Answer:
1/4
Step-by-step explanation:
The common ratio in a geometric sequence is the number you multiply to previous term to get the term after.
Dividing by a number is the same as multiplying by that 1/number.
So the common ratio here is 1/4.
This is a geometric sequence since you are able to find all the terms in this sequence by multiplying 1/4 to it's previous term.
Examples:
160(1/4)=40
40(1/4)=10
10(1/4)=10/4=2.5
2.5(1/4)=2.5/4=0.625.
Part A
(h + t)(x)
(5x - 2 + 4x + 6)(x) First plug in the numbers
(9x + 4)(x) Add h(x) and t(x)
(9x² + 4x) Then multiply it by x
x(9x + 4) Lastly, simplify x out (I'm including both answers because I don't know whether your questions will ask for either one)
Unsimplified Answer: 9x² + 4x Simplified Answer: x(9x + 4)
Part B
(h x t)(x)
(5x - 2)(4x + 6)(x) First step is to of cource, plug in the numbers
(20x² + 30x -8x -12)(x) Next we multiply h(x) and t(x)
(20x² + 22x -12)(x) Simplify it a little
(20x³ + 22x² - 12x) After that, multiply the whole thing by x
(2x)(10x² + 11x - 6) Simplify 2x out of the equation
(2x)(5x - 2)(2x + 3) Lastly, simplify the rest
Unsimplified Answer: (20x³ + 22x² -12x) Simplified Answer: (2x)(5x - 2)(2x + 3)
Part C
h[t(x)]
(5x - 2) [(4x + 6)(x)] Plug in the numbers
(5x - 2)(4x² + 6x) Multiply t(x) and x
(20x³ + 30x² - 8x² -12x) Multiply that by h(x)
(20x³ + 22x² -12x) Simplify a little... Wait! That looks like the answer to Part B! Perhaps we did something wrong, let's go back and alter the third step
(5x -2)(2x)(2x + 3) This time, simplify before multiplying oh wait, that's part B's simplified answer, isn't it.
Well, there's a good explanation for this: Part B and Part C are essentially the same equations, just in slightly different orders!
So, it will have the same answers and Part B! (At least, in theory, I'd recommend checking this for yourself too!)
Unsimplified Answer: (20x³ + 22x² - 12x) Simplified Answer: (2x)(5x-2)(2x+3)
Well, that's a wrap, Parts A, B, and, C with work and explanations; if you find that I made a mistake or did something wrong let me know. I hope this helped, and good luck!
Answer:
Option B.
Step-by-step explanation:
The given exponential equation is
...(1)
It is given that the graph of above equation passes through points (−3, 24) and (−2, 12).
The graph passes through the point (-3,24), so substitute x=-3 and y=24 in equation (1).
...(2)
The graph passes through the point (-2,12), so substitute x=-2 and y=12 in equation (1).
...(3)
Divide equation (3) by equation (2).
Substitute b=0.5 in equation (2).
Substitute a=3 and b=0.5 in equation (1).
Therefore, the correct option is B.
Answer:
A
Step-by-step explanation:
The base angles of an isosceles triangle are congruent
The sum of the 3 angles in a triangle = 180°, hence
180° - 112° = 68°
base angle = 
= 34°
Thus each base angle equals 34° → A
