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6 in. Math

The single logarithm of log 3 + 4 log x is = log (3x^4).

What is a logarithmic function?

A logarithmic function in mathematics is defined as the function which is the inverse of the exponential function. It is denoted by using the word log. For example log 10 = 1

Write the given logarithmic expression in a single logarithm. log 3 + 4 log x

Given logarithmic expression is log 3 + 4 log x

Applying given properties of logarithmic function;

log a + log b = log (ab)

2 log a = log a²

Now, log 3 + 4 log x = log 3 + log x^4

= log (3x^4)

Hence, the single logarithm of log 3 + 4 log x is = log (3x^4).

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Answer: 1 = e

Step-by-step explanation:

The percentage of decay for the exponential function: y = 18(0.75) x is 25%.

This equation represents exponential decay. Whenever the base is less than 1, the function represents decay. When the base is greater than 1, the function represents growth. In this case, the base is 0.75 which is less than 1, representing decay.

The formula for exponential decay is y=a(1-r)x.

r is the decay rate, expressed as a decimal.

In this case, r = 1 - 0.75 = 0.25 which represents 25%.

Therefore, the percentage of decay for the exponential function: y = 18(0.75) x is 25%.

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Solving for the variable 'a' gives the equation a = u - k

A subject of formula can be defined as a variable written in terms of other variables in an equation or given expression.

It is also recognized as the variable that is being worked out in an equation or expression.

Given the equation:

u=a+k

To make the variable 'a' the subject of formula, we have to take all other variables to the other side of the equality sign, making the variable 'a' stand alone.

We then have;

u - k = a

This is also written as;

a = u - k

Thus, solving for the variable 'a' gives the equation a = u - k

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The price of the cheaper vehicle is $39,000

From the question, we are to determine the price of the cheaper vehicle

Let the cost of one of the cars b $x

and the cost of the other car be $y

From the given information,

The total price for two cars at a dealership is $108,000

That is

x + y = 108000   ----------- (1)

and

one car’s price is $9000​ less than twice the other

x = 2y - 9000       ----------- (2)

Put equation (2) into equation (1)

x + y = 108000

2y - 9000 + y = 108000

2y + y - 9000 = 108000

2y + y = 108000 + 9000

3y = 117000

y = 117000/3

y = 39000

∴ The price of one of the vehicles is $39,000

Substitute this value into equation (2)

x = 2y - 9000

x = 2(39000) - 9000

x = 78000 - 9000

x = 69000

The price of the other vehicle is $69,000

Hence, the price of the cheaper vehicle is $39,000

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Answer: [tex]x=\Large\boxed{\frac{2}{5} }[/tex]

Step-by-step explanation:

Given equation

[tex]-5x-(-6-4x)=-2(3x-4)[/tex]

Expand the parenthesis

[tex]-5x+6+4x=-2\times3x-2\times(-4)[/tex]

[tex]-5x+6+4x=-6x+8[/tex]

Combine like terms

[tex]-x+6=-6x+8[/tex]

Add 6x on both sides

[tex]-x+6+6x=-6x+8+6x[/tex]

[tex]5x+6=8[/tex]

Subtract 6 on both sides

[tex]5x+6-6=8-6[/tex]

[tex]5x=2[/tex]

Divide 5 on both sides

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

[tex]x=\Large\boxed{\frac{2}{5} }[/tex]

Hope this helps!! :)

Please let me know if you have any questions

 In the foreign exchange market, if a Pound is equal to 1.59 USD, one Euro is equal to 1.46 USD. So roughly speaking, one Pound is equal to 1.09 Euro.

given,

a ) £1 = €1.16

    = £60 x 1.16 = 69.60

b) 0.87 pound = 1 euro

    €98.60 ,

    therefore , 98.60/0.87 = 113.33

Convert Euro to British Pound

EUR GBP

1,000 EUR 876.24 GBP

5,000 EUR 4,381.2 GBP

10,000 EUR 8,762.4 GBP

50,000 EUR 43,812 GBP

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answer :

so this is the answer of the value of x

The solution of the linear equation is x = 21.

Here we have the linear equation:

5x - 2x + 5 = 2x + 26

To solve this for x, move all the terms with x to the left side and all the others to the right side:

5x - 2x - 2x = 26 - 5

5x - 4x = 21

x = 21

The solution of the linear equation is x = 21.

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The decay factor for the annual rate of change of - 55 % is 0.45.

A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.

