Identify the simplest polynomial function having integer coefficients with the given zeros. 0,-4,√3.

A. P(x) = x^4 + 4x³ - 3x² -12x
B. P(x) = x^4 + 4x³ -12x² - 3x
C. P(x) = x³ + 4x² - 12x - 3
D. P(x) = x³ + 4x² - 3x - 12

Step-by-step explanation:

[tex]midpoint = ( \frac{(2 + 8)}{2} , \frac{(3 + 9)}{2} ) \\ = (5,6)[/tex]

Answer:

√(x2-x1)²+(y2-y1)²

√(8-2)²+(9-3)²

√6²+6²

√36+36

√72

8.48528137424≈8.5

Step-by-step explanation:

Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex],

where a and b are positive integers.

The value of a + b is 96.

Let mid-point of DC be E and mid-point of AB be F.

Since [tex]$\mathrm{O}_1$[/tex] and [tex]$\mathrm{O}_2$[/tex] are circumcenters, therefore both lie on the perpendicular bisectors of DC and AB passing through E and F.

Now, [tex]$\mathrm{O}_1 \mathrm{P}=\mathrm{O}_1 \mathrm{~B}$[/tex] and [tex]$\mathrm{O}_2 \mathrm{P}=\mathrm{O}_2 \mathrm{D}$[/tex]

Also [tex]$\angle \mathrm{CAB}=\angle \mathrm{ACD}=45^{\circ}$[/tex]

Therefore [tex]\angle \mathrm{BO}_1 \mathrm{P}=2 \times 45^{\circ}=90^{\circ}=\angle \mathrm{DO}_2 \mathrm{P}$[/tex]

Angle subtended by an arc of a circle at its center = 2 × the angle subtended at its circumference

Therefore [tex]\angle \mathrm{O}_1 \mathrm{~PB}$[/tex] and [tex]$\angle \mathrm{O}_2 \mathrm{PD}$[/tex] are isosceles right triangles.

Using the above information and symmetry,

[tex]$\angle \mathrm{DPB}=120^{\circ}$[/tex]

Also, [tex]$\triangle[/tex]ABP is congruent to [tex]$\triangle[/tex]ADP (SAS)

and [tex]$\triangle[/tex]CPB is congruent to [tex]$\triangle[/tex]CPD (SAS)

Therefore [tex]\angle \mathrm{APB}=\angle \mathrm{APD}=60^{\circ}[/tex]

And [tex]\angle \mathrm{CPB}=\angle \mathrm{CPD}=120^{\circ}[/tex]

Now, [tex]$\angle \mathrm{ABP}=(180-60-45)^{\circ}=75^{\circ}$[/tex]

[tex]\Rightarrow \angle \mathrm{O}_1 \mathrm{BF}=30^{\circ}[/tex]

And [tex]$\angle \mathrm{PDC}=(180-120-45)^{\circ}=15^{\circ}$[/tex]

[tex]\Rightarrow \angle \mathrm{O}_2 \mathrm{DE}=30^{\circ}[/tex]

Therefore [tex]\triangle \mathrm{O}_1 \mathrm{BF}$[/tex] and [tex]$\triangle \mathrm{O}_2 \mathrm{DE}$[/tex] are right angled triangles.

BF = DE = [tex]\frac{12}{2}[/tex] = 6

[tex]\Rightarrow O_1 B=O_2 D=4 \sqrt{3}[/tex]

And  PB = PD = [tex]\frac{4 \sqrt{3}}{\cos 45^{\circ}}=4 \sqrt{6}[/tex]

Now, Let x = AP

Using law of cosine on [tex]$\triangle[/tex]ABP, we have

[tex]& 96=x^2+144-24 x \times \frac{1}{\sqrt{2}} \\[/tex]

[tex]& \Rightarrow x^2-12 \sqrt{2} x+48=0 \\[/tex]

[tex]& \Rightarrow x=\sqrt{72} \pm \sqrt{24}[/tex]

Taking the positive root, AP = [tex]\sqrt{72}+\sqrt{24}$[/tex]

Therefore a + b = 72 + 24 = 96

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Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex], where a and b are positive integers. Find a + b. (correct answer +5, wrong answer 0 )

On solving the provided question, we can say that - here in the given equation we got x- 1 = 0; x = 1, y = 2

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

y = 2x +1

y = 3x - 1

x- 1 = 0

x = 1, y = 2

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Answer: x = 3

Step-by-step explanation:

-3 +9x = 24

9x= 24+3

9x=27

9x/9= 27/9

x=3

Answer:

x = 3

Step-by-step explanation:

-3 + 9x = 24

rearrange:

9x - 3 = 24

Add 3 to both sides of the equation:

9x - 3 + 3 = 24 + 3

9x = 27

Divide both sides by 9:

9x/9 = 27/9

x = 3

Have a nice day!

Answer:

a = 4√2, h = 2√3

Answer:

The vertex is (-4, -9)

Step-by-step explanation:

The two roots are located at x = -7 and x = -1, which come from (x + 7) and (x + 1).  The axis of symmetry is located halfway between these values, at x = -4.  This axis passes through the vertex.  The y-value at the vertex is (-4 + 7)(-4 + 1), or -9.  The graph is a parabola that opens up.  The vertex is (-4, -9).

Answer:

114.12

Step-by-step explanation:

The measure of the missing length of the trapezoid is equal to 3√39 units.

Trapezoids are quadrilaterals with only one pair of congruent sides and two pairs of congruent angles. The relationship between the longest and shortest legs (D, d) in a trapezoid is defined below:

D = d + 2 · c

Where c is the length of the horizontal leg of the right triangle in a trapezoid.

And the missing leg can be found by means of Pythagorean theorem:

x = √(r² - c²)

Where:

First, determine the length of shortest leg: (D = 40, d = 26)

40 = 26 + 2 · c

14 = 2 · c

c = 7

Second, find the longest leg by Pythagorean theorem:

x = √(20² - 7²)

x = 3√39

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Answer:

Step-by-step explanation:

For every 3 quetzals there are four axolotls and for every 8 axolotls there are 5 Mexican wolves, if there is a population of 150 quetzals, how many axolotls are there? And how many Mexican wolves are there?

Answer:

look at the photo x is the red and y is the blue

The 40 50 90 triangle can be solved using Pythagoras theorem.

A triangle in which both legs are congruent, and the length of the hypotenuse is the length of a leg times the square root of 2.

Given:

We have 40 50 90 triangles.

A triangle with two equal legs whose hypotenuse measures one leg's length multiplied by the square root of two.

Because the length of the hypotenuse in the triangle above equals the length of one of its legs times sqrt(2), which is 3, the triangle is a 40-50-90 triangle.

So, Such type of Triangles can be solved using Pythagoras theorem.

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Answer: 20$

5$ for each person attending. Hope it helps.

Answer:

$20

Step-by-step explanation:

the unit rate (cost per person) is

 $15

-------------- = $5/person

3 people

For four people the total cost would be (4 people) ($5/person) = $20

Answer:

yes

Step-by-step explanation:

according to pythagoras theorem = hypotenuse² = √ base²+perpendicular²

so 21² + 28² = 35²

Answer:

A. 35 million

B. $1519 increase

$7719 year end

Step-by-step explanation:

Answer:

40,000

Step-by-step explanation:

can I have branliest

Answer: 40,000

Step-by-step explanation: Well it doubles every 440 minutes. Since it is asking for the size after 880 minutes, and the starting size is 20,000 just double 20,000 because 440 times 2 equals 880.

Answer:

300 words in 6 minutes

300/6 words in 1 minutes

50 words in 1 minutes

Therefore,Lee can type 50 words in 1 minute.

Answer:

Infinutely many solutions

Step-by-step explanation:

y = 10x + 2 --------- (1)

y = 8x +2x +2

=> y = 10x + 2---------- (2)

(1) -> 10x -y + 2 = 0

(2) -> 10x -y + 2 = 0

a1=10 ; b1=-1 ; c1 = 2

a2=10 ; b2=-1 ; c2= 2

a1/a2 = 10/10 = 1

b1/b2 = -1/-1 = 1

c1/c2 = 2/2 = 1

therefore, a1/a2 = b1/b2 = c1/c2

Therefore the line coincides and there are infinitely many solutions.

The percent discount on the new phone is 15%.

Discount refers to a reduction in the original price of a product or service. It is a way for businesses to incentivize customers to purchase their products by offering a lower price than the original price.

To find the percent discount, we need to divide the amount of the discount by the original price, and then multiply by 100 to express the answer as a percentage.

Discount = Original Price - Sale Price

Discount = $46 - $39.10

Discount = $6.90

Percent Discount = (Discount / Original Price) x 100

Percent Discount = ($6.90 / $46) x 100

Percent Discount = 15%

Therefore, the percent discount is 15%.

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Answer:

7

Step-by-step explanation:

a^2 + b^ = c^2

x^2 + 24^2 = 26^2

x^2 = 100

x=10

Can i have brainliest please

Answer:

x = 10

Step-by-step explanation:

This is a right triangle problem

use the Pythagorean Theorem

a^2 + b^2 = c^2

x^2 + 24^2 = 26^2

x^2 + 576 = 676

Subtract 576 from both sides

x^2 = 100

Take the square root of both sides

x = 10

Answer:

80

Step-by-step explanation:

[tex]6\frac{2}{3} *12[/tex]

First, write the fractions as improper fractions.

[tex]\sf\frac{20}{3} *\frac{12}{1}[/tex]

Multiply.

[tex]\sf\frac{240}{3}[/tex]

Divide.

80

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6\dfrac{2}{3}\times 12}[/tex]

[tex]\mathsf{= \dfrac{6\times3+2}{3}\times\dfrac{12}{1}}[/tex]

[tex]\mathsf{= \dfrac{18 + 2}{3} \times\dfrac{12}{1}}[/tex]

[tex]\mathsf{= \dfrac{20}{3} \times\dfrac{12}{1}}[/tex]

[tex]\mathsf{= \dfrac{20\times12}{3\times1}}[/tex]

[tex]\mathsf{= \dfrac{240}{3}}[/tex]

[tex]\mathsf{= 240\div 3}[/tex]

[tex]\mathsf{= 80}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{80}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

184ft^2

Step-by-step explanation:

W have to find the area of triangles and rectangles and add them together to get the total area of the figure:

Area of triangles = 1/2(b)(h)

Area of rectangles = l x w

6 x 10 = 60

1/2(6)(4) = 12 (We can make this 12 a 24 because there are two of these triangles)

5 x 10 = 50 (We can also make this 50 a 100 because there are two of these rectangles)

100 + 24 + 60 = 184ft^2

Answer:

V  =  38.47 in^3

Step-by-step explanation:

The container base radius is half the diameter, that is, 1.75 in, and the height is 12 in.  The formula for the volume of a cylinder of radius r and height h is V = (1/3)(pi)(r)^2h, which in this particular case comes out to:

V = (1/3)(3.14)(1.75 in)^2*(12 in), or

V  =  38.47 in^3

Answer:

115.40 in3

that is the correct answer to this question.

The partial fraction expansion of (x³ + 4)/ ((x² - 1)(x² + 3x + 2)) is -3/ 4(x + 1) + 5/12(x - 1) + 4/3(x + 2) - 3/ 2(x + 1)². So the coefficients A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2.

A partial fraction expansion is a way of expressing a rational function (a function that can be written as the ratio of two polynomials) as the sum of simpler fractions, each with a numerator that is a constant or a simple polynomial. The process of finding the partial fraction expansion of a rational function is also known as partial fraction decomposition.

The denominator is

(x² - 1)(x² + 3x + 2) = (x² - 1)(x² + x + 2x + 2)

(x² - 1)(x² + 3x + 2) = (x + 1)(x - 1)(x + 1)(x + 2)

So by  partial fraction expansion

(x³ + 4)/ ((x² - 1)(x² + 3x + 2)) = (x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2))

(x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2)) = A/ (x + 1) + B/(x - 1) + C/(x + 2) + D/ (x + 1)²

A(x - 1)(x + 1)(x + 2) + B(x + 1)²(x + 2) + C(x + 1)²(x - 1) + D(x - 1)(x + 2) = x³ + 4

(A + B + C)x³ + (2A + 4B + C + D)x² + (-A + 5B - C + D)x + (-2A + 2B - C - 2D) = x³ + 4

Thus from coefficients of x³, x², x and 1,

A + B + C = 1

2A + 4B + C + D = 0

-A + 5B - C + D = 0

-2A + 2B - C - 2D = 4

Solving

A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2

--The question is not clear, the question is given below--

"Enter (A,B,C,D) in order below if A, B, C, and D are the coefficients of the partial fractions expansion of

[tex]$$12\cdot\frac{x^3 + 4}{(x^2-1)(x^2 +3x+ 2)}[/tex]  "

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Answer:

Step-by-step explanation: If the sides are a,b,c (in ascending order) and c squared = the sum of the squares of a and b, then it's a right triangle.

Answer:

No, it is not a right triangle.

Step-by-step explanation:

Right triangle fulfill the pythagorean theorem:

[tex]a^2+ b^2 = c^2[/tex]

Where, c is the hypothenuse or the longest side, and b and a are the remaining two sides.

[tex]12^{2} = 144\\16^2 = 256\\256 + 144 = 400\\\sqrt {400} = 20 \neq 18[/tex]

Answer:

80x

Step-by-step explanation:

There is no substitution for the variable so the expression is 80x

Answer:

yes

Step-by-step explanation:

yes

yes

yes

yes

yeyed

yes

answer: 47.5 cups

Step-by-step explanation:

2.50 x 19 = answer