Answer:
c.) 16in
Step-by-step explanation:
40/5 = 8
8 x 2 = 16
The solution to the given inequality as represented in the task content are; z < - 1.00485413 OR z > 1.00485413.
<h3>What is the solution to the given inequality?</h3>
It follows from the task content that the solution of the given inequality; ( 29 / 289z ) < ( 16 / 161 ) z is to be determined.
Since the given inequality is;
( 29 / 289z ) < ( 16 / 161 ) z
By cross multiplication; we have;
161 × 29 < ( 16z × 289z )
( 161 × 29 ) / ( 16 × 289 ) < z²
1.00973183 < z²
Therefore;
1.00485413 < z. OR. -1.00485413 > z.
Ultimately, z < - 1.00485413 OR z > 1.00485413.
Read more on inequalities;
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The transformations done are option A. A reflection over the y-axis, then a reflection over the x-axis
Step-by-step explanation:
Step 1:
First, we plot the points of triangle ABC and A''B''C''.
The points of triangle ABC are A (-8, -5), B(-4, -3), and C(-4,-7).
The points of triangle A''B''C'' are A'' (8, 5), B'' (4, 3), and C'' (4,7).
The points of both triangles ABC and A''B''C'' are the same values but different symbols for x and y values.
Step 2:
If a shape is reflected across an axis, the values remain the same but the symbols vary according to the quadrant.
If a shape is translated, all coordinates of all the points vary accordingly.
As triangles ABC and A''B''C'' have exactly the same coordinates it means that two reflections have occurred but no translations have occurred.
So the answer is the option with two reflections. So option A. A reflection over the y-axis, then a reflection over the x-axis is the answer.
Answer:
1. the y-intercept is 9.5 and it means the starting length of the candle
2. the slope is -1/2 and it means that the candle burns 1/2 an inch every hour
3. it burns an inch every 2 hours, it is 9.5 inches long, so 19 hours it'll take to burn.
