write the equation of the graph below in factored form
f(x) = (x + 1)(x-2)(x-3)
f(x) = (x - 1)(x + 2)(x + 3)
f(x) = (x + 1)(x + 2)(x + 3)
f(x) = (x - 1)(x - 2)(x - 3)

Answer:  \(\frac{7}{120}\)

Step-by-step explanation:

Step-by-step explanation:

2x+y=7

(A) (0,7),(72,0)and(3,1)

(B) (0,6),(72,0)and(3,1)

(C) (0,7),(52,0)and(3,1)

(D) (0,7),(72,0)and(2,1)

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Related Questions

Find three solutions of the equation: 2x+y=7

(A) (0,7),(72,0)and(3,1)

(B) (0,6),(72,0)and(3,1)

(C) (0,7),(52,0)and(3,1)

(D) (0,7),(72,0)and(2,1)

Given:

The linear equation having variables x and y is given as –

2x+y=7

For the initial solution of the equation, put x=0 in the linear equation and obtain the value of variable y .

So, substituting x=0 in the equation, we get,

2×0+y=7y=7

So, the first solution of the linear equation is

x=0

y=7

In two-dimensional coordinates form (x,y) , the first solution is (0,7) .

Now, similarly,

Substituting y=0 in the linear equation we have,

⇒2x+0=7⇒2x=7⇒x=72

So, the second solution of the linear equation is

x=72

y=0

In two-dimensional coordinates form (x,y) , the second solution is (72,0) .

And finally,

Substituting y=1 in the linear equation we have,

⇒2x+1=7⇒2x=6⇒x=62⇒x=3

So, the third solution of the linear equation is

x=3

y=1

In two-dimensional coordinates form (x,y) , the third solution is (3,1) .

Therefore, the three solutions of the equation 2x+y=7 are (0,7) , (72,0) and (3,1) .

The correct answer is –

(A) (0,7),(72,0)and(3,1)

Answer:

Therefore, the three solutions of the equation 2x+y=7 are (0,7) , (72,0) and (3,1) . So, the correct answer is “Option A”.

Step-by-step explanation:

Henry had deposited approximately $8,000.32 if he received $13,299.23 after 5 years. Rounded to the nearest dollar, the answer is $8,000.To solve this problem, we can use the formula for compound interest:

\($$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$\)

where A is the amount after t years, P is the principal (the amount deposited), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

In this case, we have:

A = $13,299.23

r = 0.08 (8%)

n = 4 (quarterly compounding)

t = 5 years

We can rearrange the formula to solve for P:

\(P = \frac{A}{(1 + \frac{r}{n})^(nt) }\)

Plugging in the values, we get:

\(P = \frac{ $13,299.23}{(1 + \frac{0.08}{4} ) ^ {(4*5)} }\)

P ≈ $8,000.32

Therefore, Henry had deposited approximately $8,000.32 if he received $13,299.23 after 5 years. Rounded to the nearest dollar, the answer is $8,000.

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Answer:

1.8 and 14.3

Step-by-step explanation:

Our equation is a quadratic equation so we will use the dicriminant method

Answer:

1. Angle forming a linear pair sum to 180°

2. Transitive property of equality

3. Algebra

4. Definition of congruency

Step-by-step explanation:

The given statement and reasons are presented as follows;

Statement      \({}\)                          Reason

1. m∠GKH + m∠HKI = 180°    \({}\) 1. Angle forming a linear pair sum to 180°

m∠HKI + m∠IKJ = 180°

2. m∠GKH + m∠HKI = m∠HKI + m∠IKJ \({}\)2. Transitive property of equality

3. m∠GKH = m∠IKJ  \({}\)              3. Algebra

4. m∠GKH ≅ m∠IKJ               4. Definition of congruency

The explanation are;

1. The sum of angles on a straight line is 180°

2. The transitive property of equality can be written as follows;

Given a = c and b = c, therefore, a = b

3. The addition property of equality states that given a + b = c + b, therefore a = c

4. Two geometric figures are said to be congruent when they are equal.

Equation shows that Tom's indirect utility function V(p, w) is convex in p, as desired.

V(λ\(p1\) + (1-λ)\(p2\), w) ≤ λV(\(p1\), w) + (1-λ)V(\(p2\), w)

To prove that Tom's indirect utility function V(p, w) is convex in p, where p is the price vector and w is the wealth, we need to show that for any two price vectors p1 and p2, and for any λ ∈ [0,1], the following inequality holds:

V(λ\(p1\) + (1-λ)\(p2\), w) ≤ λV(\(p1\), w) + (1-λ)V(\(p2\), w)

To prove this, we can use the concept of homothetic preferences.

Homothetic preferences imply that the utility function is homogeneous of degree zero, meaning that multiplying prices and income by the same positive constant does not affect the consumer's preferences.

Let's assume Tom's utility function is U(x), where x represents the consumption bundle.

Tom's indirect utility function can be defined as:

V(p, w) = max { U(x) | px ≤ w }

Now, consider two price vectors p1 and p2, and let x1 and x2 be the optimal consumption bundles for p1 and p2, respectively.

Since U(x) is homogeneous of degree zero, we have:

U(λ\(x1\)+ (1-λ)\(x2\)) = U(x1 + λ(x2 - x1)) = U(x1) [using homogeneity]

From the definition of the indirect utility function, we know that V(p, w) = U(x), where x is the consumption bundle that maximizes U(x) subject to the budget constraint.

Therefore, we have:

V(λp1 + (1-λ)p2, w) = U(x1) [since λx1 + (1-λ)x2 is the optimal consumption bundle for λp1 + (1-λ)p2]

Now, let's consider the right-hand side of the inequality:

λV(p1, w) + (1-λ)V(p2, w) = λU(x1) + (1-λ)U(x2) [using the definition of the indirect utility function]

Since U(x1) = U(x2) (as shown above), we can simplify the right-hand side:

λV(p1, w) + (1-λ)V(p2, w) = U(x1)

Therefore, we have:

V(λp1 + (1-λ)p2, w) ≤ λV(p1, w) + (1-λ)V(p2, w)

This shows that Tom's indirect utility function V(p, w) is convex in p, as desired.

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Step-by-step explanation:

= 7 × 4/3

= (7 × 4)/3

= 28/3

7 × 4/3 = 28/3

Answer:

\( \sf 9 \frac{1}{3} \)

Step-by-step explanation:

\( \sf = 7 \times \frac{4}{3} \)

\( \sf = \frac{7}{1} \times \frac{4}{3} \)

\( \sf = \frac{28}{3} \)

\( \sf = 9 \frac{1}{3} \)

Answer:

34

Step-by-step explanation:

34

Answer:

24

Step-by-step explanation:

4×6=24

you need to multiply one side with the other side

first side - 4

second side - 6

Answer: plan B is cheaper

Step-by-step explanation:

Answer:

x = 2 & y = 8

And this means-

x+y=10

Note:- These type of questions can have infinite solutions

Answer:

y=x+6

Step-by-step explanation:

In triangle ABC, side AC and the perpendicular bisector of BC meet in point D, and BD bisects ∠ABC。 If AD = 9 and DC = 7, 145–√5  is the area of a triangle.

I supposed here that [ABD] is the perimeter of ▲ ABD.

As  BD  is a bisector of  ∠ABC ,

ABBC=ADDC=97

Let  ∠B=2α

Then in isosceles  △DBC

∠C=α

BC=2∗DC∗cosα=14cosα

Thus  AB=18cosα

The Sum of angles in  △ABC  is  π  so

∠A=π−3α

Let's look at  AC=AD+DC=16 :

AC=BCcosC+ABcosA

16=14cos2α+18cosαcos(π−3α)

[1]8=7cos2α−9cosαcos(3α)

cos(3α)=cos(α+2α)=cosαcos(2α)−sinαsin(2α)=cosα(2cos2α−1)−2cosαsin2α=cosα(4cos2α−3)

With  [1]

8=cos2α(7−9(4cos2α−3))

18cos4−17cos2α+4=0

cos2α={12,49}

First root lead to  α=π4  and  ∠BDC=π−∠DBC−∠C=π−2α=π2 . In such case  ∠A=π−∠ABD−∠ADB=π4, and  △ABD  is isosceles with  AD=BD. As  △DBC  is also isosceles with  BD=DC=7,  AD=7≠9.

Thus first root  cos2α=12  cannot be chosen and we have to stick with the second root  cos2α=49. This gives  cosα=23  and  sinα=5√3.

The area of a triangle ABD=12h∗AD  where h  is the distance from  B  to  AC.

h=BCsinC=14cosαsinα

Area of  triangle ABD=145–√5

= 145–√5.

Incomplete question please read below for the proper question.

In triangle ABC, side AC and the perpendicular bisector of BC meet in point D, and BD bisects ∠ABC。 If AD = 9 and DC = 7, what is the area of triangle ABD?

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To determine whether the points a(2, 4, 0), b(3, 5, −2), and c(1, 3, 2) lie on a straight line or not, we can use the slope formula.

Let's calculate the slope of AB:$$m_{AB}=\frac{y_B-y_A}{x_B-x_A}=\frac{5-4}{3-2}=1$$Now let's calculate the slope of BC:$$m_{BC}=\frac{y_C-y_B}{x_C-x_B}=\frac{3-5}{1-3}=-1$$We have the slope of both the lines AB and BC. As the slopes of both the lines are not equal, the three points do not lie on a straight line.Therefore, it is concluded that the points a(2, 4, 0), b(3, 5, −2), and c(1, 3, 2) do not lie on a straight line.Three points are said to be collinear or lie on the same line if the slope of the line joining any two of the points is the same. When the points are collinear, the slope of any two lines is the same. In other words, the slope of AB should be the same as the slope of BC.However, if the slope of one of the lines joining any two points is not the same as the slope of the other lines, the points are not collinear. This is exactly the case with the points a(2, 4, 0), b(3, 5, −2), and c(1, 3, 2).By applying the slope formula, we have found that the slope of AB is 1 and the slope of BC is -1. Since the slopes of both the lines are not equal, the three points do not lie on a straight line.

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The three points a(2, 4, 0), b(3, 5, −2), c(1, 3, 2) do not lie on a straight line.

To determine whether the points a(2, 4, 0), b(3, 5, −2), and c(1, 3, 2) lie on a straight line or not, we can use the slope formula.

Let's calculate the slope of AB:

m_{AB}={y_B-y_A}/{x_B-x_A}={5-4}/{3-2}=1

Now let's calculate the slope of BC:

m_{BC}={y_C-y_B}/{x_C-x_B}={3-5}/{1-3}=-1

We have the slope of both the lines AB and BC. As the slopes of both the lines are not equal, the three points do not lie on a straight line.

Therefore, it is concluded that the points a(2, 4, 0), b(3, 5, −2), and c(1, 3, 2) do not lie on a straight line.

Three points are said to be collinear or lie on the same line if the slope of the line joining any two of the points is the same. When the points are collinear, the slope of any two lines is the same.

In other words, the slope of AB should be the same as the slope of BC.

However, if the slope of one of the lines joining any two points is not the same as the slope of the other lines, the points are not collinear.

This is exactly the case with the points a(2, 4, 0), b(3, 5, −2), and c(1, 3, 2).

By applying the slope formula, we have found that the slope of AB is 1 and the slope of BC is -1.

Since the slopes of both the lines are not equal, the three points do not lie on a straight line.

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Answer:

A

Step-by-step explanation:

Answer:

b i think

Step-by-step explanation:

Answer:

x = 0

Step-by-step explanation:

3(x + 6) = 18

distribute

3x + 18 = 18

Subtract 18 from both sides

3x = 0

Divide both sides by 3

x = 0

The correct statement regarding Python indentation is that incorrect indentation will result in an "IndentationError."

The correct output for the given "for" loop and "range" function is:

99 88 77 66 55 44 33 22 11 0 -11

Regarding the statement about a "Fatal" logic error in Python, the correct answer is:

In script mode - Python displays a traceback, then terminates the script.

When a fatal logic error occurs in Python during script execution, Python will display a traceback message that provides information about the error, such as the line where it occurred, and then terminates the script. This traceback message helps in debugging the code and identifying the cause of the error.

In interactive mode, if a fatal logic error occurs, Python will also display a traceback message but will not terminate the entire session. Instead, it will allow you to continue entering new commands or snippets of code.

Regarding Python indentation, the correct statement is:

Incorrect indentation will result in an "IndentationError."

Python relies on indentation to define the grouping and structure of code blocks. It uses consistent indentation to determine which lines of code belong to a particular block, such as loops or conditional statements. If the indentation is incorrect or inconsistent, Python will raise an "IndentationError" and the code will not run successfully.

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Answer:

  A.  7 units

Step-by-step explanation:

The volume of this triangular prism can be found from ...

  V = 1/2LWH

  21 = 1/2(2)(3)h . . . fill in the given values

  7 = h . . . . . . . . . divide by 3

The height of the prism is 7 units.

Answer:

(6, -1)

Step-by-step explanation:

Solve the System of Equations

2x + 3y = 9 and x − 2y = 8

Add 2y to both sides of the equation.

x = 8 + 2y 2x + 3y = 9

Replace all occurrences of x with 8 + 2y in each e quation.

Replace all occurrences of x in 2x + 3y = 9 with 8 + 2y. 2 (8 + 2y) + 3y = 9

x = 8 + 2y

Simplify 2 (8 + 2y) + 3y.

16 + 7y = 9

x = 8 + 2y

Solve for y in the first equation.

Move all terms not containing y to the right side of the equation.

7y = −7

x = 8 + 2y

Divide each term by 7 and simplify.  

y = −1

x = 8 + 2y

Replace all occurrences of y with −1 in each equation.

Replace all occurrences of y in x = 8 + 2y with −1. x = 8 + 2 (−1)

y = −1

Simplify 8 + 2 (−1).

x = 6

y = −1

The solution to the system is the complete set of ordered pairs that are valid solutions.

(6, −1)

The result can be shown in multiple forms.

Point Form:

(6, −1)

Equation Form:

x = 6, y = −1

Answer:

(6, -1)

Step-by-step explanation:

Answer:

5, 1 , -5, -9

Step-by-step explanation:

This seem's difficult but in reality its easy... just alot of work.

(Domain means x and range means Y)

You have all the x points (-3,-1,2,4)  but you need the Y's.

You have to fill in the points for x in the equation.

Example:

F(x)= - 2x- 1 will now be F(x)=-2(-3)-1

- you'll do that for each x point.

Next you solve.

F(x)= -2(-3)-1

- first we mutiply -2 times -3.

- that equals 6

- now we have 6-1

- solve that and you get 5

Thats all it is. Do that for each point and you'll have your Ranges.

I hope this helps for future questions. Good Luck!!!

Answer:

14/46

Step-by-step explanation:

Given data: Height of inverted cone = h = 30 feet. Diameter of circular base = 15 feet.Radius of circular base = r = (15/2) feet = 7.5 feet.

The volume of the inverted cone (tank) can be calculated as:

V = 1/3πr²hIn this case,

the volume of the water in the tank will decrease as it flows out of the bottom.

As water flows out, the height of water in the tank will decrease at some rate.

We need to find the rate at which the height of water is decreasing when the height of water is 20 feet.

Let the radius of water in the tank at some instant be R and height of water in the tank be h_w.

The volume of water in the tank at some instant can be calculated as:

V_w = 1/3πR²h_wFrom the given data,

we know that water is flowing out at the rate of 2 cubic feet per hour.

Therefore, the rate at which the volume of water in the tank is decreasing is 2 cubic feet per hour.

At some instant, the radius and the height of water in the tank are given by:

R = r × (h_w/h) and h_w = 20 feet

So, the volume of water at this instant can be calculated as:

V_w = 1/3π(r/h)²× h_w³

So, the rate at which the height of water is falling can be calculated as follows:

2 = d(V_w)/dt

= (πr²/3)×(dh_w/dt)

=> dh_w/dt

= (6/πr²) feet per hour

On substituting the given values in the above expression,

we get:

dh_w/dt = (6/π×7.5²) feet per hour

Answer: dh_w/dt = 0.0546 feet per hour (rounded to four decimal places).

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Answer:

21.91 meters

Step-by-step explanation:

Since they already give you the hypotenuse, you will find the other missing side using this formula:

A= \(\sqrt{c^2 - b^2}\)

So c² = 1,156

and b² = 676

1156 - 676 = 480

------

The square root of 480 is around 21.91

Let's double check, to double check, pretend that you don't know the hypotenuse, but you know the a and b sides.

So: 480.05 + 676 = 1,156.05

\(\sqrt{1156.05}\) ≈ 34

-------

Have a good day :)

To compute a basis of the eigen space corresponding to eigen value -2, we need to find the null space of the matrix A + 2I, where A is the 3x3 matrix and I is the identity matrix.

The null space will give us the basis vectors of the eigen space

To find the eigen space corresponding to the eigen value -2, we start by constructing the matrix A + 2I, where A is the given 3x3 matrix and I is the 3x3 identity matrix. Next, we solve the homogeneous system of linear equations (A + 2I)x = 0, where x is a vector. The solutions to this system form the null space of the matrix A + 2I.

By finding a basis for this null space, we can obtain the basis vectors of the eigen space corresponding to the eigen value -2.

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The two correct answers are:

If f(x) = (x + 6)(x^2 + 3), then f'(x) = 2x^3 + 12x + 9.

If y = (x^2 - 1)(x^2 + 6), then dy/dx = 4x^3 + 14x.

The product rule states that if we have two functions, u(x) and v(x), then the derivative of their product is given by (u*v)' = u'v + uv'. In other words, we differentiate the first function and multiply it by the second function, then add it to the product of the first function and the derivative of the second function.

Let's analyze each given option:

If f(x) = (x + 6)(x^2 + 3), using the product rule, we differentiate the first function, which is x + 6, to get 1. Then we multiply it by the second function, x^2 + 3, to get (x + 6)(2x) = 2x^2 + 12x. Similarly, we differentiate the second function to get 2x and multiply it by the first function to get (x + 6)(2x) = 2x^2 + 12x. Adding these two results together, we get f'(x) = 2x^2 + 12x + 2x^2 + 12x = 4x^2 + 24x.

If ||,y y = (t^3 + 2t)(t^2 + 2t + 1), the given expression is incorrect. It is not using the product rule correctly to differentiate the function y.

If h(z) = (z^4 + 3z - 2)(z + z^2 + 1), the given expression is incorrect. It is not using the product rule correctly to differentiate the function h(z).

If f(t) = (t^2 + 1)*t^3, the given expression is incorrect. It does not correctly apply the product rule to differentiate the function f(t).

If y = (x^2 - 1)(x^2 + 6), using the product rule, we differentiate the first function, x^2 - 1, to get 2x. Then we multiply it by the second function, x^2 + 6, to get (x^2 - 1)(2x) = 2x^3 - 2x. Similarly, we differentiate the second function to get 2x and multiply it by the first function to get (x^2 + 6)(2x) = 2x^3 + 12x. Adding these two results together, we get dy/dx = 2x^3 - 2x + 2x^3 + 12x = 4x^3 + 10x.

Therefore, options 1 and 5 are the correct answers.

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Answer:

in the thousandths

Step-by-step explanation:

because it would go

hundreds,tens,ones (decimal) tenths, hundredths,then thousandths

Answer:

Thousandths place and 0.009

Step-by-step explanation: