Answer:
C, E
Step-by-step explanation:
A. INCORRECT
A is wrong because a reflection across the x-axis DOES move the position of the figure (as it is flipped, so the position changes), but it DOES NOT change the angle (since a shift in position doesn't equal to a change in angle measure)
B. INCORRECT
Although a reflection across the x-axis does change the position of the angle, it DOES NOT change the measure of the angle.
C. CORRECT
A reflection across the x-axis does in fact move the position of the figure and does not change the angle measure. Reflections only deal with flipping a figure, not changing it's shape/distorting it so that the angle will change.
D. INCORRECT
A translation right will change the position of the figure but will not change the measure of the angle.
E. CORRECT
Yes, a translation right WILL change the position of the figure but will NOT change the measure of the angle. This is because a translation is simply moving a figure up and down; it has nothing to do with changing the shape of the figure/distorting it so that the angle is different.
The answer is 140 feet because 10×14 is 140
X = measure of each of the legs
"perimeter is 8 more than 2 times one of the legs" ---> P = 2x+8
P = 28 is the given perimeter
So,
P = 2x+8
28 = 2x+8
2x+8 = 28
2x = 20
x = 10
If x = 10, then the two legs add up to x+x = 10+10 = 20
Leaving P-20 = 28-20 = 8 inches left over for the base
You have the correct answer (choice D, 8 inches) though your steps are a bit confusing at some parts. Such as the part where you wrote 2x = 10 twice. I think I know what you were trying to say.
Answer: the value of population standard deviation is 3.87
Step-by-step explanation:
From the information given,
Number of sample, n = 8
For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.
We will apply the formula
Confidence interval
= mean ± z ×standard deviation/√n
Since confidence interval = 2.694,
It becomes
2.694 = 1.96 × standard deviation/√8
Dividing both sides of the equation by 1.96, it becomes
1.37 = standard deviation/√8
Standard deviation = 1.37 × √8
Standard deviation = 3.87
Answer: The central angle of the arc is 162 degrees.
Step-by-step explanation: The information available are as follows;
Circumference of the circle equals 10. Length of an arc equals 9/2. The circumference of a circle is given as;
Circumference = 2Pi x r
That means 2Pi x r = 10.
Also the length of an arc along the same circle is 9/2. Length of an arc is calculated as;
Length of arc = (X/360) x 2Pi x r
Where X is the central angle of the arc
That means;
9/2 = (X/360) x 2Pi x r
We can now substitute for the known values as follows
Length of an arc = (X/360) x 2Pi x r
9/2 = (X/360) x 10
9/2 = 10X/360
By cross multiplication we now have
(9 x 360)/(2 x 10) = X
3240/20 = X
162 = X
The angle at the center of the arc is 162 degrees.
