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Write f(x) = 2×2 44x + 185 in vertex form. to write f(x) = 2×2 44x + 185, factor out from the first two terms. next, form a perfect square trinomial keeping the value of the function equivalent: f(x) = 2(x2 22x + 121) + 185 242 the function written in vertex form is f(x) = (x )2 + .

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Answer:

To write f(x) = 2×2 – 44x + 185, factor out   2 from the first two terms.

Next, form a perfect square trinomial keeping the value of the function equivalent:

f(x) = 2(x2 – 22x + 121) + 185 – 242

The function written in vertex form is f(x) = 2 (x –
11
)2 +  -57.

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A circle has an area of 12. If the radius is increased by a factor of 2, what is the new area of the circle?

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Answered by answersmine AT 22/10/2019 – 02:38 AM

A=12. A=π×r^2(area of a circle)
π×r^2=12
r×2:
π×(r×2)^2= π×r^2×4. Here you can see that the calculation is exactly the same as above except from the Factor 4. This Shows that the area is four times bigger than before: 12×4

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Given f(x)=x^3+4x^2+5x+2 and that -1 is a zero of f(x). What is the factor of f(x)

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From the context, the question is asking “What are the factors of f(x)”.
As Sxerks indicated in the comments, (x-1) is a root => (x+1) is a factor.

To factor completely, a long division or synthetic division can be done to find
f(x)/(x+1)=(x^3+4x^2+5x+2)/(x+1)=x^2+3x+2 with no remainder.

Factor the resulting quadratic,
x^2+3x+2=(x+2)(x+1)
factors f(x) completely into
f(x)=(x+1)^2(x+2)

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Factor: 5x^2 + 37x + 14

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Factor: 5x^2 + 37x + 14

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Which factor, industrialization or race, had the greatest influence on the Age of Imperialism?

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Which factor, industrialization or race, had the greatest influence on the Age of Imperialism?

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If a pyramid has a side length of 230 meters and a height of 146 and I'd the model has a side length of 0.575 meters and a height of 0.365 what is the scale factor of model

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If a pyramid has a side length of 230 meters and a height of 146 and I’d the model has a side length of 0.575 meters and a height of 0.365 what is the scale factor of model

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Which polynomial is represented by the factor (x-8)(x+5)

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Which polynomial is represented by the factor (x-8)(x+5)

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Triangle PQR is transformed to similar triangle P’Q’R’. A coordinate grid is shown from negative 10 to 0 to positive 10 on both x- and y-axes at increments of 1. A triangle PQR has P at ordered pair 4, 4, Q at ordered pair 8, 4, R at ordered pair 4 and 8. A polygon P prime Q prime R prime has P prime at ordered pair 1,1, Q prime at ordered pair 2,1, R prime at ordered pair 1, 2. What is the scale factor of dilation?

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Answered by answersmine AT 22/10/2019 – 03:37 AM

The length of the legs, PQ and PR are 4 units.
The lengths of the legs, P’Q’ and P’R’ are 1 unit.
Since the legs (and triangle) got smaller we know that the scale factor is between 0 and 1.
So.. 4 * x = 1
divide both sides by 4
       x = 1/4
The scale factor is 1/4

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Factor completely 21x3y4 + 15x2y2 − 12xy3.

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Factor completely 21x3y4 + 15x2y2 − 12xy3.

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Rewrite 35 +63 as two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor

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Answered by answersmine AT 22/10/2019 – 03:45 AM

To find this answer you would need to first find the GCF, which would be 7. Next, you would take both numbers (35 and 63) and divide them by 7, getting 5 and 9, and adding them together you would get 14. So your answer would be 7 and 14, since when you multiply those numbers, you get 98, which is the sum of 35 and 63.

Post your answer

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Explain why intensity level is an important factor in your workouts.

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Answered by answersmine AT 22/10/2019 – 03:52 AM

Raising the intensity is raising your heart rate. If your workout is high intensity, you burn more fat! It is very important. If you are working out with no intensity, means you are not sweating.

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Which factor was a key reason for the economic success of the Greek city-states? A. new farming techniques B. geographical isolation C. war and conquest D. a booming system of trade

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Answer:

D. a booming system of trade

Explanation:

The sea (the Aegean and the whole Mediterranean) became the best means to put the Greek polis in contact with each other and with other civilizations, establishing an active trade of all kinds of products at long distances (reaching North Europe and Central Asia), to the point that many of the city-states depended heavily on maritime trade. The Greeks became excellent sailors, an ability used in civil as well as military affairs.

