find the equation of the line containing the points shown​

Answer:

[tex]\boxed{\textsf{ The value of x is \textbf{ 8 + 6}$\sqrt{3 }$.}}[/tex]

Step-by-step explanation:

Here we are given a equation which we need today simplify and solve for x .The given equation to us is :-

[tex]\sf\implies \dfrac{1}{x {}^{2} - 3 } = \dfrac{ \sqrt{3} }{x + \sqrt{3} } - \dfrac{2}{ \sqrt{3} - x } [/tex]

Let's simplify the equation :-

[tex]\sf\implies \dfrac{1}{x {}^{2} - 3 } = \dfrac{ \sqrt{3} }{x + \sqrt{3} } - \dfrac{2}{ \sqrt{3} - x } \\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3}{x+\sqrt3}-\dfrac{2}{-(x-\sqrt3)}\\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3}{x+\sqrt3}+\dfrac{2}{x-\sqrt3}\\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3(x-\sqrt3)+2(x+\sqrt3)}{(x+\sqrt3)(x-\sqrt3)}\\\\\sf\implies \dfrac{1}{x^2-3}=\dfrac{\sqrt3x-3+2x+2\sqrt3}{x^2-3}\\\\\sf\implies 1=\sqrt3x-3+2x+2\sqrt3 \\\\\sf\implies \sqrt3x+2x = 4-2\sqrt3\\\\\sf\implies x(\sqrt3 +2)=4-2\sqrt3\\\\\sf\implies x =\dfrac{4-2\sqrt3}{\sqrt3+2}\\\\\sf\implies x =\dfrac{ (4-2\sqrt3)(\sqrt3-2)}{(\sqrt3+2)(\sqrt3-2)}\\\\\sf\implies x =\dfrac{-8-6\sqrt{3}}{3-4}\\\\\sf\implies \boxed{\pink{\sf x =8+6\sqrt3}}[/tex]

Answer:

total -70

Step-by-step explanation:

x =18

y=-28

Z = -60

An Arithmetic series: 14 + 6 + (–2) + (–10) + (–18) + (–26) + (–34)

The Total value is =  -70

x = 18

y = -28

Z = -60

An Arithmetic series: 14 + 6 + (–2) + (–10) + (–18) + (–26) + (–34)

1st an 2nd element difference is = 14 - 6 = 8

2nd and 3rd element difference is = - 6 - 2 = -8

3rd and 4th element difference is = - 2 + 10 = 8

4th and 5th element difference is = -10 + 18 = 8

The difference (x,y and z) is 8 and also it's negative because the series is lowering the previous value.

Now, Proof of x,y and z = - 8

14 - 8 = 6

6 - 8 = - 2

- 2 - 8 = - 10

- 10 - 8 = - 18

- 18 - 8 = - 26

-26 - 8 = -34

Therefore, The value is = total -70

x = 18

y = -28

Z = -60

Find more information about Arithmetic Series here:

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Answer:

That is an entire worksheet.  Also just download PhotoMath on your phone and it will give you the answers.

Step-by-step explanation: I'll get you started

1) 1

2) 2

3) 4

4)

5) 20

6) 1

7) 2

8) 20

Answer:

1. 1/2

2. 2/3

3. 4/7

4. 10/25

5. 20/40

6. 1/10

7. 2/6

8. 20/90

9. 27/36

10. 1/6

11. ?

12. 2/5

13. 2/3

14. 11/12

15. 17/25

16. 2/8

17. 6/7

18. 42/70

Step-by-step explanation:

Answer:

25 = 9y+3

Transposing (3) to the L.H.S.:

= 25-3 = 9y

= 22 = 9y

Transposing (9) to L.H.S.:

= 22÷9 = y

= 2.444444444444444.......................

= 2.44

Answer:

y=2.44......

Step-by-step explanation:

25 = 9y+3

Transposing (3) to the L.H.S.:

= 25-3 = 9y

= 22 = 9y

= 22÷9 = y

= 2.444444444444444.......................

= 2.44

Answer:

Andre  y=5x+100

Elena y=20x+10

the rate Elena is 20

the rate  Andre is 5

Step-by-step explanation:

Answer:

x =44

Step-by-step explanation:

180 - 86 - 50 = 44

Answer:

t - b >= e

Step-by-step explanation:

There are few actual necessities that a person actually needs in order to survive, everything else is actually a want and not a necessity. Such necessities include food, water, and rent. These can be represented as

Budget = b

We can use them in the following equality. While e would be representing the entertainment and t represents the total money he has.

t - b >= e

You can now plug in the actual values for t and b to find out how much you would have left for entertainment.

The circumference is 615.44.

The formula is

R = C/(pi)*2

( 2 is square)

( I can't find the pi symbol sorry)

So meaning  in simple term, it would look like this

R = 615.44/2*(3.14)

615.44/6.28

then we divide which we will get 98

ANSWER: 98

Given:

The radical expression is

[tex]\pm \sqrt{-22}[/tex]

To find:

The simplified form of the given expression by using the imaginary unit i.

Solution:

We have,

[tex]\pm \sqrt{-22}[/tex]

It can be written as

[tex]\pm \sqrt{-22}=\pm \sqrt{22}\sqrt{-1}[/tex]       [tex][\because \sqrt{ab}=\sqrt{a}\sqrt{b}][/tex]

[tex]\pm \sqrt{-22}=\pm \sqrt{22}i[/tex]      [tex][\because \sqrt{-1}=i][/tex]

Therefore, [tex]\pm \sqrt{-22}=\pm \sqrt{22}i[/tex].

