How many integers between 50 000 and 60 000 are squares of integers?

Answers

Answer 1

Perfect squares are the squares of integers

There are 990 integers between 50000 and 60000 that are squares of integers

There are 1000 perfect squares, and 100 perfect cubes between 1 and 1000000

This is because:

[tex]\mathbf{100000 = 1000^2 = 100^3}[/tex]

Rewrite as:

[tex]\mathbf{100000 = x^2 = y^3}[/tex]

Where x lies between 1 and 1000, and y lies between 1 and 100.

If y^3 is a perfect square, then y is a perfect square

List out the perfect squares from 1 to 1000

[tex]\mathbf{y = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100}[/tex]

Take the cube of these numbers

[tex]\mathbf{y^3 = 1^3, 4^3, 9^3, 16^3, 25^3, 36^3, 49^3, 64^3, 81^3, 100^3}[/tex]

[tex]\mathbf{y^3 = 1, 64, 729, 4096, 15625, 46656, 117649, 262144, 531441, 1000000}[/tex]

So, the count of numbers that are perfect squares and perfect cubes between 1 and 1000000 is 10.

The count of integers between 50000 and 60000 that are squares of integers is:

[tex]\mathbf{n = x -10}[/tex]

Substitute 1000 for x

[tex]\mathbf{n = 1000 -10}[/tex]

[tex]\mathbf{n = 990}[/tex]

Hence, there are 990 integers between 50000 and 60000 that are squares of integers

Read more about perfect squares at:

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Related Questions

What is the volume of an oblique square pyramid with base edges 25 ft and height 24ft?
A. 5,000 ft^3
B. 7,500 ft^3
C. 10,000 ft^3
D. 15,000 ft^3

Answers

Check the picture below.

Find the measure of

Answers

Answer:

∠ A = 43°

Step-by-step explanation:

Since the triangles are similar then corresponding angles are congruent, so

∠ B = ∠ T  = 55°

The sum of the 3 angles in a triangle = 180°

sum the 3 angles in Δ ABC and equate to 180

2x - 9 + 3x + 4 + 55 = 180 , that is

5x + 50 = 180 ( subtract 50 from both sides )

5x = 130 ( divide both sides by 5 )

x = 26

Then

∠ A = 2x - 9 = 2(26) - 9 = 52 - 9 = 43°

Solve the problem using a system of equations: The difference of the squares of two numbers is 15. The difference of twice the square of the first number and the square of the second number is 30. Find the numbers.
(__,__),(__,__)

Answers

The numbers which hold true for the situation modelled in the task content are; (-√15, 0) and (+√15, 0).

Which numbers hold true for the situation?

The system of equations which model the situation is;

x²- y² = 15

2x² - y² = 30.

Hence, by subtracting equation 1 from 2; we have;

x² = 15

x = ±√15.

and hence by substitution; the value of y is;

(√15)² + y = 15

y = 0.

Hence, the required values of the numbers are;

(-√15, 0) and (+√15, 0).

Read more on system of equations;

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4. A) Joe types 200 words in 12 minutes, how many does he type per minute?

Answers

Answer:

Step-by-step explanation:

So, we divide 1200 by 25 to find out how many words per minute he types.

1200 / 25 = 48

So, he types 48 words per minute.

Now, we multiply this by 45 to find out how many words he can type in 45 minutes.

48 x 45 = 2,160

Joseph can type 2,160 words in 45 minutes!

Which expression has the same value as − 4 1/5 + 9 3/5?

