Solve each equation. Check your answers.
2 log x=-1

In the Law of Syllogism , Long sentences and phrases can occasionally be perplexing and written imprecisely at first glance.

What is the purpose of a syllogism?

Long sentences and phrases can occasionally be perplexing and written imprecisely at first glance.

Therefore, using symbols to denote various statements is quite helpful.

because the number of various statements we have and the relationship between them will then be much more obvious.

To put it another way, it would be simpler to decide which logical law to apply to a certain issue.

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Answer:  E

Step-by-step explanation:

4 x 4 = 16

7 x 7 = 49

16 + 49 = 65

8.062 is the square root of 65.

Round 8.062 I guess you could round it to 9 but I believe the actual answer should be 8.

Answer:

1. roots may be +/-1,2,3,6 and fractions

A root must be minus since if they were positive, the function would be >0.

-1 works by inspection, so (x+1) is a factor.

-1/1==6==11==6

1===5===6==0

the factors are (x-1)(x^2+5x+6)=(x+1)(x+2)(x+3)

Roots are -1, -2,-3

-

2.x^3-7x+6, Try+/-1,2,3,6

start with 1, and1-7+6=0; (x-1) is a factor

can divide

1/1=0==-7===6

1---1-- -6===0

The factors are (x+1)(x^2+x-6)=(x-1)(x+3)(x-2)

roots are 1,2,-3

-

3.x^3+x^2-12x

factor out an x

x(x^2+x-12)=x(x+4)(x-3)

roots are 0, -4, 3

-

4.9x^3-7x+2

roots can be +/-1, and +/-2 along with (1/3) (2/3),(1/9), (2/9)

-1

(x+1) is a factor.

-1/9===0== -7===2

9----- -9===2====0

(x+1)(9x^2-9x+2)

factor the last with +/- 1, 2.

second factors by noting x^2-9x+18 factors Into (x-6)(x-3)

divide the constant by 9 and put the denominator in front

(3x-2)(3x-1)

so the roots are -1, (2/3), and (1/3)

-

5x³+4x²-31x+6, note: I will assume 31 x.

Roots include (1/5)(2/5)(3/5)(6/5) along with

+/- 1,2,3,6, and 1, -1 do not work by inspection

2/5===4=== -31===6

5------14---- -3===0

so (x-2)(5x^2+14x-3)

or (x-2)(5x-1)(x+3) are the factors

roots are 2, (1/5), -3

hope this helps

The value of the expression 2x^2 where x = 5 and y = 2 is 8

The expression is given as

2x^2

From the question, we have the values of the x and y to be

x = 5 and y = 2

Substitute x = 5 and y = 2 in the expression 2x^2

So, we have

2x^2 = 2 x 2^2

Evaluate the exponent

So, we have

2x^2 = 2 x 4

Evaluate the product

So, we have

2x^2 = 8

Hence, the value of the expression 2x^2 where x = 5 and y = 2 is 8

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The result of simplifying each number 10,000⁰.⁷⁵ using the properties of exponents is 1

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

(10,000⁰)⁷⁵

Using the zero exponent rule that indicates that: any base with an exponent of zero is equal to one, we have:

1⁷⁵

One multiplied by itself many time will be one

1

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:

=-1.66

Step-by-step explanation:

2 nickles, 6 dimes. Not 100% sure but I think it's right

Answer:

26

Step-by-step explanation:

Answer: 26

Step-by-step explanation: When rounding you have to look and see if your number is above or below 5. Let's take your number for example.

25.9

Focus on the decimal point. If you notice, the number after the decimal point is above 5, therefore you should round it off to 26.

Hope it helps ^^

The solution to given equation 5x - 12 - 6x = -10x + 7 - 1 is x = 2.

In this question,

we have been given an equation  5x - 12 - 6x = -10x + 7 - 1

We need to solve above equation using given steps.

5x - 12 - 6x = -10x + 7 - 1                   .................(Given equation)

Step 1. Collect like terms

⇒ (5x - 6x) - 12 = -10x + (7 - 1)

⇒ -x - 12 = -10x + 6

Step 2.Move variables to one side of the equation (addition/subtraction property of equalities)

⇒ -x + 10x -12 = 6

Step 3. Move constant to the other side of equation (Addition/subtraction property of equalities)

⇒ 9x = 6 + 12

⇒ 9x = 18

Step 4.(multiplication/division property of equalities)

⇒ x = 18 ÷ 9

⇒ x = 2

Therefore, the solution to given equation 5x - 12 - 6x = -10x + 7 - 1 is         x = 2.

