Answer:
x = 16
Step-by-step explanation:
SR = ST ⇒ Two sides are equal. So, ΔSRT is an isosceles triangle.
The angles opposite to equal sides are equal.
⇒ ∠STR = ∠R
∠STR = 4x - 28
Linear pair: If a ray stands on a line, then the adjacent angles are supplementary and they are called linear pair
∠STR + ∠STU = 180° {linear pair}
4x - 28 + 9x = 180
4x + 9x - 28 = 180 {Combine like terms}
13x- 28 = 180
Add 28 to both the sides
13x = 180 + 28
13x = 208
Divide both sides by 13
x = 208/13
Answer:
vertex = (- 1, 1 )
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
x = -
y = x² + 2x + 2 ← is in standard form
with a = 1 and b = 2 , then
x = - = - 1
substitute x = - 1 into the equation for y- coordinate of vertex
y = (- 1)² + 2(- 1) + 2 = 1 - 2 + 2 = 1
vertex = (- 1, 1 )
Answer:
32, <u>16</u>, <u>8</u>, <u>4</u>, <u>2</u>, 1
Explanation:
The geometric mean can be represented by .
Which is the mean of the product of n numbers, used to find the average of a geometric progression.
Don't get confused by geometric mean, it is only asking you about the next numbers in the geometric sequence given the first and sixth term.
The explicit rule for a geometric sequence can be modeled by:
Where is the nth term,
is the first term in the sequence, n is the term number, and r is the common ratio.
Since we already know the first term, will simply be 32.
Since we know it's geometric, there will be an exponential relationship, which means that we will use the geometric mean to find the common ratio.
There are 6 total terms, r is raised to the n – 1 so 6 – 1 = 5, and that will be the degree of this root.
=
=
.
Therefore: .
Using all the information we have, we can find the explicit rule:
→
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We can test that this works by substituting the number location of the term you want to find.
For instance: