One of the zeros of the polynomial function is 3.


f(x)=x4−x3−7x2+x+6

What is the factored form of the function?




f(x)=(x−3)2(x+1)(x+2)

f(x)=(x−3)(x+1)(x−1)(x+2)

f(x)=(x−3)(x+1)(x+2)2

f(x)=(x−3)(x+1)2(x+2)

Answer:

A. Commutative property

Step-by-step explanation:

The commutative property states that multiplication can be performed in any order. This means that a*b=b*a. Therefore, it does not matter whether \(\sqrt{2}\) or 3 is first in the multiplication problem. So, the first answer is correct.

Answer:

See below

Step-by-step explanation:

Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.

Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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Answer:

1.x=3/4y + 2

Step-by-step explanation:

Add 3y to both sides then after youdidnt that divide both sides by 4 Thereyougo the answer.

i have school myself so i only did one.

Answer:

Brainliest??!!!

Step-by-step explanation:

The probability for the given case is 1/3.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

A spinner has numbers indicated on it from one to six.

Suppose A be the event spinner lands on 1.

And, B be the event the spinner land on 4.

Now, the probability of any event is the ratio of number of favorable outcome to the total number of outcomes which is given as,

P(A) = 1/6

And, P(B) = 1/6

Thus, the probability of event A or B is given as,

P(A or B) = P(A) + P(B)

              = 1/6 + 1/6

              = 1/3

Hence, the probability that the spinner lands on 1 or 4 is 1/3.

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The number of iPhones that should be sold in 2017 (since growth is exponential) is $ 6,476,635 x 10⁶. See the explanation below.

Exponential growth is a data pattern that exhibits greater increases with time. Compounding produces exponential profits in finance. Compounding interest savings accounts may provide exponential growth.

The calculation for the above solution is as follows:

Recall that the formula for exponential growth is:

f(x) = a (1+r)ˣ

Where:

f(x) = exponential growth function

a = initial amount

r = growth rate

{x} = number of time intervals

Hence f(x) = 1.7 (1+ r)⁵

Note that x = 2017-2012 =5

r = (present value - past value)/ past value

Present value = 35.2

Past Value = 1.7

Hence r = (35.2-1.7)/1.7

r = 19.7058823529

Approximately 19.71

Hence,

f(x) = 1.7 (1+ 19.71)⁵

= 1.7 (20.71)⁵

= 1.7 x 3809785.2361

= 6476634.90137

Which is approximately = 6,476,635

Recall that our computation was done in millions hence the answer if left in standard notation is:

Increase in 2017 = $ 6,476,635 x 10⁶

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The graph that represents the given inequalities are attached below.

To find the solution graph of the inequalities y ≤ x² + 1 and x > y²  – 5, you would first graph the equations y = x²  + 1 and x = y²  – 5 separately.

The inequality \(y \leq x^2 + 1\) represents the shaded region below the graph of the equation y = x²  + 1.

This region includes the curve and all the points below it.

The inequality x > y²  – 5 represents the shaded region to the right of the graph of equation x = y²  – 5. This region includes the curve and all the points to the right of it.

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The Gini coefficient is 2(−13/30) = -13/15.

The Lorenz curve L(p) can be expressed as the cumulative distribution function of a random variable X. The Gini coefficient is then given by the area between the diagonal line (representing perfect equality) and the Lorenz curve L(p).

In other words, the Gini coefficient is the ratio of the area between the diagonal line and the Lorenz curve to the total area under the diagonal line.

The Lorenz curve for the state can be given as L(p)=p^4/3.Ron can compute the Gini coefficient by finding the area between the diagonal line and the Lorenz curve.

The diagonal line goes from (0,0) to (1,1).The area under the diagonal line is 1/2.

The area between the diagonal line and the Lorenz curve is given by∫[0,1](L(p)−p)dp=

∫[0,1](p^4/3−p)dp

=(1/15)−(1/2)

= -13/30

The Gini coefficient can be negative when the Lorenz curve lies above the diagonal line, which indicates that the distribution is more equal than the hypothetical distribution of perfect equality.

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Answer:

x=81 degrees

y=132 degrees

z=60 degrees

Answer:

x=81 degrees

y=132 degrees

z=60 degrees

Answer:

9^1 has a power of 1.  it evaluates to 9

Step-by-step explanation:

Answer:

  (4,8)

Step-by-step explanation:

One of the marked points on the black line is (4,8).

__

You will notice that the only combination worth $3.00 is (12,0).

Answer:

The  probability is  \(P(0.35 <X < 0.55) = 0.9921772\)

Step-by-step explanation:

From the question we are told that

  The sample size is  n =  175

   The population proportion is  p =  0.45

Generally the mean of the sampling distribution is  \(\mu_{x} = 0.45\)

 Generally the standard deviation is mathematically represented as  

        \(\sigma_{x} = \sqrt{\frac{p (1-p)}{n} }\)

=>      \(\sigma_{x} = \sqrt{\frac{0.45 (1-0.45)}{175} }\)

=>      \(\sigma_{x} = 0.0376\)

Generally the probability of  that the sample proportion of orange candies will be between 0.35 and  0.55 is  

      \(P(0.35 < X < 0.55) = P( \frac{0.35 - 0.45}{0.0376} < \frac{X -\mu_{x}}{\sigma_{x}} < \frac{0.55 - 0.45}{0.0376} )\)

=>   \(P(0.35 <X < 0.55) = P( -2.696 < \frac{X -\mu_{x}}{\sigma_{x}} < 2.6595 )\)

Generally \(\frac{X - \mu_{x}}{\sigma_{x}} = Z (The \ standardized \ value \ of X)\)

So

    \(P(0.35 <X < 0.55) = P( -2.6596 < Z< 2.6595 )\)

=>  \(P(0.35 <X < 0.55) =P( Z< 2.6595 ) - P( Z < -2.6596 )\)

From the z-table  

    \(P( Z< 2.6595 ) = 0.99609\)

and

    \(P( Z< - 2.6595 ) = 0.0039128\)

So

   \(P(0.35 <X < 0.55) =0.99609 - 0.0039128\)

=> \(P(0.35 <X < 0.55) = 0.9921772\)

Answer:

this will give you the answer: for cylinder

V = 3×2^2×7 = 84cm

this will give you the answer for cone:

V = 3× 2^2 × 6/3 = 24cm

then we just add

84 + 24 = 108cm^3

Step-by-step explanation:

hope it helps!

