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Crank
3 years ago
11

Solve the system of equations y=2x+3 and 4x-2y=-6

Mathematics
1 answer:
SashulF [63]3 years ago
6 0
Substitute 2x + 3 for y

4x - 2(2x+3) = -6
4x - 4x - 6 = -6
-6 = -6
true, so the solution is all real numbers
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Convert 34.0 dm to km. Show all work.
larisa [96]

Step-by-step explanation:

Convert 34 Decimeters to Kilometers (dm to km) with our conversion calculator and conversion tables. To convert 34 dm to km use direct conversion formula below.

34 dm = 0.0034 km.

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6 0
3 years ago
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What are the solutions to the equation 3(x – 4)(x + 5) = 0?
iris [78.8K]

Answer:

x=4 and x= - 5

Step-by-step explanation:

In order to solve this we should re-arrange the equation:

(x-4)(x+5)=\frac{0}{3}

This is equal to:

(x-4)(x+5)=0

Then we can seperate this into:

(x-4)=0\\(x+5)=0

So solving for x in both cases we get

x-4=0 \\x=4\\And\\x+5=0\\x=-5\\

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3 years ago
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Lena [83]
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7 0
2 years ago
Question 2 of 5
AlekseyPX

Given:

The different recursive formulae.

To find:

The explicit formulae for the given recursive formulae.

Solution:

The recursive formula of an arithmetic sequence is f(n)=f(n-1)+d, f(1)=a,n\geq 2 and the explicit formula is f(n)=a+(n-1)d, where a is the first term and d is the common difference.

The recursive formula of a geometric sequence is f(n)=rf(n-1), f(1)=a,n\geq 2 and the explicit formula is f(n)=ar^{n-1}, where a is the first term and r is the common ratio.

The first recursive formula is:

f(1)=5

f(n)=f(n-1)+5 for n\geq 2.

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:

f(n)=5+(n-1)(5)

f(n)=5+5(n-1)

Therefore, the correct option is A, i.e., f(n)=5+5(n-1).

The second recursive formula is:

f(1)=5

f(n)=3f(n-1) for n\geq 2.

It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:

f(n)=5(3)^{n-1}

Therefore, the correct option is F, i.e., f(n)=5(3)^{n-1}.

The third recursive formula is:

f(1)=5

f(n)=f(n-1)+3 for n\geq 2.

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:

f(n)=5+(n-1)(3)

f(n)=5+3(n-1)

Therefore, the correct option is D, i.e., f(n)=5+3(n-1).

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