Solve each equation. If necessary, round to the nearest ten-thousandth. log (5 x-4)=3

(x+√y)(x-√y) = x² - y is always an integer.

Given that x and y are integers.

Then x + √y is an irrational number.

The conjugate of (x + √y) is (x - √y).

We need to find the product (x + √y)(x -√y).

Use the identity, (a +b)(a-b) = a²-b²

So  (x + √y)(x -√y) = x² - (√y)²

                             = x² - y

Given that x is an integer. The square of an integer is always an integer.

Since x² and y are integers, their difference is also an integer.

So we can conclude that x²-y is an integer.

Hence, (x+√y)(x-√y) = x² - y is always an integer.

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12[tex]y^{-2}[/tex] = 20 => y = 0.774, by basic algebra.

Given: 12[tex]y^{-2}[/tex] = 20

=> [tex]\frac{12}{y^2}[/tex] = 20

=> [tex]\frac{12}{20} = y^2[/tex]

=> [tex]y^2 = \frac{3}{5} = 0.6[/tex]

=> y = 0.774.

Hence, 12[tex]y^{-2}[/tex] = 20 => y = 0.774, by basic algebra.

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YES , both the function will have same domain and range.

Domain and Scope The domain of a function is the set of values that we are allowed to enter into our function. This collection includes the x values for a function like f. (x).

The range of values that a function can accept as input is known. When we enter an x value, the function returns this list of values.

All Real x, x not = 0 is the domain (the range of potential values for x).

Since 6/0, 8/0, and 12/0 are not defined, x = 0 is not considered.

All Real f(x), f(x) not = 0 is the range.

Because 6 / and 6 / - will never equal 0, f(x) = 0 is not included. The same is true for 8/x and 12/x.

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[tex]763 \times 10 {}^{3} = 7.63 \times 10 {}^{5} [/tex]

Answer:

D)21

Step-by-step explanation:

I hope I can help. You won't make a mistake there

Answer:

Answer is D) 21

[tex]{ \tt{ {x}^{2} - 7x + 3 = 0}}[/tex]

Sum of roots [L + M]: -(-7) = 7

Product of roots [ LM ]: 3

[tex]{ \rm{L {}^{2} M +LM {}^{2} = LM(L + M )}} \\ \\ = { \rm{3(7)}} \\ \\ = 21[/tex]

[tex]\displaystyle\\Answer:\ 6\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\4\frac{2}{3} -(-1\frac{1}{2})=\\\\ 4\frac{2}{3} +1\frac{1}{2}=\\\\\frac{4*3+2}{3} +\frac{1*2+1}{2}=\\\\\frac{12+2}{3}+\frac{2+1}{2}=\\\\\frac{14}{3}+\frac{3}{2}=\\\\\frac{(14)(2)+(3)(3)}{(3)(2)} =\\\\\frac{28+9}{6} =\\\\\frac{37}{6} =\\\\\frac{36+1}{6}=\\\\\frac{36}{6} +\frac{1}{6}=\\\\\frac{(6)(6)}{6}+\frac{1}{6}=\\\\6+\frac{1}{6}=\\\\6\frac{1}{6}[/tex]

The density of iodine is about 6.281 times the density of acetone. The density of acetone is about 785 kilograms per cubic meter. What is the density of iodine as a repeating decimal?

The density of iodine as a repeating decimal is 4930.585 kilogram.

Given the density of iodine is about 6.281 times the density of acetone.

We can write as x=6.281y      (take x=6.281y as equation(1))

Here, x is the density of iodine and y is the density of acetone

Now take the density of acetone is about 785 kilograms per cubic meter.

We can write as y=785 kg.

Now substitute y=785 kg in equation (1)

We get x=6.281[tex]\times\\[/tex]785 kg

x=4930.585 kg

Therefore, The density of iodine as a repeating decimal is 4930.585 kilogram.

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The density of iodine as a repeating decimal is 4930.585 kilogram. when the density of iodine is about 6.281 times the density of acetone, the density of acetone being 785 kilograms per cubic meter.

As given in the question the density of iodine is about 6.281 times the density of acetone.

It can be written as x=6.281y      (take x=6.281y as equation(1))

Here, x is the density of iodine and y is the density of acetone

Now the density of acetone is about 785 kilograms per cubic meter as given in question

So, y=785 kg.

Now substituting y=785 kg in equation (1)

it is calculated as x=6.281 x 785 kg

x=4930.585 kg

Therefore, The density of iodine as a repeating decimal is 4930.585 kilogram.

