Solve the following radical equations.
∛x-1=√x-1

Answer: 0.004 = 4.0 x [tex]10^{-3}[/tex]

Step-by-step explanation:

Rules guiding exponential notation :

Writing numbers in exponential notations have some guiding rules. These include:

The base is always 10

The exponent cannot be zero and must be an integer. It can be positive or negative.

The coefficient can take any form - negative or positive, integer or decimal. All significant digits must be included after the decimal.

Following these rules :

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Answer:

5000

Step-by-step explanation:

5x1000=5000

The result of simplifying the number 4¹/₂ . 4¹/₂  using the properties of exponents is 4

To solve this exercise we have to resolve algebraic operations following the exponent properties.

4¹/₂ . 4¹/₂

Base= 4

Using the product rule that indicates that: the exponent result will be the addition of these exponents, we have:

(4) ⁽¹/₂ ⁺ ¹/₂⁾

(4) ⁽¹⁺¹⁾/₂

(4) ⁽²/₂⁾

(4)⁽¹⁾

4

In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.

Example: 3² = 3*3 = 9

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Answer:

1920 rings

Step-by-step explanation:

Our equation: 16 x 10 x 12

16 x 10= 160

160 x 12= 1920

Answer: -13

Step-by-step explanation: so order of operations is also PEMDAS.

and u go from left to right so using this you would multiply 8 x 5 and then you get 35. after this subtract 23-36 and u get -13.

According to the question, to express the rational function for the vertical asymptote whose equation is [tex]x=8[/tex] and horizontal asymptote whose equation is at [tex]y=0.[/tex]

As per the question, the function 'f(x)' is vertical at [tex]x=8[/tex]. Therefore, the denominator be [tex](x-8)[/tex]

[tex]f(x)=\frac{g(x)}{(x-8)}[/tex]

The function 'g(x)' should have same degree as the denominator function has and it is defined as[tex]y=0[/tex]

The rational function can be written as:

Rational function = [tex]\frac{y}{(X-8)}[/tex]

What is rational function?

Rational function is a function whose numerator and denominator terms are in polynomials. Basically, it is a ratio of polynomials. The important condition for these type of function is that denominator should be of degree one.

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The factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4 and the value of the maximum profit is 680

The given parameters are

f(x) = x^3 + 5x^2 - 16x - 80

x = -4 is a root

To set up the synthetic division, we start by writing out the coefficient of each term

So, we have

-4 |  1    5    -16    -80

Bring down the first coefficient

-4 |  1    5    -16    -80

      1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)

      1

Add

-4 |  1    5    -16    -80

           (-4)

      1     1

Multiply by -4

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1

Add

So, we have

-4 |  1    5    -16    -80

           (-4)  (-4)

      1     1     -20

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20

Add

So, we have

Multiply by -4

-4 |  1    5    -16    -80

           (-4)  (-4)    80

      1     1     -20    0

This means that,

Quotient = x^2 + x - 20

Remainder = 0

Expand x^2 + x - 20

x^2 + x - 20 =x^2 + 5x - 4x - 20

Factorize

x^2 + x - 20 = (x + 5)(x - 4)

Recall that the initial root is

x = -4

Rewrite as

x + 4 = 0

So, we have the complete factor to be

f(x) = (x + 4)(x + 5)(x - 4)

Set to 0

(x + 4)(x + 5)(x - 4) = 0

Solve for x

x = -4,  = -5 and x = 4

Hence, the factors are (x + 4), (x + 5) & (x - 4) and the solution is x = -4,  = -5 and x = 4

The equation of the profit function is given as

P(x) = 230 + 30x - 0.5x^2

Differentiate the function

So, we have

P'(x) = 0 + 30 - x

Evaluate the like terms in the function

So, we have

P'(x) = 30 - x

Set the function to 0

So, we have

30 - x = 0

Evaluate

x = 30

Substitute x = 30 in the equation P(x) = 230 + 30x - 0.5x^2

So, we have

P(30) = 230 + 30 x 30 - 0.5 x 30^2

Evaluate

P(30) = 680

Rewrite as

Pmax = 680

Hence, the value of the maximum profit is 680

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Answer: 2.2

Step-by-step explanation: twenty percent of 11 is 2.2

[tex]f(x) = \alpha (x - 4) {}^{2} (x - 2) {}^{2} \\ f(x) = \alpha (x {}^{2} - 8x +16 )(x - 4x - 4) \\ f(x) = \alpha (x {}^{4} - 12x {}^{3} + 52x {}^{2} - 96 x + 64) \\ where \: \alpha ∈ \: \real[/tex]

After solving the given equation 25²x=144, the value of x = 144/625.

