When you reflect a function in the <em>x</em>-axis, the first coordinate of a point stays the same, and the second coordinate changes sign (what was positive is now negative and vice versa). See the attached picture.
Question 11: f(x) = -5x + 2. The function changes to its opposite, so g(x) = -(-5x + 2) = 5x - 2.
When you reflect a function in the <em>y</em>-axis, the first coordinate of a point changes to its opposite, but the second coordinate stays the same. Replace <em>x</em> with -<em>x</em> .
Question 14: f(x) = |2x - 1| + 3. Replacing <em>x</em> with -<em>x</em> produces g(x) = |2(-x) - 1| + 3 which simplifies to g(x) = |-2x -1| + 3.
Question 15 works the same way as #14.
In this question, the speed of the dolphin is already given, but the unit is different. The speed of the dolphin is given as 40 miles per hour and it has to be converted to feet per hour.
We already know that 1 mile = 5280 feet
Then
40 mile = 5280 * 40 feet
= 211200 feet
So the speed in feet per hour will be 211200 feet per hour. I hope the procedure is clear enough for you to understand. You can always use this method for solving similar problems without requiring any help from outside.
Answer:
22.5 cm
Step-by-step explanation:
9 inches=9×2.5 cm =22.5 cm
Answer:
shorter piece = 6. longer piece = 12
Step-by-step explanation:
short piece = s
long piece = l
l+s= 18
l= 6+s , substitute
6+s+s = 18
6+2s= 18
2s= 18-6
2s= 12
s=12/2
s= 6= shorter piece
l= 6+s
l= 6+6= 12 = longer piece
Answer:
2.6
Step-by-step explanation:
The Mean Absolute Deviation (MAD) is the average amount that each point is from the overall average of the data set.
So, first find the overall average (also called the mean):
avg = (1 + 1 + 2 + 3 + 5 + 7 + 9) / 7
= 28 / 7
= 4
The average (mean) is 4, so now you calculate how far each point is from 4 and average those numbers:
Note: Remember to use absolute values, since distance can't be negative.
4 - 1 = 3
4 - 1 = 3
4 - 2 = 2
4 - 3 = 1
4 - 5 = |-1| = 1
4 - 7 = |-3| = 3
4 - 9 = |-5| = 5
And finally, average (or find the mean) the new data set:
avg = (1 + 1 + 2 + 3 + 3 + 3 + 5) / 7
so 18 / 7 is the MAD of the data set.
Finally, round it to the nearest tenth:
18 ÷ 7 = 2.57142857143 ≈ 2.6
