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Part 1
Complete the table to find the value of a nonzero number raised to the power of 0.

According to the question, the given expression is a single natural logarithm and the expression is as follows:

Expression: [tex]ln7+2ln5[/tex]

Using logarithmic formulas, the above expression can be written as:

Expression: [tex]ln7+2ln5 = ln7+ln5^{2} =ln7+ln25[/tex]

Using multiplication logarithmic formula that is [tex]log(ab)=log(a)+log(b)[/tex]

Now the above expression can be written as:

Expression: [tex]ln7+ln25 = ln(7X25) = ln(175)[/tex]

The solution for the given expression is: [tex]ln(175)[/tex].

What is logarithmic function?

In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.

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Each logarithm as the quotient of two common logarithms is :

[tex]\frac{log\\ 2}{log \\7}[/tex]

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

   [tex]log_ax=N[/tex]

where, a is the base of function or equation

           x define expression

Mathematically, if  [tex]a^N=x[/tex]  is an exponential function then, this can be converted to logarithmic function as  [tex]log_ax=N[/tex].

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations.

Some important formulas of logarithms are :

The given expression is,

[tex]log_7{2}[/tex]

as, [tex]log_bm= \frac{log_cm}{log_cb}[/tex]

therefore ,

[tex]log_7{2}[/tex] =  [tex]\frac{log \ 2}{log \ 7}[/tex]

Hence,  logarithm as the quotient of two common logarithms is :

[tex]\frac{log \\2}{log \\7}[/tex]

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Answer:

C. b || c

Step-by-step explanation:

Answer:

c) b // c

Step-by-step explanation:

Two lines are said to be parallel when one of the conditions is true.

1) Corresponding angles are equal.

2) Alternate interior angles are equal.

3) Co interior angles are supplementary.

∠1 =115°   {Vertically opposite angles}

∠1 = ∠2 = 115°

If corresponding angles are equal, then the lines are parallel. So, b // c

Answer:

-1

Step-by-step explanation:

2 – (9 ÷ 3)

divide 9 and 3

2 - 3

subtract 2 from 3 and you get

-1

Answer:

-1

Step-by-step explanation:

Its just the answer.

Answer:

6n-2

Step-by-step explanation:

Write the expression

subtracted from  means it comes after

product of 6 and a number means multiply

6n

2 is subtracted from

6n-2

Answer:

It can be expressed as:

6x-2

6(coefficient)

x(variable)

2(constant)

Answer:

Step-by-step explanation:

Explanation:

I would write the growth function as:

y

=

100

e

k

t

So that at

t

=

0

we get:

y

=

100

e

0.02

⋅

0

=

100

bacteria.

At

t

=

5

hours we will get:

y

=

100

e

5

⋅

0.02

=

110

bacteria.

To double the initial number we need to solve:

200

=

100

e

0.02

t

e

0.02

t

=

2

Apply natural logs to both sides:

ln

(

e

0.02

t

)

=

ln

(

2

)

0.02

t

=

ln

(

2

)

t

=

ln

(

2

)

0.02

=

34.65

≈

34.6

34

hours and 36 minutes approx.

This is the same as g(x) which, therefore the functions are inverse of each other.

What does a math inverse mean?

for any point (x, y), that appears in one function, the point (y, x) must appear in the other function. for any point (x, y), that doesn't appear in one function, the point (y, x) must not appear in the other function.  

so if you find any point that doesn't meet the above rules, you can prove that the functions are not inverses of each other.  

to prove that they are inverses of each other, you need to check all points in the functions, and there is an infinity of them, so instead, you can write f(x) like this:  

y = 3x - 5  

solve for x:  

y + 5 = 3x  

x = (y + 5) / 3  

swap x and y:  

y = (x + 5) / 3  

this is the same as g(x) which, therefore the functions are inverse of each other.

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For the given equation 10x=1/100, the value of x is 0.001

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

It has the formula Ax + B = 0, with A and B being any two real integers and x being an ambiguous variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.

Given,

10x = 1/100

x = 1/1000

x = 0.001

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According to basic algebra and the logarithm, the bone is roughly 16384 years old.

