i need help with this one

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

Answer:

  14 pounds

Step-by-step explanation:

The given equations can be solved for y by substituting for x. The first equation is convenient for writing x in terms of y.

  x = 20 -y . . . . . . . subtract y from the first equation

  7(20 -y) +5.5y = 119 . . . . . substitute for x in the second equation

  140 -1.5y = 119 . . . . . . . . simplify

  21 = 1.5y . . . . . . . . . . . add 1.5y -119 to both sides

  14 = y . . . . . . . . . . . .divide by 1.5

14 pounds of soy nuts should be used in the mixture.

__

Additional comment

There are many ways to solve a system of two linear equations. The attachments shows a matrix solution using a suitable calculator. It tells us that x=6 and y=14, as we found above.

Thw statement that's true for the function g is g(-13) = 20.

From the information given, the function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45.

In this case, g(-13) = 20. Here, x = -13 is in the domain and 20 is also in the range. Therefore, this is true for g.

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361 lollipop candies or 697 gummy bear candies fills the bag of volume 528 in.³, which gives the following possible equation;

Volume of candy bag = 528 in.³

Number of lollipop candies the bag can hold = 361 candies

Number of gummy bear candies the bag can hold = 697 candies

Therefore;

[tex]1 \: lollipop = \frac{528}{361} = 1.46[/tex]

[tex]1 \: gummy \: bear = \frac{528}{697} = 0.76[/tex]

Which gives the following equation;

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Answer:

l/361 + g/697= 1

Khan Academy Sat Practice

Trigonometric ratios are defined as the ratio of different sides of a right angle triangle with respect to one angle of the right angled triangle.

Length of the wire = Hypotenuse of the triangle =  X

Base of the triangle = Distance from the bottom of the tower to the point where wire is attached on ground = 20 m

Angle b/w Hypotenuse and Base of triangle = 46°

cos(θ) = Base / Hypotenuse

cos(46) = 20 / X

X = 20 / cos(46)

X = 28.79 m

Hence, the length of the wire is 28.79 m.

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We can write the ordered pairs that meet this condition as:

(x, y) = (x, (9 + x)/4 )

An ordered pair on the X-Y plane is written as (x, y).

Here we also have the relation:

-x + 4y = 9

If we isolate y, we get:

4y = 9 + x

y = (9 + x)/4

Now, we can write the ordered pairs that meet this condition as:

(x, y) = (x, (9 + x)/4 )

To get the particular ones you can replace the value of x, for example, if x = 0, then:

(x, (9 + x)/4 ) = (0, 9/4)

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Answer:

the second option: [tex]7x+4y=44[/tex]

Step-by-step explanation:

So when a line is parallel, it means that it has the same slope and a different y-intercept, it's important that there is a different y-intercept, otherwise it would be the same line, and the "two lines" would intersect at infinite points.

Anyways by looking at the graph you have two points (-8, 5) and (-4, -2). So the run in this case was 4 and the rise was -7. This is a slope of -7/4. So we have the equation: [tex]y=-\frac{7}{4}x+b \text{ where b}\ne-9}[/tex]. Since it passes through the point (8, -3) we can plug that in as (x, y) to solve for b (the y-intercept)

Plug in (8, -3) as (x, y)

[tex]-3=-\frac{7}{4}(8)+b[/tex]

Multiply the -7/4 and 8

[tex]-3 = -14+b[/tex]

add 4 to both sides

[tex]11 = b[/tex]

So this gives us the equation:

[tex]y=-\frac{7}{4}x+11[/tex]

Since it's asking for it in standard form you move the 7/4 x to the other side

Add 7/4x to both sides

[tex]\frac{7}{4}x+y=11[/tex]

Multiply both sides by 4 to cancel out the fraction

[tex]7x+4y=44[/tex]

So he needs to sell $2,000 in merchandise.

