What is the smallest positive integer that will make x^x > 500,000? What
is the largest negative integer that will make x^(-x) >500000?

Answers

Answer 1

Answer:

For [tex]x^x > 500,000[/tex]  [tex]x=7[/tex]

For [tex]x^{(-x)} > 500,000[/tex]  [tex]x=-7[/tex]

Step-by-step explanation:

We need to find the smallest positive whole number that satisfies the inequality:

[tex]x^x > 500,000[/tex]

We tested with x = 6

[tex]6^6=46,656[/tex]

[tex]46,656 > 500,000[/tex]

Inequality is not met because [tex]46,656 < 500,000[/tex]

We test with the following integer x = 7

[tex]7^7=823,543[/tex]

[tex]823,543 > 500,000[/tex]

Then the smallest positive integer that will make [tex]x^x > 500,000[/tex] is 7

Inequality is met.

In the same way the largest negative integer that will make [tex]x^{(-x)} >500000[/tex] is [tex]x=-7[/tex] Beacuse [tex]7^{-(-7)}=823,543[/tex]

Answer 2

Answer:

Smallest positive integer value for [tex]x^x>5000[/tex] is,

x = 7,

Largest negative integer value for [tex] x^{-x} >500000[/tex] is,

x = -8

Step-by-step explanation:

If [tex]x^x>500000[/tex]

∵ If x is a positive integer then the possible values of x = 1, 2, 3, 4, 5, 6, 7.....

Case 1 : If x < 7,

[tex]x^x < 500000[/tex]

Case 2 : If x ≥ 7,

[tex]x^x > 500000[/tex]

Hence, smallest positive integer value of x is 7.

Now, if [tex]x^{-x}>500000[/tex]

∵ If x is negative integer then the possible value of x = -1, -2, -3, -4,.....

Case 1 : if x is odd negative integer,

[tex]x^{-x} < 50000[/tex]

eg : -1, -3, -5, -7,...

Case 2 : If x is even negative integer then there are further two cases,

(i)  x is more than or equal to -6,

[tex]x^{-x} < 500000[/tex]

eg x = -6, -4, -2,

(ii) x is less than -8,

[tex]x^{-x} > 50000[/tex]

eg : x = -10, -12, -14,...

Hence, the largest negative integer value that will make [tex]x^{-x}> 500000[/tex] is x = -8.


Related Questions

Which represents a perfect cube?
8.8.8
8+8+8
9.9.9.9
9+9+9+9+9

Answers

Answer:

8.8.8.

Step-by-step explanation:

8.8.8  = 8^3  = 512    Perfect cube.

8+8+8 =24

9.9.9.9 = 6561

9+9+9+9+9 = 45.

None of the others are perfect cubes.

Answer:A 8.8.8

Step-by-step explanation:i did the quiz

What is the greatest common factor of 8x and 40y

Answers

Answer:

The GCF of both the terms is 8....

Step-by-step explanation:

Given:

What is the greatest common factor of 8x and 40y.

The GCF of 8x and 40y is 8.

We will use the method of prime factorization to find the greatest common factor.

The prime factorization of 8x is:

8x = 2*2*2*x

The prime factorization of 40y is:

40y = 2*2*2*5*y

Therefore the common factors in both the terms are 2*2*2 which becomes 8

Thus the GCF of both the terms is 8....

Answer:

8

Step-by-step explanation:

7.
chef has 50 pounds of strip Zebra. The trim loss on the strip zebra is
40% and the cooking loss is 60% of the trimmed weight. How many
pounds of trimmed, cooked strip zebra will the chef have left to serve to
his customers?

Answers

Answer:

12 pounds

Step-by-step explanation:

After trimming:

50 − 0.40 (50) = 0.60 (50) = 30

After cooking:

30 − 0.60 (30) = 0.40 (30) = 12

What is the solution to 2x-8 <12?

Answers

Answer:

[tex]x < 10[/tex]

Step-by-step explanation:

[tex]2x - 8 < 12 \\ 2x - 8 + 8 < 12 + 8 \\( 2x < 20) \div 2 = x < 10[/tex]

x<10 is the solution to the inequality 2x - 8 < 12

To solve the inequality 2x - 8 < 12, you can follow these steps:

Add 8 to both sides of the inequality:

2x - 8 + 8 < 12 + 8

This simplifies to:

2x < 20

Divide both sides of the inequality by 2:

(2x)/2 < 20/2

This simplifies to:

x < 10

Therefore, the solution to the inequality 2x - 8 < 12 is x < 10.

Learn more about inequalities here:

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Which properties of equality are used to solve the following (in no particular order)?

3(x + 12) - 2 = 50

Addition Property of Equality


Subtraction Property of Equality


Division Property of Equality


Combine Like Terms


Distributive Property

Answers

All except combine like terms. Since you only have 1 variable.

Hope this helps.

r3t40

in 135 space shuttle missions, there were two failures. Based on these data, what's the probability of a successful mission?​

Answers

Answer:

98.518 repeating prercent

Step-by-step explanation:

2 out of 135 can also be written as 2/135

2 divided by 135 is 0.014814814814

that number is the percentage of failures

100% in decimal form is 1.00

1.00 subtracted by the percentage of failures is the percentage of successes

which is .98518518518, 518 repeating move the decimal over 2 and you got the percentage 98.518 repeating

Use the graph of f(x) to evaluate the following:

The average rate of change of f from x=0 to x=4 is_____.

Give your answer as an integer or reduced fraction

Answers

Answer:

-5/4

Step-by-step explanation:

The average rate of change of f from x=0 to x=4 is_____.

This means we are being asked to evaluate [tex]\frac{f(4)-f(0)}{4-0}[/tex].

To do this we will need to find f(0) and f(4).

f(0) means what y-coordinate corresponds to x=0 on the curve.  Find x=0, the curve is above there, go straight up and see  y=5 there.  This means f(0)=5.

f(4) means what y-coordinate corresponds to x=4 on the curve. Find x=4, then curve is above there, go straight up and see y=0 there.  This means f(4)=0.

So we have:

[tex]\frac{f(4)-f(0)}{4-0}=\frac{0-5}{4-0}=\frac{-5}{4}[/tex].

Which one of the following equations could describe the graph above?

Answers

What’s the graph above?

Answer: A. y=(1/2)^x+6

Step-by-step explanation: If this is the graph you’re talking about-

When “a” is less than one, the graph increases exponentially to the left. The smaller the value of a, the steeper the slope of the line.

There is a vertical shift up 6 as well

What is 7(x+6)=3(x+9)

Answers

Answer:

x= -3.75

Step-by-step explanation:

Answer:

x = -15/4

Step-by-step explanation:

7(x+6)=3(x+9)

Distribute

7x+42 = 3x+27

Subtract 3x from each side

7x-3x+42 = 3x-3x+27

4x +42 = 27

Subtract 42 from each side

4x+42-42 = 27-42

4x =-15

Divide each side by 4

4x/4 =-15/4

x = -15/4

Which expression is equivalent to log3(x + 4)?
log3 - log(x + 4)
log12 + logx
log3 + log(x + 4)
log 3/log(x+4)

Answers

Answer:

log[3(x+4)] is equal to log(3) + log(x + 4), which corresponds to choice number three.

Step-by-step explanation:

By the logarithm product rule, for two nonzero numbers [tex]a[/tex] and [tex]b[/tex],

[tex]\log{(a \cdot b)} = \log{(a)} + \log{(b)}[/tex].

Keep in mind that a logarithm can be split into two only if the logarithm contains the product or quotient of two numbers.

For example, [tex]3(x + 4)[/tex] is the number in the logarithm [tex]\log{[3(x + 4)]}[/tex]. Since [tex]3(x + 4)[/tex] is a product of the two numbers [tex]3[/tex] and [tex](x + 4)[/tex], the logarithm [tex]\log{[3(x + 4)]}[/tex] can be split into two. By the logarithm product rule,

[tex]\log{[3(x + 4)]} = \log{(3)} + \log{(x + 4)}[/tex].

However, [tex]\log{(x + 4)}[/tex] cannot be split into two since the number inside of it is a sum rather than a product. Hence choice number three is the answer to this question.

Answer:

c

Step-by-step explanation:

16. The dimensions of a window are 3x + 10 and 2x + 6. What is the area of the window?

Answers

Answer:

Answer in factored form (3x+10)(2x+6)

Answer in standard form 6x^2+38x+60 ( I bet you they want this answer)

Step-by-step explanation:

The assumption is this is a rectangle.

If you have the dimensions of a rectangle are L and W, then the area is equal to L times W.

So here we just need to multiply (3x+10) and (2x+6).

The answer in factored form is (3x+10)(2x+6).

I bet you they want the answer in standard form.

So let's use foil.

First: 3x(2x)=6x^2

Outer: 3x(6)=18x

Inner: 10(2x)=20x

Last: 10(6)=60

----------------Add up!

6x^2+38x+60

The area of the window is 3x² + 19x + 30

The dimension of the window are  3x + 10 and 2x + 6.

The area of the window can be calculated as follows;

area = lw

Therefore,

area = (3x + 10)(2x + 6)

area = 6x² + 18x + 20x + 60

area = 6x² + 38x + 60

area  = 3x² + 19x + 30

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[tex] - 3 + 5i \div - 3 - 4i[/tex]

Answers

Answer:

[tex]\frac{-11}{25}+\frac{-27}{25}i[/tex] given you are asked to simplify

[tex]\frac{-3+5i}{-3-4i}[/tex]

Step-by-step explanation:

You have to multiply the numerator and denominator by the denominator's conjugate.

The conjugate of a+bi is a-bi.

When you multiply conjugates, you just have to multiply first and last.

(a+bi)(a-bi)

a^2-abi+abi-b^2i^2

a^2+0         -b^2(-1)

a^2+-b^2(-1)

a^2+b^2

See no need to use the whole foil method; the middle terms cancel.

So we are multiplying top and bottom of your fraction by (-3+4i):

[tex]\frac{-3+5i}{-3-4i} \cdot \frac{-3+4i}{-3+4i}=\frac{(-3+5i)(-3-4i)}{(-3-4i)(-3+4i)}[/tex]

So you will have to use the complete foil method for the numerator. Let's do that:

(-3+5i)(-3+4i)

First: (-3)(-3)=9

Outer::  (-3)(4i)=-12i

Inner: (5i)(-3)=-15i

Last: (5i)(4i)=20i^2=20(-1)=-20

--------------------------------------------Combine like terms:

9-20-12i-15i

Simplify:

-11-27i

Now the bottom (-3-4i)(-3+4i):

F(OI)L (we are skipping OI)

First:-3(-3)=9

Last: -4i(4i)=-16i^2=-16(-1)=16

---------------------------------------------Combine like terms:

9+16=25

So our answer is [tex]\frac{-11-27i}{25}{/tex] unless you want to seprate the fraction too:

[tex]\frac{-11}{25}+\frac{-27}{25}i[/tex]

Solve this inequality: 36 - 7 < 32

Answers

You already did. That is a true statement.

32 > 29 [and vice versa]

I am joyous to assist you anytime.

The inequality 29 < 32 is true.

After calculating 36 - 7 which equals 29, we compare this result to 32. The inequality 29 < 32 holds true, so the original inequality 36 - 7 < 32 is correct.

The student has asked to solve the inequality 36 - 7 < 32. To solve this inequality, we need to perform the subtraction on the left side of the inequality first.

