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3 years ago

Identify the conclusion of the statement.

Mathematics

1 answer:

Marina CMI [18]3 years ago

6 0

Answer:

D) The slope of the line is undefined

Step-by-step explanation:

A vertical line will have an undefined slope, because it does not run horizontally.

To find the slope, you calculate it with rise over run, however, a vertical line will not run horizontally, meaning the run is 0.

And, dividing anything by 0 will get you an undefined answer.

So, D is correct. the slope of the line is undefined

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Kayla squared a number x and added this result to -6.5. This gave her an answer of 42.5.

ladessa [460]

Answer:

7, -7

Step-by-step explanation:

x^2-6.5= 42.5 add 6.5 to both sides

x^2= 49

The square root of 49 is 7 and -7.

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2 years ago

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marta [7]

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2 years ago

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.