help me with the fonction please im stuck U_U

The actual roots of the function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex] are -9/2, 3/5 and 1.

Given  function [tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex].

Function is a relationship between two or more variables expressed in equal to form.

The roots of a polynomial function are the zeroes of the polynomial function. A polynomial function is a function that involves only non negative integer powers in an equation.

The polynomial function is given as:

[tex]f(x)=10x^{3}+29x^{2} -66x+27[/tex]

factorize the above function

[tex]f(x)=(2x+9)(5x-3)(x-1)[/tex]

Now put the function f(x) equal to zero.

f(x)=(2x+9)(5x-3)(x-1)

split the function means put all the expressions equal to zero as under:

(2x+9)(5x-3)(x-1)=0

solve each for the value of x

x=-9/2,x=3/5,x=1

Hence the roots of the function [tex]f(x)=10x^{3} +29x^{2} -66x+27[/tex] are which are also the values of x are -9/2,3/5,1.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

"integral" means here that the factors in the polynomial are integers.

we have 3 zeros.

the least degree of a polynomial with 3 zeros is 3.

and yes, that works also for 2 zeros (the degree must be at least 2, it must be at least a quadratic equation).

or 4 zeros (at least 4th degree).

it in general n zeros (at least nth degree).

constructing this out of the given zeros is easy.

what happens, when I multiply something by 0 ? the total result will be 0.

and so, we simply multiply 3 short terms with each other, where each term turns 0 for one of the given zeros.

what expression in x turns 0, when x = -1/3 ?

well : x + 1/3 or with integers 3x + 1 (multiplied by 3)

and for x = 2/3 ?

x - 2/3 or with integers 3x - 2

and for x = -1/4 ?

x + 1/4 or with integers 4x + 1

so, our polynomial function (of at least 3rd degree) is then

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

basically this could be already the result, depending on what your teacher wants.

for the fully extended form we need to do the multiplications :

(3x + 1)(3x - 2) = 9x² - 6x + 3x - 2 = 9x²- 3x - 2

(9x²- 3x - 2)(4x + 1) = 36x³ + 9x² - 12x² - 3x - 8x - 2 =

= 36x³ - 3x² - 11x - 2

the requested polynomial function is

f(x) = 36x³ - 3x² - 11x - 2

The length of C'B' after dilation using a scale factor of 3 is: D. 15 units.

Dilation is the reduction or enlargement of an image by a scale factor, whereby the original and new images are similar.

Applying the distance formula, we have:

BC = √[(8−12)² + (10−13)²]

BC = √(−4)² + (−3)²]

BC = √(16+9)

BC = √25

BC = 5 units

Applying the scale factor:

Length of C'B' = 3(5) = 15 units.

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Answer:

Perpendicular: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]

Parallel: [tex]y=3x-7[/tex]

Step-by-step explanation:

So when two lines are perpendicular, that means the the slope is the reciprocal with the opposite sign so: [tex]\frac{a}{b} \text{ has a slope perpendicular to } -\frac{b}{a}[/tex]. In this case we have the equation in slope-intercept form, so it's easy to determine the slope, it's 3. So that means the perpendicular line will have a slope of: [tex]-\frac{1}{3}[/tex]. Since you have a slope of 3/1 which becomes 1/3 and also an opposite sign. This gives you the equation: [tex]y=-\frac{1}{3}x+b[/tex]. We can solve for b, by plugging in a coordinate it passes through. This is given in the problem, with it being (4, 5) = (x, y). So plugging these values in as (x, y) gives you the equation: [tex]5=-\frac{1}{3}(4)+b\implies\frac{15}{3}=-\frac{4}{3}+b\implies\frac{19}{3}=b[/tex]. This gives you the complete equation: [tex]y=-\frac{1}{3}x+\frac{19}{3}[/tex]

So when two lines are parallel, that means they have the slope, and a different y-intercept. This is because if they had the same y-intercept, then the two lines would be the same exact line. We already know the slope, it's 3. So we have the general equation: [tex]y=3x+b\text{ where b}\ne-3[/tex]. The restriction on b, was explained on the previous sentence, if b=-3, then we have the same equation, which is not parallel, they would be the same line, meaning they would intersect at infinite points, which is completely different than two lines that never intersect. So now we can plug in the given point (4, 5) to solve for b. Plugging these coordinates in gives you: [tex]5=3(4)+b\implies5=12+b\implies-7=b[/tex]. This gives you the complete equation: [tex]y=3x-7[/tex]

Considering the given equation of the circle, the true statements are given as follows:

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The equation given is:

x2 + y² - 2x - 8 = 0.

