Expand each logarithm.
logb b/x

Answer:

x=3

Step-by-step explanation:

Adult tickets that were sold were 210 .

Let the no. of children be x and no. of adults be y .

According to ques .

x + y = 385     - eq 1

4 x + 6 y = 1960          - eq 2

Solving linear equation in 2 variable by method of substitution ,

multiply   - eq 1 by 4 ,

4 x + 4 y = 1540     - eq 3

multiplying  - eq 3 by - 1

- 4 x - 4 y = - 1540         - eq 4

Adding  - eq 2 and   - eq 4

2 y = 420

y = 210

Hence , 210 adult tickets were sold .

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The statement that shows Sam's purpose for making the investment,  is; Sam wants an investment that offers a higher return than stocks.

We know that bonds refers to a type of investment that could be held for a while the hope of making returns. Both the bonds and the stocks are common types of investments that are traded in the equities market. They are held by buyers with the sole hope that they could yield returns.

However, the bonds tend to be more secure than the stocks. The stocks are actually an overly volatile kind of investment. The bonds when mature tends to provide a high return on investment for the investor compared to the stocks.

Hence, the statement that shows  Sam's purpose for making the investment,  is; Sam wants an investment that offers a higher return than stocks.

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Answer: 4

Step-by-step explanation: Divide both sides by -3 so the x is by itself. When you divide both sides by -3, you get x =4.

Answer:

4

Step-by-step explanation:

Divide -3 on both sides so that x is by itself

-3x = -12

-3      -3

-3 is cancelled out

-12 divided my -3 is 4

Since both numbers are negative it would end up positive.

If the numbers are both positive then it would be positive as well.

And if one number is positive and the other is negative then the answer would be negative.

The answer would be: 4

I hope it helps! Have a great day!

The closest side length of each side of the garden is 7 feet .

It is given that Billy is planting a square garden that is 48 ft.²

Putting A = 48 ft.² in equation (1) , we get

       [tex]48=a^2\\a=\sqrt{48} \\a=6.92[/tex]

which is approximately equal to 7

Hence , closest side will be 7 ft.

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Answer:

4

Step-by-step explanation:

because if it has two Pairs that's 2 on each side of the side of the shape

so, when you have a figure of 2 parallel sides id would be a parallelogram

Answer to this question is:

Domain of given function is (0,∞),{x|x>0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is 9/x²

The domain is all values of x that make the expression defined.The entire range of independent variable values is the domain of a function.

This definition can be stated simply as follows: The domain is the collection of all x-values that can be used to make the function "work" and produce actual y-values.

When choosing the domain, keep in mind that a fraction's denominator (bottom) cannot be 0.

Interval Notation:(0,∞)

Set-Builder Notation:{x|x>0}

The set of all valid y values constitutes the range.Graph may be used to find the values.

Interval Notation:(0,∞)

Set-Builder Notation:{y|y>0}

For calculation of inverse:

∴Domain of given function is (0,∞),{x|x>0}

Range of given function is (0,∞),{y|y>0}

Inverse of given function is 9/x²

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The value of x for the equation log₈2=x is 0.333

Logarithmic function properties. You have encountered several characteristics during your study of algebra, including the commutative, associative, and distributive properties. These characteristics make it easier to simplify a complex statement or equation. With logarithms, the same holds true.

Given,

log₈2=x

It can be expressed in the form -

2 = 8ˣ

2 =  2³ˣ

As base is same -

1 = 3x

x = 1/3

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Answer: A, C and F

Step-by-step explanation:

Here we need to evaluate some mathematic expressions in some given values, we will get:

3x-  4 is equal to 17 when x = 7.

-5x + 8 is equal to -7 when x = 3.

Here we have some expressions that we need to evaluate. Evaluating an expression means that we replace the variables (usually denoted by letters) with numerical values.

The first expression is:

3x-  4

And we we want to evaluate it in x = 7.

So just replace the x by the number 7 and then do the operations:

3*7 - 4 = 21 - 4 = 17

The expression is equal to 17 when x = 7.

Now let's do it again for second expression:

-5x + 8  with x = 3.

Replacing the variable by the number we get:

-5*3 + 8 = -15 + 8 = -7

So that is the basic procedure to evaluate mathematic expressions.

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The values of  f(−4), f(−2), and f(3) for given piecewise function are 0, -4, and -3.5 respectively.

What is piecewise function ?

Whenever the summation of two functions is different over different intervals, the sum is a piecewise function.

