I need help with this exercise on Simplifying Logarithms.
Evaluate the following showing steps. Round the answer to three significant digits.

e^(4x-2) when x = 2

Answer:

Theorems are stated below

x = 6

Step-by-step explanation:

The following theorems can prove that 2 lines are parallel

Two lines are parallel if they’re cut by a transversal such that

The two angles shown are corresponding angles. They are corresponding because each is in the same position left side) in its group of four angles.

Corresponding angles are equal

Therefore,15x + 9 = 21x - 27

Subtract 9 from both sides:
15x = 21x - 27 - 9

15x = 21x  - 36

Subtract 21x from both sides

15x - 21x = - 36

-6x =  36

Divide by -6 both sides

-6x/-6 =  36/-6

x = 6

The two angles are
15x + 9 = 15(6) + 9 = 90 + 9 = 99°

and

21x - 27 = 21(6) - 27 = 126 - 27 =99°

And indeed they are equal

$202.50 is your answer

Answer:

Step-by-step explanation:

Solve for X:

Solve for 19:

Answer:

6 I belive it should land on 6

Simple interest , 4368 is  the amount of money Marty would have at the end of the second year.

What does the term "simple interest" mean?

P = $4000 R = 4% T = 1

then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]

                = [tex]\frac{4000 * 4 * 1}{100}[/tex]  = 160

So, the total amount is ( 4000 + 160) = 4160

Second year

P = 4160 , R = 5%  T = 1

then substitute the value into the formula = [tex]\frac{P * R * T }{100}[/tex]

                      =  [tex]\frac{4160 * 5 * 1}{100}[/tex]  = 208

So, the total amount is ( 4160 + 208 ) =   4368

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Answer: 2.12

Step-by-step explanation:

it's in the hundredths place

2       .   1           2

ones    tenths  hundredths

A quadratic function is one that has the formula f(x)=ax2+bx+c, where a, b, c, and an are all real values and a 0 a 0. The conventional form of a quadratic function is this form.

The quadratic function's graph is a U-shaped curve known as a parabola.

Below is a graph of the equation y=x2y=x2; it is a parabola.

The parabola rises if a>0a>0 in f(x)=ax2+bx+cf(x)=ax2+bx+c.  In this case, the vertex is the smallest or lowest point of the parabola.

The vertex of the y=x2y=x2 graph is (0, 0). (0,0).

The parabola opens downhill if a0a0 in f(x)=ax2+bx+cf(x)=ax2+bx+c is true. The maximal or highest point of the parabola in this instance is called the vertex.

The value of cc for an equation in standard form yields the graph's yy-intercept.

The axis of symmetry is the line that divides the parabola into two symmetric sections and runs through the vertex.

In the case of the graph y=ax2+bx+cy=ax2+bx+c, where a=0a=0, the equation for the axis of symmetry is x=b2ax=b2a.

The yy-axis, with x=0x=0, is the axis of symmetry in all of the graphs above. The axis of symmetry in the graphs below is different (marked in red.) As you can see, cc still provides the yy-intercept.

If you write a quadratic function like x=f(y)=ay2+by+cx=f(y)=ay2+by+c, instead of writing yy as a function of xx, you obtain a parabola with a horizontal axis of symmetry.

Hence, that the xx-intercept in this situation is cc. When aa is positive, the graph opens to the right; when aa is negative, it opens to the left.

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Value of n is 4

The area of a rectangle is equal to the product of its length and width.

we know ,

the area of  rectangle, multiply the length, , and the width, ,

and set the product equal to the area.

area of rectangle        = length * width

            54                  = 3(n - 1) * (n + 2)

             54                 =( 3n - 3) * (n + 2)

multiply ( 3n - 3) with  (n + 2)

we get,

              54                = [tex]3n^{2} + 6n - 3n -6[/tex]

              54                = [tex]3n^{2} + 3n -6[/tex]

              54                = 3([tex]n^{2} + n -2[/tex])

             [tex]\frac{54}{3}[/tex]                  =  ([tex]n^{2} + n -2[/tex])

             18                 =  ([tex]n^{2} + n - 2[/tex])

 [tex]n^{2} + n - 2[/tex] - 18           = 0

 [tex]n^{2} + n - 20[/tex]                = 0

solve them

 [tex]n^{2} + 5n + 4n -20[/tex]       = 0

 n (n + 5) - 4 (n + 5)   = 0

(n + 5)(n -4)  

then we get,            

n = -5 , n = 4

value of n should not be negative . so value of n is 4

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area

Area of rectangle = Length x Breadth

A = lb

how to Factoring Quadratic Equation

Step 1: Consider the quadratic equation ax2 + b x + c = 0

Step 2: Now, find two numbers such that their product is equal to ac and sum equals to b.

(number 1)(number 2) = ac

(number 1) + (number 2) = b

Step 3: Substitute these two numbers in the formula given below:

(1/a) [a x + (number 1)]  [a x + (number 2)] = 0

Step 4: Finally simplify the above equation.

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Answer: 59

Step-by-step explanation:

Using linear functions, it is found that:

1. The functions are given as follows:

2. They will have the same elevation after 18.4 minutes.

3. At that time, the elevation is of 18,150 feet.

A linear function is modeled in slope-intercept form by:

y = mx + b

In which:

For the functions in this problem, we have that:

Hence the functions are given as follows:

They will have the same elevation when:

E1(t) = E2(t)

28270 - 550t = 5270 + 700t

1250t = 23000

t = 23000/1250

t = 18.4.

They will have the same elevation after 18.4 minutes.

This elevation will be of:

28270 - 550(18.4) = 18150.

At that time, the elevation is of 18,150 feet.

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Answer: 5358

Step-by-step explanation:

282

x 18

----------

2538

+282

-----------

5358

The function is written in vertex form the equation for is  mathematically given as

f(x) = 3(x – 4)2 – 38

This is further explained below.

Generally, To convert the expression "f(x) = 3x2 – 24x + 10," which is in quadratic form, into vertex form, which will look like this "y = a(x-h)2 + k," you will need to apply the technique of completing the square. This will allow you to convert the expression. In the beginning, we shall separate the x2 and x terms.

y = 3(x² - 8x) + 10

We start with a negative eight, divide that number by two to obtain a negative four, and then we square that number, which gets us sixteen. We combine these so that it forms a perfect square, and then we remove 16 so that it is not altered in any way. We will get:

y = 3(x² - 8x + 16 - 16) + 10

y = 3((x - 4)² ) - 48 + 10

y = 3(x - 4)² - 38

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Answer: option D

Step-by-step explanation:

Answer:3 and 5/7

Step-by-step explanation:

Solution  : y = -7

One Variable in the linear equation :

The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2. Whereas if we speak about linear equations in two variables, it has two solutions.

-6y+6= -2(4y + 4)

-6y = -8y -8 -6

-6y +8y = -14

2y = -14

y = -14/2

y = -7

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Step-by-step explanation:

vertex of A = (x1,y1) =(2,4)

vertex of B = (x2,y2)= (12,2)

vertex of c = (x3,y3) = (8,6)

Midpoint :

The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.

x= x1+x2/2

y=y1+y2/2

Now ,

D(7,3) is the midpoint of AB.

D (x',y') = (7,3)

vertex of A = (x1,y1)

vertex of B = (x2,y2)

x' = x1+x2/2

7 = x1+x2/2

14 = x1+x2 ...1

y' = y1+y2/2

3= y1+y2/2

6= y1+y2 .....2

E (x'',y'') = (10,4)

vertex of c = (x3,y3)

vertex of B = (x2,y2)

x''= x3+x2/2

y''=y3+y2/2

20= x3+x2 ....3

8 =y3+y2.......4

F (x''',y''') = (5,5)

vertex of c = (x3,y3)

vertex of A = (x1,y1)

10= x1 +x3 ...5

10 =y1+y3 .....6

For 1 & 3 & 5

14 = x1+x2 ...1

20= x3+x2 ....3

10= x1 +x3 ...5

Add all  1 & 3 & 5

44 = 2(x1+x2+x3)

22 = (x1+x2+x3) .....7

For 1 & 7

x3 = 8

For 3 & 7

x1 = 2

For 5&7

x2 = 12

For 2 , 4 & 6

6= y1+y2 .....2

8 =y3+y2.......4

10 =y1+y3 .....6

Add all  2 & 4 & 6

24 = 2 (y1+y2+y3)

For 2 & 8

y3 = 6

For 4 & 8

y1 = 4

For 6 & 8

y2 = 2

vertex of A = (x1,y1) =(2,4)

vertex of B = (x2,y2)= (12,2)

vertex of c = (x3,y3) = (8,6)

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Answer: He could put 8 blocks in 8 stacks

Step-by-step explanation:

Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

To find out how many blocks Ken could put in each stack, we need to divide the total number of blocks by the number of stacks.

So we have:

Number of blocks = 64

Number of stacks = x

To find out how many blocks can be put in each stack, we can set up the following equation:

64 / x = y

where y is the number of blocks in each stack.

Solving for y, we get:

y = 64 / x

So if Ken wants to put all 64 blocks into the same number of stacks, he can put:

64 blocks in 1 stack

32 blocks in 2 stacks

16 blocks in 4 stacks

8 blocks in 8 stacks

4 blocks in 16 stacks

2 blocks in 32 stacks

1 block in 64 stacks

Therefore,

Ken could put the blocks in stacks of 1, 2, 4, 8, 16, 32, or 64.

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The probability that the lot of the bulbs will fail inspection of the quality control inspector is 0.9856

Given data

p = 20%

sample drawn = 19 bulbs

20% of the bulbs in the lot are defective

n = 19

p = 20% = 0.20

if 20% of the bulbs are defective to find the non defective bulbs we solve as follows

q = 1 - p

= 1 - 0.20

= 0.80

Using binomial theorem,

[tex]P ( X = x) = (^n C _{x} ) * p x * (1 - p)n - x[/tex]

[tex]= 1 - P ( x < 1 )[/tex]

[tex]= 1 - P ( X = 0)[/tex]

[tex]= 1 - ( ^{19} C _{0} ) * 0.20^0 * (0.80)^{19}[/tex]

[tex]= 1 - 1 * 1 * 0.01441[/tex]

[tex]= 1 - 0.01441[/tex]

= 0.98559

= 0.9856 (to four decimal place)

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The number of positive integers n, that satisfy 3^n+81 the square of an integer is infinite.

Based on the information given, let 3n + 82 = p².

Therefore, 3n = p² - 81

= (p - 9)(p + 9)

Let p = 3q.

3n = (3q - 9)(3q + 9(

= 9(q - 3)(q + 4)

n = 3(q - 3)(q + 3)

n > 0 ; q >= 4 for n = 4, 5, 6....

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Answer:

1/16

Step-by-step explanation:

32= 2^5

Thus:

(2^5) ^-4/5

= (2)^ - 4

= (16) ^ - 1

= 1/16

The probability of a random probability of a random student being chosen who is a female and is not between the ages of 18 and 20 will be 0.06.

From the information, 53% of its students are male (M), 37% of its students are between the ages of 18 and 20 (A), and that 31% are both male and between the ages of 18 and 20.

Probability to females = 100% - 53% = 47%

Therefore, the probability of a random student being male or between the ages of 18 and 20 will be:

= 37% - 31%

= 6%

Therefore, the probability of a random student being female or between the ages of 18 and 20 will be 6%.

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Answer:

Step-by-step explanation:

17

12

-----

do 7 x 2

14

then carry the 1

2x1 is 2 plus the 1 from before. it becomes 3

then do 1 x 7 then 1 x 1 but with an extra zero

so it becomes

17

12

---------

34

170

---------

then add it all together

34+170=204

Answer: 17*12=204

Step-by-step explanation:  because of G O O G L E

In linear equation, 2x - 5 is an expression for John's test grade.

What is linear equation in one variable?

Let Ariana's test grade = x

twice Ariana's test grade =  2x

then, John's test grade  = 2x - 5

an expression for John's test grade = 2x - 5

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Answer:

List A: 2√2, 3√2, 4√2, …

List B: 2π, 3π, 4π, …

List C: 2log35, 3log35, 4log35, …

Step-by-step explanation:

In the last half hour 4  miles did Jesse ride his bike.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

Jesse rode his bike for 2 hours at a constant rate.

First 1.5 hours, he rode 12 miles.

According to given question we have

1.5 hours=12 miles

1 hours=12/1.5

0.5 hours=12*0.5/1.5

0.5 hours=4  miles

Therefore, in the last half hour 4  miles did Jesse ride his bike.

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The length of AB is 11.40 units.

The length of two points can be calculated using the distance formulae.

The distance formulae comes under the Co-ordinate geometry section.

The distance between two points is measured by squaring  the sum of the difference between the x and y co-ordinates and then applying the square root to the result.

Here the two points given are A(-3,7) and B(6,14).

The length of the line segment AB is = √(-3-6)²+(7-14)²

                                                              = √(-9)²+(-7)²

                                                              = √81+49

                                                              = √130

                                                              = 11.40 units

So, the length of line segment AB is 11.40 units.

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It is recommended that the expressions

d = 400 - 256 and

d = 256 - 400 be considered when attempting to determine how much farther Adam can see to the horizon.

Since, the eye-level height of Pam is 256 feet above sea level, whereas the eye-level height of Adam is 400 feet above sea level.

Therefore, the formula that indicates how much farther Adam can see to the horizon should be taken to be

d = 400 - 256 and

d = 256 - 400.

This expression may be found by subtracting 400 from 256.

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CQ

Pam's eye–level height is 256 feet above sea level and Adam's eye–level height is 400 feet above sea level. What expression shows how much farther Adam can see to the horizon? In simplest terms, Adam can see a√b feet farther than Pam.

Answer:

A= 2 B= 6

Step-by-step explanation:

the dude above me is wrong

Answer: so assuming this is a d6, it's 3/6

Step-by-step explanation:

on a d6, there are 6 sides (duh). three out of the six numbers are even, two four and six. so, three out of the six numbers you can roll are even.

Answer:

bjuk

Step-by-step explanation:

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