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3 years ago

Is 6 to the 3rd power equal to 2•2•2•3•3•3? Full explaination and reasoning.

Mathematics

1 answer:

Zolol [24]3 years ago

4 0

Answer:

yes

Step-by-step explanation:

if you do 6^3 you get 216

6*6*6=216

6*6=36

36*6=216

2*2*2*3*3*3=216

2*2=4

4*2=8

8*3=24

24*3=72

72*3=216

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If the subspace of all solutions of Ax 0 has a basis consisting of vectors and if A is a matrix, what is the rank of A

Nuetrik [128]

Question: If the subspace of all solutions of

Ax = 0

has a basis consisting of vectors and if A is a matrix, what is the rank of A.

Note: The rank of A can only be determined if the dimension of the matrix A is given, and the number of vectors is known. Here in this question, neither the dimension, nor the number of vectors is given.

Assume: The number of vectors is 3, and the dimension is 5 × 8.

Answer:

The rank of the matrix A is 5.

Step-by-step explanation:

In the standard basis of the linear transformation:

f : R^8 → R^5, x↦Ax

the matrix A is a representation.

and the dimension of kernel of A, written as dim(kerA) is 3.

By the rank-nullity theorem, rank of matrix A is equal to the subtraction of the dimension of the kernel of A from the dimension of R^8.

That is:

rank(A) = dim(R^8) - dim(kerA)

= 8 - 3

= 5

4 0

3 years ago

The graph shows the number of students enrolled in a high school over a seven years period.

Olegator [25]

D.2600 2200+40=2600. hope this helps!!

8 0

2 years ago

Read 2 more answers

Which recursive formula can be used to generate the sequence shown, where f(1) = 5 and n > 1?

saveliy_v [14]

You can try them out and see which one works.

a: f(2) = f(1) +6 = 5+6 = 11 . . . . . . not this one

b: f(1) = f(2) -6 = -1-6 = -7 . . . . . . not this one (5 ≠ -7)

c: f(2) = f(1) - 6 = 5 - 6 = -1 . . . . . this gives the right f(2)

d: f(2 = -6(f(1) = -6(5) = -30 . . . . not this one

_____

The appropriate choice is ...

... f(n +1) = f(n) - 6

— — — — —

You can also recognize that the next term is 6 less than the current one, so f(n+1) = f(n) - 6, which corresponds to the 3rd selection.

7 0

2 years ago

Read 2 more answers

Describe and correct the error the student made when writing the equation of the line that passes through (-8,5)

pshichka [43]

Option D (The student should have used as the slope of the perpendicular line.) is correct.

Step-by-step explanation:

We need to identify the error that the student made in finding equation of the line that passes through (-8,5) and is perpendicular to y = 4x + 2

The slope of the required line would me -1/m because both lines are perpendicular.

So, slope of new line will be: -1/4

because the equation of slope-intercept form is: $y=mx+b$ where m is the slope

Now, for finding equation the student used point slope form i.e $y-y_1=m(x-x_1)$

where y_1 and x_1 are the points and m is the slope.

Putting values:

x_1=-8, y_1=5 and m=-1/4

$y-5=-\frac{1}{4}(x-(-8))\\y-5=-\frac{1}{4}(x+8)\\y-5=-\frac{1x}{4}-2\\y=-\frac{1x}{4}-2+5\\y=-\frac{1x}{4}+3$

This is the correct solution.

The student made error by using the wrong slope he used 2 instead of -1/4

in the step $y-5 = 2(x-(-8))$

So, Option D (The student should have used as the slope of the perpendicular line.) is correct.

Keywords: Equation of line using Slope

Learn more about Equation of line using Slope at:

#learnwithBrainly

3 0

2 years ago

Read 2 more answers

Write an equation of the perpendicular bisector of the segment with endpoints G 9,8       and H 3,2      .

Norma-Jean [14]

Answer:

y = -x + 11

Step-by-step explanation:

The equation of a straight line is is given by:

y = mx + b; where m is the slope and b is the y intercept

The equation of the line joining G(9, 8) and H(3, 2) is given as:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\y-8=\frac{2-8}{3-9}(x-9)\\\\y-8=x-9\\\\y=x-1$

The perpendicular bisector of the line joining G(9, 8) and H(3, 2) is perpendicular to the line joining G(9, 8) and H(3, 2) and passes through the midpoint of line joining G(9, 8) and H(3, 2).

Let (x, y) be the midpoint of the line joining G(9, 8) and H(3, 2). Hence:

x = (9 + 3)/2 = 6

y = (8 + 2)/2 = 5

The midpoint = (6, 5)

Two lines are perpendicular if the product of their slopes is -1.

The line joining G(9, 8) and H(3, 2) has a slope of 1, hence, the slope of the perpendicular bisector would be -1.

This means that the perpendicular bisector has a slope of -1 and passes through (6, 5). Using:

$y-y_1=m(x-x_1)\\\\y-5=-1(x-6)\\\\y-5=-x+6\\\\y=-x+11$

The equation of the perpendicular bisector is y = -x + 11

8 0

3 years ago