Bonus question: what is the relationship between the circumference of a tire and the rotations necessary to cover a given distance? (i.e. are they directly proportional or inversely proportional) Explain your answer choice. Hint: think about the rotations necessary for a miniature toy car versus a massive tractor.​

The actual roots of the function P(x) = x^4 - 4x^3 - 4x^2 + 36x - 45 are its real roots

The actual roots ordered from least to greatest are -3 and 3

From the complete question, the polynomial function is:

P(x) = x^4 - 4x^3 - 4x^2 + 36x - 45

Expand the above equation

P(x) = x^4 - 4x^3 + 5x^2 - 9x^2 + 36x - 45

Factorize the equation

P(x) = x^2(x^2 - 4x + 5) - 9(x^2 - 4x + 5)

Factor out x^2 - 4x + 5

P(x) = (x^2- 9)(x^2 - 4x + 5)

Express x^2 - 9 as a difference of two squares

P(x) = (x + 3)(x - 3)(x^2 - 4x + 5)

The expression (x^2 - 4x + 5) cannot be factorized.

So, we have:

P(x) = (x + 3)(x -3)

Equate to 0

(x + 3)(x -3) = 0

Expand

x + 3 = 0 or x - 3 = 0

Solve for x

x = -3 or x = 3

Hence, the actual roots ordered from least to greatest are -3 and 3

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Answer:

answer in picture

Step-by-step explanation:

Answer:

The odds of drawing a heart are 13:52

Explanation: A standard deck of card contains 52 card. There are 4 types of playing cards: clubs, diamonds, hearts and spades. Every type of them has 13 cards. How do u know that? Well just divide 52 by 4 and then you get 13.

The small does 2 1/2 for 1/4 of the large. Multiply by 4 to get a full rotation of the large one:

2 1/2 x 4 = 10

answer: D. 10

Answer:

Step-by-step explanation:

Since the prices increase at a monthly rate of 0.1% per month. To find the percentage do they increase a year, we need to convert 0.1% to a decimal.

So here how we do it. We put 0.1 percent on the numerator because it a small number which is what we want over 100 like this:

[tex]\frac{0.1}{100}[/tex]

Now when plugging this into your calculator you get:

0.001

.So what do we do with this number?

We now times it by 12 like this:

0.001 x 12 which gives us:

0.012

So we can convert this back to a percentage by moving the decimal by 2 places to the right which gives us 1.2%.

Another way we could of done this without doing the long way to figure it out is by multiplying 0.1 times 12 which still gives us 1.2%

Answer:

f−1(x)=x5+45

Step-by-step explanation:

Answer:

Below in bold.

Step-by-step explanation:

z = 87 degrees ( vertical angles)

9x - 87 = 180 - z   ( adjacent angles are supplementary)

9x - 87 = 180 - 87  

9x = 180

x = 20 degrees.

Answer:

[tex]\red{\frac{ {c}^{10}}{{d}^{10} } }[/tex]

Step-by-step explanation:

[tex] \huge \: \frac{ {c}^{ - 6} {d}^{4}}{ {c}^{ - 16} {d}^{14} } \\ \\ = \huge \: \frac{ {c}^{16 - 6}}{{d}^{14 - 4} } \\ \\ = \huge \: \red{\frac{ {c}^{10}}{{d}^{10} } }[/tex]

Answer:

Below

Step-by-step explanation:

64-133+32+3-12= -46

-46/2= -23

There is no remainder

Answer:

Midsegment = 3√13

Step-by-step explanation:

The length of the mid segment of trapezoid is half the sum of the lengths of the two parallel sides, AB and CD

Answer:

20times bc u times 5 by 10 then divide 8 u get 6.2

Answer:

They were out side for 21 minutes

Step-by-step explanation:

you just add 11:43 and add 21 minutes  to it and you get 12:04

Answer:

4/13

Step-by-step explanation:

The pattern is that every number is multiplied by 2 starting at 1/52. To find the next fraction in the sequence, multiply 2/13 by 2:

[tex]\frac{2}{13} (\frac{2}{1} )=\frac{4}{13}[/tex]

4/13 is our final simplified answer

I hope this helps!

Answer:

Answer:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

Step-by-step explanation:

Standard equation of a circle:  \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2

(where (a, b) is the center and r is the radius of the circle)

Substitute the given center (-14, -5) into the equation:

\sf \implies (x-(-14))^2+(y-(-5))^2=r^2⟹(x−(−14))2+(y−(−5))2=r2

\sf \implies (x+14)^2+(y+5)^2=r^2⟹(x+14)2+(y+5)2=r2

Now substitute the point (-7, 5) into the equation to find r²:

\sf \implies ((-7)+14)^2+(5+5)^2=r^2⟹((−7)+14)2+(5+5)2=r2

\sf \implies (7)^2+(10)^2=r^2⟹(7)2+(10)2=r2

\sf \implies 149=r^2⟹149=r2

Final equation:

\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149

The amount that Jo will have less towards next years holiday, if all other expenses, wage and bonus stay the same is $146.88.

The initial amout that Jo paid for the phone is calculated as follows;

amount per month = ($49) / (1 + ¹/₃)

amount per month = ($49) / (1.333)

amount per month = $36.76

For 1 year (12 months), = $36.76 x 12 = $441.12

$49 x 12 = $588

= $588 -  $441.12

= $146.88

Thus, the amount that Jo will have less towards next years holiday, if all other expenses, wage and bonus stay the same is $146.88.

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Answer:

1.98Gal

Step-by-step explanation:

Randy soda total is 1.5 gal + 2.25 Gal = 3.75 Gal

Andy soda total is 1.15 + 0.62 Gal = 1.77 Gal

3.75-1.77=1.98Gal

1.98

Step-by-step explanation:

1.5+2.25=3.75

1.15+0.62=1.77

3.75-1.77=1.98

Answer:

448 is the answer

Step-by-step explanation:

If u need complete solution do let me know

Answer:

448 yd^2.

Step-by-step explanation:

The surface area consists of 3 rectangles and 2 congruent triangles

= 12*11 + 2 * 10*11 + 2 * 1/2 * 12*8

= 132 + 220 + 96

= 448 yd^2.

Answer:

$ 25.86 is the answer

Step-by-step explanation:

Answer:

Hopefully, this helps you!!

:3

Here's a graph!

Have a great day!!

[tex]Sokkachan[/tex]

Answer:

Point W

Step-by-step explanation:

Answer: B (2.9 x 10)

Step-by-step explanation: (4.35 x 10^2)/15 = 29 = 2.9 x 10

In order to solve a proportion, you should cross-multiply:-

[tex]\bf{\displaystyle\frac{3x}{10} =\frac{3}{2}}[/tex]

Multiply 3x times 2 and 10 times 3:-

[tex]\bf{6x=30}[/tex]

Divide both sides by 6:-

[tex]\boxed{\bf{x=5}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

Bob

Step-by-step explanation:

Answer:

..............................

Answer:

6.25 years

(6 years 3 months)

Step-by-step explanation:

Simple interest formula

A = P(1 + rt)

where:

Given:

Substitute given values into the formula and solve for t:

⇒ 1500 = 1000(1 + 0.08t)

⇒ 1500 = 1000 + 80t

⇒ 500 = 80t

⇒ t = 6.25 years

Answer:

S

ThenSn=n(a1+an)2Sn=n(a1 + an)2 , where nn is the number of terms, a1a1 is the first term and anan is the last term. The sum of the first nn terms of an arithmetic sequence is called an arithmetic series .

Step-by-step explanation:

Answer:

1st one is 0.021

2nd one is 0.009

the last question is 0.015 tho

Answer:

for the first one it will be 0.021

the second one it's 0.009

and for the third one it will be 0.015

The marginal tax bracket of Dave shows that the amount of the federal tax is $28000.

Let the federal tax be represented by x.

From the information, Dave’s marginal tax bracket is 25%, and he contributed 7000.

Based on the information, the amount will be:

25% of x = 7000

0.25 × x = 7000

0.25x = 7000

x = 7000/0.25

x = $28000

In conclusion, the amount is $28000.

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Answer:

[tex]Y=-\frac{1}{3} + 6[/tex]

Hope This Helps! :) Please Mark Brainliest!

Answer:

^EKF and^HKI

Step-by-step explanation:

answer:

127.2345in²

explanation:

attached

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