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3 years ago

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Alexia used three teams of paper in her first semester of school. Each team has the same number of sheets. She used another 40 s

heets after that. Write an expression to represent the total number of sheets Alexa used

1 answer:

AysviL [449]3 years ago

6 0

3x + 40, where x is the amount of sheets in each team

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If S_1=1,S_2=8 and S_n=S_n-1+2S_n-2 whenever n≥2. Show that S_n=3⋅2n−1+2(−1)n for all n≥1.

Snezhnost [94]

You can try to show this by induction:

• According to the given closed form, we have $S_1=3\times2^{1-1}+2(-1)^1=3-2=1$ , which agrees with the initial value <em>S</em>₁ = 1.

• Assume the closed form is correct for all <em>n</em> up to <em>n</em> = <em>k</em>. In particular, we assume

$S_{k-1}=3\times2^{(k-1)-1}+2(-1)^{k-1}=3\times2^{k-2}+2(-1)^{k-1}$

and

$S_k=3\times2^{k-1}+2(-1)^k$

We want to then use this assumption to show the closed form is correct for <em>n</em> = <em>k</em> + 1, or

$S_{k+1}=3\times2^{(k+1)-1}+2(-1)^{k+1}=3\times2^k+2(-1)^{k+1}$

From the given recurrence, we know

$S_{k+1}=S_k+2S_{k-1}$

so that

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 2\left(3\times2^{k-2}+2(-1)^{k-1}\right)$

$S_{k+1}=3\times2^{k-1}+2(-1)^k + 3\times2^{k-1}+4(-1)^{k-1}$

$S_{k+1}=2\times3\times2^{k-1}+(-1)^k\left(2+4(-1)^{-1}\right)$

$S_{k+1}=3\times2^k-2(-1)^k$

$S_{k+1}=3\times2^k+2(-1)(-1)^k$

$\boxed{S_{k+1}=3\times2^k+2(-1)^{k+1}}$

which is what we needed. QED

6 0

2 years ago

Solve for x <br> 3(2)^3x+1

lubasha [3.4K]

Answer:

24

Step-by-step explanation:

the simplified version of this expression would be 24 x + 1

5 0

3 years ago

50 BIG POINTS! Help me on math please! @ Apologiabiology, @ Bookishfairy73

nekit [7.7K]

Rate of change is also knkown as slope which is found by
$\frac{y2-y1}{x2-x1}$ =slope if you know 2 points/ordered pairs
aos, if x incheases while y decreases then slope is negative
when x increases while y increases then slpe if positive
also, if you can convert to y=mx+b, m=slope
another thing if you have ax+by=c then slope=-a/b

so first one
2x-5y=15
a=2
b=-5
-2/-5=2/5
slope=2/5
positive

next
y=-4x
-4 =slope=negative

x increases while y decreases
negative

x increases while y decreases
negative

so
Positive
Negative
Negative
Negative

A. 6x-3y=12
sloope=-6/-3=2

B. y=5x+b
slope=5

C. (8-2)/(3-1)=6/2=3
sloope=3

D. goes up 4 units and goes right 1 unit, 4/1=4
sloope=4

5 is greates
B is the answer

A. (6-3)/(4-3)=3/1=3
slope=3

B. y=4+6x
slope=6

C.12x+6y=18
slope=-12/6=-2

D. goes down 5 units as it goest 1 uniit to right aka -5./1
slope=-5

greatest is 6
B is answer

the starting value I would guess si when x=1 what is the greats y value

look at each
first one
A. x=1 and =-3

B.y=3x-8
y=3(1)-8
y=3-8
y=-5

C. 8x+4y=16
8(1)+4y=16
8+4y=16
4y=8
y=2

D. at 1 unit to right it is 1 nit up so y=1

greatest is 2 or C

so just subsitute 1 for x since x represents how many teaspoons
y=16(1)560
y=16+560
y=576 caloris for 1 sugar teaspoon

for honey, just read off the graph
for when x=1
y=504

so calores of sugar=576
calories in honey=504

ANSWERS

Postive
Negative
Negative
Negative

B

B

C

sugar=576
honey=504

4 0

3 years ago

Read 2 more answers

Complete 5^9/5^3=5^a

Goryan [66]

Answer:

6=a

Step-by-step explanation:

5^9/5^3=5^a

We know that b^c = b^d = b^(c-d)

5^9/5^3=5^a

5^(9-3) = 5^a

5^6 = 5^a

The bases are the same so the exponents are the same

6=a

7 0

2 years ago

Read 2 more answers

What is the GCF of 4and 2

Hoochie [10]

Answer:

2

Step-by-step explanation:

GCF stands for the "greatest common factor." Therefore because 2 can go into both 2 and 4 evenly, it is the GCF.

3 0

3 years ago