Solve. Check for extraneous solutions. ∛x=8

-3 is equation in logarithmic form.

What is the purpose of logarithm?

A logarithm is a mathematical formula that calculates how many times the base, or initial number, must be multiplied by itself to produce the target number.

A logarithm is defined simply?

10⁻³=0.001

log. 001 = -3 log 10 = -3

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If I were George Washington, I would have put two very different people to advise me because I would have a broader vision of government affairs.

George Washington (1732-1799) was an American politician and military man who stands out for being one of the most influential people in history and for having served as the first president of the United States between 1789 and 1797. He is considered the most important father of the Nation of the United States.

In 1789 he was unanimously elected by the other founding fathers as the first president of the United States. During his rule he tried to create a nation capable of maintaining peace with its neighboring countries, so he proclaimed neutrality to avoid any involvement in foreign conflicts.

For George Washington it was a challenge to occupy the position of the first president of the United States because he was going to lead a country that was just being formed. Due to the above, it was of vital importance to include all forms of thought and all visions in its government plan and way of governing.

Therefore, when assuming office as president of the United States, it would be of great importance to have advisers who would help him see from the point of view of other people so that his decisions would take into account the interests of all citizens to avoid uprisings and divisions.

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If two water tanks are 50 inches tall and tank a is empty and for each minute the water increases by 3.7 inches and tank b is draining and the water decreases by 1.9 inches each minute, then the minutes after which the height of the water in each tank is the same is equal to 9.

The time in minutes after which the height of the water in each tank is the same can be determined by using a linear equation.

The equation for this problem can be given as,

0 + 3.7(x) = 50 - 1.9(x)

Here x is equal to minutes. To find the minutes after which the water level will be the same can be determined by calculating the value of x in this linear equation.

3.7(x) + 1.9(x) - 50 = 0

5.6(x) = 50

x = 50 / 5.6

x = 8.92 ≈ 9

Hence, the height of the water in tank a and tank b is equal after 9 minutes.

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The minimum number of weeks it will take for Eduardo to make a profit

850w > 7500 + 300w. Option D

This is further explained below.

Generally, the Total cost  is  mathematically given as

X= $7500+$300w

Where he is earning each week

=$850

Therefore,

He will be paid in n weeks=$850n

The information that has been presented states that the very bare minimum number of weeks that it will take for Eduardo to earn a profit is by.

Total revenue is more than total expenditures

850w > 7500 + 300w

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Answer:

Question 1 is x = 2, y = 2, z = 2

Question 2 is x = 1, y = 1, z = -3

Question 3 is x = 13, y = -10, z = -7

Question 4 is x = 5, y = -2, z = -3 (C)

Question 5 is x = 2, y = 0, z = -2

Step-by-step explanation:

I did not have time to do this...

Step-by-step explanation:

1. -9x

2. 2(5x -3)

3.. -4x + 4y -9

4. 6x+18

5.-5x +42

6. (2x+5)

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ L(\stackrel{x_1}{7}~,~\stackrel{y_1}{-1})\qquad M(\stackrel{x_2}{-2}~,~\stackrel{y_2}{4})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ LM=\sqrt{(~~-2 - 7~~)^2 + (~~4 - (-1)~~)^2} \implies LM=\sqrt{(-2 -7)^2 + (4 +1)^2} \\\\\\ LM=\sqrt{( -9 )^2 + ( 5 )^2} \implies LM=\sqrt{ 81 + 25 } \implies LM=\sqrt{ 106 }[/tex]

Answer:

A

Step-by-step explanation:

∠ A and ∠ B are alternate exterior angles and are congruent , then

∠ B = ∠ A , that is

8x - 28 = 5x - 4 ( subtract 5x from both sides )

3x - 28 = - 4 ( add 28 to both sides )

3x = 24 ( divide both sides by 3 )

x = 8

Answer:

1 - 1/4 - 2/3 = r

Step-by-step explanation:

N=1/4, D=2/3

whole pizza=1

r=remainder pizza

1 - 1/4 - 2/3 =r

(1 - 1/4 - 2/3 =r)*12 ==> multiply by 12 to get rid of denominators

12 - 12/4 - 12*2/3=12r

12-3-24/3=12r

9-8=12r

12r=1

r=1/12 of a pizza left

Answer:

1/12

Step-by-step explanation:

the common number of 3 and 4 is 12. You multiply 1/4 by three and you get 3/12, and you multiply 2/3 by 4 and you get 8/12. You add 8 and 3 and you get 11, that's the number that indicates the part of the eaten pizza. 12-11=1. 1/12 left from the pizza.

Answer:

just add more to the milk and another scoop of chocolate

Step-by-step explanation:

1.5 cups milk

6 scoops of chocolate

The formula for calculation of circumference of the circle = d π or 2πr where d is diameter of circle and r is the radius of circle

As given in the question the circumference of the circle whose diameter is 2 cm is 6.28cm and we come to know that value of π used here is 3.14 and not 22/7

So, the circumference of the circle whose diameter is 1cm = d π

              = 1 π

            = 1 3.14

                                                                                          = 3.14 cm

Hence the circumference of the circle whose diameter is 1cm using the value of pi as 3.14 comes out to be pi that is 3.14 cm

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Answer:

y = 3x² + 2

Step-by-step explanation:

I'm help to number on more this, thank for subject on help for today.

Using the mass ratio, the spacecraft's velocity was determined to be 7.7025 km/s.

Here, c = 2.7 km/s, t = 30s, R = 20

On substituting the values of 'R', 't', 'v', we get:

v = -0.0098 ( 30) + 2.7 ( ln (20))

=> v = - 0.294 + 2.7 (2.995)

=> v = 7.7025 km/s

A spaceship is a machine or vehicle built to travel through space. Spacecraft are a form of artificial satellite used for a wide range of tasks, such as communications, Earth observation, meteorology, navigation, space colonization, planetary exploration, and cargo and person transfer.

Following are the main distinctions between spaceships and rockets: The spacecraft is launched into space by rockets, which then crash to Earth. Rockets are never manned, whereas spacecraft can be either manned or unmanned. Additionally, spacecraft cannot match the power of rockets.

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Answer:1

Step-by-step explanation if c is for 6 its 1 p

Answer:

C/6

Step-by-step explanation:

you have c pieces to share with 6 friends.

A radical function such that y≤3 is given by y=-√|x|+3 .

A radical function is defined as a function which has the independent variable within a radical sign.

A radical sign is also defined as the power of the variable to be a fraction.

We know that the n-th root of x is similar to x to the power of (1/n) .

The domain of the function is onto the set of real numbers which means that the domain contains all real numbers.

The range of the function is given as y≤3, that is the value of y can take a maximum value of 3.

Hence we can write a function where x ∈ R and y ≤ 3 .

Let us consider the function y=-√|x|+3

The above functions satisfies all the criteria for the question. It is a radical function and the maximum value can be 3 as -√|x| can have a max value of 0 for all  x ∈ R .

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Answer:9

Step-by-step explanation:draw a line threw the equal sign, add 36 instead of subtracting it, which then would be 9.

Answer:

down below

Step-by-step explanation:

In order for you to get a negative number, you need to put in the variables place, 9.

9 is your answer.

Answer:

Heya genial Gracia dispute

Answer:

2.61625

Step-by-step explanation:

209.3 divided by 80

1) Solve each inequality individually.

[tex]\dfrac{2x-3}5 - \dfrac{4x-9}6 > 1 \\\\ 6(2x-3) - 5(4x-9) > 30 \\\\ (12x-18) - (20x+45) > 30 \\\\ -8x > 3 \\\\ x < -\dfrac38[/tex]

and

[tex]5(x-1) + 7(x+2) > 3 \\\\ (5x-5) + (7x+14) > 3 \\\\ 12x > -6 \\\\ x > -\dfrac12[/tex]

Then the solution set is

[tex]-\dfrac12 < x < -\dfrac38[/tex]

since -1/2 = -4/8 is smaller than -3/8.