When we calculate 36 - 7, we get 29. Now we can compare this result to 32 to determine if the inequality holds true.

Since we are dealing with an inequality, we know that if a value a is less than a value b, then a is indeed smaller in quantity or value compared to b. Here, 29 is indeed less than 32. Therefore, the inequality 29 < 32 is true.

What is the length of the hypotenuse in the right triangle shown below?

Answers

Answer:

C.  6√2.

Step-by-step explanation:

Since this is a right angled isosceles triangle bot legs are 6 units long

So h^2 = 6^2 + 6^2 = 72

h = √72 = 6√2.

Answer:

The correct option is C) 6√2.

Step-by-step explanation:

Consider the provided triangle.

The provided triangle is a right angle triangle, in which two angles are 45° and one is 90°.  

As both angles are equal there opposite side must be equal.

Thus, the leg of another side must be 6.

Now find the hypotenuse by using Pythagorean theorem:

[tex]a^2+b^2=c^2[/tex]

Substitute a = 6 and b = 6 in [tex]a^2+b^2=c^2[/tex].

[tex](6)^2+(6)^2=(c)^2[/tex]

[tex]36 + 36=(c)^2[/tex]

[tex]72=(c)^2[/tex]

[tex]6\sqrt{2}=c[/tex]

Hence, the length of the hypotenuse in the right triangle is 6√2.

Therefore, the correct option is C) 6√2.

The digits of a two-digit number sum to 8. When the digits are reversed, the resulting number is 18 less than the original
number. What is the original number?

Answers

Answer:

It's 53.

Step-by-step explanation:

Let the number be xy so the digits are x and y, so:

x + y = 8...........(1)

Reversing the 2 digits we have the number 10y + x and this equals

10x + y - 18 so we have the equation:-

10x + y - 18 = 10y + x

9x - 9y = 18

x - y = 2...........(2)   Adding equations (1) and (2) we have:

2x = 10

x = 5

and y = 8 - 5 = 3.

So the original number is  53.

We can check this  as follows

Original number is 53 so the reverse is 35 .

53 - 35 = 18  which checks out.

Need The Answer Plz And Thank You!! I’m Failing

Answers

Angle BCA

Step-by-step explanation:

You can see this due to the angle having the name amount of congruent angle marks.

Let f(x) = 4x - 7 and g(x) = 2x - 3. Find (fog)(4).

Answers

Answer:

13

Step-by-step explanation:

(f∘g)(4) is another way of writing f(g(4)).

First, find g(4).

g(x) = 2x − 3

g(4) = 2(4) − 3

g(4) = 5

Now substitute into f(x).

f(x) = 4x − 7

f(g(4)) = 4g(4) − 7

f(g(4)) = 4(5) − 7

f(g(4)) = 13

[tex](f\circ g)(x)=4(2x-3)-7=8x-12-7=8x-19\\\\(f\circ g)(4)=8\cdot4-19=13[/tex]

When solving -1/5 (x − 25) = 7, what is the correct sequence of operations?


A:Multiply each side by negative one over five , add 25 to each side
B:Multiply each side by 5, subtract 25 from each side
C:Multiply each side by negative one over five , subtract 25 from each side
D;Multiply each side by −5, add 25 to each side

Answers

Answer:

It is C. Multiply each side by negative one over five , subtract 25 from each side.

Hope this helped you! :3

Answer:

D;Multiply each side by −5, add 25 to each side

Step-by-step explanation:

-1/5 (x − 25) = 7

To solve this equation, we will first multiply both-side of the equation by -5

-5 × -1/5(x-25) =7 × 5

(At the left-hand side of this equation, the  5 we multiplied will cancel the 5 at the denominator, leaving us with just '1' since negative multiply by negative is positive), Hence our equation becomes;

(x - 25) = 35

x - 25 = 35

Then the next thing to do is to add 25 to both-side of the equation in other to get the value of your x

x -25 + 25 = 35 + 25

x=60

Therefore,  option D is the correct sequence of operation to follow to enable you solve the equation.

Three terms of an arithmetic sequence are shown below. Which recursive formula defines the sequence? f(1) = 6, f(4) = 12, f(7) = 18 f (n + 1) = f(n) + 6 f (n + 1) = 2f(n) f (n + 1) = f(n) + 2 f (n + 1) = 1.5f(n)

Answers

Answer:

f(n + 1) = f(n) + 2

Step-by-step explanation:

A recursive formula gives any term in the sequence from the previous term.

the n th term of an arithmetic sequence is

f(n) = f(1) + (n - 1)d ← d is the common difference

Given

f(1) = 6 and

f(4) = 12, then

f(1) + 3d = 12, that is

6 + 3d = 12 ( subtract 6 from both sides )

3d = 6 ( divide both sides by 3 )

d = 2

To obtain a term in the sequence add 2 to the previous term, hence

f(n + 1) = f(n) + 2 ← recursive formula

Answer:

c

Step-by-step explanation:

its c

HELPPPP WILL NAME BRAINIEST

Answers

Answer:

Triangle APB is an isosceles triangle ⇒ 3rd answer

Step-by-step explanation:

* Lets explain the how to solve the problem

- ABCD is a square

∴ AB = BC = CD = AD

∴ m∠A = m∠∠B = m∠C = m∠D = 90°

- DPC is equilateral triangle

∴ DP = PC = DC

∴ m∠DPC = m∠PCD = m∠CDP = 60°

- In the Δs APD , BPC

∵ AD = BC ⇒ sides of the square

∵ PD = PC ⇒ sides of equilateral triangle

∵ m∠ADB = m∠BCP = 30° (90° - 60° = 30) ⇒ including angles

∴ Δs APD , BPC are congregant ⇒ SAS

- From congruent

∴ AP = BP

Triangle APB is an isosceles triangle

Two tins are geometrically similar. If the ratio of their volume is 27:64 find the ratio of their curved surface area.

Answers

Answer:

9 : 16

Step-by-step explanation:

Given 2 similar figures with linear ratio = a : b, then

area ratio = a² : b² and

volume ratio = a³ : b³

Here the volume ratio = 27 : 64, hence

linear ratio = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{64}[/tex] = 3 : 4

Hence area ratio = 3² : 4² = 9 : 16

4x – 9y = 7
–2x + 3y = 4
What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?

Answers

Answer:

By 2.

Step-by-step explanation:

You need to eliminated the x-terms, so the first step is to focus only in those terms.

So yo have 4x and -2x, since you are thinking in eliminate then you have this equation>

[tex]4-2*K=0[/tex]

Note that we dont put the x variable, since we are studying its coefficients in the equations system.

Solving for K, Gives us that K=2

So.

Multiplying the second equation by 2 results in

[tex]-4x+6y=8[/tex]

When you put them together, it gives you the following

[tex]4x-9y -4x+6y- 7+8[/tex]

and the final equation is

[tex]-3y=15\\[/tex]

giving you the answer for y, that is [tex]y=-5[/tex]

Answer: 2 and 3.

Step-by-step explanation:


Rowena walks 3 kilometers a day. How many meters does she walk in three days?

Answers

3km times 3 = 9km. 9km equals to 9000m.

[tex]\huge{\boxed{\text{9,000 meters}}}[/tex]

There are 1,000 meters in each kilometer, so multiply to find the daily number of meters.  [tex]3*1000=3000[/tex]

Multiply this by 3 to find the number of meters Rowena walks in three days.  [tex]3000*3=\boxed{9000}[/tex]

Find the value of x.
A. 1.1
B. 6.6
C. 8.8
D. 5.5

Answers

Answer:

B. 6.6

Step-by-step explanation:

AC is a midsegment of the trapezoid DFBE.