Answers

Answer:

27 / 5

Step-by-step explanation:

− 4 1/5 + 9 3/5 = 5.4 or 5 2/5

27/5 = 5.4 or 5 2/5

Simplify (-2)^4(-2) =
(3st)^2 =
7^0=

Answers

Answer:

-32

Step-by-step explanation:

The lines shown below are parallel. If the green line has a slope of 5, what is
the slope of the red line?
A. 5
O B. //
1
C.
091
D. -5

Answers

Answer:

its C. 1/5

Mark me BRAINLIEST

Help please Its about functions

Answers

I only got the first one, but i hope this helped :/

A father wants to buy a total of five milk drinks for his son and spend $7.95. Eggnog costs $1.55 and a peanut punch costs $1.65. Determine the number of each milk drink bought​

Answers

Answer:

2

Step-by-step explanation:

$ 1.55 + $1.65 = $3.11

the budget is $7.95

$7.95 ÷ $3.11 = 2.5 but since you can't get half a milk it's 2

Write an equation in slope-intercept form that has a y-intercept at (0, -3) and also contains the point
(4, 5).
Write your answer as an equation with numbers, letters, and symbols - no spaces.

Answers

Answer: y = (1/2)x + 3

Step-by-step explanation:

The equation in slope-intercept form  y = (1/2)x+3

How do you write an equation in slope-intercept?

To determine how to write an equation from two points, we must determine the value of the slope and the yy-intercept. First, we will calculate the slope. This will be the value of mm in the slope-intercept form equation:

y=mx+b

Let’s answer the question, “What is the slope-intercept form of a line going through the points (1,5)(1,5) and (-4,7)(−4,7)?”

Remember, to calculate the slope we use the equation:

y2-y1/x2-x1

Therefore, the slope of the line is

-2/5

We can substitute

-2/5 for m.

To learn more about equation in slope-intercept refer to:

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please give explanation and answers for brainlist

Answers

Answer:

y - (-1) = 6/15 (x - 4)

(y + 1) 15 = 6 (x - 4)

15y + 15 = 6x - 24

15y = 6x -24 -15

15y = 6x - 39

Step-by-step explanation:

try hard

Helps plz and no links

Answers

Answer:

1+2+3- -9+236359

Step-by-step explanation:

Answer:

y=-4x-7

Step-by-step explanation:

if you use the slope formula, y2-y1 over x2-x1 using any two points from the grid, you get a slope of -4.

if you use the slope intercept form, y=mx+b, and plug in y, m the slope, and x, you get -3=-4(-1)+b

if you solve that, you get -3=4+b

and if you isolate 4 by subtracing 4 from both sides, b=-7.

then you plug slope and y intercept into formula, and get y=-4x+b

can find anything to answer this

Answers

Answer:

where?

Step-by-step explanation:

maybe I can help to your question

Answer: C
Explain bc MN is not midsegment

If f(x)=8-5x, what is f(4p+3)

Answers

Answer:

-20p - 7

Step-by-step explanation:

f(x)=8-5x

f(4p+3) = 8 - 5(4p + 3)

= 8 - 20p - 15

= -20p -7

la quinta parte de 20​

Answers

Answer:

4

Step-by-step explanation:

20/5 = 4

Solve for the missing variable

Answers

Answer:

x = 7.5.

The two lines on the side of the triangle in the screenshot show us that the two lines made are the same length. So the difference between the first two values, i.e. 22.3 and 14.9 is the same difference between 14.9 and x.

Step-by-step explanation:

hope this helps. . .<3

good luck!    uωu

Answer:

Step-by-step explanation:

14.9 is the middle value of x and 22.3. So your formula looks like this.

(x + 22.3) / 2 = 14.9          Multiply both sides by 2

2(x + 22.3) / 2 = 14.9*2    Remove the brackets.

x + 22.3   = 29.8              Subtract 22.3 from both sides

x = 29.8 - 22.3                

x = 7.5

Use a calculator to solve the following equation for θ on the interval [−π2,π2]. csc(θ)=−5 Select all correct answers.

