The point-slope form:
m - slope
(x₁, y₁) - point
The formula of a slope:
We have the points (-2, 7) and (1, 1). Substitute:
<em>point-slope form</em>
<em> slope-intercept form</em>
<em>standard form</em>
Consider the sequence of numbers 3/8,3/4, 1 1/8,1 7/8 Which statement is a description of the sequence?
2 answers:
The complete question in the attached figure
Let
for n=1
f(1)=3/8
for n=2
f(2)=3/4
for n=3
f(3)=1 1/8
for n=4
f(4)=1 1/2
for n=5
f(5)=1 7/8
we know that
f(2)-f(1)=3/4-3/8=3/8------> f(2)=f(1)+3/8
f(3)-f(2)=1 1/8-3/4----> 9/8-6/8----> 3/8-----> f(3)=f(2)+3/8
f(4)-f(3)=1 1/2-1 1/8-----> 12/8-9/8----> 3/8-----> f(4)=f(3)+3/8
f(5)-f(4)=1 7/8-1 1/2-----> 15/8-12/8---> 3/8-----> f(5)=f(4)+3/8
therefore
the answer is the option
The sequence is recursive and can be represented by the function f(n + 1) = f(n) + 3/8
Let
for n=1
f(1)=3/8
for n=2
f(2)=3/4
for n=3
f(3)=1 1/8
for n=4
f(4)=1 1/2
for n=5
f(5)=1 7/8
we know that
f(2)-f(1)=3/4-3/8=3/8------> f(2)=f(1)+3/8
f(3)-f(2)=1 1/8-3/4----> 9/8-6/8----> 3/8-----> f(3)=f(2)+3/8
f(4)-f(3)=1 1/2-1 1/8-----> 12/8-9/8----> 3/8-----> f(4)=f(3)+3/8
f(5)-f(4)=1 7/8-1 1/2-----> 15/8-12/8---> 3/8-----> f(5)=f(4)+3/8
therefore
the answer is the option
The sequence is recursive and can be represented by the function f(n + 1) = f(n) + 3/8
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First option: correct. This is because angles WOX and XOZ are supplementary, so
Second option: correct. By the inscribed angles theorem, we have
Angles WOX and YOZ are congruent because they form a vertical pair; they both have measure 76 degrees. This means angles WXY and WZY are also congruent, since the interior angles of any triangle sum to 180 degrees in measure. Therefore triangles WXO and YZO form a side-side-side pair, and all SSS triangles are similar.
Third option: not correct. There is a theorem (not sure what the name is) regarding intersecting chords that asserts the average of the measures of arcs WY and XZ is the same as the measure of angle XOZ. This means
Fourth option: not correct. This is because arcs WX and XZ are not "supplementary" in the sense that they do not form a semicircle and their measures do not add to 180 degrees. We know this because it's clear that point O is not the center of the circle. If it was, then angle XOZ would be a central angle and its measure would be the same as the arc XZ it subtends.
Fifth option: correct. The theorem mentioned in the assessment of the third option makes itself useful here. We have