The list price on a winter coat is $84. It is being sold at a 23% discount. What is the sale price of the coat?
A)$64.68
B)$61.32
C)$47.48
D)$22.68

Answer:

x=4

Step-by-step explanation:

on edge

The extraneous solution to the logarithmic equation log₇(3x²+x)-log₇x=2 is x=16

When you raise a number with an exponent, there comes a result.

Lets say you get[tex]a^b = c[/tex]

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

[tex]b = \log_a(c)[/tex]

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We are given the function as;

log₇(3x²+x)-log₇x=2

Domian: 3x²+x>0

x(3x+1)>0

x∈(-∞,-1/3)U(0,∞)

Hence, x∈(0,∞), Thus x∈(0,∞)

In this problem we use the following formula:

 [tex]\boxed {log_ax-log_ay=log_a\frac{x}{y}}\displaystyle\\log_7(3x^2+x)-log_7x=2\\\\log_7(x(3x+1))-log_7x=2(1)\\\\log\frac{x(3x+1)}{x} =2(log_77)\\\\log(3x+1)=log_77^2\\\\log_7(3x+1)=log_749\\\\\\\\3x+1=49\\\\3x+1-1=49-1\\\\3x=48\\\\x=16[/tex]

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Answer:

3.444

Step-by-step explanation:

3.444

Answer:

  32

Step-by-step explanation:

  [tex]\log a=7\hspace{15px} \log b=10\hspace{15px} \log c=3\\\\ \log \dfrac{a^8c^2}{b^3}=8\log{a}+2\log{c}-3\log{b}=(8)(7)+(2)(3)-(3)(10)\\\\=56+6-30=\boxed{32}[/tex]

__

The applicable rules of logarithms are ...

  log(ab/c) = log(a) +log(b) -log(c)

  log(a^b) = b·log(a)

Answer:

h = 15

Step-by-step explanation:

Use Pythagorean Theorem to solve for h.

a² + b² = c²

8² + h² = 17²

64 + h² = 289

h² = 225

h = 15

Answer:

Try searcing it up

Step-by-step explanation:

chances are its already been answered

Answer:

3.4

Step-by-step explanation:

5x=12x-28

28=12x-5x

28=8x

28÷8=3.4

Step-by-step explanation:

There ya go my laddie. enjoy.

Answer:

1. 8v^4 + 6v^2

2. -7n - 3

3. 2a^3 - 6a

4. -2x^4 + 8x

Step-by-step explanation:

you remove the parentheses, group( or put )the terms together, then combine the like terms, and you'll get your answers.

Answer:

360ft

Step-by-step explanation:

Answer:

(from top)

in the first box, type $9

in the second box, type 4

in the third box, type $45

in the last box, type $112.50

Step-by-step explanation:

divide 22.50 by 2.5 = 9

so in the first box, type 9

36 divided by 9 = 4

5 * 9 = 45

12.5 * 9 = 112.5

Answer:

She makes $9 per hour. 9*2.5=22.50.

4 hours=$36

5hrs=$45

12.5 hours=112.50 dollars

Step-by-step explanation:

Answer:

1.) The product of 12 and 3/4 is less than 12. This is because you are multiplying 12 by a number less than 1.

2.) The product of 5 and 1/2  is less than 5, this is because you are multiplying 5 by a number less than one.

Step-by-step explanation:

If multiplied by a number less than one then it will be smaller than original

If multiplied by one will be the same as original

If multiplied by a number greater than one it will be greater than original

Answer:

This is your answer

Answer:

[tex]6x^2 + 2x[/tex]

Step-by-step explanation:

2x * (6x+2) = 12x^2 + 4x = 2 * area

area = 6x^2 + 2x

Answer:

3.21 x 10^8

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

volume of hexagonal prism = area of base * perpendicular height

Step-by-step explanation:

Answer:

this image is unclear i cant answewr this

Step-by-step explanation:

Answer:i think 6x+3 is 9x and 2x-5 is 3x

Step-by-step explanation:

Answer:

201.06

Step-by-step explanation:

A=πr2

R= 16/2= 4cm

A= 22/7 x 4 x 4

A= 201.06

Answer:

A. Census

Step-by-step explanation:

You would simply ask ALL of the employees at your workplace as to whether or not they visit the dentist for regular check-ups. Thus, it is a census.

The type of study which will be the best help the company discover this information is survey sample, the correct option is B

Sample space is the set of all possible outcome the considered random experiment can result to.

Thus, suppose we toss a coin, then tossing a coin is a random experiment, and the  sample space is {'head', 'tail'}. We ignore other outcomes like slant coin, or standing coin by assuming that coin is very thin to stand and always falls down.

We are given that;

The number of its employees who go to the dentist.

Now,

A census involves collecting data from every individual in a population, which can be time-consuming, expensive, and may not be feasible for a large company with a large number of employees.

An observational study involves observing individuals and collecting data without intervening or manipulating any variables. This type of study may not provide information about the number of employees who visit the dentist for regular checkups since it does not involve asking individuals directly about their behavior.

An experiment involves manipulating one or more variables to observe the effect on another variable. This type of study may not be appropriate for studying employee behavior related to dentist visits since it may not be ethical or practical to manipulate employees' behavior in this way.

A survey sample, on the other hand, involves selecting a subset of employees and asking them directly about their behavior related to dentist visits. This can be an effective and efficient way to gather information about the number of employees who visit the dentist for regular checkups.

Therefore, by sample space the answer will be survey sample.

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Answer:

h

Step-by-step explanation:

Answer:

Step-by-step explanation:

7) The tangent angles are 90° each.

The angles of a quadrilateral add up to 360°, so ? = 360°-90°-90°-73° = 107°.

8)  Solve this the same way as question 7). ? = 360°-90°-90°-57° = 123°.

Questions 9) and 10) are cut off, so I assume you don't need to know those.

Answer:

All equilateral triangles are acute angle triangles.

The value of expression for x > 5 is,

⇒ x + 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Expression is,

⇒ |x + 3|

if x > 5

Now, For  x > 5;

Expression is,

⇒ x + 3

At x = 5;

⇒ 5 + 3

⇒ 8

Thus, The value of expression for x > 5 is,

⇒ x + 3

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Answer:

31 cm

Step-by-step explanation:

A rectangle has 4 sides.

27 cm + 4 cm = 31 cm.

The perimeter is 31 cm.

If you are confused, to find perimeter you add all the sides up. That is why I added 1 + 1 + 1 + 1 / 4.

For inches or a different measure I recommend just converting it. You never mentioned the measure so I decided with cm.

Answer:

35

Step-by-step explanation:

just because i saw a guy who commented on first answer

There are 10 perfect squares between 1 and 100, and 10 powers with an exponent of 2 between 1 and 100.

A number system is defined as a system of writing to express numbers.

Between 1 and 100, the perfect squares (numbers that can be expressed as the square of an integer) have exponents of 2.

We need to count the number of perfect squares between 1 and 100. These include:

1² = 1

2² = 4

3²= 9

4² = 16

5² = 25

6² = 36

7²= 49

8² = 64

9² = 81

10² = 100

So, there are 10 perfect squares between 1 and 100, and therefore 10 powers with an exponent of 2 between 1 and 100.

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live to be 80 years old and sleep 8 hours a day, How many years have I slept

Solution

A day has 24 hours

24 = 8 + 8 + 8

So you spent 1/3 of your time sleeping.

You can get the same answer if you do 8/24

8/24 = (8 ÷ 8) / ( 24 ÷ 8) = 1/3

All you need to do now is to find 1/3 of 80

1/3 of 80 = 1/3 × 80 = 80/3

80 / 3 = (78 + 2) / 3 = 78 / 3 + 2 / 3 = 26 + 2/3

So that is 26 years + ( 2/3 of a year)

What is 2 / 3 of a year?

Since 2 /3 of a year is a fraction of a year, the answer for 2 / 3 of a year will be in months.

1 year = 12 months.

Just find out what 2/3 of 12 is

2/3 of 12 is 2/3 times 12

2/3 times 12 = (2 times 12) / 3 = 24 / 3 = 8 months

Putting everything together, you slept for 26 years and 8 months during your lifetime.

Hope it helped!

Answer:

D

Step-by-step explanation:

multiplying the day with 54 gives you its amount earned

Answer:

13.3 (rounded in the tenth place)

Step-by-step explanation:

equation: a^2 + b^2 = c^2

What we know :

a = 20^2 = 400

b = what we are looking for

c = 24^2 = 576

Our equation will be looking like :

20^2 + b^2 = 24^2

400 + b^2 = 576

Now we  subtract 400 into 576

which equals 176 now we square root it

and get 13.2664 but we gotta square root it and that will lead you to have 13.3 as your answer

Answer:

31.24

Step-by-step explanation:

a^2+b^2=c^2

20^2=400

24^2=576

576+400=976

√976=31.24

Answer:

n = 8.2

Step-by-step explanation:

54 - 13 = 41

5n = 41

41/5 = 8.2

n=8.2