2)

[tex]\dfrac{x+1}2 - \dfrac{x+2}3 < \dfrac{x+12}6 \\\\ 3(x+1) - 2(x+2) < x+12 \\\\ (3x+3) - (2x+4) < x + 12 \\\\ x - 1 < x + 12 \\\\ -1 < 12[/tex]

This is true for all values of [tex]x[/tex].

For the second inequality, (I use periods in place of commas because it renders better as TeX)

[tex]0.3x - 19 \le 1.7x - 5 \\\\ -1.4x \le 14 \\\\ x \ge -10[/tex]

Taken together, the solution set is

[tex]\boxed{x\ge-10}[/tex]

3)

[tex](x-6)^2 < (x-2)^2 - 8 \\\\ x^2 - 12x + 36 < (x^2 - 4x + 4) - 8 \\\\ -8x < -40 \\\\ x > 5[/tex]

and

[tex]3(2x-1) - 8 < 34 - 3(5x-9) \\\\ (6x - 3) - 8 < 34 - (15x - 27) \\\\ 21x < 72 \\\\ x < \dfrac{72}{21} = \dfrac{24}7[/tex]

But [tex]x[/tex] cannot be both larger than 5 = 35/7 and smaller than 24/7, so there are no solutions.

4)

[tex]\dfrac{3x-2}3 - \dfrac{4x+1}4 \le 1 \\\\ 4(3x-2) - 3(4x+1) \le 12 \\\\ (12x-8) - (12x + 3) \le 12 \\\\ -11 \le 12[/tex]

This is true for all [tex]x[/tex].

[tex](x-1)(x-2) > (x+4)(x-7) \\\\ x^2 - 3x + 2 > x^2 - 3x - 28 \\\\ 2 > -28[/tex]

This is also true for all [tex]x[/tex].

Any value of [tex]x[/tex] is a solution.

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

We want to find the value of 'x':

   [tex]\hookrightarrow \text{ thus we must first find the value of '4x'}[/tex]

         [tex]\hookrightarrow \text{EC and GH are parallel lines intersected by the same line BG}[/tex]      

              [tex]\hookrightarrow \text{angles formed by the parallel lines and a intersecting lines}[/tex]                                  [tex]\hookrightarrow \text{ are equal in measure }[/tex]

                         [tex]\hookrightarrow \text{thus angles BEC and EGH are equal in measure}[/tex]

Angle EGH is made up of two angles, ∠EGC and ∠CGH

            ⇒ ∠EGH = ∠EGC + ∠CGH = 78 + 14 = 92 degrees

Since ∠BEC = ∠EGH

 [tex]\hookrightarrow 4x = 92\\\hookrightarrow x = 92/4 = 23[/tex]

Answer: 23

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Vertical Angle Theorem: two angles that are formed by two intersecting lines and are opposite each other are equal

The value of x is 23 because Angle FGI and Angle HGC are vertically opposite angles, the answer is 23.

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

It is given that:

The triangle and two parallel lines are shown in the picture.

As we know, from the definition of the vertically opposite angle, two lines intersect each other at the intersecting point.

Angle FGI = Angle HGC = 14 degrees

4x = 78 + Angle HGC

4x = 78 + 14

4x = 92

x = 92/4

x = 23

Thus, the value of x is 23 because Angle FGI and Angle HGC are vertically opposite angles, the answer is 23.

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The length of AB is 4.47 units, the length of CD is 2.83 units and the length of EF is 5 units.

We are given different right angled triangles.

We need to find AB, CD and EF

We will do this by using the Pythagoras theorem.

Pythagoras theorem states that:

Hypotenuse² = Base² + Perpendicular²

For AB,

Hypotenuse = AB

Base = 2 units

Perpendicular = 4 units

So, we get that:

AB² = 2² + 4²

AB² = 4 + 16

AB² = 20

AB = √ 20

AB = 2√5 units

AB = 4.47 units.

