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Solnce55 [7]
3 years ago
7

How many terms are in the arithmetic sequence 9, 2, −5, . . . , −187?

Mathematics
1 answer:
Fantom [35]3 years ago
4 0
9, 2, -5... so is going down by 7 each time, meaning the "common difference" is -7.

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
a_1=9\\
d=-7\\
a_n=-187
\end{cases}
\\\\\\
-187=9+(n-1)(-7)\implies -187=9-7n+7
\\\\\\
7n=9+7+187\implies 7n=203\implies n=\cfrac{203}{7}\implies \boxed{n=29}
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Select the two binomials that are factors of this trinomial x2+10x+16
Zigmanuir [339]

So for this trinomial, I will be factoring by grouping. Firstly, what two terms have a product of 16x^2 and a sum of 10x? That would be 8x and 2x. Replace 10x with 2x + 8x:

x^2+2x+8x+16

Next, factor x^2 + 2x and 8x + 16 separately. Make sure that they have the same quantity inside the parentheses: x(x+2)+8(x+2)

<u>Now you can rewrite this as (x+8)(x+2) , which is your final answer.</u>

5 0
3 years ago
2 x -1^2 + 1<br><br> please show me how to get to the answer of 1
OLga [1]

Answer:

-1

Step-by-step explanation:

2 × (-1²) + 1 = 2 × (-1) + 1 = -2 + 1 = -1

7 0
2 years ago
Read 2 more answers
Please help me! Thanks
Yuki888 [10]

Answer:

The answer is D. 22

Step-by-step explanation:


4 0
3 years ago
"If a ball is thrown into the air with a velocity of 44 ft/s, its height in feet t seconds later is given by y = 44t − 16t2. (a)
Nataly_w [17]

Answer:

i) -28 ft/s

ii) -21.6 ft/s

iii) -20.8 ft/s

iv) -20.16 ft/s

b)  -20 ft/s

Step-by-step explanation:

if v represents vertical velocity then if the height y is

y = 44*t − 16*t²

and the instant velocity v is the derivative with respect to the time

v= dy/dt = 44*(1) - 16*(2*t) = 44- 32*t

while the average velocity is va= (y-y₀)/(t-t₀)

where t₀ = 2 and y₀=y(t₀) =  44*2 − 16*2² = 24

then

va= (y-y₀)/(t-t₀) = (44*t − 16*t² -  24)/(t-2)

for

i) t= 0.5s + 2 s= 2.5 s

va = (44* 2.5  − 16* 2.5 ² -  24)/( 2.5 -2) = -28 ft/s

ii) t= 0.1s + 2 s= 2.1 s

va = (44* 2.1  − 16* 2.1 ² -  24)/( 2.1 -2) = -21.6 ft/s

iii) t= 0.05 s + 2 s= 2.05 s

va = (44* 2.05  − 16* 2.05 ² -  24)/( 2.05 -2) = -20.8 ft/s

iv) t= 0.01s + 2 s= 2.01 s

va = (44* 2.01  − 16* 2.01 ² -  24)/( 2.01 -2) = -20.16 ft/s

b) the instantaneous velocity when t=2

v (t=2) =  44- 32*(2) = -20 ft/s

6 0
2 years ago
A team played 20 games and won 18. what % did they win?
maxonik [38]

<u>Answer:</u> 90%

<u>Reasoning:</u> To solve this divide 18 by 20

18/20= 0.9

Now multiply 20 by 0.9 to check

20 x 0.9= 18


8 0
2 years ago
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