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The inverse function of  f(x) = √x + 2 would be f⁻¹(x) = x² - 2.

The domain of the function would be {x ∈ R, x ≥ −2}.

The range would be {y ∈ R, y ≥ 0}.

The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.

Considering f(x) = y, to find the inverse function, the x and y values are switched giving the new equation of

x = √y + 2

Simplifying the above equation, we get

x - 2 = √y

x² - 2 = y

x² - 2 = y is the inverse of the function f(x)=√x+2

The domain of the function would be all x, such that x + 2 ≥ 0, or x ≥ −2.

Hence it is {x∈R, x ≥ −2}

For range, consider y =√x + 2.

Since√x+2 ≥ 0, it is obvious that y ≥ 0.

The range would be {y ∈ R, y ≥ 0}

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The number of newspapers that each bundle have contained will be 23373 newspapers.

From the information, the printing press printed 934,920 newspapers, which were bound into 40 identical bundles for easy transportation.

Therefore, the number of newspapers that each bundle have contained will be:

= Total newspaper / Number of bundle

= 934920 / 40

= 23373

Therefore, the number of newspapers that each bundle have contained will be 23373 newspapers.

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Last month, a printing press printed 934,920 newspapers, which were bound into 40 identical bundles for easy transportation. How many newspapers could each bundle have contained

The give expression can be written in the simplest form by solving the exponents.

The rules applicable to the expression are rule for negative exponent and power rule of exponents. Either one can be used first. In this case we will multiply the exponents and then solve for the negative exponent.

According to the power rule of exponents, when an exponential expression is raised to a new power, the exponents are multiplied i.e. (a^x)^y=a^xy

(x^2/3)^-3=x^(2/3)*-3=x^-2

According to the rule of negative exponents, the term with the negative exponent can be solved by expressing it as a reciprocal of the term i.e. a^-x=1/a^x

x^-2=1/x^2

The simplest form of the expression (x^2/3)^-3 is 1/x^2.

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The expression to find the temperature at the end of the day is Morning temperature + (Change in temperature) and we get the temperature as -24 degree Fahrenheit.

Given,

The Morning temperature = 15°F

Change in temperature during day time = fall by 39 degree Fahrenheit

The temperature of the end of the day:

Morning temperature + (change in temperature)

Fall by 39° = decrease in temperature by 39° = - 39°

Therefore,

Substitute the values in the expression:

That is,

15°F + (-39°F)

15°F - 39°F

= - 24°F

Therefore, the expression to find the temperature at the end of the day is Morning temperature + (Change in temperature) and we get the temperature as -24 degree Fahrenheit.

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Factorization of 25 yields 5×5. In index form, this is written as 5^2. Use the power rule (a^m)^n = a^mn

25=5^2

25^(3/2) = (5^2)^(3/2)

5^(2x3/2)= 5^3

5x5x5 = 125

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After simplification of m9m - 3 the answer is 3(3[tex]m^{2}[/tex] - 1).

Given that :

= m9m - 3

a. Reordering terms:

= 9mm - 3

b.Exponents combining:

= 9mm -3

= 9[tex]m^{2}[/tex] - 3

c.Common value factor:

= 9[tex]m^{2}[/tex] - 3

Take 3 has common

= 3(3[tex]m^{2}[/tex] - 1)

Therefore after simplification of m9m - 3 the answer is 3(3[tex]m^{2}[/tex] - 1).

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In 5 weeks Joe's brother will have more money than Joe

Joe and his brother are collecting money for charity

Joe has collected $170 and he plans to earn $20 weekly

His brother has already collected $80 and he plans to earn $40 weekly

Let's start off with Joe and the amount he will be earning weekly

First week: 170 + 20 = 190

Second week: 190 + 20 = 210

Third week: 210 + 20 = 230

Fourth week: 230 + 20= 250

Fifth week: 250+20= 270

Next is to calculate Joe's brother earnings

First week: 80 + 40 = 120

Second week: 120 + 40 = 160

Third week: 160 + 40 = 200

Fourth week: 200 + 40= 240

Fifth week: 240 + 40 = 280

In five weeks Joe's brother will earn $280 while Joe will earn $270

Hence Joe bother will have more money that joe in 5 weeks

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Answer:

line J and line L are parallel so C.

