As a math citizen, why is it important to be able to interpret and analyze graphs?​

The provided in its extended form logarithms ( log₃2/x).  = 2log3 + log x.

The fact that logs represent exponents gives rise to four fundamental properties. The first three are easy to remember: A product's log equals the total of its elements' logs. The log of a quotient is proportional to the distinction between the numerator as well as denominator logs. Power multiplied by that of the logarithmic of the base equals the log of power.

log₃2/x

Applying the property of log  (log a/b = log a +log b)

log₃2/x

log₃2 + log x

Applying the property (logₐᵇ = a log b)

log₃2

2log3

we get substituting the.(log₃2 + log x)

2log3 + log x

The provided in its extended form logarithms ( log₃2/x).  = 2log3 + log x.

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Answer:

10 pencils

Step-by-step explanation:

16-x = 36-3x

16-36 = -3x+

thus x = 10

If the expression is log₂9-log₂3, then it will look like [tex]log_{2}3[/tex] in single logarithm.

Given that the expression is log₂9-log₂3.

We have to give the single logarithm for the given expression.

The quotient rule for logarithms tells us that the logarithm of a quotient is equal to a difference of logarithms. Just as with the product rule we also can use the inverse property to derive the quotient rule. The quotient property basically says that log (m/n)=log m-log n.

The expression is log₂9-log₂3.

log₂9-log₂3=[tex]log_{2}[/tex](9/3)

We can write it as [tex]log_{2}3[/tex].

Hence if the expression is log₂9-log₂3, then it will look like [tex]log_{2}3[/tex] in single logarithm.

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Answer:

= 17

Step-by-step explanation:

If f(x)=3x+2, then replacing x=5 we get f(5)=3x5+2=15+2=17

Answer:

the answer to the equations is 17

Step-by-step explanation:

The answers will be :

a. The length of the line segment will be equal to 8.24 units.

b. The midpoint of the line segment will be ( -2 , -2 ).

c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0

What is slope of a line segment ?

The ratio of the difference in y-coordinates over the equivalent x-coordinates between two different locations on a line.

It is given that a line segment has endpoints of Y(2,-3) and Z(-6,-1).

Let's solve the given parts based on the above data.

a.

The length of the line segment will be given by :

YZ = [tex]\sqrt({x_{2} - x_{1})^2 + (y_{2}- y_{1})^2}[/tex]

YZ = √ [( -6 -(2)]^2 + [ -1 - (-3)]^2}

YZ = √ (-8)² + 2²)

YZ = √68

YZ = 8.24 units

b.

The midpoint (say M) of the line segment will be given by :

M = ( [tex]\frac{x_{1} + x_{2} }{2} , \frac{y_{1} + y_{2} }{2}[/tex])

M = [(2-6)/2 , (-3-1)/2]

M = ( -2 , -2 )

c.

And the equation of line passing through points Y and Z will be :

[tex]y_{2} - y_{1}[/tex] = m ( [tex]x_{2} - x_{1}[/tex] )

Let's calculate value of slope (m) firstly which will be :

m =([tex]y_{2} - y_{1}[/tex]) / ( [tex]x_{2} - x_{1}[/tex] )

m = ( -1 + 3 ) / (-6 - 2)

m = 2 / -8

m = -1 / 4

or

m = -0.25

Using the value of slope (m) : we get the equation of line as :

[tex]y - y_{1}[/tex] = - 0.25 ( [tex]x - x_{1}[/tex] )

or

(y + 3) = - 0.25 ( x - 2)

y + 3 = -0.25 x + 0.50

or

y + 0.25 x - 2.5 = 0

If we multiply by 4 throughout the equation ; then the equation of line can also be written as :

4y + x - 10 = 0

Therefore the answers will be :

a. The length of the line segment will be equal to 8.24 units.

b. The midpoint of the line segment will be ( -2 , -2 ).

c. The equation of line passing through points Y and Z will be 4y + x - 10 = 0

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Expression as a single natural logarithm of 4 ln 3  is 4.39444915467

4 ln 3  

=[tex]ln 3^{4}[/tex]

= ln 81

=4.39444915467

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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Answer:

4(2)³+A×2²+7(2)-1=7

4×8+4A+14-1=7.