With the function displayed to the right, you may represent exponential growth or decay.

A(x) = a( 1 + r)ˣ

Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.

Now, we have the annual rate of change as:

r = - 55 % = - 55 / 100 = - 0.55

From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.

So, let B = 1 + r

B = 1 + r

B = 1 + (- 0.55)

B = 1 - 0.55

B = 0.45

Now, the value of B is less than 1 therefore, the corresponding decay factor is 0.45.

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Answer: 50

Step-by-step explanation:

8x4 =32

6x3=18

32+18=50

The equation in the form of slope-intercept for Macario's hourly wage is y=9x+0.12s

What is a slope-intercept function?

A slope-intercept equation comprises the total amount paid as wages to Macario which includes the hourly rate of $9 multiplied by the number of hours spent working plus the 12% of total sales achieved by Macario, in essence, if we assume that the number of hours spent working is x and that total sale is s, the slope-intercept form that  represents Macario's hourly wage y is shown thus:

y=9x+0.12s

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well, let's keep in mind that a meter has 100 centimeters, thus 1.3 meters will be 1.3 * 100 cm, namely 130 cm.

[tex]\begin{array}{ccll} cm&year\\ \cline{1-2} 2 & 1\\ 130& x \end{array} \implies \cfrac{2}{130}~~=~~\cfrac{1}{x}\implies \cfrac{1}{65}=\cfrac{1}{x}\implies x=65[/tex]

$1.051271 is the exponential function to explain why continuous compounding does not give you much of an investment advantage.

With an example, what is compound interest?

Simple Interest: A = P(1+rt)

P: the principal, the amount invested

A: the new balance

t: the time

r: the rate, (in decimal form)

Ex 1 -  If $1000 is invested now with simple interest of 8% per year. Find the new amount after two years.

P = $1000, t = 2 years, r = 0.08.

A = 1000(1+0.08(2)) = 1000(1.16) = 1160

B) Suppose you invest $1 at 5% compounded yearly.

Suppose you invest $1 at 5% compounded continuously.

The 1st case gives you $1*(1.05)1 = $1.05

The 2nd case gives you $1*e0.05 = $1.05127

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Hey there!

3x + 8x

= 3 + 8

= 11x

= 11

Therefore, your answer should be:

11x

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

q3: -9, 1

q4: No

The reason there are multiple answers for this question is because of the absolute value sign. to solve this you can isolate the absolute value onto one side and solve for the positive and negative possibilities.

step 1: isolate the absolute value

|3(x+4)|+8=23 ----> |3(x+4)|=15

step 2: remove the absolute value sign the remember that now it has two answer possibilities where 15 can be both negative and positive and still be right. Then just solve just like you would a normal equation.

3(x+4)= +-15 ----> x+4= +-5

x = -9, 1

The rational number between the square root of 7 and the square root of 8 is 27/10

Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.

This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals

The features of the rational number are given as

Value = between the square root of 7 and the square root of 8

Rewrite the value properly

So, we have

Value = between √7 and √8

Evaluate the values of √7 and √8

So, we have

√7 = 2.65

√8 = 2.83

This means that the rational number is between 2.65 and 2.83

A number between 2.65 and 2.83 is 2.7

Express as fraction

value = 27/10

Hence, the rational number between the square root of 7 and the square root of 8 is 27/10

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The probability of the new boy being paired up with a boy who does not love camping is 2/3 or 66.66%

Total no. of troop members = 15

No. of boys who love camping = 5

No. of boys who love fishing = 10

No. of boys who love archery = 3

No. of boys who love hiking = 12

The boy who enjoys carving = 1

Boys who do not like camping = 1 - 5/15 = 10/15 = 2/3*100 = 66.66%

So, the probability that the new boy will be paired up with a boy who does not love camping is 66.66% or 2/3.

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The rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).

Given that, a rotation and reflection composition is equivalent to other compositions.

Reflection is flipping an object across a line without changing its size or shape. Rotation is rotating an object about a fixed point without changing its size or shape.

Rotation rule:

Rotation of a point through 180°, about the origin when a point A (x, y) is rotated about the origin O through 180° in the anticlockwise or clockwise direction, it takes a new position A' (-x, -y).

Reflection rule:

A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis.

Therefore, the rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).

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If he plans to spend 200 per month, then the number of months he can make withdrawals from his savings account until his balance is zero dollars is equal to 5.

