2.16=?2, point, 1, start overline, 6, end overline, equals, question mark

Answer:

c. tr(AB) = tr(A)tr(B)

Step-by-step explanation:

The trace of a matrix is only valid for a square matrix, that is a n by n matrix. The trace of a matrix is the sum of all its diagonal elements. The following properties of trace holds for a matrix A and B with size n by n and a real number c.

i) The trace sum of two matrix is equal to the sum of their individual traces. That is:

tr(A + B) = tr(A) + tr(B)

ii) The trace of the product of a scalar and a matrix is the same as the product of the scalar and the trace of the product, that is:

tr(cA) = ctr(A)

iii) The trace of a transpose of a matrix is equal to the trace of the matrix, that is:

[tex]tr(A^T)=tr(A)[/tex]

iv) The trace of a product of matrix is given as:

tr(AB) = tr(BA)

Answer:

c. tr(AB) = tr(A)tr(B)

Answer:

10x+8=4x+(-4).

10×+8=4x-4.

collect like terms.

10x-4x=-4-8.

6x=-12.

x=-12/6.

x=-2.

Answer:

10

Step-by-step explanation:

xy + 5x + 4y = -5

(x + 4) y + 5x = -5

(x + 4) y = -5x − 5

y = -5 (x + 1) / (x + 4)

For y to be large as possible, (x + 1) / (x + 4) must be negative.  That means -4 < x < -1.  So x is either -2 or -3.

The possible values of y are:

y = -5 (-2 + 1) / (-2 + 4) = 5/2 (not an integer).

y = -5 (-3 + 1) / (-3 + 4) = 10.

Answer:

a.  Point E

b  Line AB

Step-by-step explanation:

The lines AB and CD will intersect at a point

The Point is Point E

Planes will intersect at a line

Planes X and Plane Y intersect at line AB

Answer:

a.  point E

b.  points A and B ( which is line AB )

Step-by-step explanation:

a.  the intersection of AB and CD = point E

b.  the intersection of plane X and Y = points A and B ( which is line AB )

Answer:

C) 1 5/16

Step-by-step explanation:

(3/4)/(4/7)=(3/4)(7/4)=21/16=1 5/16

Answer:

32 miles per gallon

Step-by-step explanation:

351 divided by 11 = 31.90909090909090909090909090 e.t.c

Answer:

10626 ways

Step-by-step explanation:

Given

Number of students = 23

Prizes = 3

Required

Number of different outcomes for the top 3

This question will be solved using permutation formula because it implies selection of 3 students from 23

[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]

Where n = 23 and r = 3

The formula becomes

[tex]^{23}P_3 = \frac{23!}{(23-3)!}[/tex]

[tex]^{23}P_3 = \frac{23!}{(20)!}[/tex]

[tex]^{23}P_3 = \frac{23!}{20!}[/tex]

[tex]^{23}P_3 = \frac{23 * 22 * 21 * 20!}{20!}[/tex]

[tex]^{23}P_3 = 23 * 22 * 21[/tex]

[tex]^{23}P_3 = 10626[/tex]

Hence, there are 10626 ways

Answer:

Separate the stones into 3 groups of 3.

Let's call each the three groups A, B, and C.

1) Place group A and group B on the two plates of the scale. There are two possible outcomes i) and ii) below:

i) The groups have different weights. A is heavier than B or B is heavier than A. Take the heavier group. Place two stones from this group on the scale. If one is heavier than the other, this is it. If they are equal, the stone not on the scale is it.

ii) Groups A and B have equal weights. The heavier stone in in group C. Using group C, place two stones from this group on the scale. If one is heavier than the other, this is it. If they are equal, the stone not on the scale is it.

The Histogram is attached blow.

A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of data items in a series of equal-sized numerical intervals. The independent variable is represented along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.

Given:

Data: 4,4,6, 11, 11, 12, 14, 14, 21, 21, 24, 26

So, Interval           Frequency

      0- 5                     4 , 4 (2)

       5-10                      6(1)

      10- 15                    11, 11, 12, 14, 14  

     15- 20                      _

     20- 25                  21, 21, 24

     25- 30                        26

Hence, the Histogram is attached blow.

Learn more about Histogram here:

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Answer:

T will equal 4

Step-by-step explanation:

T-4=T-4

T+4=T+4

Answer:

the volume of the 2nd box is 1200 cubic inches

Step-by-step explanation:

Answer:

198

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

So we know that the point-slope form of the line that passes through the points (-4,-3) and (12,1) is:

[tex]y-1=\frac{1}{4}(x-12)[/tex]

And we want to convert this to standard form.

The standard form of a linear equation is:

[tex]Ax+By=C[/tex]

Where A, B, and C are integers, and, traditionally, A is positive.

