Solve the equation 6(x-5) =12

The question is missing. Here is the complete question.

Let y = [tex]\left[\begin{array}{ccc}2\\6\end{array}\right][/tex] and u = [tex]\left[\begin{array}{ccc}7\\1\end{array}\right][/tex]. Write y as the sum of a vector in Span(u) and a vector orthogonal to u.

Answer: y = [tex]\left[\begin{array}{ccc}\frac{21}{10} \\ \frac{3}{10} \end{array}\right] + \left[\begin{array}{ccc}\frac{-1}{10}\\ \frac{57}{10} \end{array}\right][/tex]

Step-by-step explanation: The sum of vectors is given by

y =  [tex]y_{1}[/tex] + z

where  [tex]y_{1}[/tex] is in Span(u);

vector z is orthogonal to it;

First you have to compute the orthogonal projection [tex]y_{1}[/tex] of y:

[tex]y_{1}[/tex] = proj y = [tex]\frac{y.u}{u.u}.u[/tex]

Calculating orthogonal projection:

[tex]\left[\begin{array}{c}2\\6\end{array}\right][/tex].[tex]\left[\begin{array}{c}7\\1\end{array}\right][/tex] = [tex]\left[\begin{array}{c}9\\6\end{array}\right][/tex]

[tex]\left[\begin{array}{c}7\\1\end{array}\right][/tex].[tex]\left[\begin{array}{c}7\\1\end{array}\right][/tex] = [tex]\left[\begin{array}{c}49\\1\end{array}\right][/tex]

[tex]y_{1} = \frac{9+6}{49+1}.u[/tex]

[tex]y_{1} = \frac{15}{50}.u[/tex]

[tex]y_{1} = \frac{3}{10}.u[/tex]

[tex]y_{1} = \frac{3}{10}.\left[\begin{array}{c}7\\1\end{array}\right][/tex]

[tex]y_{1} = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right][/tex]

Calculating vector z:

z = y - [tex]y_{1}[/tex]

z = [tex]\left[\begin{array}{c}2\\6\end{array}\right] - \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right][/tex]

z = [tex]\left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right][/tex]

Writing y as the sum:

[tex]y = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right] + \left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right][/tex]

Answer:

Kindly check explanation

Step-by-step explanation:

Given the Coefficient of correlation (r) = 0.864

The Coefficient of determination (R^2) :

0.864^2 = 0.747 ( 3 decimal places)

B) the Coefficient of determinationR^2 tells about the proportion of variation in the dependent variable that is predicted by the independent variable, Hence, a proportion of about 0.75 should fall within the regression line.

C) percentage variation explained :

Coefficient of determination * 100%

0.747 * 100% = 74.7%

D) unexplained variation due to other factors or sampling error :

(total variation - explained variation) = (100 - 74.7)% = 25.3%

Answer:

E

Step-by-step explanation:

So we already know that:

[tex]\lim_{x \to 5} f(x)=2 \text{ and } \lim_{x \to 5} g(x)=-6[/tex]

So, go through each of the choices and see which ones are correct.

I)

We have:

[tex]\lim_{x \to 5} (f(x)+g(x))[/tex]

This is the same as saying:

[tex]\lim_{x \to 5} f(x)+ \lim_{x \to 5} g(x)[/tex]

And since we already know the values:

[tex]=(2)+(-6)\\=-4[/tex]

So, the limit does indeed exist.

II)

We have:

[tex]\lim_{x \to 5} \frac{f(x)}{g(x)+6}[/tex]

This is the same as:

[tex]\frac{ \lim_{x \to 5} f(x)}{ \lim_{x \to 5} g(x)+ \lim_{x \to 5} 6 }[/tex]

The bottom right one is just 6. Simplify:

[tex]\frac{ \lim_{x \to 5} f(x)}{ \lim_{x \to 5} g(x)+6}[/tex]

Substitute the values we know:

[tex]=\frac{(2)}{(-6)+6} \\=2/0[/tex]

This is a value over zero. Unlike the indeterminate form 0/0, this limit does not exist.

III)

We have:

[tex]\lim_{x \to 5} \frac{f(x)-2}{g(x)}[/tex]

Again, this is the same as:

[tex]\frac{ (\lim_{x \to 5} f(x))-2}{ \lim_{x \to 5} g(x)}[/tex]

Substitute in the values we know:

[tex]=\frac{(2)-2}{(-6)}\\ =0/-6=0[/tex]

The limit does exist and it is 0.