Answers

[tex]csc(\theta )=-5\qquad -\frac{\pi }{2}<\theta <\frac{\pi }{2} \\\\[-0.35em] ~\dotfill\\\\ csc(\theta )=-5\implies \stackrel{\textit{using the reciprocal of } csc(\theta )}{\cfrac{1}{sin(\theta )}=-5}\implies \cfrac{1}{-5}=sin(\theta ) \\\\\\ sin^{-1}\left( -\frac{1}{5} \right) = sin^{-1}[sin(\theta )]\implies sin^{-1}\left( -\frac{1}{5} \right) = \theta \implies \begin{array}{llll} -11.54^o\\ ~\hfill or\\ 348.46^o \end{array} \approx \theta[/tex]

The value of θ is -11.54⁰ or 348.86⁰ for cosec(θ)=−5 for interval  [−π/2,π/2].

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

cosec(θ)=−5 for interval [−π/2,π/2].

We know Sinθ=1/cosecθ

Cosecθ=1/sinθ

Now cosec(θ)=−5

-5=1/sinθ

sinθ=-1/5

θ=sin⁻¹(1/5)

θ=sin⁻¹(1/5)

θ=-11.54⁰ or 348.86⁰

Hence the value of θ is -11.54⁰ or 348.86⁰ for cosec(θ)=−5 for interval  [−π/2,π/2].

To learn more on trigonometry click:

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9/10 - _ = 1/5 mathematics

Answers

Answer:

x=7/10

Step-by-step explanation:

1/5=2/10

9/10-       =2/10

Substitute the blank with X

9/10-  X  =2/10

x=7/10

Answer:

7/10

Step-by-step explanation:

9/10 - _ = 1/5

Let's represent the unknown as x

Therefore,

9/10 - x = 1/5

9/10 - 1/5 = x

x = 9/10 - 1/5 = 7/10

i will mark as brainliest PLZ HELPPPPPP

Answers

A because The area of the pen = 10*6 = 60 sq. ft.
we know square gives maximum area.
so 8*8 =64
He could have gained 4 sq.ft

The hypotenuse of a right triangle is three times the length of one of its legs. The length of the other leg is four feet. Find the lengths of the three sides of the triangle. For non-integer answer(s), round your answer(s) to the nearest tenth.
___feet, ___feet, ___feet

Answers

then then then

okokokokokokok

Hello. I am trying to figure out how to convert 17cm2 or cm squared to in2 (in squared)

Answers

Answer:

1 cm2 = 0.155 in2; 1 in2 = 6.4516 cm2

Step-by-step explanation:

Welcome, Brainlest Please?

can someone please help!!!

Answers

Answers:

System 1:  x = 3 and y = -5System 2: x = 1 and y = 2

==========================================================

Explanation:

For now, let's focus on system 1.

We have identical copies of "2y" in each equation, which means that if we were to subtract the equations straight down, then the y terms cancel out. That allows us to solve for x.

The x terms subtract to 7x-x = 6xThe y terms subtract to 0 and go awayThe right hand sides subtract to 11 minus (-7) = 11-(-7) = 11+7 = 18

After doing those subtractions, we have the new equation 6x = 18 which solves to x = 3. Divide both sides by 6 to isolate x.

Once we know x, we can find out y.

7x+2y = 11

7(3)+2y = 11

21+2y = 11

2y = 11-21

2y = -10

y = -10/2

y = -5

or we can say

x+2y = -7

3+2y = -7

2y = -7-3

2y = -10

y = -10/2

y = -5

We should lead to the same y value either way. This helps confirm we have the correct x value.

Overall, the solution to system 1 is (x,y) = (3, -5)

----------------------------

Now onto system 2.

Unfortunately, we don't have identical y terms this time. But what we can do is double everything in the second equation to go from -x+y = 1 to -2x+2y = 2.

The new equivalent system is

[tex]\begin{cases}7x+2y = 11\\-2x+2y = 2\end{cases}[/tex]

Now we have the same situation as before: Subtract straight down, solve for x.

The x terms subtract to 7x-(-2x) = 7x+2x = 9xThe y terms go away when subtractingThe right hand sides subtract to 11-2 = 9

So we have 9x = 9 and that solves to x = 1.