Completing the squares, the equation is given as follows:

(x - 1)² + y² = 8 + 1

(x - 1)² + y² = 9.

Researching the problem on the internet, the true statements are:

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Answer:

43.2 m square is ur answer .

Answer:

43.2 m^2

Step-by-step explanation:

The area of a rectangle is the width times the length.

Area = (9.6 m)*(4.5 m)

Area = 43.2 m^2

Answer:

2x³+3x²-8x+3

Step-by-step explanation:

So we know x=½,x=1 and x=-3

Then (2x-1)(x-1)(x+3) are the factors

(2x-1)[(x²+3x-x-3)]

(2x-1)[(x²+2x-3)]

2x³+4x²-6x-x²-2x+3

2x³+3x²-8x+3

Since it has a variable in the denominator, the function f(x) is a parent function classified as rational.

Rational functions are functions that have the input variable, be it x, t, or any other, in the denominator.

The most simple example is given by:

[tex]f(x) = \frac{1}{x}[/tex].

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Answer: Reciprocal

Step-by-step explanation:

Reciprocal functions are functions that contain a constant numerator and x as its denominator. Its parent function is y = 1/x.

option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

The area of the parallelogram is:

A = b×h

Here b is the base length and h is the height

In ABCD parallelogram:

A = (3)×(3)

A = 9 square units

EFGH parallelogram:

a = (3)×(3)

A = 9  square units

The area of parallelogram ABCD is equal to the area of parallelogram EFGH.

Thus, option third "The area of parallelogram ABCD is equal to the area of parallelogram EFGH" is correct.

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The side of the edge of the cube is 7. 07cm

Given that a  diagonal of a cube measures the square root of 150 cm and the diagonal of a face measures 10 cm.

Let's find the edge of the face

Note that the face of the cube is in the shape of square .

The diagonal of the face is 10 cm.

The formula for  diagonal of square = [tex]\sqrt{2a}[/tex]

a is the side of the square face

We have that,

[tex]\sqrt{2a} = 10[/tex]

Make 'a' subject of formula

a = [tex]\frac{10}{\sqrt{2} }[/tex]

Find the surd of the equation, we have

a = [tex]\frac{10}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex]

a = [tex]\frac{10\sqrt{2} }{2}[/tex]

a = [tex]5\sqrt{2}[/tex]

a = [tex]7. 07cm[/tex]

Thus, the side of the edge of the cube is 7. 07cm

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The meter mark at which Ario wil be when Miguel starts the race is; 7.4 meters

A ratio such as the ratio 1:4 shows the proportion of two factors. In this case, it shows the ratio between the completed meters vs the remaining meters.

To find the distance, we will have to determine how much 1:4 represents in the total distance.

Total distance = 25 meters - 3 metes = 22 meters

Thus; 22 * 1/ 5 = 22/5 = 4.4

However, we also know they are three meters behind the start.

Thus, the meter mark at which Ario will be when Miguel starts the race

4.4 + 3 =7.4 meters

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\textbf{Which set of data does not have a mode?}[/tex]

[tex]\huge\textbf{The choices that you have provided:}[/tex]

[tex]\textbf{(A) 1, 2, 5, 6, 8}[/tex]

[tex]\textbf{(B) 1, 3, 5, 5, 6}[/tex]

[tex]\textbf{(C) 1, 5, 5, 5, 5}[/tex]

[tex]\textbf{(D) 1, 1, 1, 2, 2}[/tex]

[tex]\huge\textbf{Okay, so let's get the understanding}\\\\\huge\textbf{of the word mode is:}[/tex]

[tex]\large\textbf{The best way to understand what \boxed{\bf mode} it is known as}\\\\\large\textbf{the number you see MORE THAN once. }[/tex]

[tex]\huge\textbf{Now that we got that information out of}\\\\\huge\textbf{the way, we can answer your question by}\\\\\huge\textbf{doing process of elimination.}[/tex]

[tex]\huge\textsf{Option A.}[/tex]

[tex]\textbf{1, 2, 5, 6, 8}[/tex]

[tex]\large\textbf{None of the numbers r.e.p.e.a.t so this cann be your}\\\\\large\textbf{answer.}[/tex]

[tex]\huge\textsf{Option B.}[/tex]

[tex]\textbf{ 1, 3, 5, 5, 6}[/tex]

[tex]\large\textbf{1}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{3}\rightarrow\large\textbf{ is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}\\\large\textbf{6}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}[/tex]

[tex]\large\textbf{Just because majority of your numbers r.e.p.e.a.t.e.d}\\\\\large\textbf{once that doesn't mean it does have a mode rarely.}\\\\\\\\\\\large\textbf{So, Option B. isn't your answer because it has a mode.}[/tex]

[tex]\huge\textsf{Option C.}[/tex]

[tex]\textbf{ 1, 5, 5, 5, 5}[/tex]

[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d once}\\\large\textbf{5}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d four times}[/tex]

[tex]\large\textbf{Option C. isn't your answer because it has a mode.}[/tex]

[tex]\huge\textsf{Option D. }[/tex]

[tex]\textbf{1, 1, 1, 2, 2}[/tex]

[tex]\large\textbf{1}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d three times}\\\large\textbf{2}\rightarrow\large\textbf{is r.e.p.e.a.t.e.d twice}[/tex]

[tex]\large\textbf{Just because we have like two modes, it still doesn't mean}\\\large\textbf{you don't have a mode. It 's kind of cool that you have more}\\\large\textbf{than once mode.}[/tex]

[tex]\large\textbf{Option D. isn't your answer because it has a mode though}\\\large\textbf{because it has like 2 sets of modes.}[/tex]

[tex]\huge\textsf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\textsf{Option\ A. 1, 2, 5, 6, 8}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The value of x in the equation (x - 5)² = 25 is 10.

(x - 5)² = 25

Take the square root of both sides

Therefore,

√(x - 5)² = √25

x - 5 = 5

add 5 to both sides

x - 5 + 5 = 5 + 5

x = 10

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The angle of rotation of triangle ABC to A'B'C is 105°

It should be noted that the rotation from ABC to A'B'C is in a clockwise direction.

Point B is also on the x axis and point B' is in the second quadrant.

In this case, the angle that depicts the second quadrant is 105°.

In conclusion, the correct option is D.

The complete question is:

Triangle A’ B’ C’ is the image of A B C under a rotation about the origin, (0,0)

Determine the angle of rotation

A. -105 degrees

B. -75 degrees

C. 75 degrees

D. 105 degrees

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Answer:

=================

Use the intersecting chords theorem, according to which, the products of the lengths of the line segments on each chord are equal,

or

Substitute the lengths and solve for x:

The matching answer choice is A.

Answer:

A. 100

Step-by-step explanation:

Angle 1 = 40

Angles 1 and 2 are equal. Add the angles 1 and 2 together.

40+40=80

The last step is to subtract 80 from 180.

180-80=100.

∠3=100

Hope this helps!

If not, I am sorry.

The ratio of orange juice to apple juice to grape juice is 6: 3 : 2

A ratio says how much of one thing there is compared to another thing.

Therefore, we are comparing the numbers of juice produce by a bottling company.

Hence,

number of orange juice = 24

number of apple juice = 12

number of grape juice = 8

Therefore, the ratio of orange juice to apple juice to grape juice is as follows:

ratio = 24 : 12 : 8

divide through by 4

ratio = 6: 3 : 2

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Considering the area of the rectangle, it is found that she will need 17 tiles to cover the floor.

The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:

A = lw

The dimensions in feet are given as follows:

Hence the area in square feet is given by:

A = 4.5 x 3.75 = 16.875 ft².

Each tile has 1 square foot, hence, rounding, she will need 17 tiles to cover the floor.

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Answer:

Graph is below

Brainliest, please :)

Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.

The triangle is geometric shape which includes 3 sides and sum of interior angle should not grater than 180°

Solution is supposed to be

[tex]tan_ (-1) (28/21) = 53.33[/tex]

Thus,Stacie did the mistake that he put the value of base in place of perpendicular and vice versa.

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[tex]f(x)=x(x-3)(x+3)[/tex]

If the biologist catches and tags 32 bass and from sample of 55 he found only 5 tagged then there are 352 bas in the lake.

Given Biologist catches and tags 32 bass, when sample of 55 bass is taken  then 5 are found tagged.

Population is basically number of living thing exists in a particular area.

Number of bass which are tagged in lake=32

Sample size=55

Number of bass found tagged=5

means percentage of tagged bas found is 5/32*100=1.6%

We have to calculate number of times 5 is multiplied to get 32 which is 6.4.

Number of bass in the lake=55*6.4

=352 basses.

Hence there are 352 basses in the lake if 5 are found tagged in a sample of 55.

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The distance would be 231 miles.

Speed can be calculated as the ratio of distance traveled to the time taken

Given information;

Time taken = 3 hours 30 minutes

Speed = 70 mph

We know that,

Distance = speed x time

Distance = 70 x 3.30

Distance = 231 miles

Thus, the distance would be 231 miles.

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The price of the light as a function of x is given by the exponential function:

[tex]p(x) = \$375*(0.98)^x[/tex]

We know that the original price of the light is $375.

This value decreases a 2% each year, so each year we need to multiply the above price by (1 - 2%/100%) = (1 - 0.02) = 0.98

Then, if x represents the number of years, the price of the light as a function of x is given by the exponential function:

[tex]p(x) = \$375*(0.98)^x[/tex]

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Answer:

All of these definitions are correct.

Answer:

5*8 = 40

Step-by-step explanation:

2(3) -1 = 5

3 +5 = 8

area = 5*8 = 40

Answer:

formula-Area=l×b

Step-by-step explanation:

Length (l)=2x-1

Breadth(b)=x+5

We know that,

Area(A)=l×b

=(2x-1)×(x+1)

=(2×3-1)×(3+1)

=5×4

=20cm*2*

Kelly used a volume of [tex]\frac{3}{4}[/tex] liters of milk at dinner.

Given we have, Initial amount of milk is [tex]2[/tex] liters.

The amount of milk used in the morning is [tex]\frac{1}{2}[/tex] Liters.

Now, Milk left = [tex]2[/tex] liters- [tex]\frac{1}{2}[/tex] liter= [tex]\frac{3}{2}[/tex] liters

[tex]\frac{3}{2}[/tex] liters used in half:

[tex]\frac{1}{2} \frac{3}{2}[/tex] = [tex]\frac{3}{4}[/tex] liters.

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Answer:

1) Equation's:

2) Number of guest and the charge:

Part 1

Turn sentences into equation's (Let 'y' be total cost and x per meal) :

(i) charges $500 and $15 per meal

(ii) charges $350 and $18 per meal

Part 2

            y  =  y

500 + 15x = 350 + 18x

18x - 15x = 500 - 350

3x = 150

x = 150/3

x = 50

Charge at guest's 50 meal:

y = 500 + 15(50)

y = $1250

Point : (50, 1250)

1 atom of C has a mass of 12 amu (atomic mass unit).

1 atom of O has a mass of 16 amu.

1 molecule of CO₂ thus has a mass of 12 + 2×16 = 44 amu.

C thus makes up 12/44 ≈ 0.27 of the total mass of CO₂, while O makes up the remaining 32/44 ≈ 0.73.

Then in a 2 kg = 2000 g block of CO₂, carbon makes up about 12/44 × 2000 ≈ 545 g.