Given the functions, f(x)=30x4+9x3+27x2−21x−17 and g(x)=6x+3, divide f(x) by g(x) and simplify.

Question options:

a.5x3−x2+5x−6+16x+3

b.5x3−x2+5x−6−36x+3

c.5x3−x2+5x−6+66x+3

d.5x3−x2+5x−6+86x+3

This value is approximate.

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Explanation:

The entire paragraph of text given to you is not needed. It's interesting that the height used to be 480 ft 11 in, but we don't use that anywhere in our calculations to get the current shorter height. Instead we rely solely on the diagram.

Refer to the diagrams I have posted below. Figure 1 is the same diagram more or less, but I've added the variables x and h.

Both h and x are in feet.

I've also added the point labels A through E.

I've split figure 1 into two pieces. Figure 2 focuses on triangle ADE and figure 3 focuses on triangle BDE.

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Let's put our attention on triangle ADE in figure 2.

Set up the tangent ratio shown below and solve for h.

[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(\text{A}) = \frac{\text{DE}}{\text{AD}}\\\\\tan(40.3) = \frac{h}{x+200}\\\\h = (x+200)\tan(40.3)\\\\[/tex]

Now move onto triangle BDE in figure 3.

Set up the tangent ratio and apply substitution.

[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(\text{B}) = \frac{\text{DE}}{\text{BD}}\\\\\tan(46.27) = \frac{h}{x+100}\\\\\tan(46.27) = \frac{(x+200)\tan(40.3)}{x+100}\\\\[/tex]

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Let's solve for x.

[tex]\tan(46.27) = \frac{(x+200)\tan(40.3)}{x+100}\\\\(x+100)\tan(46.27) = (x+200)\tan(40.3)\\\\x\tan(46.27)+100\tan(46.27) = x\tan(40.3)+200\tan(40.3)\\\\[/tex]

[tex]x\tan(46.27)-x\tan(40.3)=200\tan(40.3)-100\tan(46.27)\\\\x(\tan(46.27)-\tan(40.3))=200\tan(40.3)-100\tan(46.27)\\\\x=\frac{200\tan(40.3)-100\tan(46.27)}{\tan(46.27)-\tan(40.3)}\\\\x\approx 329.87238475414\\\\[/tex]

Use this to find h.

[tex]h = (x+200)\tan(40.3)\\\\h \approx (329.87238475414+200)\tan(40.3)\\\\h \approx 449.364461010933\\\\h\approx 449.364[/tex]

The height of the pyramid is currently 449.364 feet approximately.

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Lastly we'll convert to feet,inches format since the "480 ft 11 in" figure is in that format.

h = 449.364 ft

h = 449 ft + 0.364 ft

h = 449 ft + (0.364 ft)*(12 in/1 ft)

h = 449 ft + 4.368 in

h = 449 ft + 4 in

h = 449 feet, 4 inches

Answer:

1/32

Step-by-step explanation:

(1/2)^3 /4= (1/8)/ 4= 1/8 x 1/4= 1/32

Answer:

12

Step-by-step explanation:

Answer:

Choice D

Step-by-step explanation:

11.21 x 100% = 1,121%

Answer:

D. 1,121%

Step-by-step explanation:

100% = 1

so 11 = 1,000%

.01 = 1%

so .21 = 21%

Answer:

Leia is incorrect; 10 should not be in the domain.

Step-by-step explanation:

the domain is x, the range is y. The domain really should be '1, 4, 7, 13, 16 ,19' and the 10 should not be there.

Answer:

Money Market account

Step-by-step explanation:

Money Market accounts typically allow you to earn money at a higher interest rate than other types of savings accounts.

Answer:

B

Step-by-step explanation:

Step-by-step explanation:

calculate the total area of the bottom sections of the back and the two side walls which should be tiled.Give your answer in squared metres rounded a

accurately to 2 decimals

Answer:

789÷2=11 nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

Answer:

C. 7 ft

Step-by-step explanation:

The radius and height of the cone are the legs of a right triangle. The slant height is the hypotenuse.

24² + h² = 25²

576 + h² = 625

h² = 49

h = 7

Answer: C. 7 ft

Based on the angle-side relationship theorem, we would have the following:

The angle-side relationship theorem states that the longest side of a triangle is opposite the largest angle, and vice versa.

Given the following:

Therefore, based on the angle-side relationship theorem, we would have the following:

Learn more about angle-side relationship theorem on:

https://brainly.com/question/18980866

Answer:

yes

Step-by-step explanation:

becaise you can solve it

Answer:

See explanation

Step-by-step explanation:

First, because it is a quadratic function, we know that its graph is a parabola that opens up, as x is positive. Because x has no coefficients, we also know that it is a basic parabola, with no vertical stretches or compressions, and a vertex at x=0. Because of the -3, we know the parabola has a verticle shift down 3 units, making the parabola's vertex at (0,3). Hope this helps!

Answer: Am I wrong for getting no solution ?

Step-by-step explanation:

Answer:

0.035 decimeters.

Step-by-step explanation:

Google

Answer:

The length of the insect in decimeters is 0.035.

Step-by-step explanation:

Conversion of unit questions can be solved by rule of three.

Each millimeter has 0.01 decimeter. How many decimeters are there in 3.5 millimeters? So:

1 ml - 0.01dm

3.5ml - x dm

The length of the insect in decimeters is 0.035.

Using the uniform distribution, it is found that there is a 0.3 = 30% probability that Samantha has to wait less than 4.5 minutes to catch the bus.

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The probability of finding a value of at lower than x is:

[tex]P(X < x) = \frac{x - a}{b - a}[/tex]

In this problem, the time is uniformly distributed between 0 and 15 minutes, hence the bounds are a = 0 and b = 15.

The probability that Samantha has to wait less than 4.5 minutes to catch the bus is given by:

[tex]P(X < 4.5) = \frac{4.5 - 0}{15 - 0} = 0.3[/tex]

More can be learned about the uniform distribution at https://brainly.com/question/13889040

Answer:

x = 30 cm

solve proportionality:

[tex]\sf \dfrac{larger \ side}{larger \ base} = \dfrac{shorter \ side}{shorter \ base}[/tex]

solve:

[tex]\hookrightarrow \sf \dfrac{x}{45} = \dfrac{18}{27}[/tex]

[tex]\hookrightarrow \sf {x}{} = \dfrac{18*45}{27}[/tex]

[tex]\hookrightarrow \sf {x}{} = 30[/tex]

Answer:

[tex]x=30\:cm[/tex]

Step-by-step explanation:

[tex]\frac{x}{45}=\frac{18}{27}[/tex]

[tex]x=\frac{18*45}{27}[/tex]

[tex]x=\frac{810}{27}[/tex]

[tex]x=30[/tex] [tex]cm[/tex]

-{ModPatrol}

Answer:

1/8 hours

Step-by-step explanation:

First, we have to make our 2 fractions denominators the same to be able to subtract them! We want both of our denominators to be 8 so 5/8 already had 8 so we just need to change 1/2 to do that we are going to multiply the fraction by 4 so 1 x 4 = 4/2 x 4 = 8. Now we have 5/8 and 4/8. All we need to do now is subtract our fractions! 5/8 - 4/8 = 1/8

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

Answer:

[tex]spent \:extra \: \frac{1}{8} hrs [/tex]

Step-by-step explanation:

[tex]haha.....its \: quite \: logical \\ she \:spent \: \frac{5}{8} - \frac{1}{2} = \frac{1}{8} hrs \: more.[/tex]

Answer:

10000.

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hope its useful

Answer:

12,000

Step-by-step explanation:

Multiply 2,000 by 6 to get your answer

Hope that helps!

Answer:

$4.4

Step-by-step explanation:

22/5

I believe the answer is $4.4

Step-by-step explanation:

so if you take $22.00 divided by 5 you would get the answer

Answer:

151 Centimeters if using 3 centimeters   or 158 Centimeters if using 3.14 Centimeters

Step-by-step explanation:

Sorry if this isn't what you asked for, but i tried my best ^^

Answer:

A, C, E

Step-by-step explanation:

Answer:

(6, 11)(8, 15)(9, 17)(10, 19)

Step-by-step explanation:

ohhhh

sooo

y = 2(6) - 1

y = 12 - 1

y = 11

(6, 11)

y = 2(8) - 1

y = 16 - 1

y = 15

(8, 15)

y = 2(9) - 1

y = 18 - 1

y = 17

(9, 17)

y = 2(10) - 1

y = 20 - 1

y = 19

(10, 19)

Answer:

30 cm and 20 cm

Step-by-step explanation:

hope it helps

Answer:

23°

Step-by-step explanation:

243° + 94° + b = 360°

337 + b = 360

337 - 337 + b = 360 - 337

b = 23°

243+94=337

337-360=23

Answer is 23

Answer:

Step-by-step explanation:

since 90 hundredths is 90/100, 90 hundredths is a fraction.  if you divide 90 by 100 you get 0.90  

since 7 thousandths is 7/1000 divide that as a fraction also.

You will get 0.007

add them together 0.907

Hope that helps

Answer:

a

[tex]P(A_4) =  0.077[/tex]  

b

[tex]P(A_5) =0.7542 [/tex]

Step-by-step explanation:

From the question we are told that

    The chance that a new authors first article will be submitted is  [tex]P(A) =  0.40[/tex]

    The chance that a new authors next article will be submitted is  [tex]P(N) =  0.20[/tex]

Generally the probability that a new author first article is not published is

      [tex]P(A)' = 1 - 0.4 =  0.6[/tex]

Generally the probability that a new author next articles are not published is  

      [tex]P(N)' = 1 - 0.2 =  0.8[/tex]

Now from the question we are told to obtain the probability that a new author will be published for the first time when he or she  submits a 4th article, which implies that the new authors first three articles where not published

So the probability is mathematically represented as

   [tex]P(A_4) =  P(A)' *  P(N)' * P(N)' * P(N)[/tex]    

=> [tex]P(A_4) =  0.6 * 0.8 * 0.8* 0.2[/tex]  

=> [tex]P(A_4) =  0.077[/tex]  

Generally the probability that a new author will be published for the first time within his or her first 5  articles submitted is equivalent to

1 - [The probability that a new author will not be published for the first time

    within his or her first 5  articles submitted]

Now the  probability that a new author will not be published for the first time within his or her first 5  articles submitted. is mathematically represented as

    [tex]P(A_5)' = P(A)' * P(N)' * P(N)'*P(N)'* P(N)'[/tex]

=> [tex]P(A_5)' = 0.6 *0.8 * 0.8'*0.8* 0.8[/tex]

=>   [tex]P(A_5)' = 0.24576 [/tex]

Generally the probability that a new author will be published for the first time within his or her first 5  articles submitted is mathematically represented as

    [tex]P(A_5) = 1 - P(A_5)'[/tex]

=>  [tex]P(A_5) = 1 -0.24576 [/tex]

=>  [tex]P(A_5) =0.7542 [/tex]