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Murljashka [212]
3 years ago
6

Find the distance between the points (-5, 3) and (7, -2).

Mathematics
2 answers:
denpristay [2]3 years ago
6 0

Answer: have a good day :)

<em>the distance between the two points is 13.</em>

aksik [14]3 years ago
5 0
The distance between the two points is 13
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What’s the slope of the line that passes through 5,10 and 7,12
Marrrta [24]

Slope of the line passes through (5,10) and (7,12) is 1.

Step-by-step explanation:

Given,

The two points are (5,10) and (7,12).

To find the slope passing through the given points.

Formula

The slope of the line passing through (x_{1} ,y_{1}) and (x_{2} ,y_{2}) is \frac{y_{2} -y_{1} }{x_{2} -x_{1} }

Now, putting x_{1} =5,y_{1}=10, x_{2}=7, y_{2} =12 we get,

Slope = \frac{12-10}{7-5} = \frac{2}{2} = 1

Hence,

Slope of the line passes through (5,10) and (7,12) is 1.

7 0
3 years ago
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A is an m×n matrix.Check the true statements below:A. The kernel of a linear transformation is a vector space.B. If the equation
Bess [88]

Answer:

Results are (1) True. (2) False. (3) False. (4) True. (5) True. (6) True.

Step-by-step explanation:

Given A is an m\times n matrix.  Let T :U\to V  be the corresponding linear transformationover the field F and \theta be identity vector in V. Now if x\in Ker( T)\implies T(x)=\theta.

(1) The kernel of a linear transformation is a vector space : True.

Let x,y\in Ker( T), then,

T(x+y)=T(x)+T(y)=\theta+\theta=\theta\impies x+y\in Ker( T)

hence the kernel is closed under addition.

Let \lambda\in F, x\in Ker( T), then

T(\lambda x)=\lambda T(x)=\lambda\times \theta=\theta

\lambda x\in Ker(T) and thus Ket(T) is closed under multiplication

Finally, fore all vectors u\in U,

T(\theta)=T(\theta+(-\theta))=T(\theta)+T(-\theta)=T(\theta)-T(\theta)=\theta

\implies \theta\in Ker(T)

Thus Ker(T) is a subspace.

(2) If the equation Ax=b is consistent, then Col(A) is \mathbb R^m : False

if the equation Ax=b is consistent, then Col(A) must be consistent for all b.

(3) The null space of an mxn matrix is in \mathbb R^m

: False

The null space that is dimension of solution space of an m x n matrix is always in \mathbb R^n.

(4) The column space of A is the range of the mapping x\to Ax

: True.

(5) Col(A) is the set of all vectors that can be written as Ax for some x. : True.

Here Ax will give a linear combination of column of A as a weights of x.

(6) The null space of A is the solution set of the equation Ax=0.

: True

5 0
3 years ago
Factor the expression using the GCF.
ss7ja [257]

Answer:

= 3 (3x + 5y)

Step-by-step explanation:

First find the GCF of 9 and 15 which would be 3. Then the GCF which is 3 is placed on the left of the parentheses. then you plug in the numbers. So 9x divided by 3 is 3x, and 15y divided by 3 is 5y.

7 0
2 years ago
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PLEASE HELP!! Which graph represents the function y=sin(1/2x) after a shift of 3 units down?
dybincka [34]

Answer:

a

Step-by-step explanation:

correct on edge

3 0
2 years ago
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Four pieces of rope unknown(but equal) length and 10 more feet of rope are attached together. The resulting rope is 30 feet long
attashe74 [19]
The 4 pieces of rope equals 5 feet each one
7 0
3 years ago
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