Write an equation that represents a horizontal translation 10 units left of the graph of g(x) = |x|
2 answers:
Answer: h(x) = |x+10|
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Explanation:
To shift the graph 10 units to the left, we replace x with x+10. What's really going on is that the xy axis shifts 10 units to the right (because x is now x+10; eg, x = 2 ---> x+10 = 2+10 = 12) so it appears that the graph is moving to the left. The general rule is h(x) = g(x+10).
So,
g(x) = |x|
g(x+10) = |x+10| ... every x has been replaced with x+10
h(x) = g(x+10)
h(x) = |x+10|
We can use a graphing tool like GeoGebra to visually confirm we have the right answer (see attached). Note how a point like (0,0) on the green graph moves to (-10,0) on the red graph.
---------------------------------------------------------
Explanation:
To shift the graph 10 units to the left, we replace x with x+10. What's really going on is that the xy axis shifts 10 units to the right (because x is now x+10; eg, x = 2 ---> x+10 = 2+10 = 12) so it appears that the graph is moving to the left. The general rule is h(x) = g(x+10).
So,
g(x) = |x|
g(x+10) = |x+10| ... every x has been replaced with x+10
h(x) = g(x+10)
h(x) = |x+10|
We can use a graphing tool like GeoGebra to visually confirm we have the right answer (see attached). Note how a point like (0,0) on the green graph moves to (-10,0) on the red graph.
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Note necessary facts about isosceles triangle ABC:
- The median CD drawn to the base AB is also an altitude to tha base in isosceles triangle (CD⊥AB). This gives you that triangles ACD and BCD are congruent right triangles with hypotenuses AC and BC, respectively.
- The legs AB and BC of isosceles triangle ABC are congruent, AC=BC.
- Angles at the base AB are congruent, m∠A=m∠B=30°.
1. Consider right triangle ACD. The adjacent angle to the leg AD is 30°, so the hypotenuse AC is twice the opposite leg CD to the angle A.
AC=2CD.
2. Consider right triangle BCD. The adjacent angle to the leg BD is 30°, so the hypotenuse BC is twice the opposite leg CD to the angle B.
BC=2CD.
3. Find the perimeters of triangles ACD, BCD and ABC:
4. If sum of the perimeters of △ACD and △BCD is 20 cm more than the perimeter of △ABC, then
5. Since AC=BC=2CD, then the legs AC and BC of isosceles triangles have length 20 cm.
Answer: 20 cm.