Y and t may have the following values: t = 16384, y = 16380. (a). (as determined using logarithm and elementary algebra).

The logarithm is exponentiation's opposite function in mathematics.

The power to which a number must be increased in order to obtain another number is known as a logarithm. This shows that the logarithm of a fixed integer base b represents the exponent to which that number must be raised in order to reach a specific number x.

The logarithm with a base of 10 is the common logarithm, commonly referred to as the value of log base 10. The common logarithm of 10 has a value of 1, or 1.

Let 'a' be the original amount of the object.

Then, according to question, for y = amount of carbon in the object, y = 0.14(a) (as the bone contains 14% of its original carbon-14).

We are also given that: y = a [tex]e^{-0.00012t}[/tex]

On substituting the value of y, we get: 0.14a = a  [tex]e^{-0.00012t}[/tex]

By basic algebra, we can solve it as:

=> 0.14 =  [tex]e^{-0.00012t}[/tex]

=> ln (0.14) = ln ( [tex]e^{-0.00012t}[/tex]) (taking natural logarithm on both sides)

=> ln (0.14) = - 0.00012t (as [tex]log_{b} a^{m} = m log_{b} a[/tex] ; further: [tex]log_{e} e=1[/tex]  )

=>  ln(0.14)/-0.00012= t

=> t = 16384 years (approx.)

The values of y and t can be as follows: t = 16384, y = a (0.9998(16384)) = 16380(a).

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The number of caps they can buy is 2 and the number of shirts they can buy is 6.

The system of equations that can be used to represent this question is:

6s + 3c = 36 equation 1

s + c = 8 equation 2

Where:

In order to determine the required values, take these steps:

Multiply equation 2 by 6

6s + 6c = 42 equation 3

Subtract equation 1 from equation 3

3c = 6

c = 6/3

c = 2

Substitute for c in equation 2:

s + 2 = 8

s = 8 - 2

s = 6

Here is the complete question:

Eight friends started a business. They will wear either a baseball cap or a shirt imprinted with their logo while working. They want to spend exactly $36 on the shirts and caps. Shirts cost $6 each and Caps cost $3 each. How many of each item can they afford?

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Based on the given graph, the average rate of change from x=1 to x = 4 is - ²/₃

To find the average rate of change which is the slope, the formula is:

= (Y₂ - Y₁) / (x₂ - x₁)

The coordinates of x = 1 and x = 4 are:

(1, 5) and (4, 3)

Average rate of change is:
= (3 - 5) / (4 - 1)

= -2 / 3

= - ²/₃

In conclusion, the average rate of change is - ²/₃.

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Answer:

[tex]-\frac94 \to -2\frac3{20} \to-2.05\to\frac78 \to 89(percent) \to 0.9[/tex]

Step-by-step explanation:

[tex]-2\frac3{20} = -2.15\\89(percent) = 0.89\\-\frac94 = -2.25\\\frac78 = 0.875[/tex]

Answer:

[tex]-\frac{9}{4}, -2\frac{3}{20} ,-2.05, 7/8, 89%, 0.9[/tex]

Step-by-step explanation:

We know that the number line goes from negative to positive

Convert everything to decimal

89% = 0.89

[tex]-2\frac{3}{20} =-2.15[/tex]

-9/4 = [tex]-2\frac{1}{4} = -2.25[/tex]

7/8 = 0.875

[tex]-\frac{9}{4}, -2\frac{3}{20} ,-2.05, 7/8, 89%, 0.9[/tex]

Hope this helps  :)

Have a great day!

On the outside to the left of the L shape is K, then the synthetic division used to represent the dividend is[tex]2x^{3} +10x^{2} +x+5[/tex].

A more straightforward method of dividing a polynomial using a degree one polynomial equation is known as synthetic division.

a simplified method for dividing a polynomial by another polynomial of the first degree by writing down only the coefficients of the several powers of the variable and changing the sign of the constant term in the divisor so as to replace the usual subtractions by additions.

Here,

An L shape is created when a vertical line and a horizontal line are combined.

Within the form, there are two rows of entries.

Entries 2, 10, 1, and 5 are in row 1.

