Which expression has been solved with the following number line?

The value of [tex]n[/tex] such that [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex] is [tex]280[/tex].

In this question we need to find the root of the radical function [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex], which must be simplified by algebraic means.

First, we need to elevate each side of the expression by third power:

[tex]\left(\sqrt[3]{n+\sqrt{n^{2}+8}} + \sqrt[3]{n+\sqrt{n^{2}+8}} \right)^{3} = 512[/tex]

[tex]2\cdot n + 3\cdot \sqrt[3]{(n+\sqrt{n^{2}+8})^{2}\cdot (n-\sqrt{n^{2}+8})} + 3\cdot \sqrt[3]{(n-\sqrt{n^{2}+8})^{2}\cdot (n+\sqrt{n^{2}+8})} = 512[/tex]

[tex]2\cdot n -6\cdot (\sqrt[3]{n+\sqrt{n^{2}+8}} + \sqrt[3]{n-\sqrt{n^{2}+8}}) = 512[/tex]

[tex]2\cdot n - 6\cdot (8) = 512[/tex]

[tex]n = 280[/tex]

The value of [tex]n[/tex] such that [tex]\sqrt[3]{n+\sqrt{n^{2}+8}}+ \sqrt[3]{n-\sqrt{n^{2}+8}} = 8 [/tex] is [tex]280[/tex]. [tex]\blacksquare[/tex]

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should be 4

Step-by-step explanation:

Answer: (0,-5) or just -5

Step-by-step explanation:

gradient = change in y/change in x = (-7+15)/(1-5) = -2

y = -2x + c

-7 = -2 x 1 + c

c = -7 + 2 = -5

y intercept is (0, -5)

Answer:

x< 0

Step-by-step explanation:

[] An open circle means we will be using < or > and not ≤ or ≥ because the number is not included in the inequality

[] The direction of the inequality sign will go in the direction of the graph, so we will be using < as our number is less than the value given

[] Our final answer, assuming we can use x for this graph, is x < 0

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

Assuming the 2 in 3x2 is an exponent, then it is binomial.

Step-by-step explanation:

A binomial is an expression with two terms, in this case those two terms are 3x^2 and 5

Answer:

2.binomial

Step-by-step explanation:

3x2=1

5=2

so its a binomial

Answer:

11

Step-by-step explanation:

22x = 2 · 11 · x

33 = 3 · 11

common factor to both is 11

Answer:

Step-by-step explanation:

2.6*50=130 km

Answer:

I have a test on thursday toooooooo

Step-by-step explanation:

Step-by-step explanation:

Some expressions that are equivalent to this is: 1 - 1/5; 2 - 1  1/5; 3 - 2  1/5; etc.

Answer:

9.87

Step-by-step explanation:

6%= 0.06

0.06 +6.50 = 6.56

16.43 - 6.50 = 9.87

Answer:

80d:1t

Step-by-step explanation:

320mi:4h

80mi:1h

80d:1t

Every hour the train travels 80 miles

Answer: d = 80t

Step-by-step explanation:

320 miles / 4 hours = 80 mph

distance = rate * time

Answer:

Step-by-step explanation:

1) The slope of line with the coordinate points (10, 7) and (1, 2) is [tex]\frac{5}{9}[/tex].

2) The slope of line with the coordinate points (9, 9) and (1, 16) is [tex]-\frac{7}{8}[/tex].

3) The slope of line with the coordinate points (9, 3) and (2, 1) is [tex]\frac{2}{7}[/tex].

4) The slope of line with the coordinate points (8, 8) and (1, 2) is [tex]\frac{6}{7}[/tex].

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

From the given table, we have

1) The coordinate points are (10, 7) and (1, 2)

Here, slope [tex]=\frac{(2-7)}{(1-10)}[/tex]

[tex]=\frac{5}{9}[/tex]

2) The coordinate points are (9, 9) and (1, 16)

Here, slope [tex]=\frac{(16-9)}{(1-9)}[/tex]

[tex]=-\frac{7}{8}[/tex]

3) The coordinate points are (9, 3) and (2, 1)

Here, slope [tex]=\frac{(1-3)}{(2-9)}[/tex]

[tex]=\frac{2}{7}[/tex]

4) The coordinate points are (8, 8) and (1, 2)

Here, slope [tex]=\frac{(2-8)}{(1-8)}[/tex]

[tex]=\frac{6}{7}[/tex]

Therefore,

1) The slope of line with the coordinate points (10, 7) and (1, 2) is [tex]\frac{5}{9}[/tex].

2) The slope of line with the coordinate points (9, 9) and (1, 16) is [tex]-\frac{7}{8}[/tex].

3) The slope of line with the coordinate points (9, 3) and (2, 1) is [tex]\frac{2}{7}[/tex].

4) The slope of line with the coordinate points (8, 8) and (1, 2) is [tex]\frac{6}{7}[/tex].

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Answer:

18.7°F

Step-by-step explanation:

Difference

High temperature - low temperature

-3.6 - ( -22.3)

-3.6 + 22.3

= 18.7°F

Answer:

x = 29

Step-by-step explanation:

(x + 3) + (x - 1) + (x + 1) = 90

3x + 3 = 90

3x = 87

x = 29

Answer:

x = 29

Step-by-step explanation:

(x+3)+(x-1)+(x+1) = 90

90 = 3x +3

3x = 87

x = 29

Answer:

x = 2

Step-by-step explanation:

3x - 1 = 5

First, add 1 onto both sides. (When doing these type of questions you must do the inverse!)

3x = 6

Divide by 3 on both sides to get x.

x = 2

Hope this helps and I hope you have a good day!

Answer: 2

Step-by-step explanation: move constant to the right, calculate, divide both sides

Answer:

x <= -6.33333

(>= is greater than or equal to)

(<= is less than or equal to)

Step-by-step explanation:

7 - 3(x+5) >= 11

7 - 15 - 3x >= 11

-8 - 3x >= 11

-3x >= 19

x <= 19/-3

x <= -6.33333

please mark brainliest

The inequality 3(x + 5) - 7 ≥ 11 is satisfied for this x ≥ 1 condition.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Seven less than three times the sum of a number and 5 is at least 11.

The sum of the a number (x) and 5 is given as,

⇒ (x + 5)

Three times the sum of a number and 5 will be given as,

⇒ 3(x + 5)

Seven less than three times the sum of a number and 5 will be

⇒ 3(x + 5) - 7

Seven less than three times the sum of a number and 5 is at least 11. Then the inequality will be

3(x + 5) - 7 ≥ 11

Simplify the inequality, then the value of x will be

3(x + 5) ≥ 18

   x + 5 ≥ 6

         x ≥ 1

The inequality 3(x + 5) - 7 ≥ 11 is satisfied for this x ≥ 1 condition.

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Answer:

16%

Step-by-step explanation:

60+90=150 total students

14+10=24 left handed students

24/150= 0.16 or 16% of the population being left handed

Answer:

-2.

Step-by-step explanation:

-18/9 = -2.

36/-18 = -2.

We multiply by -2 to get the next number in the sequence.

Common ratio is -2.

#a

[tex]\\ \sf{:}\Rrightarrow 15x+30y\geqslant 150[/tex]

[tex]\\ \sf{:}\Rrightarrow x+y\geqslant 10[/tex]

And

[tex]\\ \sf{:}\Rrightarrow 0.5x+2y\geqslant 8[/tex]

#2

Attached

#3

Answer:

Third angle is [tex]130-7x[/tex]

Step-by-step explanation:

We have sum of angles is [tex]180^{0}[/tex]

Let the third angle be [tex]y[/tex]

Hence

[tex]5x+20+2x+30+y=180\\\\y=130-7x[/tex]

Third angle is [tex]130-7x[/tex]

Answer: 84.6

Step-by-step explanation: Based on the given conditions, formulate: 90 x 94%

Calculate the product or quotient: 84.6

get the result: 84.6

Hopefully that helps you! :)

Answer:

400m

Step-by-step explanation:

40% of some quantity = 0.4 times the quantity

We also know 1 km = 1000 m, therefore: 40% of 1000m = 0.4 * 1000m = 400m.

40% of 1 km in meters is 400 meters

Percentage simply means per 100. Percentage can be express as decimal or fraction.

For example 25% of 80 can be found as follows:

From the example, 25% of 80 is 20 .

Therefore, 40% of 1 km(m) can be found as follows:

Let's convert km to metres.

1000m = 1km

40% of 1000

40 / 100 × 1000 = 40000 / 100 = 400metres

Therefore, 40% of 1 km in meters is 400 meters

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Solution: ($29990)*(0.065) = $1949.35.

Answer: The sales tax is $1949.35 and the total cost is $29,990.00 + $1949.35 = $31,939.35.

Answer:

x = 7

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

undefined slope means that there's a vertical line through the x-axis.

And since the point is at (7,-9) you only need to focus on the value of x, which in this case, is 7.

[tex]4\sin^2 x - 3 = 3 \sin x\\\\\implies 4\sin^2 x -3 \sin x -3 =0\\\\\implies 4u^2 -3u -3 =0~~~~~~~~~~~~~~;[\text{Set} ~ \sin x = u]\\\\\implies u = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot 4 \cdot (-3)}}{2(4)}~~~~~~;[\text{Apply quadratic formula}]\\\\\\\implies u = \dfrac{3\pm\sqrt{57}}8\\\\\implies \sin x = \dfrac{3\pm\sqrt{57}}8~~~~~~;[\text{Substitute back}~ u = \sin x]\\\\\text{Now,}\\\\\sin x = \dfrac{3+\sqrt{57}}8\\\\\text{No solution for}~ x\in \mathbb{R} ~\text{Since}~ -1\leq \sin x \leq 1\\[/tex]

[tex]\sin x = \dfrac{3 - \sqrt{57}}8\\\\\implies x = n\pi + (-1)^n \sin^{-1} \left(\dfrac{3-\sqrt{57}}8\right)\\\\\\\text{ When n = 1,2 and}~ [0,2\pi]},\\\\\\x= \pi - \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)~ \text{and} ~x = 2\pi + \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)\\\\\text{In decimal,}\\\\x= 3.75~~~~ \text{and}~~~ x =5.68[/tex]

Based on the information given, the amount that he'll be expected to save in 30 years will be $83.

From the question given, since Buzz had $47 and had been saving for 17 years, the amount saved per year will be:

= $47/17

= $2.7647

Therefore, the amount that'll be saved in 30 years will be:

= 30 × $2.7647

= $82.941

= $83

The amount saved will be $83.

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