Pls help me solve only letter “a” and “b”

1. 3x = log6 216

3x = 3

x = 1

2. x - 4 = log3 243

x - 4 = 5

x= 9

3. log4 (4x - 20) = 5

4x - 20 = 45

4x = 65

x = 16.25

A logarithmic function is a type of mathematical function that relates two quantities by the use of logarithms. In particular, a logarithmic function describes the relationship between the input (or independent variable) and the output (or dependent variable) in terms of the logarithm of the input.

The general form of a logarithmic function is:

f(x) = loga(x)

where f(x) is the output, x is the input, and a is the base of the logarithm The logarithm of a number x with respect to a base a is the power to which a must be raised to obtain x. For example, if a is 10, then log10(100) = 2, because[tex]10^2[/tex] = 100.

Logarithmic functions are useful for expressing quantities that vary over a large range of values, such as the brightness of stars or the acidity of solutions. They can also be used to solve exponential equations or to represent data that follows a certain pattern.

In particular, logarithmic functions have the property that they can "undo" exponential functions. That is, if we have an exponential function f(x) =[tex]a^x[/tex], then its inverse function is given by [tex]f^-1(x)[/tex] = loga(x). This property is often used in calculus and other areas of mathematics.

Logarithmic functions can be graphed in a variety of ways, depending on the base and other parameters of the function. The graph of a logarithmic function typically looks like a curve that gets steeper as it moves away from the origin.

In summary, a logarithmic function is a type of mathematical function that relates two quantities by the use of logarithms. They are useful for expressing quantities that vary over a large range of values and can "undo" exponential functions.

1. 3x = log6 216

3x = 3

x = 1

2. x - 4 = log3 243

x - 4 = 5

x= 9

3. log4 (4x - 20) = 5

4x - 20 = 45

4x = 65

x = 16.25

4. log9(3 - x) = log9 (5x – 15)

3 - x = 5x - 15

4x = 18

x = 4.5

5. log81 (x + 20) = log81 (6x)

x + 20 = 6x

5x = 20

x = 4

6. log9[tex](3x^2)[/tex] = log9 (2x + 1)

[tex]3x^2[/tex] = 2x + 1

[tex]3x^2[/tex] - 2x - 1 = 0

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

x = -1/3 or x = 1 (but x = -1/3 doesn't work because it results in a negative argument of the logarithm)

7. log4(x - 1) = log4(12)

x - 1 = 12

x = 13

8. log7(5 - x) = log7 (5)

5 - x = 5

x = 0

9. logx (5x) = 2

5x = [tex]x^2[/tex]

[tex]x^2[/tex] - 5x = 0

x(x - 5) = 0

x = 0 or x = 5 (but x = 0 doesn't work because it results in an undefined logarithm)

10. log5 (-3x) < 1

-3x < 5

x > -5/3

11. log6x > log6 (4 - x)

x > 4 - x

2x > 4

x > 2

12.  log10 (x - 3) < 2

x - 3 < 100

x < 103

13. log2 (x - 5) > log2 (3)

x - 5 > 3

x > 8

14. log7 (8x + 5) > log7 (6x - 18)

8x + 5 > 6x - 18

2x > -23

x > -11.5

15. log9 (3x - 3) < 1.5

3x - 3 < 27

x < 10

16. log10 (2x - 2) < log10 (7 - x)

2x - 2 < 7 - x

3x < 9

x < 3

17. log9 (x - 1) > log9 (2x)

x - 1 > 2x

-x > -1

x < 1

18. log16 x ≥ 0.5

x ≥ √16

x ≥ 4

19. log3 (−x - 34 + 5) > log3 (x + 2)

-x - 29 >

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Answer:

x=-5, you have to rearrange the x and 12 and then subtract 12 from both sides and you get the answer -5. x+12=7

The  slope-intercept form is  y=(1/2)x+3

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

A linear equation is an equation in which each term has at max one degree. Linear equations in variables x and y can be written in the form

y = mx + c

3x + 2y = 4x + 6

Move 3x to the right

=> 2y= 4x -3x + 6

=> 2y = x+6

=> y=(1/2)x+3

This is in slope-intercept form y=mx+b

m= 1/2 = slope

b= 3 = y intercept

The  slope-intercept form is  y=(1/2)x+3

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Mr. Davis' granola snacks will last for 20 days.