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What is a factor of x^2+5x-24

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Answered by answersmine AT 22/10/2019 – 04:04 AM

-24*x^2 = -24x^2
After that, you find what two numbers multiply to make -24 and add up to make 5 (‘5x’) which are -3 + 8. After you found those two numbers you set it up like (x^2 -3x) (there is an x because you multiplied -24*x^2 which would mean you have to distribute the x’s to the other two numbers you found) (8x-24). From then, you take out a common multiple from (x^2 – 3x) and (8x-24). The common multiple of (x^2-3x) would just be ‘x’ and the common multiple of (8x-24) is ‘8’ which makes them (x-3) (x+8). A way you can check is that (8x-24) reduces to (x-3) which is the same as what we found when we reduced (x^2-3x) ***those two should always be the same*

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A bat produces pulses of sound and listens for echoes that indicate insects are near. This is an example of a _____. competition adaptation predator adaptation prey adaptation limiting factor

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A bat produces pulses of sound and listens for echoes that indicate insects are near. This is an example of a _____. competition adaptation predator adaptation prey adaptation limiting factor

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From the table below, determine whether the data shows an exponential function. Explain why or why not. (x) -5, -4, -3, -2 (y) 0.5, 2, 8, 32 A) Yes; the domain values are at regular intervals and the range values have a common factor 8. B) Yes; the domain values are at regular intervals and the range values have a common factor 4. C) No; the domain values are not at regular intervals. D) No; the domain values are at regular intervals and the range values have a common factor 4. Please help, and please give me an explanation on the answer you choose because I need to make corrections. Please.

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Answer:

Option B-  Yes; the domain values are at regular intervals and the range values have a common factor 4.

Step-by-step explanation:

Given : The data

(x) -5,   -4,  -3,   -2

(y) 0.5,  2,   8,   32

To find : The data shows an exponential function or not

Solution :

The general form of an exponential form is y=ab^x

To check whether the data give the exponential function we form equation with the help of two points and verify the other two points .

y=ab^x

Let x= -5 and y=0.5

0.5=ab^{-5}

frac{0.5}{b^{-5}}=a ……[1]

Let x= -4 and y=2

2=ab^{-4}

frac{2}{b^{-4}}=a ………[2]

Equate LHS because RHS is equal in equation [1] and [2]

frac{2}{b^{-4}}=frac{0.5}{b^{-5}}

frac{b^{-4}}{b^{-5}}=frac{2}{0.5}

b=4

Put back in [2]

frac{2}{4^{-4}}=a .

a=2times4^4

a=2times256=512

a=512 and b=4

Exponential function – y=4(512)^x

To verify this function put

1) x=-3

y=512(4)^{-3}

y=farc{512}{64}

y=8

The point satisfied.

2) x=-2

y=512(4)^{-2}

y=farc{512}{16}

y=32

The point satisfied.

Therefore, The given data is an exponential function y=4(512)^x

The domain values are at regular intervals and the range values have a common factor 4 because b=4 and the change happen but value of b remain same.

Hence, Option B is correct.

Yes; the domain values are at regular intervals and the range values have a common factor 4.

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The function y = 4x is an exponential growth function. The graph of the function increases as x increases. The variable x is a(n) coefficient term exponent factor

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The function y = 4x is an exponential growth function. The graph of the function increases as x increases. The variable x is a(n) coefficient term exponent factor

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Which expression does not factor? m3 + 1 m3 – 1 m2 + 1 m2 – 1

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Answer:

Option C. is the right option

Step-by-step explanation:

In this question we will take each option and try to factorize them.

Option A.

(m³ + 1) = (m + 1)(m² + 1² – 1.m) = (m + 1).(m² – m + 1)

[ since (a³ + b³) = (a + b).(a² + b² – ab)]

So can be factored.

Option B.

(m³ – 1) = (m – 1).(m² + m + 1)

[ since a3 + b³= (m – 1)(m² + m + 1)

So expression can be factored.

Option C.

(m² + 1) This expression is in the factored form.

Option D.

(m² – 1) = (m + 1)(m – 1)

[(a² – b²) = (a – b)(a + b)]

So expression can be factored.

Finally the answer is Option C.

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X^2-8xy+16y^2 factor completely – AnswersMine

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Answered by answersmine AT 22/10/2019 – 04:51 AM

(x-4y)(x-4y)  this is the square of (x-4y)
                                                                   
                                                                              

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The scale factor that doubles the sizes of a figure is…

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Answer:

Option C – BD=76 cm

Step-by-step explanation:

Given : You are designing a diamond-shaped kite. you know that AD = 44.8 cm, DC = 72 cm, and AC = 84.8 cm.

To find : How long BD should it be?

Solution :

First we draw a rough diagram.

The given sides were AD = 44.8 cm, DC = 72 cm and AC = 84.8 cm.

According to properties of kite

Two disjoint pairs of consecutive sides are congruent.

So, AD=AB=44.8 cm

DC=BC=72 cm

The diagonals are perpendicular.

So, AC ⊥ BD

Let O be the point where diagonal intersect let let the partition be x and y.

AC= AO+OC

AC=  x+y=84.8 …….[1]

Perpendicular bisect the diagonal BD into equal parts let it be z.

BD=BO+OD

BD=z+z

Applying Pythagorean theorem in ΔAOD

where H=AD=44.8 ,P= AO=x , B=OD=z

H^2=P^2+B^2

(44.8)^2=x^2+z^2  ………[2]

Applying Pythagorean theorem in ΔCOD

where H=DC=72 ,P= OC=y , B=OD=z

H^2=P^2+B^2

(72)^2=y^2+z^2 …………[3]

Subtract [2] and [3]

(72)^2-(44.8)^2=y^2+z^2-x^2-z^2

5184-2007.04=(x+y)(x-y)

3176.96=(84.8)(x-y)

37.464=x-y ……….[4]

Add equation [1] and [4], to get values of x and y

x+y+x-y=84.8+37.464

2x=122.264

x=61.132

Substitute x in [1]

x+y=84.8

61.132+y=84.8

y=23.668

Substitute value of x in equation [2], to get z

(44.8)^2=x^2+z^2

(44.8)^2=(23.668)^2+z^2

2007.04-560.174224=z^2

z=sqrt{1446.865776}

z=38.06

We know, BD=z+z

BD= 38.06+38.06

BD= 76.12

Nearest to whole number BD=76 cm

Therefore, Option c – BD=76 cm is correct.

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Determine the scale factor of the function f(x)=1/3root x

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Determine the scale factor of the function f(x)=1/3root x

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If the lease factor is given 0.00045, what interest rate is that equivalent to

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Answer:  The correct option is (B) dfrac{sqrt{17}+sqrt{2}}{sqrt{17}+sqrt{2}}.

Step-by-step explanation:  We are given to select the correct fraction by which the following be multiplied to produce an equivalent fraction with a rational denominator.

F=dfrac{3}{sqrt{17}-sqrt2}~~~~~~~~~~~~~~~~~~~~~~~~(i)

We know that

to rationalize the denominator having radical terms, we multiply both numerator and denominator by a common term which contains the opposite sign before the radical term as in the original denominator.

In the given denominator, both terms are radical ones, so we can change the sign of any one of them and then multiply to the denominator and numerator simultaneously.

So, we will multiply both numerator and denominator by the term sqrt{17}+sqrt2.

From (i), we have

F\\=dfrac{3}{sqrt{17}-sqrt2}\\\=dfrac{3(sqrt{17}+sqrt{2})}{(sqrt{17}-sqrt{2})(sqrt{17}+sqrt{2})}\\\=dfrac{3(sqrt{17}+sqrt{2})}{17-2},~~~~~~~~textup{since}~(a+b)(a-b)=a^2-b^2\\\=dfrac{3(sqrt{17}+sqrt{2})}{15}\\=dfrac{sqrt{17}+sqrt{2}}{5}.

Thus, the denominator is rationalized and the required fraction to be multiplied is

dfrac{sqrt{17}+sqrt{2}}{sqrt{17}+sqrt{2}}.

Option (B) is CORRECT.

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Which of the following is an abiotic factor of a desert? A) cactus B) sand C) lizards D) wildflowers

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Which of the following is an abiotic factor of a desert? A) cactus B) sand C) lizards D) wildflowers

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Factor the trinomial below. Enter each factor as a polynomial in descending order. x2 – 29x + 100

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Answer: The answer is (C) Patricia is not correct because both 3 – 4i  and -11+√2i  must be roots.

Step-by-step explanation:  Given that  (-11-√2i) , (3 + 4i), and 10 are the roots of the polynomial function f(x) that Patricia is studying.

We know that the complex roots of a polynomial function always occur in pairs. That is, if (a + bi) is a root of a function, then (a – bi) will also be a root (one is the complex conjugate of the other).

The complex conjugate of (3 + 4i) is (3 – 4i) and the complex conjugate of (-11 – √2i) is (11 + √2i).

Therefore,  (3 – 4i) and (-11 + √2i) both are the roots of f(x).

Hence, since we have 5 roots, so the degree of the polynomial function f(x) cannot be 4.

Since Patricia concludes that the degree of f(x) is 4, so she is not correct because both (3 – 4i)  and (-11+√2i)  must be roots.

Thus, option (C) is correct.

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Factor the trinomial below. Enter each factor as a polynomial in descending order x2 + 13x + 40

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Keywords:

Polynomial, identify, ascending order

For this case, we must identify the polynomial that is written in ascending order. If we want to order a polynomial of ascending form, we must organize the polynomial from least to greatest exponent. By definition, a polynomial is of the form:

P (x) = ax ^ n + bx ^ {n-1} + ... + cx ^ 3 + dx ^ 2 + ex + f

Where:

a, b, c, d, e, f: They are the coefficients of the polynomial

n, n-1,3,2,1,0: They are the exponents. This polynomial is of degree “n”, because “n” is the largest exponent.

x: It is the variable

Then, we must see among the options given a polynomial written from least to greatest exponent, that is, from the form:

P (x) = f + ex + dx ^ 2 + cx ^ 3 + ... + bx ^ {n-1} + ax ^ n

So, among the options we have:

Q (x) = - 7 + 4x-5x ^ 2 + 3x ^ 3 written ascending

Answer:

Option C

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A toy basketball hoop for toddlers has a diameter of 10 cm. A regulation basketball hoop has a diameter of 46 cm. Determine the scale factor for the diameter of the toddler size basketball hoop to the diameter of the regulation size basketball hoop. (round answer to two decimal places)

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You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

 = 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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