Row 2 has the entries -10, 0 and blank.

On the outside, to the left of the form, is entry number five.

The entry stands for the divisor's zero.

This entry for the variable, let's say x, is [tex]2x^{3} +10x^{2} +x+5[/tex].

Therefore, the Synthetic division of the dividend is [tex]2x^{3} +10x^{2} +x+5[/tex].

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Answer: Step 1: K=2, Step 2: A=1, Step 3: B=2, C=-1, D=-2 LAST QUESTION is A on edge.

Step-by-step explanation:

Answer:

5.67

Step-by-step explanation:

The quotient was 5.6671 and rounded to the nearest hundredth is 5.67. Hope it helps.

The number of hours that Jing spent on each subject will be;

Mathematics = 5.36 hours

Chemistry = 10.72 hours

History = 71.32 hours

Let the number of hours spent on Mathematics = x

Chemistry = 2x

History = 4(2x + x) + 7 = 12x + 7

Total hours = 82 hours

Therefore, the time used for each will be illustrated:

x + 2x + 12x + 7 = 82

14x + 7 = 82

14x = 82 - 7

14x = 75

x = 75 / 14

x = 5.36 hours

Mathematics = x = 5.36 hours

Chemistry = 2x = 2 × 5.36 = 10.72 hours

History = 4(2x + x) + 7 = 12x + 7 = 71.32 hours

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Answer: m<2 = 18°

Step-by-step explanation:
m<1 + m<2 = 90°

7x - 19 + x + 5 = 90°
     First add common variables; 7x + x = 8x || -19 + 5 = -14
8x - 14 = 90°
     Second add 14 on both sides;

8x - 14 = 90°

     +14   +14

8x = 104°
      Third divide 8 to 104
[tex]\frac{8x}{8} = \frac{104}{8}[/tex]

x = 13

m<1 7(13) - 19 + m<2 (13) + 5 = 90°
13 * 7 = 91
91 - 19 = 72
72 + 13 = 85
85 + 5 = 90°

m<2 = 13 + 5 = 18°

Hope this helps! :]
--Blu

The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter is 20 unit and area is 21 unit² for vertices of a polygon W(5,−1), X(5, 6), Y(2,−1), Z(2, 6).

The perimeter of a rectangle is the total length or distance of its boundary on all sides. The perimeter of a rectangle is a linear measure and is expressed in linear units of meters, feet, inches, or yards. Let us first understand the two main properties of a rectangle.

All four angles of a rectangle are 90°.

The opposite sides of a rectangle are equal in measure.

The Perimeter of a rectangle = 2(l + w).

given coordinates:

W(5,-1), X(5,6), Y(2,-1), Z(2,6).

Now, considering the coordinates we will find the width and length of rectangle :

Taking points (2,6) and (5,6):

w=5-2=3

Taking  points (5,6) and (5,-1):

l=6-(-1)=7

Now, perimeter of rectangle

= 2x(3+7)

= 20 unit

Hence, area rectangle is : 3x7=21 unit²

Therefore area is 21 unit² and perimeter is 20 units of polygon with the given vertices W(5,−1), X(5, 6), Y(2,−1), Z(2, 6).

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Answer:

50

Step-by-step explanation:

because 10 × 5 is 50

- to check 50 ÷ 4 is infact equal to 10 (make sure u always double check ur answers)

Tonya's total earnings are the sum of the basic pay and other commissions so Tonya's earnings for a month including all incentives will be $5450.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

Basic pay of Tonya = $650

3% of 32000 ⇒

3 × 32000 / 100 = $960

Now 8% on higher of $32000

Amount higher of $32000 ⇒ 80000 - 32000 = $48000

So,

8% on 48000 ⇒

8 × 48000/100 = $3840

Total earning = 650 + 960 + 3840 = $5450

Hence "Tonya's total earnings for a month including all incentives will be $5450".

