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Amiraneli [1.4K]
3 years ago
14

How Do these two equations compare? 2x + 10 = 16. 2x- 10 = 16

Mathematics
1 answer:
finlep [7]3 years ago
6 0
In 2x+10=16, x will equal 3. In 2x-10=16, x will equal 13.
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Which is the graph of the sequence defined by the function f(x) = 100(0.5)* - 1?
krok68 [10]

Answer: f  ( x)   =  − 50

Step-by-step explanation:

4 0
3 years ago
Step by step please help answer.
sweet-ann [11.9K]

Answer:

(2) 2,640 ft

Step-by-step explanation:

I'm going to assume that in this question, you are walking 1 full circle around the reservoir. That would mean you need to calculate the circumference of the circular reservoir.

The circumference formula is:

C = ⫪d

C stands for Circumference

d stands for diameter

I will use 22/7 instead of pi, so the formula looks more like this:

C = (22/7)(d)

The diameter is 840 feet, so we will substitute the variable d with 840:

C = (22/7)(840)

You can plug this part into the calculator, but by hand, it'll look something like this:

(22/7)*840 = (22*840)/7

18,480/7 = 2.640

Hope it helps (●'◡'●)

5 0
2 years ago
Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference
Bezzdna [24]

Since a_1,a_2,a_3,\cdots are in arithmetic progression,

a_2 = a_1 + 2

a_3 = a_2 + 2 = a_1 + 2\cdot2

a_4 = a_3+2 = a_1+3\cdot2

\cdots \implies a_n = a_1 + 2(n-1)

and since b_1,b_2,b_3,\cdots are in geometric progression,

b_2 = 2b_1

b_3=2b_2 = 2^2 b_1

b_4=2b_3=2^3b_1

\cdots\implies b_n=2^{n-1}b_1

Recall that

\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n

\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2

It follows that

a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n +  n(n-1)

so the left side is

2(a_1+a_2+\cdots+a_n) = 2c n + 2n(n-1) = 2n^2 + 2(c-1)n

Also recall that

\displaystyle \sum_{k=1}^n ar^{k-1} = \frac{a(1-r^n)}{1-r}

so that the right side is

b_1 + b_2 + \cdots + b_n = \displaystyle \sum_{k=1}^n 2^{k-1}b_1 = c(2^n-1)

Solve for c.

2n^2 + 2(c-1)n = c(2^n-1) \implies c = \dfrac{2n^2 - 2n}{2^n - 2n - 1} = \dfrac{2n(n-1)}{2^n - 2n - 1}

Now, the numerator increases more slowly than the denominator, since

\dfrac{d}{dn}(2n(n-1)) = 4n - 2

\dfrac{d}{dn} (2^n-2n-1) = \ln(2)\cdot2^n - 2

and for n\ge5,

2^n > \dfrac4{\ln(2)} n \implies \ln(2)\cdot2^n - 2 > 4n - 2

This means we only need to check if the claim is true for any n\in\{1,2,3,4\}.

n=1 doesn't work, since that makes c=0.

If n=2, then

c = \dfrac{4}{2^2 - 4 - 1} = \dfrac4{-1} = -4 < 0

If n=3, then

c = \dfrac{12}{2^3 - 6 - 1} = 12

If n=4, then

c = \dfrac{24}{2^4 - 8 - 1} = \dfrac{24}7 \not\in\Bbb N

There is only one value for which the claim is true, c=12.

3 0
2 years ago
Which is an expression to find the speed in m/s?
kenny6666 [7]
C. 100/20
 This is because the formula to finding speed is distance divided by time.
5 0
2 years ago
Which is the graph of the equation y-3=0.5(x+4)?<br><br>Need help​
stiv31 [10]

Answer:

Top row 2nd one

Step-by-step explanation:

Distrube out .5 first and the equation will be .5x+2

Then add 3 to both sides and you get y=.5x+5

3 0
2 years ago
Read 2 more answers
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