Answer:
= 6
Step-by-step explanation:
The n th term of a geometric sequence is
= a
where a is the first term and r the common ratio
Here a = 6 and r = 30 ÷ 6 = 5, thus
= 6
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Answer:
Step-by-step explanation:
3x%2B4y=12 Start with the given equation
4y=12-3x Subtract 3+x from both sides
4y=-3x%2B12 Rearrange the equation
y=%28-3x%2B12%29%2F%284%29 Divide both sides by 4
y=%28-3%2F4%29x%2B%2812%29%2F%284%29 Break up the fraction
y=%28-3%2F4%29x%2B3 Reduce
Looking at y=-%283%2F4%29x%2B3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-3%2F4 and the y-intercept is b=3
Since b=3 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis
So we have one point
Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun
Also, because the slope is -3%2F4, this means:
rise%2Frun=-3%2F4
which shows us that the rise is -3 and the run is 4. This means that to go from point to point, we can go down 3 and over 4
So starting at , go down 3 units
and to the right 4 units to get to the next point
Now draw a line through these points to graph y=-%283%2F4%29x%2B3
So this is the graph of y=-%283%2F4%29x%2B3 through the points and
Answer:
A rectangle
Step-by-step explanation:
The given parameters are;
The quadrilateral ABCD is a rhombus;
The length of the sides of the rhombus = 12 inches
The lengths of the sides of a rhombus are equal
The opposite interior angles of the rhombus are equal
The length of each midpoint from the vertex = 12 in./2 = 6 in.
Therefore, we have;
The line joining the midpoints form a quadrilateral with the length of the opposite sides equal
The sum of the interior angles of the rhombus = 180°
From the diagram created with Microsoft Visio, we have;
4·a + 4·b + 360 = 4 × 180 = 360 + 360
4·a + 4·b = 360
a + b = 90°
We have;
The interior angles of the quadrilateral formed = x
a + b + x = 180° Sum of angles on a straight line
∴ x = 180° - (a + b) = 180° - 90° = 90°
x = 90°
Therefore, the interior angles of the quadrilateral formed = 90°
The quadrilateral formed having equal opposite sides, and all interior angle of 90° each is a rectangle