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The solution to the system of equations is x = 7 and y = -3

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

5x + 2y = 29

5x - 2y = 41

Add both equations

So, we have

10x = 70

Divide the equation by 10

So, we have

x = 7

Substitute x = 7 in 5x - 2y = 41

5 x 7 - 2y = 41

This gives

35 - 2y - 41

Evaluate

2y = -6

Divide by 2

y = -3

Hence, the solution to the system of equations is x = 7 and y = -3

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Answer: Im not sure but have a wonderful day god bless you.

Step-by-step explanation:

The values of the variables in the ordered pair are as follows;

18. y = 10

19. x = 6

20. y = -14

21. x = -4

22. x = -5

23. x = 40

24. y = -30

25. y = 5

Ordered pairs are points located on the graph of a function.

In a direct variation, we have;

y = m•x

Where;

m = The slope of the line joining the points

18. (2, -4), (-5, y) the ordered pair is a direct variation

The slope = (y + 4)/((-5) - 2) = (y + 4)/(-7)

y = (y + 4)/(-7) × (-5)

7•y/5 = y + 4

7•y/5 - y = 4

2•y/5 = 4

19. (4, 16), (x, 24)

m = (24 - 16)/(x - 4) = 8/(x - 4)

y = 24

Which gives;

24 = (8/(x - 4))×x

24 × (x - 4) = 8•x

16•x = 96

x = 96/16 = 6

20. (12, y), (4, 7)

m = (7 - y)/(4 - 12) = (7 - y)/(-8)

y = ((7 - y)/(-8)) × 12

12•y/(-8) = 7 - y

12•y = -56 + 8•y

4•y = -56

y = -56/4 = -14

21. (x, -16), (6, 24)

m = (24 - (-16))/(6 - x) = 40/(6 - x)

-16 = (40/(6 - x))×x

16•x - 96 = 40•x

24•x = -96

x = -96/24 = -4

22. y = -18, x = 3

-18 = m×3

m = -18/3 = -6

When y = 30

x = 30/(-6) = -5

23. y = 80 when x = 32

m = 80/32 = 10/4 = 2.5

When y = 100, we have;

x = 100/2.5 = 40

24. y = 10 when x = -4

m = 10/(-4) = -2.5

When x = 12, y = 12 × (-2.5) = -30

25. y = -7 when x = -28

m = -7/(-28) = 1/4 = 0.25

When x = 20, y = 0.25 × 20 = 5

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When Nautica is making a scaled copy of a square using a scale factor of 2, the option that isn't true is D. The corresponding angles in each figure are equivalent.

It should be noted that based on the information given, we've to multiply the given figures by 2

Therefore, each angle is multiplied by 2, the corresponding side lengths are multiplied by 2, and the perimeter is multiplied by 2

Therefore, the correct option is D.

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Step-by-step explanation:

Select the correct answer from each drop-down menu. A researcher is examining the claims made by a water softener salt manufacturer. He performs an experiment using water from a variety of sources. For each water source, he has a sample with no treatment and a sample treated with the recommended amount of the water softener salt. He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true. The conclusion drawn from the study is because the sample is . In this instance, an study was

Answer:

50.27 ft

Step-by-step explanation:

hope this helps :)

If the binomial (x−7) is a factor of the polynomial function f(x), then the true statement is f(-7) = 0

The given parameters are

The binomial (x + 7) is a factor of the polynomial function f(x)

The above means that

When the function f(x) is divided by x + 7, it has no remainder

So, we have

x + 7

Set to 0

x + 7 = 0

Add -7 to both sides

x = -7

Substitute x = -7 in f(x) = 0

f(-7) = 0

Hence, if the binomial (x−7) is a factor of the polynomial function f(x), then the true statement is f(-7) = 0

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The function that represents the distance from the fountain is:

Number of minutes  Distance

0                                     50

2                                      60

4                                      70

6                                       60

8                                        50

A circle is a bounded figure which points from its center to its circumference is equidistant.

If Brady jogs around the circular park with a fountain at its center, it means that at a point as he runs he would be further away from the fountain. And with time, he would be approaching the fountain since the park is circular. Thus, the function that represents the distance Brady runs from the fountain would be increasing at a point and then start to decrease.

If the park were a straight line, the function would be increasing with time.

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Answer:

Step-by-step explanation:

C on edge

Answer:

$3.00

Step-by-step explanation: