f(x)=b x and g(x)=logbx are inverse functions. Explain why each of the following is true.
b. The inverse of f₁(x)=b x-h is equivalent to a translation of g .

Answer:

Side = 13 cm

Step-by-step explanation:

To find the side of the square:

Area = 169 square cm

   [tex]\sf \boxed{\bf Side = \sqrt{area}}[/tex]

             [tex]\sf = \sqrt{169}\\\\ = \sqrt{13*13}\\\\ =13 \ cm[/tex]

The answer to this question is 1/2

Logarithmic scale: A measurement scale in which the position is marked using the logarithm of a value rather than the actual value.

A logarithmic equation includes a logarithm in the variable x.

An exponential equation is one in which the variable is represented by an exponent. A logarithmic equation is one in which the logarithm of a variable-containing expression is used.

For logarithmic equations, log b (x) = y is equivalent to b^y = x such that x > 0, b > 0 and b is not equal to 1.

In the given problem, b = 2, x = 1/2, and y = -1.

b =2

x = 1/2

y = -1

Substituting the values of b, x and y into the equation b^y = x;

2^(-1) = 1/2

therefore, the value of the given equation log₂1/2=1 is 1/2.

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If we compare numbers -√7 and 3.12345 we find that 3.12345 is always greater than -√7.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given that there are two numbers which are  -√7 and 3.12345.

Let's compare the,.

We know that an irrational number is a number which can't be expressed other than using roots.

Here -√7 is an irrational number and if we represent that in decimal form then it can be written as :

-√7 = - 2.6467

Now , as this number is negative decimal number it is less than the other number given which is 3.12345 because 3.12345 is a positive decimal number. And we know that value of a positive number is always greater than a negative number.

i.e.,

3.1245 > -√7

Therefore , if we compare numbers -√7 and 3.12345 we find that 3.12345 is always greater than -√7.

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The equation for the relation between the number tickets Jillian sold and the amount of money she collected is m = 2.5t.

It should be noted that there's a constant relationship between the figures that are given.

This can be illustrated as:

= 25/10

= 2.5

Therefore, the equation for the relation between the number tickets Jillian sold and the amount of money she collected is m = 2.5t.

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Adult tickets costs $63.8

Children tickets costs $13.2

Let x represent the adult tickets and y to represent the cost of children tickets

x + y= 77..........equation 1

36x + 17y= 2,297........equation 2

From equation 1

x= 77-y

Substitute 77-y for x in equation 2

36(77-y) + 17y = 2297

2772 - 36y= 2297

-36y= 2297-2772

-36y= -475

y= 475/36

y= 13.2

Substitute 13.2 for y in equation 1

x + 13.2 = 77

x= 77-13.2
x= 63.8

Hence adult tickets costs $63.8 and children tickets costs $13.2

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Answer:

0 -2 -1 1

4 -4 -4 12

-3 1 2 8

Step-by-step explanation:

in that exact order, 3 by 4

Answer: y=-3x+6

Step-by-step explanation:

simplify ax+by=c into slope intercept which is y=mx+b

y=-3x+9.

since slopes are the same in parallel equations, graph the point (1,3) and go up 3, and left 1. the y intercept should be 6. I went left one because it's a negative slope, so in order for the line to be negative, you'd go left, not right.  y= -3x+6

Answer:c=7

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

The measure of PQT = 142.

We know what ray QS bisects angle PQT. If you draw out angle PQT and ray QS you can see that angle PQS is congruent to angle SQT. Because of the definition of angle bisector. This also means that angle SQT is half of PQT. Because of this we know that we can set the measure of PQT equal to 2 times the measure of SQT.

So we can set up and solve the following equation as such:

2(8x-25) = 9x +34

16x - 50 = 9x +34

7x -50 = 34

7x = 84

x = 12

Again I this doesn't seem to be your final answer. To find the answer the measures of each angle you're going to want to plug 12 in for x for one of the angles. So I'll do it for angle SQT.

8(12) - 25

96 -25

71

So the measure of angle SQT should be 71. Therefore since QS bisects PQR, the measure of angle PQS should also be 71. The measure of PQT should be double that which makes it 142.

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Answer: Usaste el 75% de la leche y queda el 25%.

Step-by-step explanation:

According to the question, the given rational expression is as follows:

Expression =  [tex]\frac{x^{2} +8x+16}{x^{2} -2x-24}[/tex]

Simplify the numerator as well as denominator by doing factors which is shown below:

[tex]x^{2} +8x+16=x^{2} +4x+4x+16=(x+4)(x+4)[/tex]

Similarly, denominator factors are as follows:

[tex]x^{2} -2x-24=x^{2} -6x+4x-24=(x-6)(x+4)[/tex]

Now, substituting these values in the given expression, we get:

[tex]\frac{x^{2} +8x+16}{x^{2} -2x-24} = \frac{(x+4)(x+4)}{(x-6)(x+4)}=\frac{x+4}{x-6}[/tex]

Therefore, the final answer for the given expression is [tex]\frac{x+4}{x-6}[/tex].

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Answer:

Step-by-step explanation:

Depreciation means value falling

10 is the scrap value which means the value that will remain after the product is properly used up.

depreciation for one year will be calculeted through

(original value - scrap value)/ no of years of use

(500 - 10)/3

= 163 is the annual rate of depreciation

If no scrap value is given, then you will simply divide the value by the no. of years of use

b. annual depreciation = 163

original value = 500

500 - 163(x) = worth of the poster after x years

worth remaining after a certain no. of years is also known as net book value.

Answer:

x= -11

Step-by-step explanation:

(x+3)/2 = -4

multiply both sides by 2

x+3 = -8

move 3 to other side through subtraction

x = -11

Answer:

The answer is supposedly 0.25

Answer:

100mi

Step-by-step explanation:

Answer:

Due to the fact that the denomonator is the same your answer will be 8/9 but if there was a different denominator you would need to find the least common multiple. Dont forget anything you do to the bottom has to be done to the top

Step-by-step explanation:

Hope this helps!!

By applying the laws of indices to each of the expression, the simplified expressions are matched as follows:

An exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.

In Mathematics, laws of indices can be defined as the standard principles and rules that are used for simplifying a mathematical equation or expression that involves powers of the same base.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In order to evaluate an expression, you should apply the PEMDAS rule, where operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the operations of addition or subtraction would be performed from left to right.

By applying the laws of indices to each of the expression, the simplified expressions are as follows:

5³ ÷ 5⁻¹ = 5⁽³ ⁻⁽⁻¹⁾ = 5⁽³ ⁺ ¹⁾ = 5⁴     ⇒ 5³ ÷ 5⁻¹ = 5⁴

5³ × 5⁻¹ = 5⁽³ ⁺ ⁽⁻¹⁾ = 5⁽³ ⁻ ¹⁾ = 5²

a⁻ⁿ = 1/aⁿ ≡ 5⁻⁴ = 1/5⁴

5⁻³ ÷ 5⁻¹ = 5⁽⁻³ ⁻⁽⁻¹⁾ = 5⁽⁻³ ⁺ ¹⁾ = 5⁻²

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Complete Question:

Directions: Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

Simplify the expressions, and match the expressions that are equal in value.

5³ ÷ 5⁻¹

5³ × 5⁻¹

5⁻⁴

1/5⁴

5⁻³ ÷ 5⁻¹

Answer:

[tex]1.6 \times 10^5[/tex]

Step-by-step explanation:

[tex](8 \times 10^3) \times (2 \times 10^1)\\\to (8 \times 2) \times (10^3 \times 10^1) \text{ / Remember rule: } a^m \times a^n = a^{m + n}\\\to 16 \times 10^{3 + 1}\\\to 16 \times 10^4\\\to 1.6 \times 10 \times 10^4\\\to 1.6 \times 10^{1 + 4}\\\to 1.6 \times 10^5[/tex]

Answer:

f(10) = 905

Step-by-step explanation:

f(x) = 9x² +5; find f(10)

~Substitute x with 10

9(10)^2 + 5

~Solve exponent first

9(100) + 5

~Multiply

900 + 5

~Add

905

Best of Luck!

The answer is:

Work/explanation:

To evaluate the given function, plug in 5 for x:

[tex]\bf{f(x)=9x^2+5}[/tex]

[tex]\bf{f(10)=9(10)^2+5}[/tex]

Remember, exponents first. So we square 10 first.

[tex]\bf{f(10)=9\cdot100+5}[/tex]

Multiply, then add:

[tex]\bf{f(10)=900+5}[/tex]

[tex]\bf{f(10)=905}[/tex]

Simplest form of expression is an expression written in its simplest of terms without changing the original value of the expression. There should be no like terms or parentheses.

In the given expression, there are two like terms and no parentheses. Hence, we solve for eliminating the like terms to find the simplest form of expression.

In order to eliminate the like terms, we need solve the square root terms to its simplest form.

√32=√2x2x2x2x2=4√2  

√72=√2x2x2x3x3=6√2

Hence, the expression becomes,

2*4√2 x2+3*6√2 x2

Simplifying,

8√2 x2+18√2 x2

Adding the like terms,

(8+18)√2 x2

26√2 x2

Hence, the simplest form of expression 2 √32 x²+3 √72 x² is 26√2 x2.

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Answer:

-8x^2+2x+5

Step-by-step explanation:

Distributive Property

1. 10 * 10 * 10 = 1000 = 10^3

2. 10 * 10 * 10 * 10 = 10,000 = 10^4

3. 10 * 10 * 10 * 10 * 10 = 100,000 = 10^5

4. 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10,000,000 = 10^7

5. Summary

Multiplication   Exp on first factor   Exp on 2nd factor    Exp on product

10^1 * 10^2                 1                                    2                             3

10^1 * 10^3                 1                                    3                              4

10^2 * 10^3               2                                   3                              5

10^4 * 10^3               4                                   3                              7

6. Multiplying two powers of ten, the product can be found by adding up the exponential values, the sum will be the exponent of the product and the base remain ten.

This refers to the exponential value of 10. Hence we can say that power as used in mathematics, is also called exponents.

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The rocket moves really fast with high speed.

A projectile that receives thrust from a rocket engine is known as a rocket (from the Italian rocchetto, which means "bobbin/spool"). All of the propellant carried by the rocket is used to create the exhaust from its engine.

In actuality, the absence of an atmosphere in space allows rockets to operate more effectively.

Due to their ability to reach Earth's escape velocity, multistage rockets can reach any maximum altitude. Rockets may produce significant accelerations and are powerful, light, and lightweight when compared to airbreathing engines.

In order for rockets to go forward and function in the vacuum of space, their action-reaction engines quickly discharge exhaust in the opposite direction.

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The values for f(x).g(x) =  2x² -6x +9

Given:

          f(x)=2 x+5 and g(x)=x²-3 x+2

         (f.g)x = f(g)x)

          g(x) = x²-3 x+2

          f(x²-3 x+2) = 2 (x²-3 x+2) +5

          f(x²-3 x+2) = 2x² -6x +9

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Answer: 1 Donut would be $1.6 and 7 donuts would be $11.2

After evaluating the expression we get 12.

Given, x³ ₊ x²

Finding the value of an algebraic expression when a specified number is used to replace the variable is known as evaluating the expression. In order to evaluate an expression, we first replace the expression's variable with the given number, then we streamline the expression using the order of operations.

A procedure called evaluation involves analyzing a program critically. It entails gathering and studying data regarding a program's operations, features, and effects. Its objective is to assess a program, enhance its effectiveness, and/or provide information to help with programming decisions.

substitute the value of x =2

2³ ₊ 2²

= 8 ₊ 4

= 12

hence we get the answer as 12.

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Kloe can make 4 flower arrangement

The number of flowers in each flower arrangement is 6 sun flowers, 4 roses and 12 white carnations.

The number of flower arrangements can be calculated as follows;

The first step is to calculate the HCF between the three numbers

24= 6 × 4

16= 4 × 4

48= 12 × 4

The HCF is 4

Hence the number of flower arrangement is 4  and the number of flowers in each flower arrangement is 6 sun flowers, 4 roses and 12 white carnations

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