I'm confused I got an answer but got it wrong help please. ​

If ɑ and β are the roots of x² + bx + c = 0, then we can write

x² + bx + c = (x - ɑ) (x - β)

Expanding the right side gives

x² + bx + c = x² - (ɑ + β) x + ɑβ

so that ɑ + β = -b and ɑβ = c.

Recall that for all real numbers m and n,

(m + n)² = m² + 2mn + n²

a) It follows that

(i) ɑ² + β² = (ɑ + β)² - 2ɑβ = (-b)² + c = b² + c

(ii) (ɑ - β)² = ɑ² - 2ɑβ + β² = b² + c - 2c = b² - c

b) I assume you mean to find the quadratic whose roots are ɑ² + β² and (ɑ - β)² (and not (ɑ - 3)²). The simplest quadratic of this form is

(x - (ɑ² + β²)) (x - (ɑ - β)²)

Using the results from part (a), this becomes

(x - (b² + c)) (x - (b² - c))

and expanding, we get

x² - (b² + c + b² - c) x + (b² + c) (b² - c)

= x² - 2b² x + b⁴ - c²

Answer:

C. x = ±4

Explanation:

Given two equation's:

Solve them simultaneously:

 y       =       y

3x² + 15 = 5x² - 17

5x² - 3x² = 15 + 17

2x² = 32

x² = 16

x = ±√16

x = ±4

The boat suspended by wire ropes AB and AD, AC is 4 units high.

An equation is an expression that shows the relationship between two or more variables and numbers.

The gradient of AB is 0.8, hence:

AC / BC = 0.8

Since BC = 5, therefore:

AC / 5 = 0.8

AC = 4

The boat suspended by wire ropes AB and AD, AC is 4 units high.

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Answer:

The square root of 2 is 1.41421

Answer:

The square root of 2 is 1.414

Answer:

  2.7 m

Step-by-step explanation:

Corresponding sides of similar triangles are proportional. This figure shows similar triangles ∆ABC ~ ∆ADE.

__

The proportion that can be used to find h = DE is ...

  DE/BC = DA/BA

  h/(0.9 m) = (12 m+6 m)/(6 m) . . . . . filling in the values given

  h = (0.9 m)(18/6) . . . . . multiply by 0.9 m

  h = 2.7 m

The value of "h" is 2.7 m.

[tex]\boxed{\sf \sum _{n=1}^{20}\:4\left(\frac{8}{9}\right)^{n-1}}[/tex]

       Identify the following:

[tex]\rightarrow \quad \sf S_n = \dfrac{a(r^n - 1)}{r-1}[/tex]

[tex]\rightarrow \sf S_{20} = \dfrac{4(\dfrac{8}{9}^{20} - 1)}{\dfrac{8}{9} -1} \quad\overset{simplify}{\longrightarrow} \quad \dfrac{4\left(9^{20}-8^{20}\right)}{3^{38}} \quad \xrightarrow{\text{In \ Decimals} }\quad 32.58609013[/tex]

The correct answer is option D.which is -4 ≤ x ≤ 1.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

in the graph, we can see that the value of x is increasing from -4 coordinate of x to the 1 coordinate of x so the interval will be given as -4 ≤ x ≤ 1.

Therefore the correct answer is option D.which is -4 ≤ x ≤ 1.

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The product of the expressions (x⁵y³z²) and (x⁴y³z⁶) is equivalent to the expression x⁹y⁶z⁸. Then the correct option is A.

The equivalent is the expressions that are in different forms but are equal to the same value.

The expression is given below.

(x⁵y³z²) and (x⁴y³z⁶)

Then the product of the expression will be

⇒ (x⁵y³z²) (x⁴y³z⁶)

⇒ x⁵x⁴y³y³z²z⁶

⇒ x⁵⁺⁴y³⁺³z²⁺⁶

⇒ x⁹y⁶z⁸

Then the correct option is A.

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Answer:

60

Step-by-step explanation:

The shaded region's area is the difference between the area of the outer rectangle and the white rectangle.

area = LW - lw

area = (4 + 4)(9 + 3) - (4)(9)

area = (8)(12) - 36

area = 96 - 36

area = 60

Answer:

16 feet

Step-by-step explanation:

her first try is 2 and you multiply by 2 every time so her first would be 2 which we would multiply to get 4 which we would multiply again to get 8 which we would multiply AGAIN to get the final answer of 16

The profit would you make if sold 23 silk flower arrangements be  $21.5.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

spend on materials = 220

Price for each flower =10.50

If 23 flowers are sold price would be,

= 10.50*23

=241.5

Hence, the profit would be = 241.5-220

                                             = $21.5

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Answer:D

Step-by-step explanation:when x is 0 we get y=2x3^0=2x1=2

The correct option is D.

A function is defined as a relation between a set of inputs having one output each. a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

Given is a function f(x) = 2·3ˣ, we need to select the correct options regarding the function,

The properties are =

y intercept: y = 2

domain: (-∞, ∞)

decreasing interval: no

Hence the correct option is D.