What is division ?

Division is a basic arithmetic operation used to find the quotient or the number of times one quantity is contained within another. In division, a dividend is divided by a divisor, and the result is the quotient. For example, 12 divided by 3 is 4, where 12 is the dividend, 3 is the divisor, and 4 is the quotient.

Division is the inverse operation of multiplication. If you know the multiplication facts, you can use them to help you divide numbers. For instance, if you know that 5 times 6 equals 30, then you also know that 30 divided by 5 equals 6, and that 30 divided by 6 equals 5.

According to given conditions:

To find out how many days Mr. Davis' granola snacks will last, we need to divide the total amount of granola by the amount he eats each day.

Let's say Mr. Davis made 10 lbs of granola snacks.

He eats 0.5 lb each day.

So we can use the formula:

Number of days = Total amount of granola / Amount eaten each day

Number of days = 10 lbs / 0.5 lb per day

Number of days = 20 days

Therefore, Mr. Davis' granola snacks will last for 20 days.

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Rhombus question:

Opposite sides are equal so we will set x+25 and 3x-55 equal to each other.

x+25=3x-55

Subtract x to both sides:

25=2x-55

Add 55 to both sides:

2x=80

Divide 2 to both sides:

x=40

Now we will find the value of y. Remember a triangle adds up to 180 degrees, so we will add all 3 angles and set it equal to 180. The square means 90 degrees.

40+25+90+y=180

Combine like terms:

155+y=180

Subtract 155 to both sides:

y=25

Rectangle question:

Given that AE=x+16 and EC=2x-4. To solve this, you will add these two given lines together because AE+EC=AC.

x+16+2x-4

Combine like terms:

3x-12

l & m, solve for x:

Using alternate angles, we will know that 95 and x are supplementary, so they add up to 180.

95+x=180

Subtract 95 to both sides:

x=85

n & m:

Use alternate angles, think about zig zag:

1=8, 2=6, 4=5, 3+5=180

l & m solve for y:

First we will need to find the x value to solve for y. Using alternate angles, the two expressions are equal. So set the equal.

29x+2=30x-1

Subtract 29x to both sides:

2=x-1

Add 1 to both sides:

x=3

Now we will solve for y. Using alternate angles, both expressions are equal to y, we can pick any.

30x-1=y

Substitute:

30(3)-1=y

Calculate:

90-1=y

Calculate:

y=89

hope this helped!

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Answer: Thor got 32 magic pencils

Step-by-step explanation: The ratio say it is 4:6:3 which means that we have to add them together to get the total. 4+6+3=13. Now that we know we have 13 parts we need to divide by 104 to get the answer, 104/13=8, Thor got 4 parts, as we know from the problem so we multiply 8 by 4 and we get 32.

One meter is equal to 39.3701 inches

To convert 1 meter to inches, we can use the following formula:

1 meter = 39.3701 inches

The conversion factor is 39.3701

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in inches = conversion factor × The length in meter

Substitute the values in the equation

1 meter = 39.3701 × 1

Multiply the numbers

= 39.3701 inches ( rounded to four decimal places )

Therefore, one meter is 39.3701 inches

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Answer:

Step-by-step explanation:  15 feet of the ladder will be under the water because at first the ladder was 10 feet long then it  rises from under water

Answer:

[tex]y = -\frac{5}{3}x-7[/tex]

Step-by-step explanation:

We are given three coordinates. First, we have to find the slope. We can do this by counting the slope of two points which we will do for simplicity's sake.

[tex]\frac{rise}{run}[/tex] gives us [tex]-\frac{5}{3}[/tex] which we will use as the slope.