We can assume that we have a proportional relation:

y = k*x

Where y is the commission and x is what Norman sells, then:

$15 = k*$200

k = $200/$15 = 0.075

$37.50 = k*$500

k = $500/$37.50 = 0.075

Then the relation is:

y = 0.075*x

If he wants a commission of $150, then:

$150 = 0.075*x

$150/0.075 = x = $2,000

So he needs to sell $2,000 in merchandise.

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The mean of the scores if 6 students in a competitive exam is 25 marks.

Given scores of 6 students are: 10,30,50,40,20 in a competitive exam.

We have to find out the mean of the mark of 6 students in a competitive exam.

Mean is the sum of all the values in a set of data, such as numbers, measurements, divided by the number of values. It is also known as average.

Mean=∑X/n

∑X=10+30+50+40+20

=150

N=6

Now to calculate the mean we have to divide 150 by number of students which is 6.

Mean=150/6

=25 marks.

Hence the mean of the scores of 6  students is 25 marks.

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Question is incomplete as it should include :

Marks of students =10,30,50,40,20.

There are 28 ways for Mary to put the plants on the sills.

We can use the Binomial Theorem to solve this problem.

We have 6 plants and 3 sills, so we have6 + 3 − 1 = 8 total objects.

Since we have 8 objects, we can use the Binomial Theorem to expand [tex](x + y)^{8}[/tex].

The coefficient   [tex]x^{6} y^{2}[/tex] will be the number of ways for Mary to put the plants on the sills. We can expand [tex](x + y)^{8}[/tex]

using the Binomial Theorem:

[tex](x + y)^{8}=(\left\ {{8}\atop {0}} \right. )x^{8}+ (\left\ {{8}\atop {1}} \right. )x^{7}y+(\left\ {{8}\atop {2}} \right. )x^{6}y^{2} +(\left\ {{8}\atop {3}} \right. )x^{5}y^{3} +(\left\ {{8}\atop {4}} \right. )x^{4}y^{4}+(\left\ {{8}\atop {5}} \right. )x^{3}y^{5} +(\left\ {{8}\atop {6}} \right. )x^{2}y^{6} +(\left\ {{8}\atop {7}} \right. )x^{1}y^{7} +(\left\ {{8}\atop {8}} \right. )y^{8}[/tex]

Since we are only interested in the coefficient of [tex]x^{6} y^{2}[/tex] , we can ignore all terms that do not have [tex]x^{6}[/tex] and  [tex]y^{2}[/tex].

Therefore, we are left with [tex](\left\ {{8}\atop {2}} \right. )x^{6}y^{2}[/tex]

[tex](\left\ {{8}\atop {2}} \right. )=\frac{8!}{2!(8-2)!} =\frac{8!}{2!6!} =\frac{8*7*6!}{2!6!} =28\\[/tex]

Therefore, there are 28 ways for Mary to put the plants on the sills.

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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:

P(1) = P(-1)

P(1) = 3 - a + b
P(-1) = -3 + a + b

-> 3 - a + b = -3 + a + b
-> 3 - a + b + 3 - a - b = 0
-> 6 - 2a = 0
-> a = 3.

P(2) = 24 - 2a + b -> 24 - (2a - b) = 16 -> 2a - b = 8
-> 6 - b = 8
b = -2.

So, a = 3 and b = -2

Recheck : P(1) = 3 - 3 + (-2) = -2
P(-1) = -3 + 3 + (-2) = -2 => P(1) = P(-1) (true)

P(2) = 24 - 6 + (-2) = 16.

I honestly have no idea how to slove this question

For real,I don't know. OK

BTW,you nice,keep going

The number of days Tayloe will take to travel 100 miles if he travels 35 miles every 2 days is 40/7 or 5 5/7 in fraction form.

A fraction is a representation of a part of the whole.

Written as a/b, read as "a by b", it functions as a number of parts of a total of b number of parts.

In the question, we are given that Tayloe travels 35 miles every 2 days to work.

Therefore, daily traveling done by Tayloe can be shown as a fraction, 35/2 miles.

The total traveling given to us is 100 miles.

