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2 years ago

Help!! (this is 13-12 year old math it's about Negative Numbers on the number line)

Mathematics

2 answers:

Feliz [49]2 years ago

7 0

The answer to this question is -10

gavmur [86]2 years ago

5 0

Answer:

-10

Step-by-step explanation:

-5

-10

-15

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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

Raju bought seven notebooks of two hundred pages and five of hundred pages, for 107 rupees. Joseph bought five notebooks of two

olga nikolaevna [1]

Answer:

Large books = 11

Small books = 6

Step-by-step explanation:

7x + 5y = 107

7x = 107 - 5y

x = 107/7 - 5y/7

5x + 7y = 97

5 (107/7 - 5y/7) + 7y = 97

535/7 - 25y/7 + 7y = 97

535/7 + 24y/7 = 97

535 + 24y = 679

24y = 679 - 535

y = 144/24 = 6: So x =

7x + 5(6) = 107

7x = 107-30

x = 77-7 = 11

8 0

3 years ago

PLEASE HELP!!

madam [21]

Answer:

k=2/3

Step-by-step explanation:

Step 1:

Step 1 in solving the exponential equations is re-writing the base same as other side of the equation

so,

$25^{3k}=625\\=> 25^{3k}=25^2$

Step 2:

Second step is equating the exponents

The rule used is:

$If\ B^m=B^n\ then\ m=n$

So in this case

$3k=2\\k = \frac{2}{3}$

So the solution is:

k=2/3 ..

3 0

3 years ago

6,500 acres of a 41,000 acre forest burned in a fire. what percentage of forest was damaged?

Tems11 [23]

Answer:

15.85%

Step-by-step explanation:

Given:

Acres damaged (burned) = 6,500 acres

Acres in total forest = 41,000 acres

Hence the amount of damaged forest as a fraction of the total forest,

= $\frac{6500}{41000}$ = $\frac{13}{82}$

expressed as percentage = $\frac{13}{82}$ x 100% = 15.85%

8 0

3 years ago

Least to greastest awnsers

Eddi Din [679]

-60 -49 -40 9

-45 -18 80 82

-74 -23 14 85

-79 -68 21 46

-48 -21 27 54

-68 -13 4 32

3 0

3 years ago

Help!! (this is 13-12 year old math it's about Negative Numbers on the number line) ​

Help!! (this is 13-12 year old math it's about Negative Numbers on the number line)