Answer:
(∠C) ≅ (∠B)
∴ tan(∠B) = tan(∠C) and
Slope AB = Slope BC
Step-by-step explanation:
Part A:
To explain why the slope from point from A to B is the same with the slope from B to C with similar triangles we have;
The angle between segment AB and the vertical is the same as the angle between segment BC and the vertical - (corresponding angles)
The angle between segment AB and the horizontal is the same as the angle between segment BC and the horizontal - (corresponding angles)
The length of a segment opposite to the angle between segment AB and the horizontal is the as the length of a segment opposite to the angle between segment BC and the horizontal
Therefore, the triangle formed by A, B and the point of intersection of the vertical line from A with the horizontal line from B is congruent to the triangle formed by B, C and the point of intersection of the vertical line from B with the horizontal line from C
Which gives the angle with the horizontal at C (∠C) is congruent to the angle with horizontal B (∠B)
The slope AB = tan(∠B)
Slope BC = tan(∠C)
(∠C) ≅ (∠B)
Therefore, tan(∠B) = tan(∠C) and slope AB = Slope BC.
Draw out a number line with the values 0, 5, 10, 15, 20, 25, 30, etc (basically multiples of 5)
Then plot a point at 25
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Or you can draw out a number line with the multiples of 10, so with the values 0, 10, 20, 30, ...
Then plot a point at the exact midway point between 20 and 30 to represent the value 25
Perimeter is adding all the outside dimensions. The left side of the shoae is a rectangle, so the bottom line is the same as the top line, 10 feet.
Perimeter = 8 + 10 + 8.9 + 10 + 4 = 40.9 ft.
Answer:
1134.62 (THE SUM OF 20 TERMS)
Step-by-step explanation:
First we write out our given information:
a8=2a2
a11=18
an is an arithmetic sequence.
Where here an means the nth term of our sequence.
What does an arithmetic sequence mean? It means to get to the next term in your sequence you add a constant (c) each time:
an+1=an+c
Equivalently:
an+1−an(n+1)−n=c
So an is of slope c (c2 is another constant):
an=cn+c2
Where here c2=a0 (Substitute in n=0 and see why that has to be the case if we let a0 exist)
Now we use the other given information to try to come up with a solution.
Let n=2:
a2=2c+c2
Let n=8, using the above equation we have:
a8=8c+c2=2a2=4c+2c2
Let n=11
a11=18
a11=11c+c2
But a11−a8=(11c+c2)−(8c+c2)=3c
Hence, a11=3c+a8
a11=3c+4c+2c2=18
a11=3c+8c+c2=18
Answer:
sinΘ =
Step-by-step explanation:
sinΘ = = =