For CD:

Hypotenuse = CD

Base = 2 units

Perpendicular = 2 units

So, we get that:

CD² = 2² + 2²

CD² = 4 + 4

CD² = 8

CD = √ 8

CD = 2√2

CD = 2.83 units

For EF:

Hypotenuse = EF

Base = 4 units

Perpendicular = 3 units

So, we get that:

EF² = 4² + 3²

EF² = 16 + 9

EF² = 25

EF = 5 units.

Therefore, we get that, the length of AB is 4.47 units, the length of CD is 2.83 units and the length of EF is 5 units.

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The composite functions of the model taking the 20 % discount and then the 15 % discount is (D ◦ E)(x) = 0.68x.

In mathematics, function composition is an operation in which two functions, f and g, generate a new function, h, in such a way that h(x) = g(f(x)). This means that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Define fog, the composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.

In math, the domain (the x-values) of one function becomes the range (the y-value answers) of the next function. Composition notation is as follows: (f o g)(x) = f(g(x)) and exists read “f composed with g of x” or “f of g of x”.

Let D(x) = cost after applying the 15% discount,

E(x) = cost after applying the 20% employee discount, and x = cost of item(s).

Then D(x) = 0.80x and E(x) = 0.85x.

(D ◦ E)(x) = 0.68x.

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Answer:

  False

Step-by-step explanation:

You want to know "what is 3/4c - 1 = 1 + 3/4c?"

Subtracting the left-side expression from both sides, we get ...

  (3/4c -1) -(3/4c -1) = (1 +3/4c) -(3/4c -1)

  0 = 2 . . . . a False statement

__

Additional comment

Since the equation is written without parentheses, we have to assume that c is in the numerator in each expression, and that its coefficient is (3/4).

It takes 60 minutes (1 hour) for the Blue Line train and the Yellow Line train to be at the station at the same time, using their running time LCM.

The time that it will take the Blue Line train and the Yellow Line train to meet again at the station is determined using the Least Common Multiple or Factor.

The LCM is the smallest positive integer that is evenly divisible by both numbers, 10 and 12.

For instance, the LCM of 10 and 12 include 60 and 120 with 60 as the least.

The time the Blue Line runs is every 10 minutes.

The time the Yellow Line runs is every 12 minutes.

The LCM of 10 and 12 is 60 because 10 and 12 can divide 60 without a remainder.

Thus, it will take 60 minutes for the two trains to meet again at the station.

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a WHOLE is always simplified to "1", and we can use any denominator for that, so 5/5 is 1, and 7/7 = 1, and [tex]\cfrac{4}{4}\implies \cfrac{113}{113}\implies \cfrac{1000000}{1000000}\implies \text{\LARGE 1}whole[/tex]

so hmmm for this case we'll be use thirds or namely the denominator of 3, so a whole bunch of basketballs was originally 3/3 of "b", "b" was the whole amount, so originally we had 3/3, but then during the day we sold 2/3 of them, so we were left with 3/3 - 2/3 = 1/3, and then 8 came back, because they were deflated or something, now the store has a total of 38 basketballs.

[tex]\stackrel{whole}{\cfrac{3}{3}b}~~ - ~~\stackrel{sold}{\cfrac{2}{3}b}\implies \cfrac{3b-2b}{3}\implies \cfrac{b}{3}\implies \stackrel{\textit{remaining in store}}{\cfrac{1}{3}b} \\\\\\ \stackrel{in~store}{\cfrac{1}{3}b}~~ + ~~\stackrel{coming~back}{8}~~ = ~~\stackrel{new~total}{38} \\\\\\ \cfrac{b}{3}+8=38\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( \cfrac{b}{3}+8 \right)=3(38)}\implies b+24=114\implies \stackrel{originally}{b=90}[/tex]

Answer: 2 11/24

Step-by-step explanation: First we have to subtract it, so 6 5/8 - 4 1/6 which is 2 11/24

The domain of f(x) to be [0,∞).

