Factor and solve the equation x^3-x^2-30x=0

Answer:

[tex]x=3.1950[/tex]

Step-by-step explanation:

Given:

The equation to solve is given as:

[tex]\log_8 12=x-2[/tex]

In order to solve this, we use the base change formula of logarithms.

The base change formula is given as:

[tex]\log_a b=\frac{\log b}{\log a}[/tex]

Therefore, the equation can be rewritten as:

[tex]\frac{\log 12}{\log 8}=x-2[/tex]

Adding 2 on both the sides, we get:

[tex]x=2+\frac{\log 12}{\log 8}[/tex]

Now, we know that, [tex]\log 12=1.07918\ and\ \log 8=0.9031[/tex]

Plug in these values and solve for 'x'. This gives,

[tex]x=2+\frac{1.07918}{0.9031}\\\\x=2+1.19497=3.19497\approx3.1950[/tex]

Therefore, the value of 'x' is 3.1950 rounded to four decimal places.

Answer:x=3.1950 on ed yw

Step-by-step explanation:

Answer:

g(x) = -x^2 - 4

Step-by-step explanation:

f(x) = x^2

To flip the graph, you need the negative of the right side,

y = -x^2

This is a parabola that opens downward, but the vertex is at (0, 0).

Now you need to translate the graph 4 units down, so subtract 4 from -x^2.

g(x) = -x^2 - 4

Answer:

b = -6

Step-by-step explanation:

Given:

y=6x+b ----- (eq 1)

and

-3x+1/2y=-3    (Rearrange this equation to look likes eq (1) , add -3x to both sides)

(1/2) y = 3x - 3   (multiply both sides by 2)

y = 2(3x -3)   (distribute the 2 into parentheses)

y = 6x - 6 -----(eq 2)

Recall that a system of equations will have an infinite number of solutions if both equations are the same line.  (i.e they have the same slope and y intercept)

In our case, if you compare eq 1 and eq 2, the way to make both equations the same line is if b = -6. (this is the answer)

Answer:

3.1415926535

I can't explain why but I tried my best, I hope it helped.

The area of the triangle is 16 square feet.

The formula for finding the area of a triangle is given by:

Area = 1/2 * base * height

Given that the base of the triangle measures 6.4 feet and the height measures 5 feet, we can substitute these values into the formula:

Area = 1/2 * 6.4 * 5 = 16 square feet

Therefore, the area of the triangle is 16 square feet.

Ima edit this-Step-by-step explanation:

Answer:

20

Step-by-step explanation:120÷6=20

Answer:

C

Step-by-step explanation:

[tex] \frac{2}{3} \times 18 = \frac{2}{5} \times x[/tex]

[tex] \frac{36}{3} = \frac{2x}{5} [/tex]

[tex]180 = 6x[/tex]

[tex]30 = x[/tex]

Two third of 18 is equal to 2/5 of 30, Option C is the correct answer.

An equation in math is an equality relationship between two expressions written on both sides of the equal to sign.

It is given in the question

two third of 18 is equal to 2/5 of what number

Let the number be x

then the expression that can be formed = (2/5)x

and (2/3)*18

These two expression are equal

Equating the expression will give

(2/5)x = (2/3)*18

(2/5)x = 12

x = 12*5/2

x = 30

Therefore the number = 30.

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The total purchase price is $ 357.75

Solution:

Joanna buys a table and 2 chairs

Cost of table = $ 250

Cost of 1 chair = $ 100

Therefore, cost of a table and 2 chairs = 250 + 2(100) = 450

Thus, cost price = $ 450

She receives a 25% discount for being a preferred customer

Therefore, discount = 25 % of cost price

[tex]discount = 25 \% \times 450\\\\discount = \frac{25}{100} \times 450\\\\discount = 0.25 \times 450 = 112.5[/tex]

Thus, amount after discount = cost price - discount

amount after discount = 450 - 112.5 = 337.5

Thus, amount after discount is $ 337.5

Then pays 6% sales tax on the discounted purchase price

Sales tax = 6 % of 337.5

[tex]sales\ tax = 6 \% \times 337.5\\\\sales\ tax = \frac{6}{100} \times 337.5\\\\sales\ tax = 20.25[/tex]

Thus, total purchase price is given as:

total purchase price = Amount after discount + sales tax

total purchase price = 337.5 + 20.25 = 357.75

Thus total purchase price is $ 357.75

Answer:

None of the above graph gives the function.

Step-by-step explanation:

The function is given by

f(x) = - x + 1 for, x ≤ 0  .......... (1) and

f(x) = x + 1 for, x > 0 ............. (2)

Now, from this definition we can write for x = 0, the value of f(x) will be governed by the equation (1) and f(0) = - 0 + 1 = 1

So, (0,1) is a point on the graph and for x < 0 the f(x) will have negative slope and for x > 0, the f(x) will have  positive slope.

So, none of the above graphs gives the function. (Answer)  

Answer:

the 4 graph

Step-by-step explanation:

Answer:

A compound is two or more types of atoms chemically joined together.

i hope this helps

have a nice day

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The statement describes a compound: "two or more types of atoms chemically bonded together". The correct answer would be an option (C).

Compounds are pure molecules made up of two or more separate elements' atoms. Compounds can be disassembled into their constituent parts. These compounds are composed of a set number of atoms. Carbon monoxide CO is an example of a chemical compound.

A compound is a substance made up of two or more different types of atoms that are chemically bonded together.

So, two or more types of atoms chemically bonded together describe a "compound".

Hence, the correct answer would be an option (C).

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Final answer:

The two numbers that add up to 29, where one number is one more than the other, are 14 and 15. The equation 2x + 1 = 29 helped determine that the smaller number is 14, and adding one gives us the larger number, 15.

Explanation:

The two numbers in question are those that sum up to 29, and one number is one more than the other. Let's denote the smaller number as x, which makes the larger number x + 1 because it's one more than the smaller one. Setting up the equation based on the information given, we have:
x + (x + 1) = 29
Combining like terms gives us:
2x + 1 = 29
To find the value of x, we subtract 1 from both sides:
2x = 28
And then divide by 2:
x = 14
Therefore, the smaller number is 14, and the larger number, being one more than 14, is 15.

Final answer:

The egg will take approximately 3.35 seconds to reach the ground.

Explanation:

To solve this problem, we can use the equation [tex]y = yo + vot + 0.5at^2[/tex] position, yo is the initial position, vo is the initial velocity, a is the acceleration, and t is the time.

In this case, yo = 90 ft, vo = 0 ft/s, a = -16 [tex]ft/s^2[/tex]y = 0 ft (since the egg reaches the ground). Plugging these values into the equation, we get 0 = 90 + (0)(t) + 0.5(-16)t^2.

Simplifying the equation, we have [tex]0 = 90 - 8t^2[/tex], we get[tex]8t^2 = 90[/tex] both sides by 8, we get [tex]t^2 = 11.25[/tex]e square root of both sides, we find that t ≈ 3.35 seconds.

Final answer:

Betty needs 13 jars to can 104 pears and 21 jars to can 126 apples, making a total of 34 jars.

Explanation:

To determine how many jars Betty needs to can 104 pears and 126 apples, we must consider the capacity of the jars. Each jar holds 8 pears or 6 apples. Therefore, we need to calculate how many jars are required for each fruit separately.

For pears:

For apples:

The total jars needed equals the sum of the jars needed for pears and the jars needed for apples, which is 13 jars for pears plus 21 jars for apples, totaling to 34 jars.

Answer:

[tex]tan(\theta)=-\frac{5}{\sqrt{119}}[/tex]

Step-by-step explanation:

The correct question is

Suppose that ∅ Is an angle with csc(∅)=-12/5 and ∅ Is not in the third quadrant. Compute the exact value of Tan(∅).

∅ Is not in the third quadrant

If csc(∅) is negative the angle lie in the III Quadrant or in the IV Quadrant

∅ Is not in the third quadrant ----> given problem

so

That means ----> ∅ Is in the fourth quadrant

step 1

Find the value of [tex]sin(\theta)[/tex]

we have

[tex]csc(\theta)=-\frac{12}{5}[/tex]

we know that

[tex]csc(\theta)=\frac{1}{sin(\theta)}[/tex]

therefore

[tex]sin(\theta)=-\frac{5}{12}[/tex]

step 2

Find the value of [tex]cos(\theta)[/tex]

we know that

[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]

we have

[tex]sin(\theta)=-\frac{5}{12}[/tex]

substitute

[tex](-\frac{5}{12})^2+cos^2(\theta)=1[/tex]

[tex]\frac{25}{144}+cos^2(\theta)=1[/tex]

[tex]cos^2(\theta)=1-\frac{25}{144}[/tex]

[tex]cos^2(\theta)=\frac{119}{144}[/tex]

[tex]cos(\theta)=\frac{\sqrt{119}}{12}[/tex] ---> is positive (IV Quadrant)

step 3

Find the value of [tex]tan(\theta)[/tex]

we know that

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

substitute the values

[tex]tan(\theta)=-\frac{5}{12} : \frac{\sqrt{119}}{12}=-\frac{5}{\sqrt{119}}[/tex]

Answer:

Step-by-step explanation:

3.38times3=10.14

5times.79=3.95

1times2.30=2.30

10.14+3.95+2.30=18.04

Answer:

3.38times3=10.14

5times.79=3.95

1times2.30=2.30

10.14+3.95+2.30=18.04

Step-by-step explanation:

Answer:

10.8 cm

Step-by-step explanation:

we know that

1) A square picture with side length 30 cm is scaled by 60% on a photocopier

Remember that

[tex]60\%=60/100=0.60[/tex]

so

The length of the first copy of the picture is

[tex]30(0.60)=18\ cm[/tex]

2) The copy is then scaled by 60% again

so

The length of the second copy of the picture is

[tex]18(0.60)=10.8\ cm[/tex]

Based on the information given, the side length of the second copy of the picture is 10.8cm.

Therefore, the side length will be:

= 30 × 60% × 60%

= 10.8cm

In conclusion, the correct option is 10.8cm.

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Answer:

The solution is 36/35

Step-by-step explanation:

5 2/3 - 1 1/6

———————-

8 5/8 - 4 1/4

17/3 - 7/6

= ———————-

69/8 - 17/4

17/3×2 - 7/6

= ———————-

69/8 - 17/4 × 2

34/6 - 7/6

= ———————-

69/8 - 34/8

9/2

= ———————-

35/8

= 9/2 ÷ 35/8

= 9/2 × 8/35

= 9(8)/2(35)

= 9(4)/35

= 36/35

Answer:

WHERE IS IT

Step-by-step explanation:

Answer:

The graph is shown below.

Step-by-step explanation:

Given:

The inequalities to solve by graphing are given as:

[tex]y>2x\\\\y<3[/tex]

Now, in order to graph them, we first replace inequality sign by equal to sign.

So, the two equations are given as:

[tex]y=2x\\\\y=3[/tex]

Now, the first equation is a straight line of the form [tex]y=mx[/tex]. This is a line that passes through origin with slope equal to 'm'.

So, the slope of the first line is 2.

In order to plot the line,we take a random value of 'x'. Let [tex]x=1[/tex]

So, [tex]y=2\times 1=2[/tex]

So, the point on the line is (1, 2)

Now, we draw a line passing through the points (0, 0) and (1, 2). This is the line for the first equation.

Now, the second equation is a straight line parallel to the x-axis.

So, the equation [tex]y=3[/tex] is a straight line parallel to x-axis passing through the point (0, 3) as shown below.

Now, since the first inequality has 'y' greater than '2x'. So, the solution region is left of the line excluding the line.

Also, the second inequality has 'y' less than 3. So, the solution region is below the line excluding the line.

The common region for both the line inequalities is the solution.

The solution region is shown below.

Answer:

o, the solution region is left of the line excluding the line.

Also, the second inequality has 'y' less than 3. So, the solution region is below the line excluding the line.

Step-by-step explanation:

Answer:

B. Heading, Body, Closing and Signature line

Step-by-step explanation:

Quiz Verified

The three main parts of a professional cover letter are:

- Introduction

- Body

- Conclusion

Option D is the correct answer.

A professional cover letter is a formal document that accompanies a job application.

It introduces the applicant to the potential employer and highlights their qualifications, skills, and experience that make them a suitable candidates for the job.

We have,

The three main parts of a professional cover letter are:

-Introduction

-Body

- Conclusion

The introduction typically includes a greeting, a brief overview of the position being applied for, and a statement of interest in the position.

The body of the cover letter is where the applicant can expand on their qualifications, skills, and experience, highlighting relevant achievements and providing examples that demonstrate their fit for the position.

The conclusion usually summarizes the applicant's interest and qualifications, and thanks the employer for considering the application.

It may also include a call to action, such as a request for an interview or an invitation for further discussion.

Thus,

The three main parts of a professional cover letter are:

-Introduction

-Body

- Conclusion

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The sum of two numbers:

x + y = 108

The difference of the same two numbers:

x - y = 78

We can use substitution to figure out x and y:

x - y = 78 can be changed to x = 78 + y

We can plug this into the first equation:

78 + y + y = 108

78 + 2y = 108

2y = 30

y = 15

Now solve for x using any of the two equations. I'll use the first equation since it's easier:

x + 15 = 108

x = 93

Final answer:

Line a and line b, being parallel, have the same slope which is the defining feature of parallel lines.

Explanation:

When two lines, line a and line b, are parallel, they will never intersect and will have the same slope. Therefore, if line a is parallel to line b, the statement 'Line a and line b have the same slope' is true.

In the context of the slope of lines, the sum of the slopes of line a and line b would not be 0 unless both slopes are zero, which is typically not the case for non-horizontal lines. The product of the slopes would not be 1 or -1 either, unless one of the lines is perpendicular to the other, which would imply that the lines are not parallel. Therefore, the characteristic feature of parallel lines is that their slopes are identical.

Option A

The simple interest earned is $ 105

Solution:

Given that, $300 at 5% annual interest for 7 years

Therefore,

Principal = $ 300

Rate of interest = 5 %

Number of years = 7

The simple interest is given by formula:

[tex]Simple\ Interest = \frac{p \times n \times r }{100}[/tex]

Where,

p is the principal

r is the rate of interest

n is the number of years

Substituting the values in formula,

[tex]Simple\ Interest = \frac{300 \times 7 \times 5 }{100}\\\\Simple\ Interest = 3 \times 7 \times 5\\\\Simple\ Interest = 105[/tex]

Thus simple interest earned is $ 105

Answer:

[ 4 2 ] x [ -2 5 7 -1 ]​ = [- 10,836]

Step-by-step explanation:

Here, the given expression is:

[ 4 2 ] x [ -2 5 7 -1 ]​

Now solving :  [ -2 5 7 -1 ]​ , we get

[ -2 5 7 -1 ]​ =  [-258]

Now simplifying

[-258] x [ 4 2 ] =  - 10,836

⇒  [ 4 2 ] x [ -2 5 7 -1 ]​ = [- 10,836]

Hence the solution is:   [- 10,836]

Answer:

D. [6 18]

Step-by-step explanation:

Edge2020

Have a great day y'all :)

Answer:

-64

Step-by-step explanation:

-32^(6/5) =-(  [tex]}\sqrt[5]{32}[/tex])^6

               = -(2)^6

               = -64

The Simplification of the given expression is -64.

Simplification is the procedure to utilize and analyze the function or expression to make the function or expression uncomplicated.

The given expression is:

[tex]-32^{6/5} =[/tex]

To simplify this expression, we have to combine like terms.

Combining the like terms  we get:

[tex]-32^{6/5} =[/tex] ( [tex]-( \sqrt[5]{32} )^6[/tex] )^6

              = [tex]-(2)^6[/tex]

              = -64

Therefore, the value of the given expression is -64.

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Answer:

Discounted percent = 42.5% and price of the discounted product compared to original is 57.5%

Step-by-step explanation:

$46 = Discount of some decimal of $80

46 = x(80)

46/80 = 0.575

Change it to percent

57.5% discount

The discount expressed as a percent of the regular price is approximately 42.5%.

Here, we have,

To calculate the discount as a percent of the regular price, we can use the following formula:

Discount Percentage = (Discount Amount / Regular Price) × 100%

Given that

the regular price is $80 and the sale price is $46, we can calculate the discount amount by subtracting the sale price from the regular price:

Discount Amount = Regular Price - Sale Price

Discount Amount = $80 - $46

Discount Amount = $34

Now we can calculate the discount percentage:

Discount Percentage = (Discount Amount / Regular Price) × 100%

Discount Percentage = ($34 / $80) × 100%

Discount Percentage ≈ 42.5%

Therefore, the discount expressed as a percent of the regular price is approximately 42.5%.

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Answer:

36/5 = 7 1/5

Step-by-step explanation: hope this help!

Answer:

  24

Step-by-step explanation:

  [tex]\dfrac{3}{7}\times 56=3\times\dfrac{56}{7}=3\times 8=24[/tex]

Even if you don't know your times tables or how to multiply fractions, you can use a calculator to compute the value.

Kevin gave 24 stamps to his friends.

Answer:

The answer is B

Step-by-step explanation:

just did

Answer:

It takes May 6 minutes and 24 seconds to run 4 laps and 1 minute and 36 seconds per lap

Statement and question:

May runs around a 400-meter track at a constant speed of 250 meters per minute. How many minutes does it take May to complete 4 laps of the track?

Source:

Previous question that can be found at brainly

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Speed of May = 250 meters per minute

Length of the track = 400 meters

2. How many minutes does it take May to complete 4 laps of the track?

Let's answer the question calculating the total distance and the time it took Mary to run around the track, this way:

Total distance = 4 * 400 = 1,600 meters

Time it takes May to run 1,600 meters = 1,600/250

Time it takes May to run 1,600 meters = 6.4 minutes

6.4 minutes = 6 minutes + 0.4 * 60 seconds = 6 minutes and 24 seconds

Time it takes May to run one lap = 6.4/4 = 1.6

1.6 minutes = 1 minute + 0.6 * 60 seconds = 1 minute and 36 seconds