fill in the box below to write an expression that is equivalent to​

Answer:

  C.) x = -3, cross; x = 0, touch; x = 1, cross; x = 3, cross

Step-by-step explanation:

You want the zeros and their multiplicity of f(x) = x^5 -x^4 -9x^3 +9x^2, along with a description of whether the graph crosses or touches the x-axis at each zero.

The equation can be factored as ...

  f(x) = x^2(x^3 -x^2 -9x +9)

The cubic can be factored as ...

  x^3 -x^2 -9x +9 = x^2(x -1) -9(x -1) = (x^2 -9)(x -1)

and the quadratic factor can be factored as the difference of square. The complete factorization is then ...

  f(x) = x^2(x -1)(x -3)(x +3)

The zeros are the values of x that make the factors zero:

When the multiplicity of a zero is even, the graph touches the x-axis. Here, that means the graph will touch at x=0, where the multiplicity of the zero is 2.

When multiplicity is odd, the graph will cross the x-axis. The graph crosses at the zeros -3, -1, +3.

__

Additional comment

As soon as you recognize that the x^2 factor means the multiplicity of x=0 is even, you can identify the correct answer choice: the only one that says "touch" for x=0.

The eccentricity of the conic section below is: A. closer to 0 than 1.

In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.

In Mathematics, there are four (4) types of conic section and these include the following with their eccentricity:

In this context, we can reasonably infer and logically deduce that the eccentricity of the conic section is closer to zero (0) than one (1) because it represents a circle.

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Five different ways to prove the given triangles are similar is given by :

SAS, SSS, ASA, AA, and RHS.

Five different ways to prove triangles are similar is given by:

1. SAS (Side-Angle-Side) : If the corresponding sides of one triangle are in proportion to the other triangle and included angle is of equal measure.

2. SSS(Side-Side-Side): If the corresponding sides of one triangle are in proportion to the other triangle

3. ASA(Angle - Side- Angle) : If the two angles of one triangle are equal to the angles of other triangle and included side is in proportion.

4. AA( Angle-Angle) : If two adjacent angle of one triangle is equal to the measure of other triangle.

5.  RHS(Right angle- Hypotenuse - side). If the hypotenuse and one of one right triangle are in proportion to another.

Therefore, five different ways to prove the given triangles are similar is given by : SAS, SSS, ASA, AA, and RHS.

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Answer:

11111111111111111111

Answer: slope= change in y-intercept and x-intercept

Step-by-step explanation:

1-9=-8

-8- -9=1

-8/1=-8

Answer:

x=12

Step-by-step explanation:

3x+7 = 5x-17

-2x=-24

x=12

Hope this helps you can thank me if this helps and 5 star if you dont mind :)

Answer:

x=12

Step-by-step explanation:

The two sides must be equal in length

3x+7 = 5x-17

Subtract 3x from each side

3x-3x+7 = 5x-3x-17

7 = 2x-17

Add 17 to each side

7+17 = 2x-17+17

24 = 2x

Divide each side by 2

24/2 = 2x/2

12 =x

The required coordinates of point B are (2, 3) which is the correct answer would be option (C).

To find the coordinates of point B, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by the formula (x₁ + x₂)/2, (y₁ + y₂)/2.

As per the question, we are given the coordinates of points A and O, which are (4, 5) and (3, 4), respectively.

We can use these coordinates to find the coordinates of point B, which is the midpoint of line segment AO.

Let the coordinates of B would be (x, y)

Substituting the coordinates of points A and O into the midpoint formula gives us :

3 = (x+4)/2 ; 4 = (y+5)/2

6 = x +4; 8 = y + 5

x = 2; y = 3

Therefore, the required coordinates of point B are (2, 3).

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Answer: 8*8=64

               6*6*=216

64-216+21=0

Step-by-step explanation:

Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

There is only one way to know the unknown variable X. As a result, d has a value of 1. To find an equation, we must know the variable(s) that are missing as well as any associated known variable(s).

