We could use the formula, derive the formula, or just work it out for this case. Let's do the latter.
The distance of a point to a line is the length of the perpendicular from the line to the point.
So we need the perpendicular to 5x-4y=10 through (-1,3). To get the perpendicular family we swap x and y coefficients, negating one. We get the constant straightforwardly from the point we're going through:
4x + 5y = 4(-1)+5(3) = 11
Those lines meet at the foot of the perpendicular, which is what we're after.
4x + 5y = 11
5 x - 4y = 10
We eliminate y by multiplying the first by four, the second by five and adding.
16x + 20y = 44
25x - 20y = 50
41x = 94
x = 94/41
y = (11 - 4x)/5 = 15/41
We want the distance from (-1,3) to (94/41,15/41)
Answer:
1620°
Step-by-step explanation:
The formula for finding that measure is ...
sum of interior angles of n-sided convex polygon = 180°×(n -2)
For n=11, this is
sum = 180°×9 = 1620°
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Another way to get there is to remember that the sum of <em>exterior</em> angles is always 360° for a convex polygon. Then the total (interior + exterior) of the angles of an n-sided polygon is 180°×n. Subtracting the sum of exterior angles gives the total of interior angles: 180°×n -360° = 180°×(n -2).
Answer:
See below.
Step-by-step explanation:
There are 4 sides of the pyramid that rise from the 4 points on the base and they all meet at the point A.
So it has 1 square face ( the base) and 4 side faces which are all triangles.
Answer:
<em>y = 8</em>
Step-by-step explanation:
330x + 1220y = 12730 (cost of coach tickets plus cost of first class tickets is total budget)
x + y = 17 (number of coach tickets plus number of first class tickets is total number of people)
Solve the second equation for y to get y = 17 - x, then plug that into the first equation and solve for x:
330x + 1220(17 - x) = 12730
330x + 20740 - 1220x = 12730
-890x + 20740 = 12730
-890x = -8010
x = 9
Sarah bought x = 9 coach tickets. Plug that into the second equation and solve for y:
9 + y = 17
y = 8
Sarah bought y = 8 first class tickets.
Answer:
23
Step-by-step explanation:
6x3=18
18+5=23