If the domain R, f(x) is not one to one, so its inverse exists not a function.

If we restrict the domain of f(x) then we can define an inverse function.

An inverse function, even comprehended as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function exists denoted by ' f ' or ' F '.

In order to have an inverse function, a function must be one to one.

In the case of f(x) = x⁴ we find that f(1) = f(−1) =1.

If f(x) exists not one to one on its implicit domain R.

If we restrict the domain of f(x) to [ 0, ∞) then it does contain an inverse function, then [tex]f^{-1}(y)=\sqrt[4]{y }[/tex]

Let the given function be y = f(x) = x⁴

Taking the square root of both ends, then we get

± √y = x²

Let the real values be x, then

We require the left hand side to be non-negative, so assume the non-negative square root.

Take the square root of both sides of the equation then

±[tex]\sqrt[]{\sqrt{y} }[/tex] = x

⇒ x = ± [tex]\sqrt{\sqrt{y} }[/tex] = ± [tex]\sqrt[4]{y}[/tex]

It  does not give us a unique value of x in terms of y.

So the inverse function exists not defined, then x ≥ 0,  

i.e., restrict the domain of f(x) to be [0,∞).

If the domain R, f(x) exists not one to one, so its inverse exists not a function.

The domain of f(x) then we can describe an inverse function.

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We need to use the concept of lines and slopes to solve the problem.The equation of the line that passes through (5,-2) and is perpendicular to y=[tex]\frac{5}{3} x-3[/tex] is [tex]y=\frac{-3}{5} x+\frac{19}{5}[/tex].

We will be using the concept of lines and slopes to solve the question. When two lines are parallel their slopes are equal and when two lines are perpendicular the product of their slopes equal to -1.

Here we know that the line passes through a point (5,-2) and is perpendicular to another line,we need to find out the slope of the line first.

Let slope of given line be m1 and slope of the line that we need to find out be m2.

[tex]y=\frac{5}{3} x-3[/tex]

slope is the coefficient of x, thus m1=[tex]\frac{5}{3}[/tex]

we know that m1xm2=-1

[tex]\frac{5}{3}[/tex]×m2=-1⇒m2=[tex]\frac{-3}{5}[/tex]

The formula that we need to find the equation of a line is

(y-y1)=m(x-x1)

here (x1,y1) is (5,-2) and m is m2

[tex]y-5=\frac{-3}{5} (x+2)\\y-5=-\frac{3}{5} x-\frac{6}{5} \\y=\frac{-3}{5} x+5-\frac{6}{5} \\y=\frac{-3}{5} +\frac{19}{5}[/tex]

Thus using the concept of lines and slopes we found out that the equation of line that has been asked for is [tex]y=\frac{-3}{5} x+\frac{19}{5}[/tex]

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The equation of the line in point-slope form is y-1 = 3 ( x + 1)

Equation of a line:

The equation of a line, in point-slope form, is designated  using:

y-y0= m( x - x0)

In which the point is given by(x0,y0)  and m is the slope.

Slope of the line below is 3 (given in the question).

This means that m = 3

(-1,1)

This means x= -1 and y =1

equation of the line

y - y0 = m( x- x0)

y-1 =m(x-(-1))

y-1=m(x + 1)

substituting the value of m is 3

y-1= 3 ( x + 1)

Therefore, The equation of the line in point-slope form is y-1= 3 (x + 1)

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[tex]2^{(x + 3)} = 512[/tex] => x = 6, by properties of exponentiation.

Now,

[tex]2^{(x + 3)} = 512[/tex]

=> [tex]2^{(x + 3)} = 8^3 = (2^3)^3[/tex]

As [tex](a^b)^c = a^{bc}[/tex],

=> [tex]2^{(x + 3)} = 2 ^9[/tex]

=> x + 3 = 9

=> x = 6

Hence, [tex]2^{(x + 3)} = 512[/tex] => x = 6, by properties of exponentiation.

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