The correct answer is D:
35 < 7 * 5 + 6
35 < 35 + 6
35 < 41
Correct!
Answer:
the geometric series is a(n) = -12(3)^(n-1)
Step-by-step explanation:
"Triple" denotes multiplication by 3. Thus, the common factor here is 3.
The general formula for a geometric series is a(n) = a(1)(r)^(n-1), where a(1) is the first term, r is the common ratio.
Here, we have a(n)= (-12)(3)^(n-1) = -972.
We need to solve this for n, which represents the last term.
The first step towards solving for n is to divide both sides by -12:
3^(n-1) = 81
To solve for n-1, rewrite 81 as 3^4. Then we have:
3^(n-1) = 3^4, implying that (n-1) = 4 and that n = 5.
Then we know that it is the 5th term that equals -972.
In summary, the geometric series is a(n) = -12(3)^(n-1).
Answer:
5x-0=25
Step-by-step explanation:
5x-0=25
5x=25
x=5
I hope I did this right :/
Answer:
C.y+8=5(×-2)
Step-by-step explanation:
I think it is c because when i do inke pongki,it is at c, but i dont know how to plot the graph like this, what if u can teach me
Answer:
- 20. The vertex is (2/3, 14/3) | p = 3, q = -2/3 and r = 14/3
- 21. 20x² + 2x - 3 = 0
Step-by-step explanation:
20.
<h3>Given</h3>
<h3>To find</h3>
- The least value of the y and the corresponding value of x
- Constants p, q and r such that 3x² - 4x + 6 = p(x + q)² + r
<h3>Solution</h3>
The given is the parabola with positive a coefficient, so it opens up and the minimum point its vertex.
<u>The vertex has x = -b/2a and corresponding y- coordinate is found below: </u>
- x = - (- 4)/2*3 = 2/3, and
- y = 3(2/3)² - 4(2/3) + 6 = 4/3 - 8/3 + 6 = 14/3
- So the vertex is (2/3, 14/3)
<u>The vertex form of the line has the equation:</u>
- y = a(x - h)² + k, where (h, k) is the vertex
<u>Plugging in the values:</u>
<u>Comparing with p(x + q)² + r, to find out that:</u>
- p = 3, q = -2/3 and r = 14/3
=====================================
21.
(i) α and β are the roots of: ax² + bx + c = 0
<u>Show that:</u>
- α + β = -b/a and αβ = c/a
<h3>Solution</h3>
<u>Knowing the roots, put the equation as:</u>
- (x - α)(x - β) = 0
- x² - αx - βx + αβ = 0
- x² - (α+β)x + αβ = 0
<u>Comparing this with the standard form:</u>
<u>Divide by </u><u>a</u><u> to make the constants of x² same:</u>
<u>Now comparing the constants:</u>
- - (α+β) = b/a ⇒ α+β = - b/a
- αβ = c/a
--------------------------------------------
(ii)
<h3>Given</h3>
- α and β are the roots of: 3x² - x - 5 = 0
<h3>To Find </h3>
- The equation with roots 1/2α and 1/2β
<h3>Solution</h3>
<u>The sum and the product of the roots:</u>
- α + β = -b/a = 1/3
- αβ = c/a = -5/3
<u>The equation is:</u>
- (x - 1/2α)(x - 1/2β) = 0
- x² - (1/2α + 1/2β)x + 1/(2α)(2β) = 0
- x² - (α + β)/(2αβ)x + 1/4αβ = 0
- x² - (1/3)/(2(-5/3))x + 1/(4(-5/3)) = 0
- x² + 1/10x - 3/20 = 0
- 20x² + 2x - 3 = 0