore, -2 is the slope of that equation.
What we need is the slope that is perpendicular to that, though. So, find the opposite reciprocal of -2. To do this, change its sign, convert it into a fraction (), and flip its numerators and denominators. Therefore, the perpendicular slope would be
.
2) Now that we have a slope and a point the line passes through, we can write an equation using the point-slope formula, . In order to write an equation, the
,
, and
have to be substitute for with real values.
The represents the slope. We already calculated that in the last step, so put
in place of the
. The
and
represent the x and y values of a point the line passes through. We know that the line has to pass through (6, -3), so substitute 6 for
and -3 for
:
Therefore, (again, assuming that the line can be put in point-slope form) the answer is .
Since the figure is a parallelogram, then SP=RQ, and SR=PQ.
To find SR, we draw right triangle SAR, as shown in the picture, where the coordinates of A are clearly (-3, -2).
Thus, we can see that SA=4 units, and AR=4 units. By the Pythagorean theorem,
Similarly, to find SP, which is equal to QR, we draw the triangle PBS, where the coordinates of B are (-2, 2).
Clearly, PB=3 and SB=1, thus using the Pythagorean theorem in right triangle PBS:
units.
The perimeter of the parallelogram is SP+RQ+SR+PQ=
.
Answer: second choice
To find SR, we draw right triangle SAR, as shown in the picture, where the coordinates of A are clearly (-3, -2).
Thus, we can see that SA=4 units, and AR=4 units. By the Pythagorean theorem,
Similarly, to find SP, which is equal to QR, we draw the triangle PBS, where the coordinates of B are (-2, 2).
Clearly, PB=3 and SB=1, thus using the Pythagorean theorem in right triangle PBS:
The perimeter of the parallelogram is SP+RQ+SR+PQ=
Answer: second choice