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The first-degree equations are linear equations. This is the formula for a straight line. Ax+by+c = 0, where a and b are both zeros, is the conventional form of a linear equation.Anything connected to a line is said to be linear.

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The equation of the quadratic function is (c) f(x) = 3(x - 1)² - 2

From the question, we have the table of values that can be used in our computation:

A quadratic equation is represented as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

From the graph, we have the vertex to be

(h, k) = (1, -2)

Substitute (h, k) = (1, -2) in f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 1)² - 2

Also, from the graph, we have the point (0, 1)

This means that

a(0 - 1)² - 2 = 1

So, we have

a(1) = 3

Divide both sides by 1

a = 3

Substitute a = 3 in f(x) = a(x - 1)² - 2

f(x) = 3(x - 1)² - 2

Hence, the equation is f(x) = 3(x - 1)² - 2

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Answer:

$48/4 pizzas

Step-by-step explanation:

⭐ A ratio is a fraction that relates one variable to another.

⭐ A proportion is when you make two ratios equal to each other to solve for one of the variables.

We want to find what it costs for Mike to buy 4 pizzas. To achieve this, we must make a proportion.

The median is the exact middle number in a sequence or set of numbers.

Steps to find the median is given below:

Finding the Median in an Odd Set of Numbers:

Step 1: Sort your set of numbers from least to greatest. If they're scrambled, line them up, starting with the lowest number and ending with the highest number.

Step 2: Find the number that is exactly in the middle. This means that the median number has the same amount of numbers in front of it as it does behind it.

Finding the Median in an Even Set of Numbers

Step 1: Sort out your set of numbers from least to greatest. An even set of numbers is going to have two numbers exactly in the middle.

Step 2: Find the average of the two numbers in the middle. If 2 and 3 are both in the middle, so you need to add 2 and 3, then divide the sum by 2. The formula for finding the average of two numbers is (the sum of the two middle numbers) ÷ 2.

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Yes, 5 is the high standard deviation which is considered very good.

85 persons responded to my survey about their capacity to carry out specific duties.

The responses are rated on a Likert scale of 1 to 5:

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The length of the guy wire, to the nearest foot, is 201 ft.

Refer to the diagram attached below for the given information

We have two similar right triangles, ΔABE and ΔCDE.

CD = 11 ft

DE = 4 ft

BD = 32 ft

Length of the guy wire (AE)

Since ΔABE ~ ΔCDE, therefore,

AB/CD = BE/DE (proportional sides)

Plug in the values:

AB/11 = (32 + 4)/2

AB/11 = 36/2

Cross multiply:

AB = (36 × 11)/2

AB = 198 ft

Apply Pythagorean Theorem to find AE:

AE = √(AB² + BE²)

AE = √(198² + 36²)

AE = 201 ft (nearest foot)

Therefore, the length of the guy wire, to the nearest foot is 201 ft.

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We have two similar right triangles, ΔABE and ΔCDE.

CD = 11 ft

DE = 4 ft

BD = 32 ft

Length of the guy wire (AE)

Since ΔABE ~ ΔCDE, therefore,

AB/CD = BE/DE (proportional sides)

AB/11 = (32 + 4)/2

AB/11 = 36/2

AB = (36 × 11)/2

AB = 198 ft

AE = √(AB² + BE²)

AE = √(198² + 36²)

AE = 201 ft (nearest foot)

The weekly average proportion of opposed feeling is 0.0375. (Option D)

A sample proportion is the proportion of individuals in a sample who have a particular characteristic of interest. It refers to the number of successes (success means that an individual possesses the characteristic of interest) of the sample divided by the sample size. According to the provided data, the number of successes in the sample size is 30 and the sample size is 100. Hence, the sample proportion is:

Sample proportion = 30/100 = 0.3

As the survey is conducted weekly for eight weeks, the average proportion of the samples is determined by sample proportion divided by number of weeks. Hence,

Average proportion = 0.3/8 = 0.0375

Note: The question is incomplete. The complete question probably is: A Glassboro township is concerned about adverse public reaction to a trash recycling project that is currently in progress. Because of this, the commissioner of public works has authorized a weekly survey to be constructed of township residents. Each week, a sample of 100 residents are questioned on their feeling toward the project. The results to date are shown below. What is the weekly average proportion of opposed feeling? (3 pts.) a. 0.0250 b. 0.1250 c. 0.3000 d. 0.0375 e. None

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The approximate area of the rectangle as per the options will be equal to 15 square units. Hence, option B is correct.

An object's area is how much space it takes up in two dimensions. It is the measurement of the amount of unit squares which completely encompass the surface of a compact figure.

The squared unit, which is frequently expressed as inches, square feet, etc., is the accepted unit of area.

As per the given information in the question,

Let the length is given as, l = √24 and,

The width is given as, w = √10

Use the formula of area of rectangle,

A = lw

A = √24 × √10

A = 4.89 × 3.16

A = 15.45 ≈ 15 square units.

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Katie needs 9.5 quartz of the 12% sugar solution to make the 10% sugar solution.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The volume of the 12% sugar solution required, 'X' for a given volume of the 8% sugar solution, 'Y' is;

X = (2·Y + 15)/2

When the volume of the 8% sugar solution, Y = 2 quartz, the volume of the 12% sugar solution required, X = 9.5 gallons

The data of the sugar solutions are;

The volume of 5% sugar solution Kate has = 3 quarts

The volume of the 12% sugar solution = X

Let 'Y' represent the volume of the 8% sugar solution, we have;

The volume of the resultant solution, Z = X + Y + 3

The concentration of the resultant solution = 10%

0.05 × 3 + 0.08·Y + 0.12·X = 0.1·(X + Y + 3)

Solving gives the relationship between the volume of the 12% sugar solution, 'X', and the 8% sugar solution, 'Y' in quartz, as follows;

X = (2·Y + 15)/2

When the volume of the 8% sugar solution, Y = 2 quartz, we have;

X = (2 × 2 + 15)/2 = 9.5 Quartz

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Negative infinity is a concept that has no direction and function. It is the lowest possible number and is represented by the symbol "-∞".

Negative infinity is the lowest possible number, meaning there is no lower number than negative infinity. It is a concept that has no direction, meaning it is not a specific point on a number line. It is represented by the symbol "-∞", which can be thought of as a point before the beginning of the number line. Negative infinity is an abstract concept, but it is still used in mathematical operations. For example, if you have a set of numbers that contains negative infinity, then the sum of all the numbers in the set will be negative infinity. This is because negative infinity is the lowest possible number, so no matter how large the other numbers in the set are, the sum will always be lower than all of them.Negative infinity can also be used to represent undefined limits. For example, if you are looking at a graph of a function, and the y-axis goes to negative infinity, then the limit of the function at that point is undefined. This is because there is no lower number than negative infinity, so the limit cannot be determined.Negative infinity is a concept that can be confusing, but it is an important part of mathematics. It is used to represent the lowest possible number, as well as undefined limits. It is represented by the symbol "-∞" and has no direction.

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Answer:

I think 11 trips to New York because it's a popular tourist attraction.

Answer:

9.6

Step-by-step explanation:

What is the mean of the following data set 4 8 11 12 13?

Mean: is the average of values so:

(4 + 8 + 11 + 12 + 13) / 5 = 9.6

The factors of the quadratic equation 3x² -4x -4 are (3x + 2)(x - 2)    .

The process of factoring the quadratic equation means expressing the given equation as the product of two linear factors.

The quadratic expression is given as 3x² -4x -4 ;

it can be written as ⇒ 3x² -6x +2x -4    ,...by using split the middle term method .

⇒ 3x(x - 2) + 2(x - 2) ..taking 3x common from first two terms and 2 common from the last two terms .