Here, the given piecewise function f(x) is :

[tex]\begin{aligned}f(x)&=\left\{\begin{matrix}\frac{-1}{2}x-2 \text{ if} \:x \neq -2&\\-4 \:\:\:\:\:\:\;\;\text{ if }x = -2\end{matrix}\right.\end{aligned}[/tex]

Now, let us find the value of f(-4) :

for x = -4 the function f(x) is (-1/2)x -2, substituting x = -4 in place x :

f(x) =  (-1/2)x - 2

f(-4) = (-1/2)*(-4) - 2  

f(-4) = 2 - 2

f(-4)  = 0

similarly, for f(-2) :

for x = -2 the function f(x) is -4 only that is :

f(-2) = -4

For, let us find the value of f(3) :

for x = 3 the function f(x) is (-1/2)x -2, substituting x = 3 in place x :

f(x) =  (-1/2)x - 2

f(3) = (-1/2)*(3) - 2  

f(3) = -3/2 - 2

f(3)  = - 3.5

Therefore, the values of  f(−4), f(−2), and f(3) are 0, -4, and -3.5 respectively.

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Expression as a single logarithm of 5 log₇2-2 log₇y is Log (2x/3y).

Log a + Log b = Log ab

Log a - Log b = Log (a/b)

so starting with the bracket, we have;

Log 2 + Log X - Log 3y

Furthermore, we have;

Log 2x - Log 3y

Finally, we have;

Log (2x/3y)

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:

11/20

Step-by-step explanation:

4/5 - 1/4

We need to get a common denominator of 20

4/5 * 4/4 = 16/20

1/4 *5/5 = 5/20

Replacing the fractions with their equivalent fractions

16/20 - 5/20

11/20

The value of x in the absolute value inequality is given as5 - 10|3x + 3| < 95 is all set of real numbers

The absolute value inequality is given as

5 - 10|3x + 3| < 95

Subtract 5 from all sides of the absolute value inequality

So, we have

- 10|3x + 3| < 90

Multiply -1/10 to all sides of the absolute value inequality

So, we have

|3x + 3| > -9

This means that the value of x is all set of real numbers

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The process of ordering objects or numbers is known as permutation. Combinations are a method of choosing items or numbers from a collection or group of items so that the order of the items is irrelevant.

Combinations are used to group objects or to determine how many subgroups can be formed from the given collection of objects. Additionally, we use permutations to determine the amount of potential combinations of unrelated objects.

Fir example, if we want to select 2 players from 6. This will be:

= 6! / 2! (6 - 2)!

= 15 ways

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Sides of Quadrilateral A is 6, 9, 9 and 12.

It is given that Quadrilateral B is a scaled copy of Quadrilateral A,

and have shortest side = 2

To find the length of sides of quadrilateral, first we will find the ratio of the shortest side of quadrilateral A to that of quadrilateral B as shown below :

B : A = 2 : 6 = 1 : 3

This shows that the quadrilateral B is 3 times smaller than A.

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Answer:

80,000 numbers.

Step-by-step explanation:

Since the number is 6-digits and is larger than 599,999, it would be between 600,000 and 999,999.

Between those two numbers (included), there are [tex]999999 - 600000 = 399999[/tex] numbers.

In addition, we know that the number is a multiple of 5. Therefore, we should divide this number by 5 to find how many of the numbers in that group are divisible by 5.
Since it's difficult dividing 399,999 by 5, I would divide 400,000 by 5, as we must also include 600,000.

[tex]\frac{400000}5 = 80000[/tex]

The solution 'x' of the expressed logarithmic expression is 17.65.

A logarithmic equation one in which the variable x contains a logarithm.

The variable in an exponential formula is signified by an exponent. To solve exponential equations, first see if both sides of the equation can be presented as powers of the same number. Because unless you can't, start taking the common logarithm of both equation sides and solve the problem using property 7.

Now, as per the stated log expression;

3 ln x + ln 5 = 7

Apply the Power Rule on the first term of the given equation;

ln x³ + ln 5 = 7

Now, by the Product Rule, we can re-write the equation in the form;

ln (x³×5) = 7

ln (5x³) = 7

Using the exponent form of the log on both side.

e∧ln (5x³)  = e⁷

As, we have the same base for the obtained expression. Use the exponent rule;

(5x³)  = e⁷

x³ = e⁷/5

Substitute the value of exponent e = 2.72

x³ = (2.72)⁷/5

x³ = 5507.5

Take cube root on both side;

x = 17.65

Thus,  solution for the value of 'x' for expressed logarithmic expression is 17.65.

