Answer:
18/35
Step-by-step explanation:
3/5 ÷ 7/6
3/5 × 6/7
18/35
Well i could tell you if you attach a picture :)
Answer: 7
Step-by-step explanation:
Let the number chosen by Michael be x.
We are told that he multiplied it by itself, added 1. This would be:
= = ( x × x) + 1 = x² + 1
We are further told that he multiplied the result by 10, and added 3. This would be:
= = [(x² + 1) × 10] + 3
= 10x² + 10 + 3
= 10x² + 13
Lastly, he multiplied the result by 4 and his final answer was 2012. This would be:
(10x² + 13) × 4 = 2012
40x² + 52 = 2012
40x² = 2012 - 52
40x² = 1960
x² = 1960/40
x² = 49
x = ✓49
x = 7
The number is 7
can be expressed as:
= ( x × x) + 1 = x² + 1
Since you're studying this stuff, you know that
.. translation right by k units: f(x) ⇒ f(x-k)
.. translation up by k units: f(x) ⇒ f(x) +k
.. horizontal stretch by a factor of k: f(x) ⇒ f(x/k) . . . . same as compressed by 1/k
.. vertical stretch by a factor of k: f(x) ⇒ k*f(x)
.. reflection across the x-axis: f(x) ⇒ -f(x)
.. reflection across the y-axis: f(x) ⇒ f(-x)
The sequence in which these are done is important.
1. f(x) = (1/2)^x
.. translated 4 units right: f(x) = (1/2)^(x -4)
.. reflected across the x-axis: f(x) = -(1/2)^(x -4)
.. vertically stretched by a factor of 1.5: f(x = -1.5(1/2)^(x -4)
2. f(x) = ln(x)
.. translated 3 units left: f(x) = ln(x +3)
.. horizontally compressed by a factor of 1/4: f(x) = ln(x/4 +3)
.. translated down 0.5 units: f(x) = -0.5 +ln(x/4 +3)
3. f(x) = e^x
.. horizontally stretched by a factor of 3: f(x) = e^(x/3)
.. reflected across the y-axis: f(x) = e^(-x/3)
.. translated 1 unit right: f(x) = e^(-(x -1)/3)
- AC is congruent to itself
- AC bisects angle BAD, so that angles BAC and DAC are congruent
- Both angles B and D are right angles, so they are congruent
This means triangles BAC and DAC are a pair of angle-angle-side triangles, so they are congruent to one another. Corresponding parts of congruent triangles are congruent, so the line segments BC and DC are congruent and have the same length.
Then