So, the limits of only I and III exist.

The correct answer is E.

Answer:

total books in library = 39

books bought from yard sale = ??

Total book in library now = 84

Now,

books bought from yard sale= 39-84

= 45

Answer:

2.75 L

Step-by-step explanation:

This is the problem of subtraction.

Total Milk sumana has = 7.5 l

Milk used in the morning = 4.75 L

Milk left for evening = Total Milk sumana has - Milk used in the morning

Milk left for evening = 7.5 l - 4.75 l = 2.75 L

Answer:

The angle of elevation of the sun is 38°

Step-by-step explanation:

We can set up the diagram for the the question by interpreting it, you can check the diagram at the attached file.

We can see that after the interpretation of the question we arrived at a triangle,. Where the vertical side represent the 92-ft. which is the height of the tree and the horizontal side represent the 120 ft. which is the shadow's lenght. Then the angle of elevation of the sun can ba calculated using tangent ratio, from our knowledge of trigonometry

Tan(θ )= opposite/adjacent

Where our opposite =92ft

Adjacent= 120ft

Tan(θ ) =92/120

θ =tan-1( 92/120)

θ = 37.48°

Therefore, the angle of elevation of the sun If we round up our decimal value to the nearest 10th, we have θ = 38°

Answer:

30000

Step-by-step explanation:

3000 / (1/10) = w

3000*10/1 = w

30000 = w

probe:

30000*1/10 = 3000

then:

30000

is 1/10

of

30000

Answer:

14

Step-by-step explanation:

7x-1+6x-1=180

13x-2=180

13x=180+2

13x=182

x=14

Answer:

change f(x) to y, switch x and y, and solve for y

y = √(x -4)

x = √(y - 4)

x² = y - 4

x² + 4 = y

y = x² + 4

f⁽⁻¹⁾ = x² + 4, where x ≥ 4

Answer:

Step-by-step explanation:

7 3/24   + 4/24

7 7/24

Answer:

y = 9

Step-by-step explanation:

So if x = 3, we can sub that into the equation.

This gives us:

6.4 (* 3) + 2.8y = 44.4

so:

19.2 + 2.8y = 44.4

25.2 = 2.8y

so

y = 9

Answer: 9

Step-by-step explanation: plug 3 into the x, then use the order of operations/ pemdas to solve. first multiply 6.4 and 3 (=19.2) then subtract the answer from 44.4 (now the equation is 2.8y=25.2) then divide 2.8 from 25.2 to get x alone and you are left with x=9

Answer:

Step-by-step explanation:

step one:

In this problem we are  expected  to substitute the value of d in the expression for velocity given as

[tex]s=24d[/tex]

step two:

Given that

d= 117 ft

Substituting the value for d in the given equation we have

[tex]s= 24*117\\\\s=2808 ft/s[/tex]

The problem basically tests our ability to perform basic substitution operation which we have performed, should you have any question or doubt, kindly respond to this question

Answer:

53

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The factors of 8 are 1, 2, 4, and 8.

60 is not divisible by 8, but it is divisible by 4:  4 * 15 = 60. So the GCF of 60 and 8 is 4.

Answer:

Step-by-step explanation:

Hello, any irrational number multiplied by 4 is an irrational number.

For instance, you can take

[tex]\boxed{\sqrt{2}}[/tex]

Thank you

Answer:

The  value is  [tex]Z_{\alpha } = 1.439[/tex]

Step-by-step explanation:

From the question we are told that

   The  confidence level is  C  =  85%  

Generally the level of significance is mathematically represented as

         [tex]\alpha = (100 - 85 )\%[/tex]

        [tex]\alpha = 0.15[/tex]

Now from the normal distribution table  the critical value  of [tex]\alpha[/tex] is  

     [tex]Z_{\alpha } = 1.439[/tex]

2 terms

Step-by-step explanation:

4[8+2x]

=4*8+4*2x

=32+8x

therefore there are 2 terms

hope it helps u if yes pls mark brainliest

Answer:

The first factor (4) consists of one (1) term, "4".

The second factor (8 +3x) consists of two (2) terms, "8" and "3x".

