What is the completely factored form of f(x)=x3+5x2+16x+80 ?

The factorization is  [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

To answer the question, w e need to know what factorization is

Factorization is the breaking down of a larger expression into smaller expression by grouping it into its factors.

So, [{(a² - 25b²}³ + {25b² - 9c²}³ + {9c² - a²}³)/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

= [{(a² - (5b)²}³ + {(5b)² - (3c)²}³ + {(3c)² - a²)})/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Using the fact that x² - y² = (x + y)(x - y) in the terms in the numerator, we have

[{(a - 5b)(a + 5b)}³ + {(5b - 3c)(5b + 3c)}³ + {(3c - a)(3c + a)}³/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Factorizing out the denominator, we have

= [{(a + 5b)/(a - 5b)}³ + {(5b + 3c)/(5b - 3c)}³ + {(3c + a)/(3c - a)}³[(a - 5b)³ + (5b - 3c)³ + (3c - a)³]/{(a - 5b)³ + (5b - 3c)³ + (3c - a)³}]​

Cancelling out the denominator, we have

= [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

So, the factorization is  [(a + 5b)/(a - 5b)]³ + [(5b + 3c)(5b - 3c)]³ + [(3c + a)(3c - a)]³

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Using the normal distribution, it is found that 2.15% of bedroom apartments in the city cost between $750 and $1,000.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 1500, \sigma = 250[/tex]

The proportion of apartments that cost between $750 and $1,000 is given by the p-value of Z when X = 1000 subtracted by the p-value of Z when X = 750, hence:

X = 1000:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1000 - 1500}{250}[/tex]

Z = -2

Z = -2 has a p-value of 0.0228.

X = 750:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{750 - 1500}{250}[/tex]

Z = -3

Z = -3 has a p-value of 0.0013.

0.0228 - 0.0013 = 0.0215.

0.02215 = 2.15% of bedroom apartments in the city cost between $750 and $1,000.

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Answer:

[tex]\bold{\green{(4x-3)(3x^{2}-1) }}[/tex]

Step-by-step explanation:

Answer:

(3x^2 - 1)(4x - 3)

Step-by-step explanation:

We can use grouping to factor this

12x^3 – 9x^2 − 4x + 3

group into: (12x^3 – 9x^2)(− 4x + 3)

Solve one side at a time:

(12x^3 – 9x^2)

3x^2(4x - 3) factor out a 3x^2

(− 4x + 3)

- 1 (4x - 3) factor out a -1

put the two equations togeth

(3x^2 - 1)(4x + 3)

Answer:

missing side: 133 cm

Explanation:

Provided 2 length sides and one angle also need to find one missing side.

So, use cosine rule:

⇒ a² = b² + c² - 2bc cos(A)

Insert values

⇒ g² = 166² + 147² - 2(166)(147) cos(50)

⇒ g² = 17794.3935

⇒ g = √17794.3935

⇒ g = 133.3956

⇒ g = 133          (rounded to nearest whole number)

Answer:

I cant help unfortunately

Step-by-step explanation:

can you help me in the comprehension of the story uncle Marcos ?

My exam is in 4 hours btw

The solution to the inequality expression is x ≥ - 5

Inequality are expressions not separated by an equal sign. Given the inequality;

–4(x + 3) ≤ –2 – 2x

Expand

-4x - 12  ≤ -2 - 2x

Collect the like terms

-4x + 2x  ≤ -2 + 12

-2x  ≤  10

Divide both sides by -2

-2x/-2  ≤ 10/-2
x ≥ - 5

Hence the solution to the inequality expression is x ≥ - 5

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Answer:

First line

Explanation: Edge2023

Answer: (6,7)

Step-by-step explanation:

Answer:

(7,6)

Step-by-step explanation:

look above as your axis x it's 7, and then down is axis y is 6.

When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other. The measure of ∠1 is 30°, while the measure of ∠2 is 60°.

When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.

for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.

Since the two angles together form a 90° angle. The angles are complementary to each other, therefore, we can write,

∠1 + ∠2 = 90°

x + x + 30 = 90°

2x = 60°

x = 30°

Thus, the measure of the angles can be written as,

∠1 = x = 30°

∠2 = x+30° = 60°

Hence, the measure of ∠1 is 30°, while the measure of ∠2 is 60°.

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Answer:

We want to get g(x) given that we know f(x) and the graphs for both functions. We will see ...

Step-by-step explanation:

The complete statement is "if everything else stays the same, the required sample size decreases as the confidence level decreases to reach the same margin of error." This is further explained below.

Generally, the margin of error is simply defined as a measure of how far your findings depart from the population average.

In conclusion, As confidence levels decline, the needed sample size reduces to provide the same margin of error, assuming all other variables remain constant.

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Two prisms with the same volume are rectangular prisms of the dimensions  1 by 4 by 9 and 2 by 3 by 6

To do this, we start by determining the type of prism to create.

Assume that we want to create a rectangular prism.

The volume of a rectangular prism is:

Volume = Length * Width * Height

Using the digits 1 - 9, we have:

Prism 1

Length = 1

Width = 4

Height = 9

The volume is

Volume = 1 * 4 * 9 = 36

This means that the second prism must have a volume of 36.

Using the digits 1 - 9, we have:

Prism 2

Length = 2

Width = 3

Height = 6

The volume is

Volume = 2 * 3 * 6 = 36

Notice that the digits are not repeated.

Hence, two prisms with the same volume are rectangular prisms of the dimensions  1 by 4 by 9 and 2 by 3 by 6

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Answer:

81920

Step-by-step explanation:

Finding the common ratio (r) :

Finding the 14th term :

Answer:

the 14th term in the sequence would be 81920.

Step-by-step explanation:

because you are multiplying by 2 each time to find the next multiply 80 by 2 giving you 160 again giving you 320 again giving you 640 than 1280 , 2560 ,5120 ,10240 ,20480 ,40960 ,finally the 14th number in the sequence multiplying 40960 by 2 would give you your answer of 81920.

a parabola with symmetry or mirror image across the x-axis, will be a horizontal parabola, namely one that opens either to the right or left.

a horizontal parabola will be a parabola whose independent variable is the "y", so it'll be an x(y) type of equation.

[tex]~~~~~~\textit{horizontal parabola vertex form} \\\\ x=a(y- k)^2+ h\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\supset}\qquad \stackrel{"a"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0 \end{cases}\implies x=a(y-0)^2+0\qquad \textit{we also know that} \begin{cases} x=5\\ y=6 \end{cases} \\\\\\ 5=a(6-0)^2 +0\implies 5=36a\implies \cfrac{5}{36}=a~\hfill \boxed{x=\cfrac{5}{36}y^2}[/tex]

Answer:

y =  x/2 - 4

Step-by-step explanation:

Answer:

factored form

Step-by-step explanation:

example

(x + 2)(x + 3) ← is an expression in factored form

= x² + 5x + 6 ← in expanded form

Answer:

Step-by-step explanation:

Factored form is opposite of expanded form.

More info:-

Expanded form:

Factored form:

Answer:

32768

Step-by-step explanation:

8^6 is 262144

then divide 262144 by 8

so 262144 / 8 = 32768

Hope This Helped

Answer:

-1

Step-by-step explanation:

We have 2 letters, x and y. what letter is in all of them? none of them. that means the HCF can't contain a letter. let's take away the letters, we have 12, -4, 15, -5. Since -5 is a prime number. the answer is -1

The length of the similar tube will be 5041 cm.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that:-

The radius of the first tube will be calculated as:-

1200 = 2πr ( 13 )

r = 12 / 2π x 113

r = 14.7 cm

Now the length of the second tube will be:-

500 = 2π x 14.7 x L

L = 500 / 2π x 14.7

L = 5.41 cm.

Therefore the length of a similar tube will be 5041 cm.

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The number that Sean counts is 27.

What number does Sean count?

When Sean counts by 2s from 15 to 35, he would be counting odd numbers. An odd number is a number that cannot be perfectly divided by 2. There would always be a remainder.

Here are the options:

13

27

16

22

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Answer:

The image has the ans.

Step-by-step explanation:

The image will help.

Answer:

Berries with any blush of red are not ripe, yet may ripen further once picked if kept at room temperature. That said though, you really want to ...

The probability will include:

P(A and 1) = 1/24

P(C and 2) = 1/12.

P(B and 3) = 1/12.

P(A and 4) = 1/12

The probability of P(A and 1) will be:

= 1/4 × 1/6

= 1/24

The probability of P(C and 2) will be:

= 1/4 × 2/6

= 1/12

The probability of P(B and 3) will be:

= 2/4 × 1/6

= 1/12

The probability of P(A and 4) will be:

= 1/4 × 2/6

= 1/12

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Answer:

(x+6)2 + (y-4)2 = 81

Step-by-step explanation:

The equation of the circle is in the for (x-a)2 + (y-b)2 = c2

The approximate difference in their volumes is 17.2 cubic inches

The given parameters are:

Diameter, d = 2.8

Diameter, D = 3.8

The radii are the half of the diameter.

So, we have:

r = 1.4

R = 1.9

The volume of the balls is then calculated using:

[tex]V = \frac{4}{3}\pi r^3[/tex]

The difference is then represented as:

[tex]D = \frac{4}{3}\pi (R^3 - r^3)[/tex]

Substitute known values

[tex]D = \frac{4}{3}* 3.14* (1.9^3 - 1.4^3)[/tex]

Evaluate

D = 17.2

Hence, the approximate difference in their volumes is 17.2 cubic inches

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The total solution for the system of nonlinear equations represented by this graph is 2 solutions

Quadratic function have a leading degree of 2. The graph of a quadratic function is parabolic in nature.

Since the given graph consists of a parabola, hence the total solution for the system of nonlinear equations represented by this graph is 2 solutions

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The height of the skyscraper if the angle of elevation to the top of a prominent skyscraper to be 17° is 91.51 meter

An equation is an expression that shows the relationship between two or more numbers and variables.

Let h represent the height of the skyscraper, hence:

tan(17) = h/294

h = 89.88 meter

Total height = 89.88 + 1.63 = 91.51 meter

The height of the skyscraper if the angle of elevation to the top of a prominent skyscraper to be 17° is 91.51 meter

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Answer:

A or 57 7/9ft3

Step-by-step explanation:

13/3x10/3x4/1 = 520/9=57 7/9

Answer:

The volume of the rectangle would be [tex]57\frac{7}{9}[/tex] ft^3. (The first answer).

Step-by-step explanation:

To solve you have to multiply [tex]4\frac{1}{3},3\frac{1}{2}, and, 4[/tex] to get an answer of [tex]57\frac{7}{9}[/tex].
I hope this helps! :)