Question: The graph of a second-order polynomial is shown below, and the intercepts with the axes are marked. Explain how you can use the graph to write the polynomial as a product of linear factors (x-a)(x-b). Be sure to state the values of a and b. NEED HELP ASAP​

Answer:

A)

The "Standard Form" for writing down a polynomial is to put the terms with the highest degree first.

For example, the polynomial f(x)=x5+2x3−x2+2x+1 is in standard form because the highest degree terms are kept first.

B)

The problem 3 + 6 = 9 demonstrates the closure property of real number addition.

Observe that the addends and the sum are real numbers.

The closure property of real number addition states that when we add real numbers to other real numbers the result is also real.

In the example above, 3, 6, and 9 are real numbers  

Part(A),

The standard form of the polynomial is 3x⁴ - 2x³ + 5x² + 7x - 1.

Part(B),

This is another polynomial, so the closure property holds. Similarly, if we subtract or multiply these polynomials, the result is always another polynomial.

2x³ - 4x² - x + 8

A polynomial is a mathematical statement made up of exponents, coefficients, and variables, which are frequently denoted by the symbol x. (numbers that indicate the power to which the variable is raised).

Part A:

An example of a polynomial in standard form is:

3x⁴ - 2x³ + 5x² + 7x - 1

This polynomial is in standard form because the terms are written in descending order of degree, and each term has a coefficient and a variable raised to a power.

Part B:

The closure property of polynomials states that if we add, subtract, or multiply two polynomials, the result is always another polynomial.

For example, consider the polynomials:

f(x) = 2x³- 5x² + 3x + 1

g(x) = x² - 4x + 7

If we add these polynomials, we get:

f(x) + g(x) = 2x³ - 4x² - x + 8

This is another polynomial, so the closure property holds. Similarly, if we subtract or multiply these polynomials, the result is always another polynomial.

The closure property is important in algebra because it ensures that the operations we perform on polynomials are always well-defined and meaningful.

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Answer:

a = -3

Step-by-step explanation:

-3 + (14 * -3) + 45 = 0

-3 + -42 + 45 = 0

-3 + 3 = 0

So, the answer is -3

Hope this helps! :)

Answer:

(f + g)(x) = 4x + 1

Step-by-step explanation:

(f + g)(x) = f(x) + g(x) = x - 4 + 3x + 5 = 4x + 1

Answer:

Step-by-step explanation:

Total songs = 8 + 4 + 2 = 14 songs

number of rock songs = 2

Number of rap songs = 4

Probability of rock songs = 2/14 = 1/7

Probability of rap songs = 4/14 = 2/7

Answer:

3

Step-by-step explanation:

Answer:

B.a=b, c≠0

C.a=b, c=0

D.a-b=1, c≠1

Step-by-step explanation:

The equation given is c = ax - bx. We can factor the right-hand side to obtain an equivalent equation which is c = (a-b)x

Let’s explore each answer choice given. We are looking for cases where there is no one solution for the equation.

A

a-b = 1 so the right-hand side becomes 1x and we have x=c. Since c is 0 we have one solution that is x=0

B

a=b so a-b =0 and the equation becomes 0=c but the answer choice says c does not equal zero. So in this case there is no solution. This is a correct answer to the problem.

C

This is the same as choice B but since C =0 both sides of the equation equal zero. We get 0=0 but notice that this is true no matter what the value of x is so this equation is called identity and any value of x will do so there isn’t one solution but rather infinitely many. This is another right answer.

D

Here a-b=1 so we end up with x = c and since c doesn’t equal one any value of x except 1 is a solution so there isn’t one solution but infinitely many. This too is an answer to the question.

E

Since a doesn’t equal b and since c = 0 we have (a-b)x = 0 so. Either a-b is zero but since a and b are different this can’t be or x is zero. This there is one solution: x=0.

From the above, the answer to the question is choices B, C, and D

Answer:

The top number in a fraction. Shows how many parts we have. (The bottom number is the Denominator and shows how many equal parts the item is divided into.)

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

⟨-5, -1⟩

Step-by-step explanation:

Vector:

A vector is given by its endpoint subtracted by its initial point.

Vector u has initial point at (3, 9) and terminal point at (–7, 5)

Then

[tex]u = (-7, 5) - (3,9) = (-7 - 3, 5 - 9) = (-10,-4)[/tex]

Vector v has initial point at (1, –4) and terminal point at (6, –1).

Then

[tex]v = (6,-1) - (1,-4) = (6-1,-1-(-4)) = (5,3)[/tex]

What is u + v in component form?

[tex]u + v = (-10,-4) + (5,3) = (-10+5,-4+3) = (-5,-1)[/tex]

⟨-5, -1⟩ is the answer.

Answer:

The proposed negation is not correct. A possible corect negation woulld be: There is an irrational number and, a rational number whose product is rational.

Step-by-step explanation:

From the given information above:

STATEMENT: "The product of ANY irrational number and ANY rational number is irrational".