First, we calculate the money earned by Nick in 6 months

Money earned per month = $400

Money earned in 6 months = 400 × 6 = 2400

If he spends $250 out of the money earned per month, then the money spent in these 6 months can be calculated as follows;

Money spent per month = 250

Money spent in 6 months = 250 × 6 = 1500

Now we calculate the money put in the saving account in 6 months by subtraction;

Money added to the saving account = 2400 - 1500 = $900

As he already had $100 in the saving account,

Total amount of money in the saving account = 900 + 100 = 1000

If he plans to spend 200 per month, then the number of months he can make withdrawals can be calculated by division

Number of months = total money in the account ÷ money spent per month

Number of months = 1000 ÷ 200 = 5

Therefore, Nick can make withdrawals for 5 months from his savings account.

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Answer: yo wassup picture isn't straight cant see

Step-by-step explanation:

The vertex of the function where the equation of the function is given as y = -2x^2 is (0, 0)

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The equation of the function is given as

y = -2x^2

A quadratic function is represented as

y = a(x - h)^2 + k

Where the vertex is

vertex = (h, k)

This means that the equation y = -2x^2 can be rewritten as

y = -2(x - 0)^2 + 0

When the equations are compared, we have

vertex = (h, k) = (0, 0)

Hence, the vertex of the function where the equation of the function is given as y = -2x^2 is (0, 0)

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The location is 63° warmer in April than in December. The correct option is the third option  61 + |−2| = 63°, 61° is the farthest from 0°

From the question, we are to determine how much warmer the location is in April than in December

From the given information,

Average temperature in April = 61°

and

Average temperature in December = -2°

To determine how much warmer the location is, we will add the absolute values of the temperatures

That is,

61 + |-2|

= 61 + 2

= 63°

61° the temperature that is farthest from 0

Hence, the location is 63° warmer in April than in December. The correct option is the third option  61 + |−2| = 63°, 61° is the farthest from 0°

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The linear equation in the slope-intercept form is:

y = (-1/3)*x + 4

Remember that if a line passes through two points (a, b) and (c, d), then the slope is given by:

slope = (d - b)/(c - a)

By looking at the graph, we can see that the points (0,4) and (3, 3), then the slope will be:

s = (3 - 4)/(3 - 0) = -1/3

And we can see that the y-intercept is y = 4 (because the line passes through the point (0,4))

Then the linear equation in the slope-intercept form is:

y = (-1/3)*x + 4

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If you buy 7 markers , each marker would cost 9.42 ( cents ) .

Given : The total cost ( in cents ) of x + 2 markers is x³ + 5 x ² + 2 x - 8 .

To find : cost of 1 marker

Cost of 1 marker = ( x³ + 5 x ² + 2 x - 8 ) / ( x + 2 )

                            = [tex]x^{2}[/tex] + 3 x - 4

Substituting value of 7 in cost function

   =  [tex]x^{2}[/tex] + 3 x - 4 at x = 7

= 49 + 21 - 4

Cost of 7 markers = 66

Cost of 1 marker = 66 / 7

                            = 9.42

Therefore , if you buy 7 markers , each marker would cost 9.42 ( cents ) .

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1. A line can be described as a one-dimensional figure without thickness or width.

2. Lines are labeled with two points (A ↔ B). Lines can be marked using lowercase letters (for example, line k).

A line is a one-dimensional figure with a length only. A line does not have width or thickness.

A line can have line segments with two endpoints. A line cannot be measured, but its segments are measurable.

There are different types of lines, including:

Thus, lines are one-dimensional with lengths and no widths or thicknesses.

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The lines represented by y = -5x + 10 and 5y = x + 15 are; Perpendicular

We are given the equation of two lines as;

Line 1; y = -5x + 10

Line 2; 5y = x + 15

Now, the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Now, for the equation in line 1, we know that;

slope = -5 while the y-intercept is 10

For line 2, the equation can be rewritten as;

y = ¹/₅x + 3

Slope = 1/5

y-intercept = 3

Now, we know that when two lines are perpendicular, it means that their slopes are negative reciprocals of each other.

Slopes of lines 1 and 2 are negative reciprocals of each other and thus they are perpendicular.

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Answer:

44/15

Step-by-step explanation:

[tex]x-\frac{2}{5}+\frac{1}{2}x-3=1 \\ \\ \frac{3}{2}x-\frac{17}{5}=1 \\ \\ \frac{3}{2}x=\frac{22}{5} \\ \\ x=\frac{44}{15}[/tex]