We'll use this x to find the y value.

7x+2y = 11

7(1)+2y = 11

7+2y = 11

2y = 11-7

2y = 4

y = 4/2

y = 2

Or you could pick on the second equation

-x+y = 1

-1+y = 1

y = 1+1

y = 2

What is the solution set for this inequality?
- 6x + 30 < -18
0x<-2
0x<&
Ox>-2
Ox>8

Answers

Answer:

x>8

Step-by-step explanation:

[tex]- 6x+ 30 < - 18 \\ - 6x < - 18 - 30 \\ - 6x < - 48 \\ \frac{ - 6x}{ - 6} < \frac{ - 48}{ - 6} \\ x > 8[/tex]

Whose statement is correct based on the expected value?

Answers

Step-by-step explanation:

only Hadley. and even that is not fully correct.

the expected value here gives us the overall most likely outcome of the scenario when throwing 2 balls.

and not ball by ball. and not directly a probability.

like rolling a die : the expected value of rolling a 6 in 6 attempts is 1 due to the individual roll probability of 1/6.

but the probabilty is NOT 1 or 100% (a guaranteed 6 in 6 attempts).

and that brings me to my concern with Hadley's statement. it says with conviction "the player will make ...". no, only "... will likely make ..." or "... on average".

Answer:

Step-by-step explanation:

neither statement is correct. right answer on khan

When the input of the function is -1, What is the output of the function?

Answers

Answer:

2

Step-by-step explanation:

The graph clearly shows that when x = -1, y = 2.

Thus, the output of this function is 2.

Dr. Brennen donated 49 duffle bags of First-aid kits to the Bahamas Red Cross. Each bag
contained 604 First-aid kits. How many First-aid kits did the Red Cross receive in all?

Answers

Answer:

29,596 first aid kits

Step-by-step explanation:

This is a multiplication problem. There are 604 kits in each duffle bag, and there are 49 duffle bags, so the equation is 604 x 49.

In the first step, we multiply 604 by 9 to get 5,436. In the second, we multiply 604 by 40 to get 25,160. Then we add the two numbers together to get 29,596.

Hope this helped :)


Find the equation for the line that passes through ( – 7,5) that has slope 3.

Answers

☆Answer : (X1, Y1) = (-7, 5)m = 3

y - Y1 = m(x - X1)

y - 5 = 3(x - (-7))

y - 5 = 3(x + 7)

y - 5 = 3x + 21

y - 5 - 3x - 21 = 0

y - 26 - 3x = 0

-3x + y - 26 = 0

while drinking 8 glasses of water a day is good for your health if each glass of water is equivalent to 148 ml how many liters of water you need to consume everyday​

Answers

Answer:

1184ml

Step-by-step explanation:

8x148= 1184

If a ≠ 0 and b ≠ 0 which of the following is equivalent to 2/3a 1/b?

Answers

Answer:

58

Step-by-step explanation:

100 points! show work or else i report

A certain microwave requires 1200 watts. How much would it cost to run the microwave for a total of 30 minutes (defrosting chicken) at a cost of $0.20 per kilowatt hour?

Answers

[tex]\boxed{\sf E=Pt}[/tex]

E is energy

P is power

t is time in hours

E=1200(0.5h)E=600WhE=0.6Kwh

Cost

0.6(0.2)$0.12

Answer:

$0.12

Step-by-step explanation:

Conversions

  1000 watts = 1 kilowatt-hour
  ⇒ 1200 watts = 1.2 kilowatt-hour

  60 minutes = 1 hour
  ⇒ 30 minutes = 0.5 hour

A microwave requiring 1200 watts will use 1.2 kilowatts per hour.

If the microwave is used for a total of 30 minutes, it will use:

⇒ 1.2 × 0.5 =  0.6 kWh

If the cost is $0.20 per kWh, the cost of running the 1200 watt microwave for 30 minutes is:

⇒ 0.6 × $0.20 = $0.12

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