The parallel line are j and l.

Hence the correct answer is c.

Given are four lines that have been graphed on the same coordinate grid.

We need to check which of these are parallel to each other.

To determine which lines are parallel to each other, we need to compare their slopes. Parallel lines have the same slope.

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Let's identify the slopes of the given lines:

Line j: y = (2/3)x + 1/2

Slope of j: 2/3

Line k: y = (1/2)x + 2/3

Slope of k: 1/2

Line l: y = (2/3)x + 3/2

Slope of l: 2/3

Line m: y = (3/2)x + 1/2

Slope of m: 3/2

Now, let's see which lines have the same slope:

A. k & m - The slopes are different (1/2 and 3/2). These lines are not parallel.

B. k & l - The slopes are different (1/2 and 2/3). These lines are not parallel.

C. j & l - The slopes are the same (2/3). These lines are parallel.

D. j & m - The slopes are different (2/3 and 3/2). These lines are not parallel.

So, the correct answer is:

C. j & l

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The square is rotated 90° clockwise about the origin to new points A'(2, 2), B'(4, 2), C'(4, 4) and D'(2, 4)

Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.

Rotation is the flipping of a figure about a fixed point.

Square ABCD have vertices at A(-2, 2), B(-2, 4), C(-4, 4) and D(-4, 2). The square is rotated 90° clockwise about the origin to new points A'(2, 2), B'(4, 2), C'(4, 4) and D'(2, 4)

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An inequality that represents the situation is 50 ≤ x ≤ 1000

And the inequality in interval notation is  [50, 1000]

In this question, we have been given a situation - an essay contest requires that entries be within 50 words of 1000 words long.

We need to write an inequality that represents the situation using the variable x.

Also, we need to write the inequality in interval notation.

Let x represents the number of words.

An essay contest requires that entries be within 50 words of 1000 words long.

So, we get an inequality,

50 ≤ x ≤ 1000

and the corresponding interval notation for above inequality would be,

[50, 1000]

Therefore, an inequality that represents the situation is 50 ≤ x ≤ 1000

And the inequality in interval notation is  [50, 1000]

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Answer:

having two side equal on triangle

Answer:

if the two side of triangle is same then we can say that the triangle is isosceles triangle

Applying the arithmetic sequence formula, the perimeter of the triangle is: 123 cm.

An arithmetic sequence formula is given as, T(n) = a + (n - 1)d, where a is the first term; n is the nth number of terms; d is the common difference.

Applying the arithmetic sequence formula to this problem, we have the following:

n = 121

a = 3

d = 1

Substitute

T(121) = 3 + (121 - 1)1

T(121) = 3 + (120)1

T(121) = 3 + 120

T(121) = 123

Therefore, applying the arithmetic sequence formula, the perimeter of the triangle is: 123 cm.

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The mean would be 23.

GIven that

list of observations is:  (12, 30, 19, 27, 21, 35)

Number of observations = 6

What is a mean?

The mean is the average or the most common value in a collection of  numbers.

Mean = Sum of the numbers / Total no. of observation

Mean = (12+ 30+ 19+27+ 21+ 35)/6

Mean = 144 / 6

Mean =24

If 17 was added to the list the number of observations = 7

new obersation list = (12, 30, 19, 27, 21, 35 , 17)

Sum of the new observation = 161

mean = 161 /7

mean = 23

Hence, the mean would be 23 if 17 were added to the given list.

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Answer:

15/50

Step-by-step explanation:

[tex]\frac{6}{20}[/tex] = [tex]\frac{x}{50}[/tex]  Cross multiply

20x = 6(50)

20x = 300   Divide both sides by 20

x = 15

Answer:

He will have it on the 15th day

They spent 1/70 of their monthly income on other things.

The family spent GH¢60,000 on clothing.

The monthly income of the family is GH¢168,000.

What is Fraction?

The number is expressed as a quotient in which the numerator is divided by the denominator is called fraction.

