Show that
[tex]\sqrt[3]{3}+\sqrt{2}\ \textgreater \ \sqrt[3]{9}\ \textgreater \ \sqrt[4]{13}[/tex]
[tex]\;[/tex]
[tex]\Large\textrm{Note}[/tex]
1. Use of calculator is not allowed.
2. Use of approximated value is not allowed.​

Answers

Answer 1

Answer:

See below

Step-by-step explanation:

Use same power to compare the values

Prove the first part:

[tex]\sqrt[3]{3}+\sqrt{2} >\sqrt[3]{9}[/tex][tex]\sqrt[6]{3^2}+\sqrt[6]{2^3} >\sqrt[6]{9^2}[/tex][tex]\sqrt[6]{9}+\sqrt[6]{8} >\sqrt[6]{81}[/tex][tex]\sqrt[6]{9}+\sqrt[6]{8}> \sqrt[6]{8}+\sqrt[6]{8}=2\sqrt[6]{8}=\sqrt[6]{8*64} =\sqrt[6]{512} >\sqrt[6]{81}[/tex][tex]512 > 81[/tex]

Prove the second part:

[tex]\sqrt[3]{9} >\sqrt[4]{13}[/tex][tex]\sqrt[12]{9^4} >\sqrt[12]{13^3}[/tex][tex]\sqrt[12]{6561} >\sqrt[12]{2197}[/tex][tex]6561 > 2197[/tex]

Related Questions

Sonia sells stuffed animals, She sells a stuffed dog for $25.10, and the sales tax is 4% of the sale price. About
how much is the sales tax on the dog?
A. $0.10
B. $1.80
C. $2.25
D. $1.00

Answers

Answer:

$1.004 so rounded it would be Answer D ($1.00)

Step-by-step explanation:

You multiply $25.10 by the decimal form of 4 percent, which gives you the tax.

25.10(.04)=1.004

1.004 is the tax, but with the way currency work, cents do not go to the thousandths place , so you round it to $1.00.

Incase you woudl also like to know, if you add that 1 dollar to the original price you get teh total price. which woudl be $26.10.

Guys help I literally don’t know how to do this

Answers

Answer:

Ok, so to find the volume of a sphere, the volume is 4/3 (3.14 which is pie) times the radius cubed so r^3

so the radius of this sphere is 2 because 4-2=2

Step-by-step explanation:

so now we do 4/3 times 3.14 times 2^3 power=

now first we multiply 4/3 times 2 to the 3rd power bc we dont need to multiply pie (3.14) your answer would be 10.66667 so its 10.66667 pie (3.14) so round 10.66667 it would just be 10.7 because the 7 round up the 6 to a 7. Hope this helps!

2 2/3 x 3 3/8=?
Please help me

Answers

Answer:

Step-by-step explanation:

2 2/3 = 8/3

3 3/8 = 27/8

8/3 * 27/8 = 216/24

= 9

One equation in a system of equations with no solution is y=-20 +5.
Which equation could be the second equation in the system?

Answers

Answer:

the answerr is i9 dont know haha bum

Step-by-step explanation:

hahay

Answer:

B. 2x + y = 8

Step-by-step explanation:

y = -2x + 5 matches with 2x + y = 8, as they have same slope of "-2".

There you go, it is the second equation with y = -2x + 5.

Solve for x in the diagram below.

Answers

Answer:

x = 12

Step-by-step explanation:

(6x-2) + 20 = 90

6x-2 = 70

6x = 72

72 / 6 = 12

x = 12

The area of a rectangle is 17 1/2 square and it’s shorter side is 3 1/2 in. Draw a diagram that shows this information. What is the length of the longer side.?

Answers

Answer:

The area of a rectangle is 17 1/2 in and it’s shorter side is 3 1/2in.draw a diagram that shows this information. What is the length of the longer side

Step-by-step explanation:

Find the volume of a prism whose area of base is 15 cm2 and hight is 10 cm

Answers

Answer:

Step-by-step explanation:

V = Bh

V = 15(10)

V = 150 cm3

Find the missing dimension of the triangle. Area is 5cm squared and the base is 4cm. what is the height.​

Answers

Answer:

  2.5 cm

Step-by-step explanation:

Put the given values into the area formula, and solve for height.

  A = 1/2bh

  5 cm² = 1/2(4 cm)h . . . . . . . . . . . . . fill in the values

  (5 cm²)/(2 cm) = h = 2.5 cm . . . . . divide by the coefficient of h

The height is 2.5 cm.

9. Rewrite in order from least to greatest. 13%, 16/100 01/5, 0.15, 1/10​

Answers

Answer:

1/10, 13%, 0.15, 16/100, 1/5

Step-by-step explanation:

Given the following question:

13%, 16/100, 1/5, 0.15, and 1/10

In order to find the answer to this question we can rewrite all the following fractions/percent into decimals and then compare.

[tex]\frac{16}{100} =16\div100=0.16[/tex]
[tex]\frac{1}{5} =1\div5=0.2[/tex]
[tex]\frac{1}{10} =1\div10=0.1[/tex]
[tex]13=0.13[/tex]

0.13, 0.16, 0.15, 0.2, and 0.1
0.1, 0.13, 0.15, 0.16, 0.2

1/10, 13%, 0.15, 16/100, 1/5

Hope this helps.

Please Help quick This is Algebra Thank you!

Answers

i think it is 2x


Explanation: if you multiply 2x by 2x you will get 4x^2

WILL MARK BRAINLIST
Find 24% of 450.

Answers

Answer:

108

Step-by-step explanation:

450*0.24

There are 30 students in Mrs. Bristow‘s class. 20% of the students receive a gold ticket on the last quiz. How many students receive a golden ticket?

Answers

Answer:

6

Step-by-step explanation:

20% of 30 is 6. You can figure this out because 100 divided by 20 is 5, so you do 30 divided by 5, which is 6

20% is 1/5 1/5 x 30/1 = 30/5 = 6 6 is ur answer

Write the expression using exponents 5.2 • y • y • y =

Answers

Answer:

5.2y^3

Step-by-step explanation:

There are 3 y's which can be presented as y^3

5.2 times y^3 = 5.2y^3

( By the way, " ^ " is a square root sign )

I do not understand this can y’all help me

Answers

n=3

Step-by-step explanation:

24=3n-15

9=3n

3=n

Answer:

n = 13

Step-by-step explanation:

24 = 3(n - 5)

divide each side by 3

8 = n - 5

add 5 to each side

13 = n

check your work

24 = 3(13 - 5)

24 = 3(8)

24 = 24

30. A store company is going to close one of its two stores and combine all the inventory from both stores. The polynomials below represent the inventory in each store. Which expression represents the combined inventory of the two stores? ​

Answers

Answer:

A

Step-by-step explanation:

hope this helps :)

Solve equation by using the quadratic formula.
9 x squared + 7 x = 0

a.
x = StartFraction 7 Over 9 EndFraction, 0
c.
x = 0
b.
x = negative StartFraction 7 Over 9 EndFraction, 0
d.
x = plus-or-minus StartFraction 7 Over 9 EndFraction

Answers

Answer: 1:  x=3, x=1

2:  x= -5

3:  There are 2 real solutions.

4:  There are 2 real solutions.

5:  There are no real solutions.

6.  There is 1 real solution.

7.  

8.  x= -6, x = -2

9.  x = -1/6, x=1

10.  

Explanation:

1.  The quadratic formula is

Substituting our known information we have:

2.  Rewriting the quadratic in standard form we have x²+10x-25=0. Substituting this into the quadratic formula gives us:

3.  The discriminant is b²-4ac.  For this problem, that is 20²-4(-4)(25)=400--400=800.  Since this is greater than 0, there are 2 real solutions.

4.  The discriminant in this problem is 7²-4(2)(-15)=49--120=49+120=169.  This is greater than 0, so there are 2 real solutions.

5.  The discriminant in this problem is 1²-4(-2)(-28)=1-224=-223.  Since this is less than 0, there are no real solutions.

6.  If the discriminant of a quadratic is 0, then by definition there is 1 real solution.

7.  Rewriting the quadratic we have 3x²-4x-2=0.  Using the quadratic formula we have:

8.  Factoring this trinomial we want factors of 12 that sum to 8.  6*2 = 12 and 6+2=8, so those are our factors.  This gives us:

(x+6)(x+2)=0

Using the zero product property we know that either x+6=0 or x+2=0.  Solving these equations we get x= -6 or x= -2.

9.  Factoring this trinomial we want factors of 6(-1)=-6 that sum to -5.  (-6)(1)=-6 and -6+1=-5, so this is how we "split up" the x term:

6x²-6x+1x-1=0

We group together the first two and the last two terms:

(6x²-6x)+(1x-1)=0

Factor the GCF out of each group.  In the first group, that is 6x:

6x(x-1)+(1x-1)=0

In the second group, the GCF is 1:

6x(x-1)+1(x-1)=0

Both terms have a factor of (x-1), so we can factor it out:

(x-1)(6x+1)=0

Using the zero product property, we know either x-1=0 or 6x+1=0.  Solving these equations we get x=1 or x=-1/6.

10.  Substituting our information into the quadratic formula we get:

Step-by-step explanation:

60 POINTS PLEASEEEEEEEEEEE

Answers

Answer:

It is B. (0,1)

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

a

Factor out a -5 of 2x-5

Answers

Answer:

2

a

x

5

a

10

x

+

25

Step-by-step explanation:

Select the sequences that are geometric. 18, 36, 54, 72, … 4. 1, 8. 2, 16. 4, 32. 8, … –7, 14, –28, 56, … 980, 784, 627. 2, 501. 76, … 5, 2, –1, –4, ….

Answers

Answer:

18, 36, 54, 72

Step-by-step explanation:

As that sequence is common in the table of 18.

A.T.Q

18 x 1 = 18

18 x 2 = 36

18 x 3 = 54

18 x 4 = 72

Correct me, if I am wrong :)

Have a great day!

Thanks!

Group like term’s please hurry.

Answers

Answer:

Step-by-step [tex]5x-4x =x \\4x^{2} -x^{2}=3x^{2} \\-24+11=-13\\3x^{2} +x-13[/tex]

Answer:

x^5 + 151x -264

Step-by-step explanation:

See the attached page.

Tarantulas are one of the largest spiders on Earth. A
tarantula can grow to be about 6.8 centimeters long.
A spitting spider can grow to be about 0.9 centimeters long.
About how much longer are the largest tarantulas than the
largest spitting spiders?

Answers

Tarantulas are 5.9 centimeters longer.

Graph 0.04x+0.02y=0.08.

Answers

Answer:

help me please

Step-by-step explanation:

pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls pls

Estimate the unit rate.
283 students in 11 classes

Answers

Answer:

So estimate.

Really depends on what needs to be estimated, the answer or the overall equation.
So doing the real one first.
283/11 = 25 8/11

You can’t have “part” of a student so rounding this you can go up since 8 is more then half of 11

So 26 students

If you were to round the overall equation then you’d get
280 / 10 which is 28 students per class

So two options.

You started the trail with 550lbs. of food.

You now have 232lbs. of food.

What percentage of your starting
amount do you have left?

Answers

Answer:

42%

Step-by-step explanation:

232 divided by 550= 0.42

0.42=42%

Written as a rate, 32 miles in 8 hours would be ____ miles per hour.

Answers

Answer:

4 mph

Step-by-step explanation:

If you divided 32 by 8 you get 4.

Please, help me. Thanks.
Subject: Hypothesis testing and margin of errors

Answers

Answer:

See below

Step-by-step explanation:

Problem 4

[tex]H_0:\mu=145\\H_a:\mu>145[/tex]

The null hypothesis, [tex]H_0[/tex], comes from the fact that the nurse initially thinks that the average height of 7th graders is equal to 145 cm.

The alternative hypothesis, [tex]H_a[/tex], comes from the fact that the average height may be greater than 145 cm since the nurse measured the average height to be 147 cm from the random sample.

Problem 5

[tex]H_0:\mu\geq273\\H_a:\mu<273[/tex]

The null hypothesis, [tex]H_0[/tex], comes from the fact that the manufacturer initially thinks that the mean lifetime of a certain type of batteries is at least 273 hours.

The alternate hypothesis, [tex]H_a[/tex], comes from the fact that the sample taken may show that it's actually less given a sample mean of 270.5 hours.

Problem 6

The mass population data set would be most suitable because the average score of a test comes from all those who have taken the test while the sample is the class with 25 students. That sample represents the population of all those that have taken the test.

Problem 7

Because it would take a lot of time and money to check every single child in Africa, it would make the most sense to use the sample data set where your samples come from each village and those samples have the children from each village.

Problem 8

This is a population characteristic because the sample that Sarah took for the average number of children per family represents the entire population.

Problem 9

This is a sample characteristic because the size of the sample was clearly large, this was a study, and other claims made.

Find the minimum and maximum value for the function with the given domain interval

Answers

Step-by-step explanation:

1) the suggested function in the condition is hyperbola, that means

[tex]w_{min}(x)=w_{min}(x_{max}) \ and \ w_{max}(x)=w_{max}(x_{min});[/tex]

2) using this

[tex]w_{min}(x)=w_{min}(\frac{1}{7} )=7;[/tex]

[tex]w_{max}(x)=w_{max}(\frac{1}{12})=12.[/tex]

45. You deposit $6000 into an account that earns 3.8% interest compounded annually.
Find the balance of the account after 7 years.

Answers

Answer: 7596

Step-by-step explanation:

3.8%x7=26.6%

6000x26.6%=1596

6000+1596=7596

During a clothing store’s Bargain Days, the regular price for T-shirts is discounted by $4. There is a state sales tax of 3.5%, and the $4 discount is applied before the sales tax is calculated.
A. Write an expression that shows the regular price r of a T-shirt minus the $4 discount.
B. Write a rule for the function p(r) that expresses the final price p of a T-shirt with the discount applied and sales tax added.
C. How much would you pay during Bargain Days for a shirt regularly priced at $15.50?
I will mark the first correct answer Brainliest!

Answers

Answer:

$4.00+0.035+$4.00=8.035=$8.35

Step-by-step explanation:

HELPPPPPPPPPP!!!!!!!

Answers

This might help if you have A then it will be a curved line which traces somewhat the line of the image good luck
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