how do you find an expression for a cubic function when given f(1)=6 and f(-1)=f90)=f(2)=0

Answer:

1.2

Step-by-step explanation:

First make -1.5 equal to 0.

We'll have to add 1.5, right?

So 1.5 is in 2.7.

So now its 0 + ? = ?

2.7 - 1.5 = 1.2

So 0 + 1.2 = 1.2

Hope this helped.

Answer:

the slope is -1/2

Step-by-step explanation:

the formula for slope is m= y2-y1/x2-x1 (m is the slope)

the points are (-12,3) and (16,-11)

label the numbers

x1: -12

y1: 3

x2: 16

y2: -11

Now plug everything in

m=-11-3/16--12

m=-14/28

m= -1/2

Hope this helps!

Answer:

p ≥ 13

13 pizzas at least

Step-by-step explanation:

$107 + $4 = $111

$111/$9 = 12.3333 round it to 13

now we know he needs to sell at least 13 pizzas so the inequality p= 13 or p > 13.

This is my go at it, I am not sure though.

Answer:

Step-by-step explanation:

Answer:

Solve Quadratic Equation by Completing The Square

Solving 2x2-6x-15 = 0 by Completing The Square .

Divide both sides of the equation by 2 to have 1 as the coefficient of the first term :

x2-3x-(15/2) = 0

Add 15/2 to both side of the equation :

x2-3x = 15/2

Now the clever bit: Take the coefficient of x , which is 3 , divide by two, giving 3/2 , and finally square it giving 9/4

Add 9/4 to both sides of the equation :

On the right hand side we have :

15/2 + 9/4 The common denominator of the two fractions is 4 Adding (30/4)+(9/4) gives 39/4

So adding to both sides we finally get :

x2-3x+(9/4) = 39/4

Adding 9/4 has completed the left hand side into a perfect square :

x2-3x+(9/4) =

(x-(3/2)) • (x-(3/2)) =

(x-(3/2))2

Things which are equal to the same thing are also equal to one another. Since

x2-3x+(9/4) = 39/4 and

x2-3x+(9/4) = (x-(3/2))2

then, according to the law of transitivity,

(x-(3/2))2 = 39/4

Step-by-step explanation:

Basically, the answer is -1.622 and 4.622.

Please mark as brainliest.

Answer:

say it is 4/16th of an inch

Step-by-step explanation

Answer:

(-2, 0), (0, -1), (-3, 0)

Step-by-step explanation:

if you know coordinates, just find it on the graph and see if it falls in the region, if it falls on a solid line, it is ok, and if it falls on a dashed line, it is not in the region

so the okay ones are

(-2, 0)

(0, -1)

(-3, 0)

Answer:

4

Step-by-step explanation:

Answer:

Well if the total equals 180-degrees you have to make an assumption or let someone smarter just do it for you. also that box means it's a 90-degree angle so the rest is cut in half; what times three and seven would equal to 90-degrees? I can't do much anymore my brain hurts lol

Step-by-step explanation:

Hope this helps :)

Answer:D

Step-by-step explanation: All equations should be balanced and equal. What you do to one side, must be done to the other.

Answer:

Louisa can make 10 doll dresses with 4 yards of fabric.

Step-by-step explanation:

We know that one doll dress requires 2/5 yard of fabric. The question is asking find how many dresses can be made from 4 yards of fabric, in which this equation can represent:

4 = 2/5x

Find x:

4 ÷ 2/5

= 4/1 x 5/2

= 20/2 or 10 (SIMPLIFIED)

So, Louisa can make 10 doll dresses with 4 yards of fabric.

I hope I helped!

Answer:

2.25

Step-by-step explanation:

Change the fraction so that the denominator is something that's a factor of 100

9/4 = x/100

9 x 25 = 225

-----------------------

4 x 25 = 100

225/100

Now divide to get your decimal

225/100 = 2.25

Given that, -3b + (-9) = (-3)

We have to find value of b[tex].[/tex]

⭆ -3b + (-9) = (-3)

⭆ -3b - 9 = -3

⭆ -3b = -3 + 9

⭆ -3b = 6

⭆ 3b = -6

⭆ b = -6/3

⭆ b = -2 [Final answer]

Answer:

1.8 x 166 = 190.8

190.8 divided by 1.5 = 127.2

Step-by-step explanation:

The total library visits per year work out to 2700000.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

To find the total number of library visits per year, we can multiply the number of residents by the average number of visits per resident per year:

total library visits per year = (number of residents) x (average visits per resident per year)

= 1.8 x 10⁶ x 1.5

= 2.7 x 10⁶

= 2700000

Therefore, the total number of library visits per year is 2.7 x 10⁶.

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Answer:

1.30$

Step-by-step explanation:

The price of the candy bar to have a 65% mark up is $1.3035.

Markdown percentage is defined as the increase in the price which is calculated as a percent of the selling price.

Given that,

Markup percentage = 65% = 65/100 = 0.65

Let x be the price of the candy bar be to have a 65% mark up.

(x - 0.79) / 0.79 = 0.65

x - 0.79 = 0.5135

Adding 0.79 to both sides,

x = 1.3035

Hence the price of the candy bar would need to be $1.3035.

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Answer:

41600

Step-by-step explanation:

4% of 40000=1600

40000+1600=41600

Answer:

first mark brainliest

Answer:

its is b, supplementary angles

Step-by-step explanation:

the parameterization of the plane that contains the three points (-4, -2, 2), (8, -12, -6), and (40, 0, 0) is: F(s, t) = (-4 + s, -2 + t, 2)

To parameterize the plane that contains the three points (-4, -2, 2), (8, -12, -6), and (40, 0, 0), we can use two vectors that lie in the plane and find their cross product. The cross product will give us the normal vector to the plane, which we can then use to parameterize the plane.

Let's take the vectors formed by the points (-4, -2, 2) and (8, -12, -6), and (-4, -2, 2) and (40, 0, 0).

Vector v1 = (8, -12, -6) - (-4, -2, 2) = (12, -10, -8)

Vector v2 = (40, 0, 0) - (-4, -2, 2) = (44, 2, -2)

Now, let's calculate the cross product of v1 and v2:

Normal vector N = v1 x v2 = (12, -10, -8) x (44, 2, -2)

To find the cross product, we can use the following formula:

N = (v1.y * v2.z - v1.z * v2.y, v1.z * v2.x - v1.x * v2.z, v1.x * v2.y - v1.y * v2.x)

Calculating the cross product:

N = ( (-10 * -2) - (-8 * 2), (-8 * 44) - (12 * -2), (12 * 2) - (-10 * 44) )

 = ( -16, -400, -568 )

Now, we have the normal vector N = (-16, -400, -568) which is perpendicular to the plane. We can use this vector to parameterize the plane.

Let's define a point on the plane as P0 = (-4, -2, 2).

The parameterization of the plane can be given by the equation:

F(s, t) = P0 + s * U + t * V

Where U and V are two linearly independent vectors lying in the plane.

Let's choose U = (1, 0, 0) and V = (0, 1, 0) as the vectors lying in the plane.

Substituting the values, we get:

F(s, t) = (-4, -2, 2) + s * (1, 0, 0) + t * (0, 1, 0)

      = (-4 + s, -2, 2) + (0, t, 0)

      = (-4 + s, -2 + t, 2)

Therefore, the parameterization of the plane that contains the three points (-4, -2, 2), (8, -12, -6), and (40, 0, 0) is:

F(s, t) = (-4 + s, -2 + t, 2)

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Answer:

35 miles

Step-by-step explanation:

d=(70)(.5)

d=35 miles

Answer:

Step-by-step explanation:

The points lie on a straight line and go through the origin

The transformation T preserves the answer: if G has a k-clique, then G' has a k-independent set, and vice versa.

a) **Problem Definition: K-Independent Set**

A k-independent set is a subset of vertices in a graph such that no two vertices in the set are adjacent (i.e., there is no edge connecting them). Formally, given an undirected graph G = (V, E), a k-independent set S is a subset of V where for every pair of vertices u and v in S, there is no edge (u, v) in E. The goal is to find the largest k-independent set in the given graph.

b) **Brute Force Method for Solving K-Clique**

The brute force method for solving the k-clique problem involves examining every possible subset of k vertices in the graph and checking if each subset forms a complete subgraph (clique) of size k. If the size of the graph is n and k is constant, then the number of possible subsets to examine is a polynomial function of n. Thus, the brute force method runs in polynomial time when k is constant.

However, when k=n/2, the brute force method becomes inefficient. The number of subsets of k vertices to examine becomes 2^n/2, which grows exponentially with the size of the input graph. This exponential growth makes the brute force method impractical for larger values of n.

c) **Transformation from K-Clique to K-Independent Set**

To transform an instance of the k-clique problem to the k-independent set problem, we define the following polynomial-time transformation T:

Given an instance of k-clique G = (V, E), construct a new graph G' = (V, E'), where E' consists of all the edges in G that are not in E. In other words, the edges in G' are complementary to the edges in G.

The transformation T is polynomial-time because constructing G' from G can be done in polynomial time since the size of E' is at most the size of E.

**Proving T is Polynomial-Time:**

The transformation T runs in polynomial time because constructing G' from G requires checking each edge in E, which can be done in polynomial time.

**Proving T is Answer-Preserving:**

Let C be a clique of size k in G. If we apply the transformation T to G and obtain G', then the vertices in C will not be adjacent in G', as they form a clique in G. Hence, C becomes a k-independent set in G'.

Conversely, if S is a k-independent set in G', then the vertices in S are not adjacent in G'. This means that there is no edge connecting any pair of vertices in S in G'. Thus, S forms a clique of size k in G.

Therefore, the transformation T preserves the answer: if G has a k-clique, then G' has a k-independent set, and vice versa.

In conclusion, the transformation T from k-clique to k-independent set is polynomial-time and answer-preserving.

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Answer/Step-by-step explanation:

First figure:

<2 and <1 lie outside the two lines cut across by the transversal, and they also lie in opposite sides of the transversal. Therefore:

<1 and <2 are Alternate Exterior Angles

Second figure:

<3 and <4 lie within the two lines cut across by the transversal. And also lie on the same side of the transversal. Therefore:

<3 and <4 are Consecutive Interior Angles

Third Figure:

<5 and <6 both lie in the same position on the two lines cut by the transversal. Therefore:

<5 and <6 are Corresponding Angles

Fourth Figure:

<7 and <8 lie inside the two lines cut across by the transversal, and also lie in opposite directions of the transversal, therefore:

<7 and <8 are Alternate Interior Angles

The statement which is not true is c. 19 = 13 + 5

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

The given statements are,

A. 7 + 7 = 19 - 5

B. 9 + 9 = 11 + 7

C. 19 = 13 + 5

D. 20 - 12 = 4 + 4

Taking each statement one by one,

A. 7 + 7 = 19 - 5

So, L.H.S. = 7 + 7 = 14

and R.H.S. = 19 -5 = 14

Thus, L.H.S = R.H.S

Therefore the statement is true.  

B. 9 + 9 = 11 + 7

So, L.H.S. = 9 + 9 = 18

and R.H.S. = 11 + 7 = 18

Thus, L.H.S = R.H.S

Therefore the statement is true.  

C. 19 = 13 + 5

So. So, L.H.S. = 19

and R.H.S. = 13 + 5 = 18

Thus, L.H.S ≠ R.H.S

Therefore the statement is not true.

D. 20 - 12 = 4 + 4

So, L.H.S. = 20 - 12 = 8

and R.H.S. = 4 + 4 = 8

Thus, L.H.S = R.H.S

Therefore the statement is true.  

Thus, the statement which is not true is c. 19 = 13 + 5.

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Answer:

More work space

Step-by-step explanation:

Step-by-step explanation:

4y=12x+20

4y=32x

4y/4=32x/4

=8x

Answer:

F

Step-by-step explanation:

Answer:

             [tex]\bold{\underline{(3m+\frac13n)^3=27m^2+9m^2n+mn^2+\frac1{27}n^2}}[/tex]

Step-by-step explanation:

[tex](3m+\frac13n)^3=(3m+\frac13n)(3m+\frac13n)(3m+\frac13n)=\\\\=\left[(3m)(3m)+(3m)\left(\frac13n\right)+\left(\frac13n\right)(3m)+\left(\frac13n\right)\left(\frac13n\right)\right]\left(3m+\frac13n\right)=\\\\=\left[9m^2+mn+mn+\frac19n^2\right]\left(3m+\frac13n\right)=\\\\=\left[9m^2+2mn+\frac19n^2\right]\left(3m+\frac13n\right)=\\\\=9m^2(3m)+9m^2(\frac13n)+2mn(3m)+2mn(\frac13n)+\frac19n^2(3m)+\frac19n^2(\frac13n)=\\\\=27m^3+3m^2n+6m^2n+\frac23mn^2+\frac13mn^2+\frac1{27}n^2=\\\\=27m^2+9m^2n+mn^2+\frac1{27}n^2[/tex]

Answer:

x = 3

Step-by-step explanation:

The required value of the x for the given rectangle is 3cm.

Given that,
For a rectangle 1
Length = 6
Width = x
Area of the rectangle = perimeter of the rectangle

The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.

Perimeter is the measure of the figure on its circumference.
Example, for square = 4 * sides or side + side + side + side

Here,
The perimeter of the rectangle, = 2 length + 2 width.
Area of the rectangle = length * width
According to question,
area of the rectangle = perimeter of the rectangle
6 * x = 6*2 + 2x
6x - 2x = 12
4x = 12
x = 3

Thus, the required value of the x for the given rectangle is 3cm.

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1. The minimum sum of their squares is achieved when the two integers are 8 and 9, resulting in a sum of 793.

2.  The greatest possible area for the rectangle is 625 square centimeters, which occurs when the length is 25 cm and the width is also 25 cm.

The sum of two positive integers is 35. To find the minimum sum of their squares, let's assume the two integers are x and y.

Given: x + y = 35

We want to minimize the sum of their squares, which can be represented as:

S = x^2 + y^2

To solve this problem using quadratic functions, we need to express one variable in terms of the other and then substitute it into the equation for S.

From the given information, we have:

x = 35 - y

Substituting this into the equation for S, we get:

S = (35 - y)^2 + y^2

Expanding and simplifying, we have:

S = 1225 - 70y + y^2 + y^2

S = 2y^2 - 70y + 1225

Now, we have a quadratic function for S in terms of y. To find the minimum value of S, we can use the vertex formula:

The x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b / (2a).

In our case, a = 2, b = -70. Substituting these values into the formula, we get:

y = -(-70) / (2 * 2)

y = 35 / 4

y = 8.75

Since the variables represent positive integers, we will consider the nearest integer values of y, which are 8 and 9.

Checking the values of S at y = 8 and y = 9:

For y = 8:

S = 2(8^2) - 70(8) + 1225

S = 128 - 560 + 1225

S = 793

For y = 9:

S = 2(9^2) - 70(9) + 1225

S = 162 - 630 + 1225

S = 757

Therefore, the minimum sum of their squares is achieved when the two integers are 8 and 9, resulting in a sum of 793.

A rectangle has a perimeter of 100 cm. To find the greatest possible area for the rectangle, let's assume the length of the rectangle is x and the width is y.

Given: 2x + 2y = 100

We want to maximize the area of the rectangle, which can be represented as:

A = xy

To solve this problem using quadratic functions, we need to express one variable in terms of the other and then substitute it into the equation for A.

From the given information, we have:

x = (100 - 2y) / 2

x = 50 - y

Substituting this into the equation for A, we get:

A = (50 - y) * y

A = 50y - y^2

Now, we have a quadratic function for A in terms of y. To find the maximum value of A, we can again use the vertex formula:

The x-coordinate of the vertex of a quadratic function in the form f(x) = ax^2 + bx + c is given by x = -b / (2a).

In our case, a = -1, b = 50. Substituting these values into the formula, we get:

y = -(50) / (2 * -1)

y = 25

Checking the value of A at y = 25:

A = 50(25) - (25)^2

A = 1250 - 625

A = 625

Therefore, the greatest possible area for the rectangle is 625 square centimeters, which occurs when the length is 25 cm and the width is also 25 cm.

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Answer:

The leading term of the given polynomial equation is (0.1)x³ ⇒ (B)

Step-by-step explanation:

To find the polynomial equation from its graph search about

From the given graph

∵ There are three x-intercepts (-2, 0), (0, 0), (4, 0)

→ That means the polynomial equation has 3 factors use the

   x-intercepts to find them

∵ The x intercept is (-2, 0)

∴ x = -2

→ Add 2 to both sides

∴ x + 2 = -2 + 2

∴ x + 2 = 0

→ That means the equation has a factor (x + 2)

∴ (x + 2) is a factor of the given polynomial equation

∵ The x intercept is (4, 0)

∴ x = 4

→ Sutract 4 from both sides

∴ x - 4 = 4 - 4

∴ x - 4 = 0

→ That means the equation has a factor (x - 4)

∴ (x - 4) is a factor of the given polynomial equation

∵ The x intercept is (0, 0)

∴ x = 0

∴ x is a factor of the given polynomial equation

→ To find the polynomial multiply its factors

∴ y = x( x + 2)(x - 4)

∵ The leading term is the first term

∵ x(x)(x) = x³ is the first term when we multiply the 3 factors

∴ The leading term is x³

→ The choices have (0.1)x³

∴ y = 0.1x(x + 2)(x - 4)

∴ The leading term of the given polynomial equation is (0.1)x³