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xenn [34]
3 years ago
6

Simplify this terms

Mathematics
1 answer:
kramer3 years ago
4 0

Answer:

i belive it to be A

Step-by-step explanation:

because it does say 6 by 7 by 3 so i would add 3+7 it would give me ten so i belive it to be A. hoped this helped lmk if it did

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Let T: Mmxn(R)Mmxn(R) be the function defined
alexandr402 [8]

Answer:

True. See the explanation and proof below.

Step-by-step explanation:

For this case we need to remeber the definition of linear transformation.

Let A and B be vector spaces with same scalars. A map defined as T: A >B is called a linear transformation from A to B if satisfy these two conditions:

1) T(x+y) = T(x) + T(y)

2) T(cv) = cT(v)

For all vectors x,y \in V and for all scalars c \in R. And A is called the domain and B the codomain of T.

Proof

For this case the tranformation proposed is t: M_{mxn} (R) > M_{nxm} (R)

Where T(A) = A^T

For this case we have the following assumption:

1) The transpose of an nxm matrix is an nxm matrix

And the following conditions:

2) T(A+B) = (A+B)^T = A^T + B^T = T(A) + T(B)

And we can express like this T(A+B) =T(A) + T(B)

3) If A \in M_{mxn}(R) and c \in R then we have this:

T(cA) = (cA)^T = cA^T = cT(A)

And since we have all the conditions satisfied, we can conclude that T is a linear transformation on this case.

5 0
3 years ago
Which of the following geometric series converges?
Artist 52 [7]

All three series converge, so the answer is D.

The common ratios for each sequence are (I) -1/9, (II) -1/10, and (III) -1/3.

Consider a geometric sequence with the first term <em>a</em> and common ratio |<em>r</em>| < 1. Then the <em>n</em>-th partial sum (the sum of the first <em>n</em> terms) of the sequence is

S_n=a+ar+ar^2+\cdots+ar^{n-2}+ar^{n-1}

Multiply both sides by <em>r</em> :

rS_n=ar+ar^2+ar^3+\cdots+ar^{n-1}+ar^n

Subtract the latter sum from the first, which eliminates all but the first and last terms:

S_n-rS_n=a-ar^n

Solve for S_n:

(1-r)S_n=a(1-r^n)\implies S_n=\dfrac a{1-r}-\dfrac{ar^n}{1-r}

Then as gets arbitrarily large, the term r^n will converge to 0, leaving us with

S=\displaystyle\lim_{n\to\infty}S_n=\frac a{1-r}

So the given series converge to

(I) -243/(1 + 1/9) = -2187/10

(II) -1.1/(1 + 1/10) = -1

(III) 27/(1 + 1/3) = 18

8 0
3 years ago
Find the equation of a line that contains the points (−3,−1) and (−4,−7). Write the equation in slope-intercept form
ikadub [295]

Answer:

  y = -8x -25

Step-by-step explanation:

The 2-point form of the equation of a line is useful when you are given 2 points.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (7 -(-1))/(-4 -(-3))(x -(-3)) +(-1)

  y = 8/-1(x +3) -1

  y = -8x -25

7 0
3 years ago
The area of a rectanglular sandbox is (5x + 40) feet. Factor 5x + 40 to find possible dimensions of the sandbox
kotegsom [21]
5x+40 factors to 5(x+8). Notice how distributing the 5 back through to each term in the parenthesis gives
5 times x = 5x
5 times 8 = 40
So 5*(x+8) = 5*x+5*8 = 5x+40

Therefore, the factors are 5 and (x+8).
The dimensions of the sandbox are 5 feet by (x+8) feet.

We don't know the numeric value of (x+8) since we don't know the value of x, so we leave it as is. 
6 0
3 years ago
The Ferrari Testarossa and the Porsche 911 Turbo are 400 miles apart and headed straight toward each other. The Ferrari is going
ryzh [129]

Answer:

1.6 hours

Step by step explanation;

1 hour would make them only 150 miles apart, 60% of 120 and 60% of 130 added together is 150 mph, so 1.6 hours

Hope this helps :)

5 0
3 years ago
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