Thus, the number of days Tayloe will take to travel 100 miles can be shown in fractional form as 100/(35/2) = (100*2)/35 = 40/7 or 5 5/7.

Thus, the number of days Tayloe will take to travel 100 miles if he travels 35 miles every 2 days is 40/7 or 5 5/7 in fraction form.

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Answer:

x=4+√5 or x=4−√5

Step-by-step explanation:

Multiply both sides by x-4.

x2−8x+16=5

x2−8x+16−5=5−5(Subtract 5 from both sides)

x2−8x+11=0

For this equation: a=1, b=-8, c=11

1x2+−8x+11=0

x=

−b±√b2−4ac

2a

(Use quadratic formula with a=1, b=-8, c=11)

x=

−(−8)±√(−8)2−4(1)(11)

2(1)

x=

8±√20

2

x=4+√5 or x=4−√5

The value of x° + y° is 216°

Note that the shape is a regular pentagon

Sum of angle in a pentagon = 540

Angle on each side = 108°

x = 108°

y = 108°

x° + y° = 108 + 108

x° + y° = 216°

Thus, the value of x° + y° is 216°

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The number that produced a rational number when added to 1/5 is D. -2/3.

A rational number is a number that can be written as a ratio (or fraction) of two integers.

For example, when 1/5 is added to -2/3, it produces a rational number, -7/15, that remains as a fractional value.

Thus, the number that produced a rational number when added to 1/5 is D. -2/3.

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Answer:

the answer is (x )

math  way  helps

Step-by-step explanation:

The requried function of function f(g(x)) is given as x² + 6x +5.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Given functions,
f(x)=x²−4 and g(x)=x+3

In order to form a function of function we have to function g(x) in function f(x)

Now,

f(g(x)) =  f(x)=(g(x))²−4

f(g(x)) =  f(x)=(x+3)²−4
f(g(x)) = x² + 6x + 9 -4
f(g(x)) = x² + 6x +5

Thus, the requried function of function f(g(x)) is given as x² + 6x +5.

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Answer:  [tex]\sqrt{13}[/tex] units

Work Shown:

[tex](x_1,y_1) = (-5,-4) \text{ and } (x_2, y_2) = (-2,-6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-5-(-2))^2 + (-4-(-6))^2}\\\\d = \sqrt{(-5+2)^2 + (-4+6)^2}\\\\d = \sqrt{(-3)^2 + (2)^2}\\\\d = \sqrt{9 + 4}\\\\d = \sqrt{13}\\\\d \approx 3.6056\\\\[/tex]

I used the distance formula.

A slightly alternate method is to form a right triangle and use the pythagorean theorem. The hypotenuse will have the endpoints (-5,-4) and (-2,-6).

The area of the rhombus WXYZ is 48 unit².

From the diagram:

Diagonal WY = 8 units, Diagonal XZ = 6 units, hence:

Area = 8 * 6 = 48 unit².

A rhombus is a special case of a parallelogram. In a diamond, the opposite sides are parallel and the opposite sides are equal in angle. In addition, all sides of the rhombus are the same length and the diagonal bisects at right angles. Diamonds are also known as diamonds.

The diagonals of the rhombus intersect at right angles to form a non-uniform triangle. The opposite angles are equal. However, if all angles of the diamond are 90 degrees, the diamond is said to be square.

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The given geometric series as shown in the question is seen to; Be converging with its' sum as 81

We are given the geometric series;

27 + 18 + 12 + 8 + ...

Now, we see that;

First term; a₀ = 27

Second Term; a₁ = 2(27/3)

Third term; a₂ = 2²(27/3²)

Fourth term; a₃ = 2³(27/3³)

Thus, the formula is;

2ⁿ(27/3ⁿ)

Applying limits at infinity gives;

2^(∞) * (27/3^(∞)) = 0

Since the  terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

S_n = a/(1 - r)

S_n = 27/(1 - (2/3)

S_n = 81

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The exact value of cos 7pi/8 is 0. 9988

It is important to note that the value for pi = 3. 142

= cos 7π

Substitute value of π

= cos(7× 3. 142)

= cos 21. 994

Divide 21. 994 by 8

= 2. 740

Let's find the vale of [tex]cos \frac{21. 994}{8}[/tex]

= [tex]cos (2. 749)[/tex]

= [tex]0. 9988[/tex]

Thus, the exact value of cos 7pi/8 is 0. 9988

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The solution for the inequalities 3y>2x+12, 2x+y<=-5 is the value of x<-27/8 and y<7/4.

Given 3y>2x+12 and 2x+y<=-5.

We are given two inequalities  3y>2x+12 and 2x+y<=-5. Inequality are like equations but in greater than ,less than or in combination with equal to. To solve them we need to first write them properly.

2x-3y<-12

2x+y<=-5

Now assume these are equalities

2x-3y=-12

2x+y=-5

now subtract 2 from 1

2x-3y-2x-y=-12+5

-4y=-7

y=7/4

put the value of y in 2x-3y=-12

2x-3(7/4)=-12

2x-21/4=-12

2x=-12+21/4

2x=(-48+21)/4

2x=-27/4

x=-27/8

Now put the signs between the values

x<-27/8

y<7/4.

Hence the solution of the inequalities 3y > 2x + 12

2x + y ≤ -5 is the value of x<-27/8 and y<7/4.

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Answer:

187

Step-by-step explanation:

Least common multiple:

To find the required number,

30 =  2 * 3 * 5

36 = 2 * 2 * 3 * 3 = 2² * 3²

45 = 2 * 3 * 3 = 2 *3²

LCM = 2² * 3² * 5

        = 4 * 9 * 5

        = 180

Required number = 180 + 7

                             = 187

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 plane reaches its destination at 12h10 minutes if the plane leaves town A for town B.at 0540hours

For legal, commercial, and social purposes, a time zone is a region that observes a uniform standard time. Instead of strictly following longitude, time zones tend to follow the borders between countries and their subdivisions.

We have:

A plane leaves town A for town B.at 0540hours.If the journey takes 6.5hours

05h40min

Total time takes = 6 hours and 30 minutes

= 5 hours + 40 minutes + 6 hours + 30 minutes

= 11 hours + 70 minutes

= 12 hours 10 minutes

or

= 12h10 minutes

Thus, the plane reaches its destination at 12h10 minutes if the plane leaves town A for town B.at 0540hours

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The translation of the given algebraic words to symbols is: C. 3(ab).

The algebraic word, "triple" connotes "3 times'. "Product" means multiplication. Therefore, we would have the following translation:

Product of ab = ab

Triple of ab = 3(ab).

Therefore, the algebraic words translated to symbols is: 3(ab).

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From the markings on the diagram, we can tell E is the midpoint of BC and D is the midpoint of AC. We can apply the triangle midsegment theorem: ED = ½BA. Substituting in the expressions for the lengths and solving for x, we get x = 5. Now, since BE = x, then BC = 10.

Triangle midpoint theorem states that the line segment which joins the midpoints of two (2) sides of a triangle is parallel to the third side, and it's congruent to one-half of the third side.

By applying the triangle midpoint theorem, we can find the value of x:

ED = ½BA

x + 2 = ½(4x - 6)

2x + 4 = 4x - 6

4x - 2x = 6 + 4

2x = 10

x = 10/2

x = 5.

BC = x + x

BC = 5 + 5

BC = 10.

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AB turns clockwise to coincide with BC.

To find the angle by which turns counterclockwise to coincide with is 243.9 degrees:

An angle -

So,

= ABD + DBC

= 33.3° + 30.6°

= 63.9°

b) If E is drawn directly opposite C.

EBC is a straight line, so the sum of angles =180°

ABE + ABD + DBC = 180°

ABE + 33.3° + 30.6° = 180°

ABE + 63.9° = 180°

ABE = 180 - 63.1

ABE = 116.9

Therefore, AB turns clockwise to coincide with BC.

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