Answer:
<em>Answer: D</em>
Step-by-step explanation:
<u>Arithmetic Sequences
</u>
The arithmetic sequences are those where any term n is obtained by adding or subtracting a fixed number to the previous term. That number is called the common difference.
The equation to calculate the nth term of an arithmetic sequence is:

Where
an = nth term
a1 = first term
r = common difference
n = number of the term
We are given the arithmetic sequence:
10, 12, 14, 16, ...
Where a1=10 and
r = 12 - 10 = 2
Thus the general term is:

Operating:


Answer: D
Answer:
The graph has a domain of all real numbers.
The graph has a y-intercept at
.
The graph has an x-intercept at
.
Step-by-step explanation:
Given: The graph is ![y=\sqrt[3]{x-1}+2](https://tex.z-dn.net/?f=y%3D%5Csqrt%5B3%5D%7Bx-1%7D%2B2)
The domain of a function is a set of input values for which the function is real and defined.
Thus, the graph has a domain of
.
To find the y-intercept: To find the y-intercept, substitute
in
.
![\begin{aligned}y &=\sqrt[3]{x-1}+2 \\&=\sqrt[3]{0-1}+2 \\&=-1+2 \\&=1\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dy%20%26%3D%5Csqrt%5B3%5D%7Bx-1%7D%2B2%20%5C%5C%26%3D%5Csqrt%5B3%5D%7B0-1%7D%2B2%20%5C%5C%26%3D-1%2B2%20%5C%5C%26%3D1%5Cend%7Baligned%7D)
Thus, the y-intercept is 
To find the x-intercept: To find the x-intercept, substitute
in
.
![\begin{aligned}y &=\sqrt[3]{x-1}+2 \\0 &=\sqrt[3]{x-1}+2 \\-2 &=\sqrt[3]{x-1} \\(-2)^{3} &=(\sqrt[3]{x-1})^{3} \\-8 &=x-1 \\-7 &=x\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7Dy%20%26%3D%5Csqrt%5B3%5D%7Bx-1%7D%2B2%20%5C%5C0%20%26%3D%5Csqrt%5B3%5D%7Bx-1%7D%2B2%20%5C%5C-2%20%26%3D%5Csqrt%5B3%5D%7Bx-1%7D%20%5C%5C%28-2%29%5E%7B3%7D%20%26%3D%28%5Csqrt%5B3%5D%7Bx-1%7D%29%5E%7B3%7D%20%5C%5C-8%20%26%3Dx-1%20%5C%5C-7%20%26%3Dx%5Cend%7Baligned%7D)
Thus, the x-intercept is 
Answer:
(d) m∠AEB = m∠ADB
Step-by-step explanation:
The question is asking you to compare the measures of two inscribed angles. Each of the inscribed angles intercepts the circle at points A and B, which are the endpoints of a diameter.
__
<h3>applicable relations</h3>
Several relations are involved here.
- The measures of the arcs of a circle total 360°
- A diameter cuts a circle into two congruent semicircles
- The measure of an inscribed angle is half the measure of the arc it intercepts
<h3>application</h3>
In the attached diagram, we have shown inscribed angle ADB in blue. The semicircular arc it intercepts is also shown in blue. A semicircle is half a circle, so its arc measure is half of 360°. Arc AEB is 180°. That means inscribed angle ADB measures half of 180°, or 90°. (It is shown as a right angle on the diagram.)
If Brenda draws angle AEB, it would look like the angle shown in red on the diagram. It intercepts semicircular arc ADB, which has a measure of 180°. So, angle AEB will be half that, or 180°/2 = 90°.
The question is asking you to recognize that ∠ADB = 90° and ∠AEB = 90° have the same measure.
m∠AEB = m∠ADB
_____
<em>Additional comment</em>
Every angle inscribed in a semicircle is a right angle. The center of the semicircle is the midpoint of the hypotenuse of the right triangle. This fact turns out to be useful in many ways.
Answer:
The correct option is option D
Step-by-step explanation:
The volume of a pyramid is:
V=1/3(B)(H)
Where
B:Base = s^2
H:Height = 2/3s
Then:
V=1/3(B)(H) = 1/3(s^2)(2/3s) = 2/9s^3
The correct option is option D