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The original price of a ticket is a  $56.95.

According to the statement

We have to find that the linear equation.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

An amusement park offers a ticket for $12.95 off the original price p.

Then

Discounted price is that the amount of sum that extracted from the initial price when buyers receive some style of leverage from the vendor. during this case, discounted price of the ticket is $44 which was $12.95 but the initial price.

Then the first price would be:

$44 + $12.95 = $56.95

So, The original price of a ticket is a  $56.95.

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Step-by-step explanation:

-by-step explanation:

y=\frac{2}{x+1}-3y=

x+1

2

−3

asymptotes:

x+1 = 0

x = -1

y = -3

asymptotes: x = -1, y = -3

x int: (-\frac{1}{3}, 0)(−

3

1

,0)

y int: (0, -1)

D: (-infinity, -1) (-1, infinity) x cannot be -1

R: (-infinity, -3) (-3, infinity) y cannot be -3

After dividing and simplifying the expression 4√162 x⁴ / 4√2 y⁸, we get the result as 9 x ² / y⁴.

We are given the expression

4√162 x⁴ / 4√2 y⁸

We need to divide the expression and simplify it.

First, cancelling the terms that are same in the numerator and the denominator:

√162 x⁴ / √2 y⁸

Now , using the properties of the exponents, we get that:

= √81 x² / y⁴

= 9 x ² / y⁴

Therefore, after dividing and simplifying the expression 4√162 x⁴ / 4√2 y⁸, we get the result as 9 x ² / y⁴.

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Answer:

  0

Step-by-step explanation:

You want the sum of numerator and denominator such that their difference is 2 and the reciprocal is equal to the original fraction.

We want a fraction such that ...

  x/y = y/x

  y = x +2

Substituting for y, we have ...

  x/(x +2) = (x +2)/x

  x^2 = x^2 +4x +4 . . . . . cross multiply

  0 = 4(x +1) . . . . subtract x^2, factor

  x = -1 . . . . . . . . the value of x that satisfies the equation

Then the denominator is ...

  y = x +2 = (-1) +2 = 1

The sum is ...

  x +y = (-1) +1 = 0

The sum of numerator and denominator is zero (0).

Answer:-55

Step-by-step explanation:

-11 times 5= -55

x=2 y+5 is a tangent line to the circle x^2+y^2=5 at the point (1,-2).

This is further explained below.

Generally, the equation for is  mathematically given as

Differentiate both sides of the equation of the circle with respect to x, treating y=y(x) as a function of x:

[tex]x^2+y^2=5 \Longrightarrow 2 x+2 y \frac{\mathrm{d} y}{\mathrm{~d} x}=0 \\\\ \frac{\mathrm{d} y}{\mathrm{~d} x}=-\frac{x}{y}[/tex]

This gives the slope of any line tangent to the circle at the point (x, y). Rewriting the given line in slope-intercept form tells us its slope is

[tex]x=2 y+5 \\\\ y=\frac{1}{2} x-\frac{5}{2} \\\\ slope =\frac{1}{2}[/tex]

In order for this line to be tangent to the circle, it must intersect the circle at the point (x, y) such that

[tex]-\frac{x}{y}=\frac{1}{2} \\ \\\\ y=-2 x[/tex]

In the equation of the circle, we have

[tex]x^2+(-2 x)^2=5 x^2=5 \\\\ x=\pm 1 \\\\ y=\mp 2[/tex]

If x=-1, then

[tex]-1=2 y+5\\\\ y=-3 \neq 2[/tex]

If x=1, then

[tex]1=2 y+5 \\\\ y=-2$[/tex]

In conclusion, as expected. Therefore x=2 y+5 is a tangent line to the circle x^2+y^2=5 at the point (1,-2).

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Answer: $75 difference per shirt

Step-by-step explanation:

Answer: 9/9^4 in Simplest form is 1 / 729

Answer: its C because when you put it in order you should easily find it in the question. So, 1, 2, 3, 4, 5, 6, 9, 12, 15 is the full order but C is the closest answer to the question. Hope its right!

Answer:

The graph of g(x) = -|x| - 8.

Answer:

x + 6 = -6

Step-by-step explanation:

Assuming x = -6

[tex]x+6=0[/tex]

Subtract 6

[tex]x+6-6=0-6[/tex]

Simplify arithmetic

[tex]x=0-6[/tex]

Simplify arithmetic(again)

[tex]x=-6[/tex]

we technically solved the equation right at the beginning when we assumed x was equal to -6 in order to group the constants to the right.

Hope this helps, have a great day!