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Answer:

$2.53

Step-by-step explanation:

Unit price = total price / quantity

Unit price = $12.65 / 5

Unit price = $2.53

The function g whose graph is a reflection in the x-axis of the graph of f is g(x) = -2x - 3

The points on the function f are given as

(0,3) and (3,9)

Calculate the slope of f using

m = (y2 - y1)/(x2 - x1)

So, we have

m = (9 - 3)/(3 - 0)

Evaluate

m = 2

A linear equation is represented as

y = mx + c

Where m = slope

i.e. m = 2

c = y-intercept

i.e. c = y, when x = 0

In (0,3), we have

c = 3

So, the equation is

y = 2x + 3

The reflection of the equation on the x-axis is

g(x) = -f(x)

So, we have

g(x) = -2x - 3

Hence, the function g whose graph is a reflection in the x-axis of the graph of f is g(x) = -2x - 3

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Answer:

1,2,5,10

Step-by-step explanation:

hope this helps

Answer:

734.52

Step-by-step explanation:

Subtract

The simplest ratio of squares to total shapes will be 2:7.

A ratio in mathematics shows how many times one number is contained in another. When two objects are related using numbers or amounts, the relationship is known as a ratio. For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3).

A ratio can have any number of quantities, such as counts of people or things or measurements of length, weight, time, etc. Both numbers must be positive in most situations. From the information, there are 4 squares as 10 triangles.

Therefore, the simplest ratio of squares to total shapes will be:

Number of squares = 4

Total shapes = 4 + 10 = 14

Ratio = 4 / 14

Ratio = 2/7

Therefore, the simplest ratio of squares to total shapes will be 2:7.

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There are4 squares and 10 triangles. What is the simplest ratio of squares to total shapes?

The value of the expression is 284 5/ 9

A fraction can be defined as the part of a whole.

Some types of fractions are;

Given the fraction;

-13(21 4/9)

First, we convert the mixed fraction in the bracket to a proper fraction

- 13( 197/ 9)

Now, let's expand the bracket

-2561/ 9

Find the quotient

284 5/ 9

Thus, the value of the expression is 284 5/ 9

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i think it is (0,-2). y=mx+b

The system of equations are:

c + b = 1285

170c + 480b = 477,300

Two equations would be derived from the information provided in the question. The equations are known as simultaneous equations. The equations would have to be solved together in order to determine the required values.

The methods that can be used to solve simultaneous equations are:

The form of the equations is:

Number of catastrophic plan sold + number of bronze plans sold = total plans sold

Cost of the catastrophic plan x number of the plan sold) + (number of bronze plan sold x cost of the plan) = total cost of the plans

c + b = 1285

170c + 480b = 477,300

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Answer:

$1,045,000,000 = $1.045 billion.

Step-by-step explanation:

Pittman–Robertson Act

The Pittman–Robertson Act (Federal Aid in Wildlife Restoration Act of 1937) requires an 11% excise tax to be paid on the sale of firearms, ammunition, and archery equipment to be used by state governments to fund wildlife restoration.

Given information:

The money raised for conservation can be calculated by finding 11% of the number of firearms sold multiplied by the average selling price.

[tex]\begin{aligned}\textsf{Money raised}&=11\% \textsf{ of }19,000,000 \times \$500\\\\& = \dfrac{11}{100} \times 19,000,000 \times 500\\\\& = \dfrac{11\times 19,000,000 \times 500}{100} \\\\& = \dfrac{104,500,000,000}{100} \\\\& = 1,045,000,000\end{aligned}[/tex]

Therefore, the total amount of money raised was $1,045,000,000 ($1.045 billion).

Answer:

Step-by-step explanation:

To calculate the amount of money raised for conservation from the sale of firearms during 2020, we'll follow these steps:

Step 1: Calculate the total revenue generated from firearm sales.

Total revenue = Number of firearms sold * Price per firearm

Total revenue = 19,000,000 * $500

Total revenue = $9,500,000,000

Step 2: Calculate the amount of excise tax collected.

Excise tax = Total revenue * Excise tax rate

Excise tax = $9,500,000,000 * 0.11

Excise tax = $1,045,000,000

Therefore, the amount of money raised for conservation from the sale of firearms during 2020, based on the given information, is $1,045,000,000.

The greatest integer that is less than the value of the logarithm log17.52 is 1.

We are required to check the value of greatest integer that is less than log17.52

As no base is mentioned, let us consider the base to be 10

Thus, we are required to find the value of log₁₀17.52

log₁₀17.52=log₁₀10+log₁₀7.52

log₁₀10=1

log₁₀7.52=log₁₀752/log₁₀100

                =log₁₀752-2log₁₀10

                = 2.876-2=0.876

Thus, log₁₀17.52=1+0.876 =1.876

Thus , log₁₀17.52 is 1.876

Therefore, The greatest integer that is less than the value of the logarithm log17.52 is 1

Disclaimer:

Since no base has been provided for the logarithm, 10 has been considered to be the base.

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The solution of each equation 2 e -x=20 is -7.281.

2 e -x=20

Here e=2.7182

e-x =10

x = -7.281

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

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the pair of points that are at a distance of 4 units are (2, 7) and (2, 3), which is option D.

For two points defined by the coordinates (a, b) and (c, d), we define the distance between these two points as:

distance = √(( a - c)^2 + (b - d)^2)

So you can just use that simple formula for the four pairs of points given and see which pair gives a distance of exactly 4 units, if we use the last pair wich is (2, 7) and (2, 3) and we replace the values in the correspondent places of the distance equation, we will get:

distance = √( (2 - 2)^2 + (7 - 3)^2) = 4

So we conclude that the pair of points that are at a distance of 4 units are (2, 7) and (2, 3), which is option D.

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Given u = [-5 3], v = [4 -3] , and w = [2 2], by applying addition and scalar multiplication of vectors, 2u + 3v = [2, -3]

In the 2D coordinate system, vectors can be split into x-component and y-component.

A vector s = [3,–1], which means:

x-component = 3

y-component = –1

Some vector operations:

In the given problem:

u = [-5 3], v = [4 -3] , and w = [2 2]

Then,

2u = 2.[-5 3]

    = [2.(-5), 2. 3] = [-10, 6]

3v = 3. [4 -3]

     = [3. 4, 3. (-3)] = [12, -9]

Hence,

2u + 3v =  [-10, 6] + [12, -9]

            = [-10+12, 6-9]

            = [2, -3]    

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The consecutive integers are 12 , 13 ,14, and 15 .

Of the four consecutive integers let us consider the smallest integer be x.

Therefore the other 3 integers are x+1 , x+2 and x+3 .

Therefore the sum of the integers are:

x +(x+1)+(x+2)+(x+3)=4x+6

The sum of the integers is given 54.

∴4x + 6 = 54

or, 4x = 54 - 6

or, 4x = 48

or, x = 48 ÷ 4

or, x = 12

Therefore the three other integers are 13,14 and 15.

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Answer: d "y, because jhk = lmk"

Step-by-step explanation:

both triangles have a 65 and a 90 degree angle, since both triangles have to add up to 180 degrees, both sides equal 25

[tex]\huge \boxed{\sf A.A\ and\ B.7}\\\\\\\displaystyle \sf Adding\ all\ sides\ equaling\ to\ perimeter\\\\x+x+x+5=26\\\\3x+5=26 \\\\\\Solve\ for\ x \\\\Subtracting \ 5\ from\ both\ sides\\\\3x+5-5=26-5 \\\\3x=21 \\\\Dividing\ both\ sides\ by\ 3 \\\\\frac{3x}{3} =\frac{21}{3} \\\\x=7[/tex]

x = -1/4 is an extraneous solution.

✓(11x + 3) - 2x = 0

Adding 2x on both sides of the equation we get

✓(11x + 3) - 2x + 2x = 0 + 2x

✓(11x + 3) = 2x

Squaring both sides of the equation we get

(✓(11x + 3))² = (2x)²

11x + 3 = 4x²

4x² - 11x - 3 = 0 : Equation 1

By middle term splitting equation 1 can be written as

4x² - 12x + x - 3 = 0

4x(x - 3) + 1(x - 3) = 0

(4x + 1)(x - 3) = 0

x = - 1/4 and 3.

Check extraneous solution by putting the value of x in the original equation -

Let x = -1/4

✓(11(-1/4) + 3) - 2(-1/4) = 0

✓(-11/4 + 3) + (1/2) = 0

✓(1/4) + (1/2) = 0

1/2 + 1/2 = 0

1 = 0

which is a contradiction, so, x = -1/4 is an extraneous solution.

Let x = 3

✓(11×3 + 3) - 2×3 = 0

✓36 - 6 = 0

6 - 6 = 0

0 = 0

Since, LHS = RHS, x = 3 is not an extraneous solution.

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Using logarithmic quotient and power rule, we expand each logarithm function log (2√x/5)³ as  3. log (2√x) - log (5).