Looking at the graph, the y intercept of the equation is -7, so our equation would be [tex]y=-\frac{5}{3}x-7[/tex]

The the rectangular prisms have their volumes as:

1). 175 cubic feet

2). 60 cubic metres

3). 140 cubic metres

4). 216 square inches.

volume for a rectangular prism is calculated using:

length × width × height

the rectangular prisms can be divided into bigger and smaller prism and their volumes calculated separately and then added to get the total volume as follows:

1). volume of bigger rectangular prism = 7ft × 7ft × 3ft = 147ft³

volume of smaller rectangular prism = 7ft × 2ft × 2ft = 28ft³

volume of object = 147ft³ + 28ft³ = 175ft³

2). volume of bigger rectangular prism = 6m × 3m × 3m = 54m³

volume of smaller rectangular prism = 3m × 3m × 1m = 6m³

3). volume of bigger rectangular prism = 7m × 6m × 3m = 126m³

volume of smaller rectangular prism = 7m × 2m × 1m = 14m³

volume of object = 126m³ + 14m³ = 140m³

4). volume of bigger rectangular prism = 12in × 4in × 4in = 192in²

volume of smaller rectangular prism = 4in × 3in × 2in = 24in³

volume of object = 192in³ + 24in³ = 216³

Therefore, the rectangular prisms have their volumes as:

1). 175 cubic feet

2). 60 cubic metres

3). 140 cubic metres

4). 216 square inches

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an example of a matrix A and a vector b such that the solution set of Ax=b is a line in R3 that does not contain the origin will be= 1 0 0 0 ,0 1 0 0 , 0 0 0 0]

[tex]AX = \left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}x\\4\\2&\end{array}\right][/tex]

and b = [tex]\left[\begin{array}{ccc}6\\14\\30&\end{array}\right][/tex]

the augmented matrix is [A:B] = [tex]\left[\begin{array}{ccc}1&1&1\\1&2&3\\1&4&7\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}6\\14\\30&\end{array}\right][/tex]

we shall reduced the augmented matrix [A;B] to echelon form by applying elementary row transformation only.

operating  [tex]R_{2} , R_{2} - R_{1} , R_{3} ,R_{3} -R_{1}[/tex]

[tex][A:B] = \left[\begin{array}{ccc}1&1&1\\0&1&2\\0&3&6\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}6\\8\\24&\end{array}\right][/tex]

operating [tex]R_{3} , R_{3} - 3R_{2}[/tex]

      ≈ [tex]\left[\begin{array}{ccc}1&1&1\\0&1&2\\0&0&0\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}6\\8\\0&\end{array}\right][/tex]

which is the row echelon form of the matrix [A:B].

A matrix that has gone through the Gaussian end is supposed to be in column echelon form or, all the more appropriately, "decreased echelon form" or "line diminished echelon form." Such a matrix has the accompanying qualities:

1. Every one of the zero columns are at the lower part of the matrix

2. The main passage of each nonzero column after the first happens to one side of the main section of the past line.

3. The main passage in any nonzero column is 1.

4. All sections in the segment above and under a main 1 are zero.

One more typical meaning of echelon form just requires zeros beneath the main ones, while the above definition additionally requires them over the main ones.

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The method to convert mililitres to litres is the formula - Quantity in litres = quantity in mililitres/1000.

Remember that ml is the unit of volume which is abbreviated to mililitres. Now, going to the relation between mililitres and litres. We are aware that 1 litre is equal to 1000 mililitres. So, converting mililitres to litres, we need to use the following formula -

Quantity in litres = quantity in mililitres/1000

Using an example to verify the mentioned relation. Let us say we have 4000 mililitres of acid. So, what will be the volume of acid in litres.

Quantity of acid in litres = 4000/1000

Performing division

Quantity of acid in litres = 4 litres

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16 is the required coordinate of point C

A line is defined as the shortest distance between 2 points

Given the following parameters from the number line

Point M = 2

Point J = 18

The coordinate of point C that is 7/8 of the distance from M to J

C = 7/8 of MJ

C = 7/8 * (18 - 2)

C = 7/8 * 16

C = 14

Hence the point C that is 7/8 of the distance from M to J is 16

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Substituting x = 2 in each function, we get:

A. f(x) = 8x – 2 --> f(2) = 8(2) - 2 = 14 (not a match)

B. f(x) = 4x + 4 --> f(2) = 4(2) + 4 = 12 (a match)

C. f(x) = 6x – 4 --> f(2) = 6(2) - 4 = 8 (not a match)

D. f(x) = –4x – 4 --> f(2) = -4(2) - 4 = -12 (not a match)

Therefore, the equation of the function could be f(x) = 4x + 4 (option B).

Answer:

La respuesta correcta es (C) 0,39 ± 1,96 (√(0,39)(0,61)/500).

Para estimar el intervalo de confianza al 90%, necesitamos encontrar el valor crítico de Z correspondiente al nivel de confianza del 90%. Para un nivel de confianza del 90%, el valor crítico de Z es 1,96.

La fórmula para el intervalo de confianza es:

p ± Z*√(p(1-p)/n)

Donde:

p es la proporción observada en la muestra

Z es el valor crítico de Z para el nivel de confianza deseado

n es el tamaño de la muestra

Sustitución

0,39 ± 1,96 (√(0,39)(0,61) /500)

lo cual nos da un intervalo de confianza del 90% para la proporción de personas que ven cómo se brinda por su raza.

Step-by-step explanation:

espero te sirva, si no puedes español traducelo

Option A. 57. Roman numerals use letters from the Latin alphabet to represent numbers. The Roman numeral LVII represents the number 57.

The basic symbols used in the Roman numeral system are I, V, X, L, C, D, and M, which represent the numbers 1, 5, 10, 50, 100, 500, and 1,000, respectively. By combining these symbols, larger numbers can be formed.

In the case of LVII, the symbol L represents 50, the symbol V represents 5, and the symbol II represents 2. To get the total value of the Roman numeral, we add up the values represented by each symbol. So:

LVII = L + V + II

= 50 + 5 + 2

= 57

Therefore, the Roman numeral LVII represents the number 57.

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What number does the roman numeral LVII represent?

A. 57

B. 58

C. 59

D. 60

2030 military time is equivalent to 8:30 PM in standard 12-hour time notation.

2030 is a military time notation for 8:30 PM in standard 12-hour time notation.

In military time, the 24-hour clock is used, where the first two digits indicate the hour and the last two digits indicate the minutes. The hour digits range from 00 to 23, and the minute digits range from 00 to 59.

To convert 2030 military time to standard 12-hour time notation, you can use the following steps:

Check if the hour digits are greater than 12. If the hour digits are 13 or higher, subtract 12 from the hour digits to get the equivalent hour in standard time notation.

Add "PM" after the hour and minute digits to indicate that it is in the evening.

Using these steps, we can convert 2030 military time to 8:30 PM in standard time notation:

Since the hour digits 20 are greater than 12, we subtract 12 from 20 to get 8.

Add "PM" after 8:30 to indicate that it is in the evening.

Therefore, 2030 is 8.30 PM

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(a) The expected profit of this policy to the insurance company is $520.10.

(b) The interpretation value of expected profit in (a) in the context of the problem is small probability of the policyholder's death.

(a) The expected profit to the insurance company can be calculated as follows:

Expected Profit = (Probability of Survival * Premium) - (Probability of Death * Death Benefit)

Probability of Survival = 0.997

Probability of Death = 1 - Probability of Survival = 1 - 0.997 = 0.003

Premium = $780

Death Benefit = $250,000

Expected Profit = (0.997 * $780) - (0.003 * $250,000) = $520.10

Therefore, the expected profit to the insurance company from selling this policy is $520.10.

(b) The expected profit of $520.10 represents the average profit that the insurance company can expect to earn from selling this type of policy to similar customers over time.

In the context of this problem, it means that if the insurance company sells many policies like this one, they can expect to make a profit of about $520.10 per policy, on average, after accounting for the small probability of the policyholder's death.

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Answer:

1ft = 0.000189394 miles

Step-by-step explanation:

A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

Therefore, for every one foot it is equivalent to 0.000189394 miles.

The solution to the system of equation y = 5x + 4 and y = 6x + 1 is (3,19).