So, first, multiply everything by 4 to remove the negative:

[tex]4(y-1)=4(\frac{1}{4}(x-12))[/tex]

Distribute the left. The right cancels:

[tex]4y-4=x-12[/tex]

Add 4 to both sides. The left cancels:

[tex]4y=x-8[/tex]

Subtract x from both sides:

[tex]-x+4y=-8[/tex]

As I mentioned previously, the coefficient of A tends to be positive. So, divide everything by -1:

[tex](-x+4y)/-1=(-8)/-1[/tex]

Simplify:

[tex]x-4y=8[/tex]

So, our answer is A

And we're done!

Answer:

5 in the 85327= five thousand units

5 in the 435= five units

Step-by-step explanation:

85,327= eighty five thousand, three hundred and twenty seven

Value of five or the position if five in the above number is the thousand position

5 in the above = five thousand unit

435= four hundred and thirty five

The position of five in the above number is the unit position

Five in the above= five unit

Answer:6

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

This set is a function because every input value only has one output value.

Answer: h(h-3)(h+4)  

Step-by-step explanation:

To find the volume of rectangular-shaped box  we will have to multiply the length by the width by the height.

Given the statements  we can determine the  length with the equation

L = h -3  where l is the length and h is the height.

the width can also be represent by the equation

w = h + 4        

The height is is h and the length is h- 3  and the width is also h+4  so the expression will be    h(h-3)(h+4)

Answer:

In exponential form

3.2615 X 10¹

Given :

A vector v = 10i - 24k.

To Find :

A vector of magnitude 3 in the direction of v = 10i - 24k.

Solution :

Unit vector in the direction  of vector v is :

[tex]\^{v}=\dfrac{v}{|v|}\\\\\^{v}=\dfrac{10i-24k}{\sqrt{10^2+24^2}}\\\\\^{v}=\dfrac{10i-24k}{26}[/tex]

Now , vector of magnitude 3 in direction v is :

[tex]r=3 \^{v}\\\\r=3\times \dfrac{ (10i-24k)}{26}\\\\r=\dfrac{3}{13} (5i-12k)[/tex]

Hence , this is the required solution .

The vector of magnitude 3 in the direction of given vector is, [tex]\frac{30i-72k}{26}[/tex]

First we have to calculate unit vector of given vector.

    Given vector,  [tex]v=10i-24k[/tex]

Unit vector of vector v is,

                     [tex]v=\frac{10i-24k}{\sqrt{(10)^{2}+(24)^{2} } }\\ \\v=\frac{10i-24k}{\sqrt{100+576} }=\frac{10i-24k}{26}[/tex]

For vector have magnitude 3 is,

        [tex]v=3(\frac{10i-24k}{26} )=\frac{30i-72k}{26}[/tex]

The vector of magnitude 3 in the direction of given vector is, [tex]\frac{30i-72k}{26}[/tex]

Learn more about the magnitude of vectors here :

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Answer:

The answer is "8 hours"

Step-by-step explanation:

by the given value we create the equation that is:

 [tex]\to 45x-40=300\\\\\to 45x=300+40\\\\\to 45x=340\\\\\to x=\frac{340}{45}\\\\\to x= 7.55\ \ hours \ or \ \ \ 8 \ hours[/tex]

Answer:

x=10

Step-by-step explanation:

Step 1: Add x to both sides

Step 2: Subtract 2 from both sides.

Step 3: Multiply both sides by 2.

Answer:

5040

Step-by-step explanation:

7 x 6 x 5 x 4 x 3 x 2 = 5040 different ways. Look at it this way: The first place can be taken by any of the 7 objects, which leaves any of 6 objects available for second place, which leaves any of 5 objects that then leaves 4 then 3 then 2 then 1

HOPE THIS HELPS

Answer:

10+14c

Step-by-step explanation:

You multiply every number inside the parenthesis by 2.

Answer:

10+14c

Step-by-step explanation:

Multiply two times what is in parentheses.

10+14c

19+(-19)=0

Step-by-step explanation:

So first lets simplify this. We can use the method keep,change, change to do this. Keep the value of positive 19. Then change the + sign to - and the - sign to plus which gets us

19-(+19).

We can remove the +since we know its positive leaving 19-19 which is 0

Answer:

width = 5k²

length = 3k² + 7k + 4

Step-by-step explanation:

(see attached)

Answer:

5 + 4i

Step-by-step explanation:

In general, the conjugate of a + bi is a - bi

Answer:

x < 6

Step-by-step explanation:

Given

5x - 9 < 21 ( add 9 to both sides )

5x < 30 ( divide both sides by 5 )

x < 6

Answer:

x < 6

Step-by-step explanation:

5x-9<21

Add 9 to each side

5x-9+9<21+9

5x < 30

Divide by 5

5x/5 < 30/5

x < 6

Answer:

Step-by-step explanation:

-x - 6 > 21 - 28x

27x - 6 > 21

27x > 27

x > 1