So,

Then,

Therefore, after solving the given equation 25²x=144, the value of x = 144/625.

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14x+70+20x+8=180

34x+78=180

34x=102

x=3

XBC= 20(3) +8

60+8

68

XBA= 14(3)+70

42+70

112

Angle XBC= 68 degrees

Angle XBA= 112 degrees

The total amount that Amy will spend is $17.98

Amy goes out to eat at El Parral. She orders a Burritos Deluxe dinner for $8.75, fried ice cream for $4, and a Coke for $2.

Amy's gross total is $8.75 + $4 + $ 2  = $14.75

Now, sales tax of 6 percent

Her net bill is $14.75 + 6% of $14.75

$ 14.75 + 0.885

= $15.635

Here, Amy also gives a tip of 15 percent

Her total spending becomes

$15.635 + 15% of $ 15.635

$15.635+ 2.345

$17.980

or $ 17.98

Hence, the total amount that Amy will spend is $17.98

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Answer:

(-4, 0) U (1, ∞)

Step-by-step explanation:

Set each factor EQUAL to zero to find the zeroes (since it is not actually equal to zero, you will use an open circle when graphing and an open bracket when writing in interval notation).

x = 0           x-1 = 0             x + 4 = 0

                  x = 1                x = -4

Next, choose a value to the far left, between each of the zeroes, and to the far right to evaluate if it makes a true statement when input into the given inequality.

far left (I choose -5): -5(-5 - 1)(-5 + 4) > 0   →  (-)(-)(-) > 0  →   negative > 0  FALSE

- 4 to 0 (I choose -2): -2(-2 - 1)(-2 + 4) > 0   →  (-)(-)(+) > 0  →   positive > 0  TRUE

0 to 1 (I choose 0.5): .5(.5 - 1)(.5 + 4) > 0   →  (+)(-)(+) > 0  →   negative > 0  FALSE

far right (I choose 2): 2(2 - 1)(2 + 4) > 0   →  (+)(+)(+) > 0  →   positive > 0  TRUE

Point A' after the dilation of the scale factor by 1/3 is (-1,2) is the correct option.

The given point is;

Point A = (3, -6), scale factor = 1/3

Fortunately, because the dilation is centered at the origin (0,0), we can multiply the scale factor by the x and y-coordinates to acquire the image point coordinates.

Point A' = (3×1/3, -6×1/3)

Point A' = (1, - 2)

As a result, if it grows larger, it should start moving away from the origin, while if it grows smaller (as it does here), this should move closer to a origin.

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The equation that shows proportionality is in the form y = kx; Where k is the constant of proportionality.

An equation is an expression that shows the relationship between two or more numbers and variables.

Two variables are said to be proportional if an increase or decrease in one variable leads to a corresponding increase or decrease in the other variable.

The equation that shows proportionality is in the form:

y = kx

Where k is the constant of proportionality.

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Answer:

2 and - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

f(x) = 2x - 1 ← is in slope- intercept form

with gradient m = 2

• Parallel lines have equal gradients , then

the gradient of a parallel line is also 2

given a line with gradient m then the gradient of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]

The correct answer is ( -2.2, -3).

We occasionally discover the value of an unknown variable while solving the system of equations. We can display the graph using the equation, but if the graph and the equation are parallel, we will not be able to solve the system of equations.

We have a condition that, if applied, allows us to determine how many solutions this equation has: if it has one solution, no solutions, or infinitely many solutions.

y = -3 _____(1)

y = x-0.8 _____(2)

to substitute the value of y in the equation in 2

-3 = x - 0.8

-3 + 0.8 =x

-2.2 = x

Thus the correct answer is  ( -2.2, -3).

