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abruzzese [7]
3 years ago
15

Need help with this problem, it's got me stuck PLZ

Mathematics
1 answer:
faust18 [17]3 years ago
6 0

24x^2 +25x - 47                     53

----------------------- = -8x -3 - ---------------

ax-2                                     ax-2

add 53/ax-2 to each side

24x^2 +25x - 47+53                    

-----------------------         = -8x -3

ax-2                                    

24x^2 +25x +6                  

-----------------------         = -8x -3

ax-2      

multiply each side by ax-2

24x^2 +25x +6   = (ax-2) (-8x-3)

multiply out the right hand side

24x^2 +25x +6  = -8ax^2 +16x-3ax +6

24 = -8a      25 = 16 -3a

a = -3          9 = -3a

                   a = -3


Choice B

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Which quadratic equation fits the data in the table? x -5,-2,-1,0,3,4,6 y 33,9,5,3,9,15,33
mojhsa [17]

Answer:

y = x² − x + 3

Step-by-step explanation:

Quadratic equation is:

y = ax² + bx + c

Pick three points and plug in.  I'll choose (-2, 9), (-1, 5), and (0, 3).

9 = a(-2)² + b(-2) + c

5 = a(-1)² + b(-1) + c

3 = a(0)² + b(0) + c

9 = 4a − 2b + c

5 = a − b + c

3 = c

We know c = 3, so substitute into the first two equations:

9 = 4a − 2b + 3

5 = a − b + 3

0 = 4a − 2b − 6

0 = a − b − 2

Solve by elimination or substitution.

b = a − 2

0 = 4a − 2(a − 2) − 6

0 = 4a − 2a + 4 − 6

0 = 2a − 2

a = 1

b = -1

Therefore:

y = x² − x + 3

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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
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