According to the question, we need to expand  we expand logarithm function log (2√x/5)³.In Logarithms, the power is raised to some numbers (usually, base number) to get some other number. It is an inverse function of exponential function.

Power rule for logarithm: log (a)ˣ = x log (a)

Quotient rule for logarithm: log (a/b) = log (a) - log(b).

⇒log (2√x/5)³

Applying power rule to the above logarithm function, we get

log (2√x/5)³ = 3. log (2√x/5)    →(1)

Applying quotient rule to the equation (1), we get

3. log (2√x/5)  = 3. log (2√x) - log (5)

Hence, using logarithmic quotient and power rule, we expand each logarithm function log (2√x/5)³ as  3. log (2√x) - log (5).

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After expanding logarithm equation is : [tex]\frac{\sqrt{2} \log_{10}(x) }{2y^2}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

            x define expression

Mathematically, if   [tex]a^N=x[/tex] is an exponential function then, this can be converted to logarithmic function as   [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression can be written as,

[tex]\frac{log_{10}(\sqrt{x})(\sqrt{2} )}{y^2}[/tex]

as, log (√x) = 1/2 log (x)

[tex]= > \frac{\sqrt{2} \frac{1}{2} log_{10}x }{y^2} \\\\= > \frac{\frac{log_{10}x}{\sqrt{2} } }{y^2}\\ \\= > \frac{log_{10}(x)}{\sqrt{2} y^2} \\\\= > \frac{\sqrt{2}log_{10}x }{2y^2}[/tex]

Thus, Simplification of given expression is : [tex]\frac{\sqrt{2} \log_{10}(x) }{2y^2}[/tex]

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If the Learning curve rate is 85%, then the painter will need 35.5 hours to pant all 20 rooms.

Learning curve rate tells us that there will be improvement or the time for the task will decrease as the person learn the repetitive task.

The time for completing n units is given by the formula:

Tₙ = T₁ . nᵇ

Where:

T₁  = time to complete 1st task

n = number of units

b = ln (learning curve rate) / ln(2)

The given parameters:

T₃  = 9 hours

learning curve rate = 85%

Hence,

b = ln (0.85) / ln(2) = 0.693

Plug the values into the formula for n = 3

T₃ = T₁ . 3ᵇ

T₁  = T₃ / 3ᵇ = 9 / 3ᵇ

Substitute the parameters for n = 20.

T₂₉ = T₁ . 20ᵇ

      = (9 / 3ᵇ) . 20ᵇ

       = 9 . (20/3)ᵇ

Substitute b = 0.693

T₂₉ = 35.5 hours

Hence, it takes 35.5 hours for the painter to pant all 20 rooms.

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Answer:

B -N

Step-by-step explanation:

A This is -1 x - N. a negative times a negative is always positive. So -1 x -N = 1N= N

C The absolute value of N is N so this is also correct.

D The absolute value of a negative number is always positive so |-N| = N

Answer: Three Equivalent ratios for 1 2/3:4/4 = 4:1, 4:1, 4:1

Step-by-step explanation:

Define Equivalent ratio:

Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not. For example, 1:2 and 2:4 are equivalent ratios.

All equivalent fractions get reduced to the same fraction in their simplest form.

Explanation:

All those fractions obtained by multiplying both the numerator and denominator of 12/3 by the same integer are equivalent to 12/3.

12/3 × 2/2  = 24/6 = 4

12/3 × 3/3 = 36/9 = 4

12/3 × 4/4 = 48/12 = 4

4, 4, 4,  ... are equivalent to 12/3.

All those fractions obtained by multiplying both the numerator and denominator of 4/4 by the same integer are equivalent to 4/4.

4/4 × 2/2  = 8/8 = 1

4/4 × 3/3 = 12/12 = 1

4/4 × 4/4 = 16/16 = 1

1, 1,1,  ... are equivalent to 4/4.  

Therefore,

Equivalent ratios for 1 2/3:4/4 = 24/6:8/8, 33/9:12/12, 48/12:16/16

Three Equivalent ratios for 1 2/3:4/4 = 4:1, 4:1, 4:1

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the number of roots of the polynomial 7 + 5 x⁴ - 3 x² is 4.

We are given a polynomial:

7 + 5 x⁴ - 3 x²

We need to tell the number of roots that the polynomial has.

a polynomial is an expression consisting of indeterminates and coefficients.

It is the one that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Example: x² − 4x + 7.

We know that:

Number of roots = highest power of the variable of the polynomial

Here, the number of roots will be:

roots = 4

Therefore, we get that, the number of roots of the polynomial 7 + 5 x⁴ - 3 x² is 4.

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