Order these number in order to least to greatest using less than or greater than signs

Determine if b is a linear combination of a1 a2, and a3. a1 = [ 1 -2 0 ], a2 = [ 0 1 3 ], a3 = [ 6 -6 18 ], b = [ 2 -2 6 ] Choos

marysya [2.9K]

Answer: Vector b is not a linear combination

Step-by-step explanation:

First of all we put the vectors in terms of different variables, such as:

a1(1,-2,0)=(a,-2a,0);

a2(0,1,3)=(0,b,3b);

a3(6,-6,18)=(6c,-6c,18c);

To know that a vector is a linear combination we need to express it like a sum of other different vectors.

(2,-2,6)=(a,-2a,0)+(0,b,3b)+(6c,-6c,18c)

(2,-2,6)=(a+0+6c,-2a+b-6c,0+3b+18c)

We express this sum like a system of equations.

a+6c=2

-2a+b-6c=-2

3b+18c=6

We solve this system of equations and we can note that the system don't have a solution, so the vector b is not a linear combination of a1, a2, and a3.

8 0

3 years ago

Read 2 more answers

To save money, you put $200 in your bank account each week. after saving for 44 weeks, you have $1,700 dollars in your account.

Evgesh-ka [11]

Y-1700 = 200(x-4) ..............

7 0

3 years ago

Which of the following is the proper name for the figure below?<br> 7<br> Y<br> X

VMariaS [17]

Answer:

B

Step-by-step explanation:

When you look at the triangle look at the 3 vertices. Now look at you answers given and choose one that combines all 3 vertices. You don't want your answer to contain a letter/number that represents the length of a side.

So in this case you don't want M or Y in you answer.

Your answer has to be made up of A X andT.

The only answer that uses AXT is answer B.

3 0

3 years ago

: A new bear population that begins with 150 bears in 2000 decreases at a rate of 20% per year.

d1i1m1o1n [39]

Answer:

2 bears in 2020.

Step-by-step explanation:

We have been given that a new bear population that begins with 150 bears in 2000 decreases at a rate of 20% per year.

We will use exponential decay formula to solve our given problem as:

$y=a\cdot (1-r)^x$ , where,

y = Final quantity,

a = Initial value,

r = Decay rate in decimal form,

x = Time

$20\%=\frac{20}{100}=0.20$

Upon substituting our given values in above formula, we will get:

$y=150(1-0.20)^x$

$y=150(0.80)^x$ , where x corresponds to year 2000.

To find the population in 2020, we will substitute $x=20$ in our equation as:

$y=150(0.80)^{20}$

$y=150(0.011529215046)$

$y=1.7293822569$

$y\approx 2$

Therefore, 2 bears are there predicted to be in 2020.

Since population is decreasing so population is best described as exponential decay.

8 0

3 years ago

Can someone help me with the first question please

snow_lady [41]

Answer:

(c) 5y -17x +99 = 0

Step-by-step explanation:

The median of a triangle is the line through a vertex and the midpoint of the opposite side. The median of ΔXYZ from vertex Y will be the line through point Y and the midpoint of XZ.

<h3>Midpoint</h3>

The midpoint of XZ is the average of the coordinates of X and Z.

M = (X +Z)/2

M = ((1, -2) +(8, -7))/2 = (9, -9)/2 = (4.5, -4.5)

<h3>Line through two points</h3>

The slope of the median can be found using the slope formula:

m = (y2 -y1)/(x2 -x1)

The slope of line YM is ...

m = (-4.5 -4)/(4.5 -7) = -8.5/-2.5 = 17/5

The point-slope form of the equation of a line is ...

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

The line with slope 17/5 through point Y(7, 4) is ...

y -4 = 17/5(x -7)

Subtracting the right side, and multiplying by 5 gives ...

5(y -4) -17(x -7) = 0

5y -17x +99 = 0 . . . . equation of the median through Y

3 0

2 years ago