⇒ (3x + 2)(x - 2)

Therefore , the factors are (3x + 2)(x - 2)  .

The given question is incomplete , the complete question is

What are the factors of the quadratic equation 3x² -4x -4 ?

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D.

The line never increases, so we can cancel out A and C.

The line starts off straight, so it's not B.

So, the answer is D. since it starts off constant and then decreases sharply.

A triangle AAA does not satisfy congruence theorem. Triangle denoted by AAA refers a triangle having three equal side lengths and three equal angles.

Congruence theorem is developed based on two triangles which have equal corresponding side lengths and equal corresponding angles.

there are four criteria in where one or more criteria needed to satisfy. if two triangles have all three equal side lengths and equal corresponding angles then they satisfy congruence theorem. if two triangles have 2 equal side lengths and angle between sides are equal, they satisfy congruence theorem. If two triangles have equal two angles along

with equal similar side length, they satisfy congruence theorem.

hence, the triangle mentioned in the question is not congruent.

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Answer:

FALSE

Step-by-step explanation:

The angles can be the same, but the lengths of the sides can differ.

The radius of the cylinder 37cm.

cylinder's entire surface area is equal to 2r(h+r).

total surface area = 1936 square cm

height=7 cm

radius is

therefore,

2πr(h+r)=1936

2πr(r+7)=1936

44(r+7)=1936

r+7 = 1936/44

r+7=44

r= 44-7 =37

r=37cm.

The radius of the cylinder 37cm.

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Answer:

1st and 3rd 4th

graph of f(x) = x² - 12x-45 has an x-intercept at x = -3

-3 is a zero of the function f(x) = x²-12x- 45

x + 3 is a factor of x² - 12x-45

Steps:

other solution is (x - 15) or x = 15

x² - 12x-45

2 numbers that when multiplied give -45 & when added give -12 are -15 & 3

(x-15) (x+3)

"zero" is a fancy way for asking for the answer or root

imaginary number is i which is √-1 so

if you have √-9 = √9 * √-1 = 3i

if you have √-20 = √4 * √-1 * √5 = 2i√5

.

A- The maximum vertical distance from the water surface to the diver’s

shoulders are 12.061 meters.

B- The time that the diver’s shoulders enter the water is 1.936 seconds.

C- The total distance traveled by the diver’s shoulders from the time

she leaps from the platform until the time her shoulders enter the water is 12.946 meters.

D- The angle, θ between the path of the diver and the water at the instant the diver’s shoulders enter the water is 1.519.

A-  

[tex]\frac{dy}{dx} =0[/tex] only when [tex]t=0.36735[/tex]. Let [tex]b=0.36735[/tex]

The maximum vertical distance from the water surface to the diver’s

shoulders is y(b)=11.4 + [tex]\int\limits^b_0 \frac{dy}{dT} dt = 12.061[/tex] meters.

B-

[tex]y(A)=11.4+\int\limits^A_0 \frac{dy}{dt} dt = 11.4+3.6A- 4.9A^{2} =0[/tex]

when A= 1.936 seconds.

C-

[tex]\int\limits^A_0 {\sqrt{(\frac{dx}{dt} )^{2} + (\frac{dy}{dt} )^{2} } } \, dt = 12.946 m[/tex]

At time A, dy/dx = [tex]\frac{dy/dt}{dx/dt} | _{t=A} = -19.21913[/tex]

D- The angle between the path of the diver and the water is [tex]tan^{-1} (19.21913) = 1.518 or 1.519[/tex]

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In Parallelogram: Area = base x height(perpendicular distance).

In rectangle: Area = base x height.

Parallelogram:

A parallelogram is a particular sort of polygon. It's a quadrilateral in which the opposite side pairs are parallel to one another.

Area = base x height(perpendicular distance)

Rectangle:

Area = base(length) x height(width).

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Step-by-step explanation: