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The orthogonal decomposition of vector [tex]\vec b = <9, 0, 0>[/tex] with respect to vector [tex]\vec a = <4, -5, 0>[/tex]  is

[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]

From the Question we are told that

Vector [tex]\vec b = <9, 0, 0>[/tex]

Vector [tex]\vec a = <4, -5, 0>[/tex]

Generally in the orthogonal decomposition of b to a we have

[tex]\vec b=\vec b"+\vec b'[/tex]

Where

[tex]\vec b"=(\frac{\vec b*\vec a}{\vec *\vec a})*\vec a[/tex]

[tex]\vec b"=(\frac{ <9, 0, 0>*<4, -5, 0>}{<4, -5, 0>*<4, -5, 0>})*<4, -5, 0>[/tex]

[tex]\vec b"=<\frac{4}{5},\frac{-8}{5},0>[/tex]

Therefore

[tex]b'= \vec b- \vec b"\\\\b'=<4,0,0>-<\frac{4}{5},\frac{-8}{5},0>[/tex]

[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]

in Conclusion

The orthogonal decomposition of vector [tex]\vec b = <9, 0, 0>[/tex] with respect to vector [tex]\vec a = <4, -5, 0>[/tex]  is

[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]

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Answer:

12

Step-by-step explanation:

40/24 = 20/x

40x = 20 × 24

40x = 480

x = 480/40

x = 12

Answer:

AC = 4

Step-by-step explanation:

For AD to be an angle bisector then it divides the opposite side into segments that are proportional to the other two sides, that is

[tex]\frac{AB}{AC}[/tex] = [tex]\frac{BD}{DC}[/tex] , substitute values

[tex]\frac{2}{AC}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

AC = 4

Answer:

12 - (1/4)x

Step-by-step explanation:

quarter of x is (1/4)x

Now, minus that from twelve.

Answer:

B. 30m2

Answer:

I think its c I hope I'm right

Answer:

1/2 and 9 is rational but 4 is not

Step-by-step explanation:

A rational number is a number that can be written as a ratio. That means it can be written as a fraction, in which both the numerator (the number on top) and the denominator (the number on the bottom) are whole numbers.

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Answer:

8

Step-by-step explanation:

The function u given me is

[tex] \tan( \frac{\pi}{4} (x - \frac{\pi}{3} ) )[/tex]

The period of a function is represented by

[tex] \frac{2\pi}{ |b| } [/tex]

where b is the coefficient of the x variable.

The coefficient is pi/4 so

[tex] \frac{2\pi}{ \frac{\pi}{4} } = 8[/tex]

8 is the answer.

Answer: 4 units

Step-by-step explanation:

Hi ;-)

[tex]s=zh-2zt^3\\\\z(h-2t^3)=s \ \ /:(h-2t^3)\\\\z=\dfrac{s}{h-2t^3}[/tex]

Answer:

z = [tex]\frac{s}{h-2t^3}[/tex]

Step-by-step explanation:

Given

s = zh - 2zt³ ← factor out z from each term

s = z(h - 2t³ ) ← divide both sides by h - 2t³

[tex]\frac{s}{h-2t^3}[/tex] = z

Answer:

null set

Step-by-step explanation:

i am not sure but i hope it will help you

Answer:

singleton set is correct

Answer:

7/12

Explanation:

Here are the steps to follow:

Write down the factors for the numerator and the denominator.

Determine the largest factor that is common between the two.

Divide the numerator and denominator by the greatest common factor.

Write down the reduced fraction.

Answer:

7/12

Step-by-step explanation:

[tex] \frac{1}{3} + \frac{1}{2} = \frac{2 + 3}{6} = \frac{5}{6} - \frac{1}{4} = \frac{20 - 6}{24} = \frac{7}{12} [/tex]

Answer:

position of objects in space

for example: up, down, in front, behind, between, left, right.

motion of objects in space

for example: Stars, planets, moons.

Step-by-step explanation:

the formula of coordinates (x, y) that reflected across the x-axis : (x, y) => (x, -y)

so,

A(3, -2) => A'(3, 2)

B(5, 5) => B'(5, -5)

C(-4, 2) => C'(-4, -2)

Coordinates of ∆ABC

Now co-ordibates of ∆A'B'C'

[tex]\\ \rm\longmapsto A'=(3,2)[/tex]

[tex]\\ \rm\longmapsto B'=(5,-5)[/tex]

[tex]\\ \rm\longmapsto C'=(-4,-2)[/tex]

Answer:

1 real solution

Step-by-step explanation:

Use discramint formula.

[tex]b {}^{2} - 4ac[/tex]

If the discramint >0, the equation is going to have 2 real solutions

If the discramint =0, we going to have one real solution.

If the discramint<0, we going to have two imaginary solution

B is -4, A is 4 and C is 1 so

[tex] { - 4}^{2} - 4( 4)(1) = 0[/tex]

So the equation had one real solution.

Answer:

im pretty sure its 250%

Step-by-step explanation:

Answer:

250%

Step-by-step explanation:

1 is 100% and double that is 200%

1/5 of 100% is 50%

200% + 50% = 250%

Number combination can be used to find the number of selecting n  items from m items

The known parameters are;

Number of days the six friends play a game of tennis = Every day = 7 days

Number of weeks the six friends the friends play for = 7 weeks

Therefore the total number of days = 7 × 7 days = 49 days

Required:

(a) The number of ways the friends can play with each other once is given as follows;

[tex]The \ number \ of \ 2 \ combinations \ in \ 6 \ options, C_6^2 = \dfrac{6!}{2!\times (6-2)!} = 15[/tex]

The number of ways the six friends can play with each other once is 15 ways

Therefore, minimum number of singles games that will be between the same friends playing each other is given as follows;

[tex]\mathbf{Number \ of \ games = \dfrac{7 \times 7}{C_6^2} }=3.2\overline 6[/tex]

Therefore, more than 3 of the games or four games will be between pairs playing the game more than four times together, and when at least four of the games of singles are counted it will be between friends playing each other for the fourth time

(b) The number of ways the friends can play game of doubles is given as follows;

[tex]C_6^4 = \dfrac{6!}{4! \times (6 - 4)!} = 15[/tex]

The number of pairs = ₆C₂ = 15

The number of games of doubles = 49

In 49 games, we have;

The number of times the same opposing  will play a game of doubles where a member of the pair can be on either side of the court will given as follows;

[tex]\mathbf{Number \ of \ games \ of \ doubles \ between \ same \ pair} = \dfrac{7 \times 7}{15 } =3.2\overline 6[/tex]

Therefore, at least four of the of the games of doubles will be between the same set of four friends playing for the 4th time, which gives; at least four games of doubles between the same set of four friends, two of which are playing (as a pair) the same opposing pair for the 4/2 = second time

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Answer:

measure of both angle is 66

Step-by-step explanation:

vertical angles are equal so,

6x+15=4x+32

6x-4x=32-15

2x= 17

X=8.5

now,

4X+32

= 4×8.5 +32

= 66

Answer:

hope it helps you........

Answer:

2n-3m

=2(4)-3(3)

=8 - 9

= -1

Answer:

-14°F

Step-by-step explanation:

Hey there!

Answer:

17) 19

19) 8

Step-by-step explanation:

17)

(6 +6² -4)÷2

(6 +36 -4)÷2

(38)÷2

19

19)

3³ ÷3 - 1

27 ÷3 -1

9 -1

8

Answer:

600

Step-by-step explanation:

since 1m=1000mm

Answer:

D. 10

Step-by-step explanation:

[tex]{ \sf{(12x + 12) \degree = 79\degree + (5x + 3)\degree}} \\ { \sf{ \{outer \: angle \: is \: equal \: to \: sum \: of \: inner \: angles \}}} \\ { \sf{12x - 5x = 79 + 3 - 12}} \\ { \sf{7x = 70}} \\ { \sf{x = 10}}[/tex]

Answer:

integers

Step-by-step explanation:

so negative and positive are numbers in questions so no.

and def not Imaginary numbers

Answer: 12 and -12

Step-by-step explanation:

Absolute value is the distance to zero (0)

Equation 1:

|(12) - 2| = 10

= 12-2

=10

Equation 2:

|(-12) - 2| = 10

= 12 - 2

= 10

Answer:

If the exponent is 0 the answer is 224/y^2

Step-by-step explanation:

Answer:

q is 4

Step-by-step explanation:

[tex]gradient = \frac{y_{2} - y_{1} }{x _{2} - x _{1} } \\ [/tex]

let gradient of the line joining (4, q) to (6, 5) be x

let gradient of the line joining (0, 0) to (4, q) be y

[tex]y = 2x[/tex]

therefore:

[tex]( \frac{q - 0}{4 - 0} ) = 2( \frac{5 - q}{6 - 4} ) \\ \\ \frac{q}{4} = \frac{2(5 - q)}{2} \\ \\ \frac{q}{4} = 5 - q \\ \\ q = 4(5 - q) \\ q = 20 - 4q[/tex]

collect like terms:

[tex]q + 4q = 20 \\ 5q = 20 \\ q = \frac{20}{5} \\ \\ q = 4[/tex]

Let,

As we know,

then,

→ [tex]\frac{q-0}{4-0} = 2(\frac{5-q}{6-4} )[/tex]

      [tex]\frac{q}{4} = \frac{2(5-q)}{2}[/tex]

      [tex]\frac{q}{4} = 5-q[/tex]

By applying cross-multiplication, we get

      [tex]q = 4(5-q)[/tex]

      [tex]q = 20-4q[/tex]

By adding "4q" both sides, we get

[tex]q+4q= 20-4q+4q[/tex]

     [tex]5q = 20[/tex]

       [tex]q = \frac{20}{5}[/tex]

       [tex]q = 4[/tex]

Thus the above value is correct.

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Answer:

Step-by-step explanation:

[tex] \frac{v}{8} = 13[/tex]

=> v = 13 × 8

=> v = 114 (Ans)

.....................

Answer:

<CAB =30°

Step-by-step explanation:

<DAB=80°

<DAC=50°

<DAB=<DAC+<CAB

<CAB=<DAB-<DAC

=80°-50°

=30°

Answer:

40

Step-by-step explanation:

137+143=280

280/7= 40

Answer:

Division/dividing/divide

Step-by-step explanation:

If Justin has 280 baseball cards, and if each page will only hold 7 cards per page, then by dividing 280 by 7 (280÷7) would equal to 40 pages.