Answer:

Included in the picture attached

Step-by-step explanation:

Desmos graphing calculator

Answer:

y=  5/3 - 2x/3

Step-by-step explanation:

Answer:

7:04 p.m.

Step-by-step explanation:

Answer:

7:04

Step-by-step explanation

12-8 + 4

5:52 + 0:08 = 6:00

6:00 + 1:00 + 7:00

7:00 + 0.04 = 7:04

Answer:

(x - 10, y - 13)

Step-by-step explanation:

We have two shapes on a graph and the question is asking for the translation of rhombus QRST to rhombus Q'R'S'T.

Looking at the graph we can see that not only does the rhombus move backwards, but also downward, this indicates that our answers will be in a subtracting symbol.

So all we have to do is count the amount of spaces rhombus QRST went to get to rhombus Q'R'S'T

Answer:

3(14+19)

Step-by-step explanation:

you have to distribute the 3, so multiply it by both the 14 and the 19.

Answer:

20 gallons of 15% solution must be mixed with 5 gallons of 40% solution.

Step-by-step explanation:

40% of 5 gallons is 2 gallons of sugar

x represents the number of gallons of solution to be added.

15% of x is sugar.

The total amount of sugar must be equal to 20% of the final mixture.

The end mixture will be x + 5 gallons

Change percent to decimal for the equation:

.2(x +5) = .15x +2

.2x +1 = .15x +2

.2x - .15x = 2 -1

.05x = 1

x = 20

Check:

.2(20 +5) = .15(20) +2

.2(25) = 3 + 2

5 = 5 true

This means that adding 20 gallons of the 15% solution is adding 3 gallons of sugar [along with 17 gallons of water] to the 2 gallons of sugar in the original mixture.

20% of the 25 gallons, 5 gallons, of the final mixture is sugar. 80% [ 3+17 = 20 gallons] is water.

Answer:

269gallons

Step-by-step explanation:

115/6=19.16

19.16*14=268.33 or round up to 269

Answer: c

Step-by-step explanation: start at -4 then add 7 to that then .5

Answer:

Day 1=15 Day 2=30 Day 3=45 Day 4= 60 Day 5= 75. The expression is N+15

Step-by-step explanation:

The complete table:

Days                  1    2     3    4     5

Total samples  15  30  45  60   75

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of bacteria samples analyze each day = 15

The equation for the number of bacteria analyzes after x days.

B = 15x

Now,

x = 1, B = 15

x = 2, B = 30

x = 3, B = 45

x = 4, B = 60

x = 5, B = 75

Thus,

Days                  1    2     3    4     5

Total samples  15  30  45  60   75

Learn more about expressions here:

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Answer:

30/90 or 1/3

Step-by-step explanation:

This is because we know that 6+4=10. So we know the odds of drawing a white marble first is 6/10. And if we draw one without replacing it. This makes the second time 5/9 for white and 4/9 for black. We can then multiply 6/10 by 5/9 and get 30/90 which is equal to 1/3.

Hope this helps!

Answer:

1/3

Step-by-step explanation:

P=6/10 ×5/9=30/90=1/3

Answer:

number 2 + 4i is one of the root to the quadratic equation x 2 + bx + c = 0, where b and c are real numbers. a) Find b and c b)

Step-by-step explanation:

Answer:

While 3/4 and 6/8 are equivalent fractions, 3/4 and 6/8 of a pizza could represent different amounts.

Answer:

14 hours

Step-by-step explanation:

Old plan :

Initial fee =. $29

Hourly fee = $2.50

New plan :

Initial fee = $19

Hourly fee = 3.25

Let number of hours = x

When new plan will be more expensive than old plan :

19 + 3.25x > 29 + 2.50x

3.25x - 2.50x > 29 - 19

0.75x > 10

x > 10 / 0.75

x > 13.3333

After 14 hours

Answer:

Step-by-step explanation:

Prove that The two triangles are congruent

Find the measure of angle C

Given

Opposite angles are corresponding to the sides.

Therefore the angles opposite to congruent sides are also congruent:

This question is incomplete, the complete question is;

Refer to the Exhibit Student Grades. A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11.

The professor has informed the class that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A

Answer:

the minimum score needed to receive a grade of A is 88.51

Step-by-step explanation:

Given the data in the question;

Let x represent the grades of the students that were normally distributed with mean μ = 73 and standard deviation σ = 11.

so, The professor has informed the class that 7.93 percent of her students received grades of A

the minimum score needed to receive a grade of A will be:

P( X > x ) = 7.93 %

P( X > x ) = 0.0793

1  - P( X ≤ x ) = 0.0793

- P( X ≤ x ) = 0.0793 - 1

- P( X ≤ x ) = - 0.9207

P( X ≤ x ) = 0.9207

⇒ P( X-μ/σ ≤ x-μ/σ ) = 0.9207

so, x-μ/σ = InvNormal( 0.9207 )  

x-μ/σ = 1.41

(x - 73) / 11 = 1.41

(x - 73) = 1.41 × 11

(x - 73)  = 15.51

x = 15.51 + 73

x = 88.51

Therefore, the minimum score needed to receive a grade of A is 88.51