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4 years ago

What is the equation for a line that goes through (0,-1) and (3,1)

Mathematics

1 answer:

ICE Princess25 [194]4 years ago

3 0

Answer:

y=2/3x-1

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(1-(-1))/(3-0)

m=(1+1)/3

m=2/3

y-y1=m(x-x1)

y-(-1)=2/3(x-0)

y+1=2/3(x)

y+1=2/3x

y=2/3x-1

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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 S₁ = 1.

• Assume the closed form is correct for all n up to n = k. 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 n = k + 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

3 years ago

Fill in the blank.

natima [27]

The correct answer is: Commutative Property

Further Explanation:

The commutative property states that the order of number doesn't matter and changing the order of numbers or variables will produce the same result.

Commutative Property of Addition:

The Commutative Property of addition means that an expression can be written as a + b = b + a.

Commutative Property of Multiplication:

The Commutative Property of multiplication means that an expression can be written as a • b = b • a

Hence, the correct answer is: Commutative Property

Keywords: Commutative property, addition, multiplication

Learn more about Properties at:

#LearnwithBrainly

4 0

3 years ago

Which description does this model and equation represent? A)Area of a square as the sides increase by 1 unit

zaharov [31]

Answer:

Step-by-step explanation:

6 0

3 years ago

F(x)=6x^2 +10x−1

KATRIN_1 [288]

Answer: It has two distinct real zeros.

Step-by-step explanation:

The formula that is used to calculate the discriminant of a Quadratic function is the one shown below:

$D=b^2-4ac$

In this case you have the following Quadractic function provided in the exercise:

$f(x)=6x^2 +10x-1$

Let's make it equal to 0:

$0=6x^2 +10x-1$

You can identify that:

$a=6\\\\b=10$

Knowing these values, you can substitute them into the formula and then evaluate:

$D=10^2-4(6)(-1)\\\\D=124$

Therefore, since:

$D>0$

You can determine that the it has two distinct real roots.

3 0

4 years ago

What expression is equivalent to 14 − 17 ?

DENIUS [597]

answer:

Step-by-step explanation:

4 0

4 years ago