32+14-1-7=-4A..

38=-4A.

A=38/-4.

The required value of z using given conditions and functions is 7.92.

What is a function?

A function is defined as an expression or rule that specifies the relationship between two variables or objects, out of which one is dependent and the other is an independent variable. The image of each and every element is unique.

Calculation for the value of z

Given value of z = 1.5, x = 9, y = 4

Consider z as a function varying directly with x and inversely with y i.e.

z = kx / y        —-- 1

Putting the values of x, y, z, we get,

1.5 = k × 9 / 4

6 = 9 × k

k  = 6 / 9

k = 2 / 3 = 0.66

Now, calculating z for x = 6, k = 0.66 and y = 0.5, using function,

z = (0.66 × 6) / 0.5

= 3.96 / 0.5

= 7.92

Hence, the required value of z = 7.92.

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the slope is 3 for the equation

Answer:

the slope is 3 for the equation

Step-by-step explanation:

Answer:

0,896

Step-by-step explanation:

The exponential function for the value of car is V = 25,000 × e^( r × T) and the value of the car after 5 years is $ 1109.26.

The original value of a car is $25,000.

The value of the car after one year is $21,250.

Let V be the value of the car after T years.

Let the rate at which the value of the car increase be r.

From, [tex]\[ A = Pe^{r \times T} \][/tex]

Then,

[tex]\[ V = 25,000 \times e^{ r \times T } \][/tex]

The value of the car after one year is $21,250.

[tex]\[ 21,250 = 25000 \times e^{ r \times T } \][/tex]

Divide both sides by 25000

[tex]\frac{21250}{25000} = e^{1 \times r }[/tex]

Now, taking the log of both sides

[tex]\[ \ln (21250/25000) =\ln e^{1 \times r} \][/tex]

By the property of logarithm,

[tex]\ln e^{(1 \times r)} = r[/tex]

Therefore,

㏑(21250/25000) = r

Now, the value of the car after 5 years will be:

[tex]\[ V = 25,000 \times e^{ r \times T} \]\\\\[/tex]

[tex]\[ V = 25000 \times e^{ \ln (\frac{21250}{25000} ) \times 5 } \][/tex]

V = 25000 × 0.4437053125

V = $ 1109.26

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The amount in a continuously compounded account for the given conditions is $2330.64 .

It is given that principal is 2000 , annual interest rate is 5.1 % , time is 3 years

Putting [tex]P=\$2000 , \ r= 5.1\% , \ t=3 \ years[/tex] in equation (1) , we get

  [tex]A=2000\times 2.71^{0.051 \times 3}\\A=200\times 2.71^{0.153}\\ \ A=2000\times1.1653\\A =\$2330.64[/tex]

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x=0 is an extraneous solution of the equation and x = 8 is not an extraneous solution of the equation.

√(3x+1) - √(x+1) = 2

√(3x+1) = 2 + √(x+1)

Squaring both the sides of the equation

(√(3x+1))² = (2 + √(x+1))²

3x + 1 = (2)² + (√(x+1))² + 2(2) (√(x+1))

3x + 1 = 4 + x + 1 + 4(√(x+1))

3x + 1 = 5 + x + 4(√(x+1))

2x - 4 = 4(√(x+1))

Squaring again on both the side of the equation, we get

(2x - 4)² = (4(√(x+1))²

4x² + 16 - 16x = 16x + 16

4x² - 32x = 0

4x(x - 8) = 0

4x = 0 and x - 8 = 0

x = 0 and 8

Check for Extraneous Solution by keeping value of x in the original equation √(3x+1) - √(x+1) = 2

Let x=0

√(3(0)+1) - √(0+1) = 2

0 ≠ 2

LHS ≠ RHS

x = 0 is an extraneous solution of the equation

Let x=8

√(3(8)+1) - √(8+1) = 2

✓25 - ✓9 = 2

5 - 3 = 2

2 = 2

LHS = RHS

∴ x=8 is not an extraneous solution of the equation.