Since, The family spend;

On food = (3/7)*x

On clothing = (5/14)*x

On rent = (1/5)*x

Let the family's monthly income = x

Now, To find the fraction of the family's income is spent on other things, we can assume that y is spent on other things, then we should have;

(3/7)*x + (5/14)*x + (1/5)*x + y*x = x

We can divide both sides by x, we get:

(3/7) + (5/14) + (1/5) + y = 1

Now, we can solve this for y as;

3/7 + 5/14 + 1/5 + y = 1

6/14 + 5/14 + 1/5 + y = 1

(6 + 5)/14 + 1/5 + y = 1

11/14 + 1/5 + y = 1

The smallest common factor of 14 and 5 =  14*5 = 70

So, we can multiply in the first fraction by 5/5 and the second by 14/14,

(5/5)*(11/14) + (14/14)*(1/5) + y = 1

55/70 + 14/70 + y = 1

69/70 + y = 1

y = 1 - 69/70

y = 1/70

Hence, They spent 1/70 of their monthly income on other things.

And, On a particular month, the family spends  GH¢2,400 on other things, then if the monthly income is x, we have:

(1/70)*x = GH¢2,400

x = 70* GH¢2,400

x = GH¢168,000

So, The monthly income of the family is GH¢168,000

And, we know that they spend (5/14)*x on clothing,

Then this month they spent on clothing,

⇒ (5/14)*GH¢168,000 = GH¢60,000

So, They spent 1/70 of their monthly income on other things.

The family spent GH¢60,000 on clothing.

The monthly income of the family is GH¢168,000.

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The numbers are 8 and 24.

Let the smaller number be x.

Larger number = 3x

Therefore, the expression will be:

3x - 10 = x + 8

Collect like terms

3x - x = 8 + 10

2x = 18

Divide

x = 18/2

x = 9

The bigger number will be:

3x = 3 × 8 = 24

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The transformations that take rectangle ABCD to rectangle A'B'C'D' are given as follows:

Transformations in the graph of a function involve operations such as multiplication/division or sum/subtraction, either in the domain of the function, involving values of x, or the range, involving values of y.

Examples of transformations are as follows:

For this problem, we have that:

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After solving the given equation  [tex]2 e^{x-2}=e^x+7[/tex], the value of [tex]x=\ln 7-\ln \left(2 e^{-2}-1\right)[/tex].

So,

Given equation: [tex]2 e^{x-2}=e^x+7[/tex]

Then,

[tex]2 e^{x-2}=e^x+7\\2 \frac{e^x}{e^2}=e^x+7\\2 \frac{e^x}{e^2}-e^x=7\\e^x\left(2 e^{-2}-1\right)=7\\e^x=\frac{7}{\left(2 e^{-2}-1\right)}\\x=\ln \left(\frac{7}{\left(2 e^{-2}-1\right)}\right)\\x=\ln 7-\ln \left(2 e^{-2}-1\right)[/tex]

Therefore, after solving the given equation  [tex]2 e^{x-2}=e^x+7[/tex], the value of [tex]x=\ln 7-\ln \left(2 e^{-2}-1\right)[/tex].

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The formula given in the question is Doughnuts are T=4 B+ 10C.

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given:

The given question is Doughnuts are sold in bags and cartoons.

It contains 4 bags of  Doughnuts and cartoon hold 10 Doughnuts.

According to given question we have

Let the total Doughnuts be T.

Let the bags of Doughnuts be B

Let the carton of Doughnuts be C.

1 bags of Doughnuts = B

4 bags of Doughnuts =4 B

1 carton of Doughnuts = C.

10 carton of Doughnuts = 10C.

To write the formula we gave,

T=4 B+ 10C.

Therefore, the formula given in the question is Doughnuts are T=4 B+ 10C.

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A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. If For a given recipe, 24 cups of flour are mixed with 16 cups of sugar. then 21 cups of flour should be used if 14 cups of sugar are used.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

24 cups of flour are mixed with 16 cups of sugar.24:16

x cups of flour should be used if 14 cups of sugar .x:14

Now

24/16=x/14

Cross multiply

24*14=16x

336=16x

x=21.

Therefore 21 cups of flour should be used if 14 cups of sugar are used.

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