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Answer:

Here's b > 4 on the number line. When greater than, the arrow always starts with an open circle. If less than, then it will start with a closed circle.

Answer:

154

Step-by-step explanation:

Use the correct order of operations.

(120 - 14) + 4² × 3 =

First, do the parentheses and the exponent.

= 106 + 16 × 3

Now do the multiplication.

= 106 + 48

Finally, add.

= 154

Answer:

.9

85%

5/6

4/5

Step-by-step explanation:

In percentages .9 is 90%

which is larger than 85%

5/6 as a percentage is 83.33r%

4/5 as a percentage is 80%

The simple way to solve such an expression; −(−8q−8.7) as given in the task content is by the distributive property which yields; 8q + 8.7.

It follows from the task content that the expression which is to be simplified, or perhaps written in a different form is; −(−8q−8.7).

Therefore, it follows from the distributive property that we have;

-(-8q) -(-8.7)

Also, since the product of two negative signs yields a positive sign.

Hence, we have; 8q + 8.7 as the equivalent of the expression given.

Ultimately, the simple way to solve such an expression; −(−8q−8.7) as given in the task content is by the distributive property which yields; 8q + 8.7.

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Answer:

the answer is the 10⁰ ok that

Answer:

$3.42 spent on folders, She will receive $6.58 back in change

Step-by-step explanation:

$0.57 times 6 = $3.42 spent on the folders. $10-$3.42=$6.58 she will receive back.

Part 1: She spent $3.42 on the folders.

This is calculated by multiplying 6 folders by $0.57 for each folder

($0.57 x 6 = $3.42).

Part 2: She will receive $6.58 in change. This is calculated by subtracting the amount spent on the folders from the amount of money Gi Gi had to begin with ($10 - $3.42 = $6.58).

Answer:

-8

Step-by-step explanation:

[tex]-2\left(-4\right)\left(-1\right)\\\left(-4\right)\left(-1\right)\\\left(-a\right) \times \left(-b\right)=(+c)\\= 4\\=-2 \times 4\\(-a) \times (+b) = -c\\=-8[/tex]

The equation is,

→ -2 (-4) (-1)

Let's solve the problem,

→ -2 (-4) (-1)

→ (-2 × -4) × (-1)

→ 8 × -1 = -8

Thus, the answer is -8.

The domain of the function is (2,∞),{x|x>2}

and the range of function is  (−∞,∞),{y|y∈R}

The domain is all values of xx that make the expression defined.

Set the argument in log(x−2)greater than 0 to find where the expression is defined.x−2>0

Add 2 to both sides of the inequality.x>2

Interval Notation:(2,∞)

Set-Builder Notation:{x|x>2}{x|x>2}

The range is the set of all valid y values.

We can find out the range by using the graph.

Interval Notation:(−∞,∞)

Set-Builder Notation:{y|y∈R}

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Answer:

12

Step-by-step explanation:

In this problem, we need to arrange 150 chairs in rows for a school play. You want each row to have the same number of chairs.

We can find the prime factorization of 150 as follows :

150 = 2, 3, 5, 5

150 is not a perfect square. 144 is a perfect square and 12² = 144. So, there are 12 possible arrangements.

Answer:

83°

Step-by-step explanation:

Supplementary angles are angles that add up to 180°.
Za + Zy = 180
Za + 97 = 180
Za + 97 - 97 = 180 - 97
Za = 83

It will take 5.689 yrs . for the account to contain $2500 .

Simple Interest = ( P * R * T ) / 100

P ( principal amount ) = 2000

R ( rate of interest ) = 4

T ( no . of yrs . for which amount is deposited ) = unknown

According to question

Account Balance = $ 2500 = A( t ) = a [tex]( 1 + r ) ^{t}[/tex]

2500 = 2000 [tex]( 1 + 0.04 )^{t}[/tex]

1.25 =  [tex]( 1 + 0.04 )^{t}[/tex]

t = [log ( 1.25 ) ] / [ log ( 1.04 ) ]

t = 5.689

Hence , it will take 5.689 yrs . for the account to contain $2500 .

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