The formula of a midsegment of trapezoid is:

[tex]m=\dfrac{a+b}{2}[/tex]

a, b - bases of a triangle

We have

a = x, b = 4.4, m = 5.5

Substitute:

[tex]5.5=\dfrac{x+4.4}{2}[/tex]          multiply both sides by 2

[tex]11=x+4.4[/tex]       subtract 4.4 from both sides

[tex]6.6=x\to x=6.6[/tex]

Events A and B are disjointed.

P(A) = 4/11 ; P(B) = 3/11.

Find P(A or B).

*Answer Options*

7/11

4/11

3/11

8/11

Answers

Answer:

7/11

Step-by-step explanation:

Two events are disjoint events if they cannot occur at the same time. It is given that A and B are disjointed events, so A and B cannot occur at the same time i.e. the intersection of two disjoint events will be 0.

For two disjoint events A and B:

P(A or B) = P(A) + P(B)

P(A) is given to be 4/11 and P(B) is given to be 3/11. Using these values in the equation, we get:

P(A or B) = [tex]\frac{4}{11}+\frac{3}{11} = \frac{3+4}{11}=\frac{7}{11}[/tex]

A group of students and workers entering a metro station
were asked whether they were riding the bus or the
subway. The two-way table shows their answers.
Types of Transportation
Bus
Subway
Students
Workers
Total

Answers

166

27 + 42 + 21 + 76 = 166

In circle O, AD and BE are diameters. What is m? 106° 132° 138° 164°

Answers

Answer:

It is 132 just took it

Step-by-step explanation:

Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle. The measure of ∠AOE is 132°. The correct option is B.

What are vertical angles?

Each of the pairs of opposite angles made by two intersecting lines is called a vertical angle.

In circle O, AD and BE are diameters. Also, the measure of ∠EOD and ∠AOB will be equal because the two angles are vertically opposite angles. Therefore,

∠EOD = ∠AOB = 3x

As it is given that the measure of ∠AOC is 90°. Therefore, we can write,

∠AOC = ∠AOB + ∠BOC

90 = 3x + 0.5x + 34

56 = 3.5x

x = 16

Now, the measure of ∠EOD will be,

∠EOD = 3x

∠EOD = 3(16°)

∠EOD = 48°

Further, we can write,

∠AOD = ∠AOE + ∠EOD

180° = ∠AOE + 48°

∠AOE = 132°

The complete question is mentioned in the below image.

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What is the midpoint of the segment shown below?

Answers

Answer:

A

Step-by-step explanation:

Calculate the midpoint using the midpoint formula

[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

with (x₁, y₁ ) = (- 1, 5) and (x₂, y₂ ) = (5, 5)

midpoint = [ 0.5(- 1 + 5), 0.5(5 + 5) ]

              = [ 0.5(4), 0.5(10) ] = (2, 5 ) → A

Answer:

The answer would be A 2,5

Step-by-step explanation:

If Sn=n^2+3 then t10=?

Answers

Answer:

T10= -21

Step-by-step explanation:

If Sn=n^2+3 then t10=?

Sn= n²+5

put n=1, 2

S1= T1 =  (1)²+5

=1+5 =6

S2= n²+5

S2=(2)²+5

S2=4+5

S2=9

T2 = S2 - S1

T2 = 9-6

T2=3

T10 = a+(n-1)d

where a = 6, d = -3, n=10

T10= 6+(10-1)*-3

T10=6+(9)*-3

T10=6+(-27)

T10=6-27

T10= -21

Therefore T10= -21 ....

-8(5x+5)+9x(10x+9)=20

Answers

[tex]-8(5x+5)+9x(10x+9)=20\\-40x-40+90x^2+81x-20=0\\90x^2+41x-60=0\\\\\Delta=41^2-4\cdot90\cdot(-60)=1681+21600=23281\\\\x=\dfrac{-41\pm \sqrt{23281}}{2\cdot90}=\dfrac{-41\pm \sqrt{23281}}{180}[/tex]

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