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Answer:x=21

Step-by-step explanation:

10/14=15/x

5/7=15x^-1

(5/7)/15=ans

ans=x^-1

ans^-1=21

Answer: x=21

Step-by-step explanation:

[tex]\frac{10}{14} =\frac{15}{x}[/tex]

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 14x, the least common multiple of 14,x.

x×10=14×15

Multiply 14 and 15 to get 210.

x×10=210

Divide both sides by 10.

x=

10

210

​

Divide 210 by 10 to get 21.

x=21

Answer:

2.5

Step-by-step explanation:

2 2/4

Simplify 2/4

2/4 = 1/2 = 0.5

2 2/4 = 2 + 0.5 = 2.5

2 2/4 = 2 1/2

2 1/2 = 2.50 (or just) 2.5

Answer: Solution is t = 905/8

Step-by-step explanation:

Given data,

         ttt:-\dfrac{7}{4}=\dfrac{2}{5}t− 47 = 52​ t

We can write,

              - 7/4 = (2/5) t - 47

Rearrange variables to the left side of the equation

               - (2/5) t = - 47 + 7/4

Find common denominator and write the numerators above common denominator

                 - (2/5) t = ( -188 + 7 ) / 4

calculate the sum or difference

                   - (2/5) t = -181/4

Divide both sides of the equation by the coefficient of variable

                      t = (-181/4) x (-5/2)

Determining the sign for multiplication or division

                       t = 181/4 x 5/2

Write as a single fraction

                          t = ( 181 x 5 ) / ( 4 x 2 )

Calculate the product or quotient

                          t =  (905/8)

Therefore,   t = 905/8

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After solving the equation the value of x in (4x - 1) = 36 is  37/4

We have been asked to find x in (4x - 1) = 36

⇒ (4x - 1) = 36

⇒ 4x = 36 + 1

⇒ 4x = 37

⇒ x = 37/4

So, x is equal to 37/4

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The required expression that describes the shaded region is (A'∩B) ∪ (A ∩ B'). Option A is correct.

GIven that,
For the given Venn diagram which expression represents the shaded area

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The total area of A and B
= AUB
Area of unshaded area,
= (A'∩B) ∪ (A ∩ B')

Thus, the required expression that describes the shaded region is (A'∩B) ∪ (A ∩ B'). Option A is correct.

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Answer:

Alternate Exterior Angles

Answer:

alternate interior angles

Answer:

B. x = (4/3)

Step-by-step explanation:

-x + (3/7) = 2x - (25/7)

(-x + (3/7) = 2x - (25/7)) × 7

-7x + 3 = 14x - 25

-14x        -14x

-21x + 3 = -25

         -3     -3

-----------------------

-21x = -28

÷-21    ÷-21

-----------------

x = (4/3)

I hope this helps!

Answer:

Triangular inequality:  Length of third side must be less than the sum of the lengths of the other 2 sides.

x < 18 + 29

x < 47

so Maximum length of third side is 46 units.

Also 29 < 18 + x

x > 11    so minimum length = 12

Difference  = 46-11 = 35

the extraneous solution for the equation √ (x + 3) - 1 = x is x = 1 or x = - 2.

We are given an equation:

√ (x + 3) - 1 = x

√ (x + 3) = x + 1

Raise both sides to the power 2, we get that:

x + 3 = x² + 1 + 2 x

x² + 2 x - x + 1 - 3 = 0

x² + x - 2 = 0

x² + 2 x - x - 2 = 0

x ( x + 2) - 1 ( x + 2) = 0

(x - 1)(x + 2) = 0

x = 1 or x = - 2.