Given the system of equation in the question;

y = 5x + 4

y = 6x + 1

To solve the system of equation, first plug equation one into equation two and solve for x.

y = 6x + 1

Plug in y = 5x + 4

5x + 4 = 6x + 1

Solve for x

6x - 5x = 4 - 1

x = 3

Now, plug x = 3 into equation one and solve for y.

y = 5x + 4

Plug in x = 3

y = 5( 3 ) + 4

y = 15 + 4

y = 19

Therefore, the value of x is 3 and y is 19.

Option A) (3,19) is the correct answer.

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The value of 0.4375 in fractional form is 7/16.

Parts of a whole numbers are represented by fractions, where the denominator represents the entire object and the numerator the equal part.

By dividing a number by 10 for each digit after the decimal, we may eliminate the decimal and turn it into a fraction.

The decimal point is followed by four integers, thus we will divide it by 10,000.

= 4375 / 10000

Simplifying fraction yields the result

= 4375 ÷ 5 / 10000 ÷ 5

= 875 ÷ 5 / 2000 ÷ 5

= 175 ÷ 5 / 400 ÷ 5

= 35 ÷ 5 / 80 ÷ 5

= 7 / 16

In addition, they are comparable fractions.

The fractional equivalent of 0.4375 is 7/16.

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Complete question - what is 0.4375 as a fraction?

To determine whether the relation is a function, we need to check if each x-value is associated with only one y-value in the mapping diagram.

A mapping diagram is a picture of two circles that shows the connection between input and output values. Illustration of a mapping diagram. The x-values (inputs) in the image are converted to the associated y-values by drawing an arrow from one x-value to its corresponding y-value (outputs).

From the given mapping diagram, we can see that the x-value -8 is associated with the y-value -4, the x-value -5 is associated with the y-value -2, the x-value -1 is associated with the y-value -2, the x-value 1 is associated with the y-value -2, the x-value 12 is associated with both the y-value -4 and -2.

Since the x-value 12 is associated with two different y-values, the given relation is not a function. To be a function, each x-value must be associated with only one y-value in the mapping diagram.

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Answer: I think its C lmk if I'm wrong

Explanation:

Answer:

ED

Step-by-step explanation:

Since,

Δ ABC ≅ Δ DEF

Side AB is congruent to side DE

Or

BA is congruent to ED.

the length of the long leg (the side opposite the 60-degree angle) is x√3, which is:

(7/2)√3 ≈ 6.06

What is the hypotenuse?

In geometry, the hypotenuse is the longest side of a right-angled triangle, opposite to the right angle.

In a 30-60-90 triangle, the ratio of the side lengths is x : x√3 : 2x, where x is the length of the shorter leg, and 2x is the length of the hypotenuse.

Since the hypotenuse of this triangle is 14, we can set 2x = 14 and solve for x:

2x = 14

x = 7/2

Hence, the length of the long leg (the side opposite the 60-degree angle) is x√3, which is:

(7/2)√3 ≈ 6.06

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Answer:

8/100 or 2/25

Step-by-step explanation:

The decimal 0.08 can be written as the fraction 8/100 or, in simplest form, 2/25.

Answer:

-4

Step-by-step explanation:

7(-1)³ + 5(-1)² -2 = ?

-7 + 5 -2 = ?

-2 -2 = ?

? = -4

Answer:

Step-by-step explanation:

195lbs to kg is 88.4505

The area of the purple ring is 10,843.079 ft²

Remember that for a circle of radius R the circumfernce is:

C = 2*3.14*R

Here we know that the circumference of the inner circle is C = 221.056 ft

Then the radius will be:

221.056 ft = 2*3.14*R

221.056 ft/(2*3.14) = R

35.2 ft = R

Then the radius of the outer circle is:

R' = 35.2ft + 33.3ft = 68.5 ft

The area of the ring is the diffence between the areas of the larger circle and the smaller circle, then:

area = 3.14*( (68.5 ft)² - (35.2 ft)²) = 10,843.079 ft²

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Answer:
Unit Rate: $10/km

Equation: x=y/10 or y=10x