From the above statement, the word "ANY" is very vital. Let assume we choose an element x from a particular set X of irrational numbers, as well as an element y from the set Y of a rational number, therefore, the statement has a use case and applies to every x and y element. Thus, in an effective mathematical way, the statement typically implies "for all x in set X and for all y in set Y, the product x*y is irrational.

However; from the negation of the "for all" statement is "there exists" (any text in discrete arithmetic will assist you to become fully aware of this fact). Any ramifications in the statement is likewise negated, i.e; if the statement infers that the resulted product of x and y is irrational, at that point the negation(invalidation) infers that the item isn't irrational. For example, it is rational. At the point when we set up every one of these facts, we get:

"There exist an element x in the set X, in addition to that; there exists an element y in set Y;  x*y is rational".

If we express that into the option given; the right option is:

"There exist an irrational number and a rational number whose product is rational"

Answer:

I have questions in physics if you know it answer it

Answer:no

Step-by-step explanation:

the (x) fators out more than once

Answer:

ITS RED

Step-by-step explanation:

Answer:

the red one/ fgh=vwh

Step-by-step explanation:

Answer:

3739.3

Step-by-step explanation:

Equation for an area of a circle: A=πr ^ 2

Radius is half the diameter, so r = 69 / 2 = 34.5

A = π * 34.5 ^ 2 = 3739.3 cm squared

Answer:

Quad III

Step-by-step explanation:

III.

Answer:

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The answer is given,

1.n - 2 = 52

2.x - 3 = 12

3.5 + x = 50 - 10

4.3 + x = 60

5.x + 6 = 10 - 2

6.x - 9 = 12

7.x + 5 = 13

8.x + 10 = 20

9.5x = 25

10.2x = 5 + 2

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

here, we have,

as the description given,

we get,

1.n - 2 = 52

2.x - 3 = 12

3.5 + x = 50 - 10

4.3 + x = 60

5.x + 6 = 10 - 2

6.x - 9 = 12

7.x + 5 = 13

8.x + 10 = 20

9.5x = 25

10.2x = 5 + 2

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Answer:

Step-by-step explanation:

There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:

P = 2w + l; solving for l and filling in our length of fencing gives us:

l = 148 - 2w

The area then for this will be:

A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:

[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:

[tex]A=-2w^2+148w[/tex]

The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.

To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:

[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:

[tex]-2(w^2-74w)=0[/tex]

The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:

[tex]-2(w^2-74w+1369)=...[/tex]

But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:

[tex]-2(w^w-74w+1369)=-2738[/tex]

The left side can be simplified down to a perfect square binomial:

[tex]-2(w-37)^2=-2738[/tex]

Now we'll add over the -2738:

[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.

Answer:

600000Ω

Step-by-step explanation:

1μA = 10⁻⁶ A

200μA = 0.0002 A

Potential difference = V = 120 V

Current = I = 0.0002 A

Resistance = R

R = V / I

  = 120 / 0.0002

  = 600000Ω

Might Want to draw this and Its very long but Hope it helped :)

Answer:

The sides are all of the same length - let's say a. The angles are all the same too, and since the angles must add up to 180∘, we conclude that the three angles in the equilateral triangle are equal to 180∘/3=60∘.

Now we do something sneaky. We draw a line all the way down from the top vertex of the triangle to the midpoint of the bottom line.

This new line cuts our equilateral triangle in half. What are the angles in one half?

The angle at the bottom is 90∘.

One of the angles is the same as one of the angles in the original equilateral triangle, so it is 60∘.

So the third angle must be 180∘−90∘−60∘=30∘.

Now the hypotenuse of this new triangle is a, the side length of the equilateral triangle. And the length of the shortest side is a/2, since the line we drew cut the bottom line in half.

Answer:

9.76

Step-by-step explanation:

area of a rectangle = length * breadth

length = (2x + 3)

breadth = x

given area is 220 sq. inches.

thus,

220 = x * (2x+3)

220 = 2x² +3x

2x² + 3x -220 = 0

x = (-b + √ ( b²-4ac) ) ÷ 2a

x = ( -3 + √ ( 3² - 4*2*220) ) ÷ 2*2

x =9.76

Answer:

∠RQS = 21°

∠TQU = 28°

Step-by-step explanation:

90° + 221° + 3x + 4x = 360°

combine like terms:

7x + 311° = 360°

subtract 311° from each side of the equation:

7x = 49°

divide both sides by 7:

x = 7°

∠RQS = 3x = 3(7°) = 21°

∠TQU = 4x = 4(7°) = 28°

Answer:

A= 160 in. squared

Step-by-step explanation:

Answer:

25 feet

Step-by-step explanation:

Use the pythagorean theorem, where the width and length of the pool are the legs of the triangle.

Solve for c, the hypotenuse/diagonal

a² + b² = c²

15² + 20² = c²

225 + 400 = c²

625 = c²

25 = c

So, the length of the diagonal is 25 feet