Step-by-step explanation:
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13. Find the measure of angle 7 if the measure of angle 1 is 84 degrees less than the measure of angle 2. Please explain how you
got your answer. Thank you.
1 answer:
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Answer:
The exact coordinates of the point where the line through B and D intersects the y-axis is
Step-by-step explanation:
For the given question, we have the following parameters;
The shape of the quadrilateral ABCD in the question = A rhombus
The diagonals of the rhombus = AC and BD
The point of intersection of the diagonals, M = (6, -11)
The equation of the line points A and C lie = 2·y + 7·x = 20
A rhombus is an orthodiagonal quadrilateral (The diagonals of a rhombus are perpendicular)
Therefore;
AC ⊥ BD and where the slope of the line with points A and C is 'm', the slope of the line with points B and D is (-1/m)
Rewriting the equation, 2·y + 7·x = 20, in slope and intercept form, we have;
2·y + 7·x = 20
y = (- 7·x + 20)/2 = -7·x/2 + 10
∴ y = -7·x/2 + 10
The slope of the line 'y = -7·x/2 + 10', m = -7/2
∴ The slope of the line having the points B and D is -1/m = -1/(-7/2) = 2/7
The equation of the line having the points B and D in point and slope form, using point (6, -11) is given as follows;
y - (-11) = 2/7 × (x - 6)
y + 11 = 2·x/7 - 12/7
∴ y = 2·x/7 - 12/7 - 11 = 2·x/7 - 89/7 = 2·x/7 -
The equation of the line having the points B and D in point is therefore;
y = 2·x/7 -
The coordinates of the point where the line having the points B and D intersects the y-axis is the y-intercept, of the equation, y = 2·x/7 - , which is
We have to triple Autumn's earning for each basket, so the table would be
We expect an equation like
where is the initial value, and
is the multiplier. Since we start with 2$, and we triple the amount with each basket, we have
This relation is exponential, because every time a new basket is made, the previous amount is multiplied by a constant. In other words, we have
For the graph, you just need to sketch the points from the table we draw above and connect them