Therefore, we get that, the extraneous solution for the equation √ (x + 3) - 1 = x is x = 1 or x = - 2.

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An explicit formula for Mallory's run will be 15 + 5x.

Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that on June 1st, she starts by running for 15 minutes, and every day after that she adds 5 minutes to her run.

Equation = 15 + 5x, where x is the number of days.

Therefore, the explicit formula for Mallory's run will be 15 + 5x.

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Answer: The monthly payment assuming that each month he paid the same amount is = 362.5 $

Step-by-step explanation:

Given data,

Johnny bought a used car for  $7,500

He had $4600 and borrowed the rest from his parents.

Johnny 8 months to pay back the money he borrowed

So, we can write ,

Let us assume,   x1 = $7,500  and  x2 = $4600

Based on the given conditions,

we use formula is :

                          x = ( x1 - x2 ) / pay back months

                          x = ( 7,500 - 4,600 ) / 8

we can subtract the values,

we can write,

                    x = 2900/8

                      x = 725/2

                      x = 362.5 $

Therefore,

The monthly payment assuming that each month he paid the same amount is = 362.5 $.

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The mentioned number in word form is three hundred ten, seven hundred sixty three, one hundred thirty six.

The arithmetic value of a number is one that is used to denote quantity. As a result, a number is a mathematical concept used for counting, measuring, and labeling. As a result, mathematics is based on numbers.

Early humans used a variety of symbols to represent numbers, as evidenced by the inscriptions discovered at archaeological sites. For instance, farmers, traders, and merchants in antiquity used tally marks to indicate quantities. A standing line is drawn for each count in tally marks, and the fifth count is indicated by crossing out the first four lines. However, this was a laborious method and it was impractical to display quantities.

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If the length of the rectangle given is larger than the width of the rectangle then the inequality which represents given situation is 13x-9 > 4.5x+8

What is an inequality?

Inequality is a kind of equation which compares two mathematical expressions instead of equating them using relations like less than, greater than, less than or equal to, greater than or equal to.

Given that Victoria drew a diagram of her laptop which is in the shape of the rectangle. The dimension are Length 13x-9 and width 4.5x+8

If the length is given greater than width, then this can be represented by  inequality: length > width

i.e. 13x-9 > 4.5x+8

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The complete question is mentioned below :

Victoria drew a diagram of her laptop that she uses at school. It is in the shape of a rectangle. The dimensions are as follows:

Length: 13x - 9 units

Width: 4.5x + 8 units

If the length is greater than the width, which inequality represents this situation?

Answer:

a) 6 hours

b) 12 hours

c) 36 hours

Step-by-step explanation:

let hours taken to mow lawns = x

baby sit hours = 2x

walk dogs hours = 3(2x) = 6x

x+2x+6x = 54

thus, x = 6

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{If we were to find the difference between the two years you have}\\\large\text{provided you would have to go back (almost like you're going}\\\large\text{back in time). You're going to take the highest year (238 B.C.)}\\\large\text{from the lowest year (15 B.C.) and you should have your equation}\\\large\text{and answer if you did what you were told.}[/tex]

[tex]\large\text{Equation: }\rm{238\ B.C. - 15\ B.C.}[/tex]

[tex]\large\text{Get your number line ready because this will make the equation easier to}\\\large\text{solve.}[/tex]

[tex]\large\text{Start at 238 and go back 15 spaces to your 15 to your left.}[/tex]

[tex]\large\text{If you did the right calculation you should be at: 223}[/tex]

[tex]\huge\text{Thus, your answer can be: \boxed{\mathsf{238\ B.C. - 15\ B.C. }}}\huge\checkmark[/tex]

[tex]\large\text{Remember: \textsf{difference} means subtraction/subtract}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]