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Airida [17]
3 years ago
5

What is the solution to the system below? y = -3x - 2 6x + 2y = -4

Mathematics
1 answer:
Alja [10]3 years ago
4 0

Answer:

Infinitely many solutions

Step-by-step explanation:

Since y=-3x-2, plug it in (2)

6x+2(-3x-2)=-4.

Distribute:

6x-6x-4=-4

-4=-4

Infinetly many solutions.

Hope this helps :)

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Given vectors u = (−1, 2, 3) and v = (3, 4, 2) in R 3 , consider the linear span: Span{u, v} := {αu + βv: α, β ∈ R}. Are the vec
julia-pushkina [17]

Answer:

(2,6,6) \not \in \text{Span}(u,v)

(-9,-2,5)\in \text{Span}(u,v)

Step-by-step explanation:

Let b=(b_1,b_2,b_3) \in \mathbb{R}^3. We have that b\in \text{Span}\{u,v\} if and only if we can find scalars \alpha,\beta \in \mathbb{R} such that \alpha u + \beta v = b. This can be translated to the following equations:

1. -\alpha + 3 \beta = b_1

2.2\alpha+4 \beta = b_2

3. 3 \alpha +2 \beta = b_3

Which is a system of 3 equations a 2 variables. We can take two of this equations, find the solutions for \alpha,\beta and check if the third equationd is fulfilled.

Case (2,6,6)

Using equations 1 and 2 we get

-\alpha + 3 \beta = 2

2\alpha+4 \beta = 6

whose unique solutions are \alpha =1 = \beta, but note that for this values, the third equation doesn't hold (3+2 = 5 \neq 6). So this vector is not in the generated space of u and v.

Case (-9,-2,5)

Using equations 1 and 2 we get

-\alpha + 3 \beta = -9

2\alpha+4 \beta = -2

whose unique solutions are \alpha=3, \beta=-2. Note that in this case, the third equation holds, since 3(3)+2(-2)=5. So this vector is in the generated space of u and v.

4 0
3 years ago
A clock chimes 4 times each hour. whixh expression can be used to find the number of times the clock chimes in a week
solong [7]

There are 24 hours in a day, so if it chimes twice in an hour it will chime 24*2 or 48 times a day. There are 7 days in a week, so it will chime 48*7 or 336 times.

8 0
3 years ago
A pipe is leaking at the rate of 32 fluid ounces per minute. Use dimensional analysis to find out how many gallons the pipe is l
lianna [129]

well first think about it, 60 min in an hour, so 32 fluid ounces times 60 = 1920 fluid ounces, from there you can convert fluid ounces to practically anything, for instance, 1920 fluid ounces = 24 cups.

go to this address to find out more.

https://www.google.com/search?q=another+name+for+observations&rls=com.microsoft:en-US:IE-Address&ie=...

4 0
3 years ago
Read 2 more answers
Which of the following correctly completes the square for the equation
rjkz [21]

Answer:

A. (x + 2)^2 = 31.

Step-by-step explanation:

x^2 + 4x = 27

x^2 + 4x - 27 = 0

A. (x + 2)^2 = 31

x^2 + 4x + 4 - 31 = 0

x^2 + 4x - 27 = 0

This option corresponds to the given equation, so it is correct.

B. (x + 2)^2 = 43

x^2 + 4x + 4 - 43 = 0

x^2 + 4x - 39 = 0

This does not correspond to the equation.

C. (x + 4)^2 = 31

x^2 + 8x + 16 - 31 = 0

x^2 + 8x - 15 = 0

This does not correspond to the equation.

D. (x+4)^2 = 43

x^2 + 8x + 16 - 43 = 0

x^2 + 8x - 27 = 0

This does not correspond to the equation.

So, your answer is A. (x + 2)^2 = 31.

Make sure to SUBMIT and check your PREVIOUS answers to make sure they are right! XD Also, hope this helps!

7 0
3 years ago
What is 127 to the nearest 10
finlep [7]

Answer:The answer is 130

Step-by-step explanation:

3 0
3 years ago
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