Answer:

x=6 is the answer

Step-by-step explanation:

4x-3=2x+9

adding 3 on both sides

4x-3+3=2x+9+3

4x=2x+12

subtracting 2x on both sides

4x-2x=2x-2x+12

2x=12

dividing 2 on both sides

2x/2=12/2

x=6 is the answer.

hope it will help you :)

Step-by-step explanation:

4x - 3 = 2x + 9

Bringing like terms on one side

4x - 2x = 9 + 3

2x = 12

x = 12/ 2

x = 6

Answer:

16/33

Step-by-step explanation:

The probability that the first ball is red and the second ball is black is:

8/12 × 4/11 = 8/33

The probability that the first ball is black and the second ball is red is:

4/12 × 8/11 = 8/33

So the total probability of drawing one ball of each color is 8/33 + 8/33 = 16/33.

Answer:

Step-by-step explanation:

8 3/5 on a number line is between 8 and nine

idk how to draw a number line on a computer so ill just tell you how

1. divided the spaces between 8 and 9 into 5 sections ( 3/5 )

2. then mark 3 of those 5 spaces and put a dot or a line at where the 3rd space ends

Answer:

  see below

Step-by-step explanation:

The ordered pairs of the inverse function are the reverse of the ordered pairs of the function.

You are given the function has ordered pairs (-3, -2), (3, -1) and so on. The inverse function will have ordered pairs (-2, -3), (-1, 3), and so on. This matches choice A.

Answer: 6 m is greater

Step-by-step explanation:

Cm is less than m

Hope it helps

Answer:

25. <

26. <

27. >

28. <

29. <

30. >

Hope it helps!

lovelymoonlight ✨

Answer & Step-by-step explanation:

For this problem, we have to find the equations that have a value of 10 for the variable y. Immediately, we can eliminate some answers. We can eliminate A, D, and E because they all have a different value for the variable y. So, that leaves us with answer choices B and C.

In order to check to see if we are correct, let's plug in 10 for the y in answer choices B and C.

B:

8 = 18 - y

8 = 18 - 10

8 = 8

C:

60 = 6y

60 = 6(10)

60 = 60

So, as you can see, we are correct and we have successfully found the correct answer to the given problem.

Answer:

B and C

Step-by-step explanation:

We want to find the equations where y=10 is a solution. Let's plug 10 into each equation and solve.

A. y+11=22

10 +11 =22

Add 10 and 11.

21 ≠ 22

21 does not equal 22. This choice is incorrect.

B. 8= 18-y

8=18-10

Subtract 10 from 18.

8=8

8 equals 8. This choice is correct.

C. 60=6y

60=6(10)

Multiply 6 and 10.

60=60

60 equals 60. This choice is correct.

D. y/5=4

10/5=4

Divide 10 by 5.

2≠4

2 does not equal 4. This choice is incorrect.

E. 10y=20

10(10)=20

Multiply 10 and 10.

100≠20

100 does not equal 20. This choice is incorrect.

The equations where y=10 is a solution are B. 8=18-y and C. 60=6y

Answer:

last row equals 333

Step-by-step explanation:

The clock showing time 9:00 should be worth 9 points, and the clock showing 3:00 should be worth 3 points, giving for the first row:

9 + 9 + 3 = 21

the three equal calculators showing 1234 are worth 10 points each:

1+2+3+4 = 10

and 10 + 10 + 10 = 30

the light bulbs should be 15 points each then giving 15 + 15 - 15 = 130 - 15 = 15 Notice also that they all have 5 rays of light coming out (so a 3 points per ray)

Now for the bottom line we have:

9 + (1+2+2+4) times 3 * 12 (only four rays on each bulb thus 4 * 3 = 12)

Notice we added the figures that appear in the calculator.

9 + 9 * 36 = 333

Answer:

[tex] \boxed{\sf 15x^2 + 2} [/tex]

Step-by-step explanation:

Simplify the expression:

[tex] \sf \implies(10 {x}^{2} - 1 + 4x) + (3 + 5 {x}^{2} - 4x)[/tex]

Grouping like terms, 10x² + 5x² + 4 x - 4 x - 1 + 3 = (10 x² + 5x²) + (4 x - 4 x) + (-1 + 3):

[tex] \sf \implies (10 x^2 + 5 x^2) + (4 x - 4 x) + (-1 + 3)[/tex]

10x² + 5x² = 15x²:

[tex] \sf \implies 15 x^2 + (4 x - 4 x) + (-1 + 3)[/tex]

3 - 1 = 2:

[tex] \sf \implies 15 x^2 + (4 x - 4 x) + 2[/tex]

4 x - 4 x = 0:

[tex] \sf \implies 15 x^2 + 2[/tex]

Answer:

X=5 Y=-4

Step-by-step explanation:

Complete Question

The complete question is shown on the first uploaded image

Answer:

The decision is to reject the null hypothesis at a significant level of significance [tex]\alpha = 0.05[/tex] There is sufficient evidence to conclude that at least one of the population mean  is different from  at least of the population  

Step-by-step explanation:

From the question we are told that the claim is

     The mean growth rates of all four species are equal.

The  null hypothesis is  

             [tex]H_o : \mu _1 = \mu_2 = \mu_3 = \mu_4[/tex]

Th alternative hypothesis is    

             [tex]H_a: at \ least \ one \ of \ the \ means \ is \not\ equal[/tex]

From question the p-value is [tex]p-value = 0.015[/tex]

  And since the [tex]p-value < \alpha[/tex] so the null hypothesis will be rejected

So  

   The decision is to reject the null hypothesis at a significant level of significance [tex]\alpha = 0.05[/tex] There is sufficient evidence to conclude that at least one of the population mean  is different from  at least of the population  

Answer:

The correct answer is:

It is a discrete random variable. (A)

Step-by-step explanation:

Discrete Random Variables are variables that have distinct values. The number of variables that can be taken on can be counted. in this example, the variables to the question Did you smoke in the last week? is one of two possibilities; yes or no. Apart from these two values, there is no other possibility for the variables, hence it is a discrete random variable

Continuous Random Variables are values that can take on any value between distinct values, even up to infinity. The number of values that the variables can take on cannot be counted or listed. For example, is there are variables for the possible temperature that a particular city can take on in a day, the values are continuous random variables because the values do not have any distinct value, and the possibilities cannot be counted. the possibilities can be; anywhere between 20°C to 50°C. between these two, temperatures, you can have infinite possibilities; 20.1, 30.5, 40.8, etc. Hence the values cannot be counted, it is thus a continuous random variable.

Answer:

c not random variable

Step-by-step explanation:

Answer:

A. The digit 8 is in the place one million position

B. The digit 3 is in the place tens position

Step-by-step explanation:

Given:

98,045,132.706

9 is in the ten million position

8 is in the one million position

0 is in the hundred-thousand position

4 is in the ten-thousand position

5 is in the one-thousand position

1 is in the hundred position

3 is in the tens position

2 is in the one position

. Decimal

7 is in the tenth position

0 is in the hundredth position

6 is in the thousandth position

Therefore,

A. The digit 8 is in the place one million position

B. The digit 3 is in the place tens position

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Hi my lil bunny!

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Answer =   [tex]\boxed {x - 2}[/tex]

[tex]3x +1(2x-1)2-1(6x)[/tex]

= [tex]\boxed {3x + 1 . ( 2x - 1 ) . 2 - 1 (6x) = x - 2}[/tex]

Steps :

[tex]3x + 1 . (2x - 1) . 2 - 1 . (6x)[/tex]

Remove the parentheses : [tex](a) = a[/tex]

[tex]= 3x + 1 * (2x- 1) * 2 - 1 * 6x[/tex]

Multiply the numbers : [tex]1 * 2 = 2[/tex]

[tex]= 3x + 2 ( 2x - 1 ) * 6x[/tex]

Multiply the numbers : [tex]1 * 6 = 6[/tex]

[tex]= 3x + 2 ( 2x - 1 ) -6x[/tex]

Expand: [tex]2 (2x - 1) : 4x - 2[/tex]

[tex]2 ( 2x - 1 )[/tex]

Apply the distributive law : [tex]a (b - c) = ab - ac[/tex]

[tex]a = 2, b = 2x, c = 1 \\= 2 * 2x - 2 * 1[/tex]

Simplify [tex]2 * 2x - 2 * 1 : 4x - 2[/tex]

= [tex]= 4x - 2[/tex]

[tex]= 3x + 4x - 2 - 6x[/tex]

Simplify [tex]3x + 4x - 2 - 6x : x - 2[/tex]

= [tex]x - 2[/tex]

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Have a great day/night!

❀*May*❀