Answer:

\(Area = 5a - a^2\) \(inches\²\)

\(Perimeter = 10\ inches\)

Step-by-step explanation:

Given

Length = a

Width = 5 - a

Required

Determine the Area and Perimeter;

Calculating Area

Area is calculated as thus;

\(Area = Length * Width\)

Substitute values for Length and Width

\(Area = a * 5 - a\)

\(Area = a * (5 - a)\)

Open Bracket

\(Area = 5a - a^2\)

Calculating Perimeter

Perimeter is calculated as thus;

\(Perimeter = 2 (Length + Width)\)

Substitute values for Length and Width

\(Perimeter = 2 (a + 5 - a)\)

Collect Like Terms

\(Perimeter = 2 (5 + a- a)\)

\(Perimeter = 2 (5)\)

Open Bracket

\(Perimeter = 10\ inches\)

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

Benjamin Moore was the first President

The number of people that went to zoo is 261.

From the information, of all the students at Pioneer Elementary, 2/5 went on a field trip to the art museum, and 3/4 of the remainder went on a field trip to the zoo, and the rest stayed at school.

Those who went to the zoo will be:

= 3/4 × ( 1 - 2/5)

= 3/4 × 3/5

= 9/20

Since there are 580 students who attended Pioneer Elementary, those that went to the zoo will be:

= 9/20 × 580

= 261

There are 261 people who went to the zoo.

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Step-by-step explanation:

\(b = k + \frac{l}{m} \\ b - k = \frac{l}{m} \\ m = \frac{l}{b - k} \\ thank \: you\)

Answer:

Step-by-step explanation:

V = \(\pi r^{2} h\)

V = (3.14)(16)(12)

V = 50.24 cm³

Although part of your question is missing, you might be referring to this full question: What is the solution to this system of linear equations 2x + y = 1 and 3x – y = –6. So, the solution to the linear equation 2x + y = 1 and 3x – y = –6 is (-1, 3).

2x + y = 1 (1)

3x – y = –6 (2)

To solve the linear equations in two variables is by adding both the equation.

2x + 3x + y – y = 1 – 6

5x = –5

x = –1

Then, substitute the value of x in equation (1).

2x + y = 1

2 (-1) + y = 1

-2 + y = 1

y = 1 + 2

y = 3

Hence, the solution to the linear equation is (-1, 3).

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The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

Given:

Court lines are 50 mm wide.

Court paint covers 7 m² per litre of paint.

The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr

Radius of the entire circle = 9 m / 2 = 4.5 m

Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m

Circumference of the centre circle = 2π(4.45 m) = 27.94 m

Next, let's calculate the circumference of the semicircles:

The semicircles are half circles, so the circumference is given by the formula: Circumference = πr

The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.

Circumference of a semicircle = π(4.5 m) = 14.14 m

Total length = Circumference of the centre circle + 2 x Circumference of a semicircle

Total length = 27.94 m + 2(14.14 m)

Total length = 56.22 m

Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

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Answer:

3.6

Step-by-step explanation:

Answer:

-x - 6 > 0

-x > 6

x < -6

(-infinity, -6)

To graph f(x), start with these points.

x y

-6 0

-7 1

-10 2

-15 3

Draw a smooth curve that goes through these points.

The recursive sequence that represents the sequence defined by the following explicit formula is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The explicit formula of the sequence is given as follows:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

The first term and the common ratio for this problem is given as follows:

\(a_1 = -32, q = -\frac{1}{4}\)

The common ratio means that each term is the previous term multiplied by -1/4, hence the recursive formula is given as follows:

\(a_{n + 1} = -\frac{1}{4}a_n\)

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Answer:

Step-by-step exAnswer:

see the attachments for the two solutions

Step-by-step explanation:

When the given angle is opposite the shorter of the given sides, there will generally be two solutions. The exception is the case where the triangle is a right triangle (the ratio of the given sides is equal to the sine of the given angle). If the given angle is opposite the longer of the given sides, there is only one solution.

When a side and its opposite angle are given, as here, the law of sines can be used to solve the triangle(s). When the given angle is included between two given sides, the law of cosines can be used to solve the (one) triangle.

___

Here, the law of sines can be used to solve the triangle:

A = arcsin(a/c·sin(C)) = arcsin(25/24·sin(70°)) = 78.19° or 101.81°

B = 180° -70° -A = 31.81° or 8.19°

b = 24·sin(B)/sin(70°) = 13.46 or 3.64

The Reflexive Property is a property of equality that states that anything is equal to itself. This property is true for numbers, shapes, angles, and more.

In the context of geometry, the Reflexive Property of Congruence states that any geometric figure is congruent to itself. This includes angles, segments, triangles, and other polygons.

So, when you see "<J ≅ <J", it's saying that angle J is congruent to angle J, which is an application of the Reflexive Property. In other words, any angle is congruent (equal in measure) to itself.