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The airplane reaches its maximum height of 81 feet in 12 seconds.

If y = [tex]x^{2}[/tex], it means that the second derivate is 2 which is positive, then there is a minimum turning point.

If y = - [tex]x^{2}[/tex], it means that the second derivative will be -2 which is negative, then there is a maximum turning point.

Analysis:

h(t) = -[tex](t - 12)^{2}[/tex] + 81

By expanding,

h(t) = -([tex]t^{2}[/tex] - 24t + 144) +81

h(t) = -[tex]t^{2}[/tex] + 24t - 144 + 81

h(t) = -[tex]t^{2}[/tex] + 24t - 63

at turning point d/dt(h(t)) = 0

d/dt (h(t)) = -2t +24

-2t +24 = 0

if we differentiate again, second derivative is -2 which is negative, so it is a maximum point.

2t = 24

t  = 12 seconds

h(t) at t = 12

h(t) = [tex]-(12)^{2}[/tex] + 24(12) - 63 = 81 feet

In conclusion, the maximum height of the airplane after 12 seconds is 81 feet.

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Answer:

the solution  is (1,-4)

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

[tex]\text{Given that,}~ (x_1,y_1) = (-2,4)~ \text{and}~ \text{slope,}~ m = -\dfrac 32\\ \\\text{Equation of line,}~\\\\~~~~~~~y -y_1 = m(x-x_1)\\\\\implies y -4 =-\dfrac 32(x+2)\\\\\implies y-4 =-\dfrac 32x - 3\\\\\implies y = -\dfrac 32x -3 +4\\\\\implies y = -\dfrac 32x +1[/tex]

The current equation of the perpendicular line;

 ⇒ is the slope-intercept form: [tex]y= mx + b[/tex]

Now for the point-slope form, we need a point on the line and the slope of the line:

⇒ we have

Since this is the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex]

 ⇒ where the (x₁,y₁) is the point on the line and m is the slope

    [tex]= > Equation: (y-4)=-\frac{3}{2}(x+2)[/tex]

To convert the equation to slope-intercept form:

  ⇒ must isolate 'y' to one side and everything to the other side

      [tex]y= -\frac{3}{2}(x+2)+4\\ y=-\frac{3}{2} x-3+4\\y=-\frac{3}{2}x+1[/tex]

Answer: [tex]y = -\frac{3}{2}x+1[/tex]

Hope that helps!

El volumen es una cantidad escalar tridimensional. El volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm es 58,904.863 cm³.

Un volumen es un número escalar que expresa la cantidad de espacio tridimensional encerrado por una superficie cerrada.

El volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm será,

Volumen del cilindro = (π/4)×diámetro ²×altura

                                = (π/4)×(50cm)²×30cm

                                = 58,904.863cm³

Por lo tanto, el volumen de la pecera con un diámetro de 50 cm y una altura de 30 cm es 58,904.863 cm³.

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Answer: [tex](x+3)^{2}+y^{2}=5[/tex]

The equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3

The expression is given as:

9q^ 2 - 2/3(3q - 7) + 5q^2

Open the bracket

9q^ 2 - 2q - 14/3 + 5q^2

Evaluate the like terms

14q^ 2 - 2q - 14/3

Hence, the equivalent expression of 9q^ 2 - 2/3(3q - 7) + 5q^2 is 14q^ 2 - 2q - 14/3

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Answer:

P(5 ≤ X ≤ 8)  = a  rectangle  with a width of 3  and height of .15   = 3(.15)  = .45

P( 4 ≤ X ≤ 5)  =  a triangle  with a base of 1  and a height of (0.15 -0.05) = .10

So....this area  =   (1/2)(1)(.10)  = .05

And  another rectangle with a width of 1 and height of .05  = (1) (.05) = .05

So

Adding these areas

P( 4 ≤ X ≤ 8 )  =  .45 + .05 + .05   =  .55

Step-by-step explanation:

Hoped this helped!

Answer:

hello how are you nice to meet you

An equation that can be used to determine how much each cookie cost originally is ($13.32 + $7) / 16.

A coupon reduces the price of an item. Thus, the amount paid by Louis would be lower than the original price.

Original price = coupon + price paid

($13.32 + $7)

The cost per cookie, can be determined by dividing the original price by the total number of cookies bought.

($13.32 + $7) / 16

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Answer:

Step-by-step explanation:

Givens

Number of cookies = 16

Deduction =  7

Final Cost = 13.31

Equation

16c - 7 = 13.31

Solution

You are not asked for a solution but I'll put it here anyway.

16c - 7 = 13.32                      Add 7 to both sides

16c -7+7 = 13.32+ 7              Combine

16c = 20.32                          Divide by 16

16c/16 =  20.32/16                

c = 1.27

The maximum displacement of the tuning fork is 0.4 mm

A tuning fork is a acoustic resonator , It is used to tune musical Instruments.

It is given in the question that the

displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d = 0.4 sine (1760 pi t).

the maximum displacement of the tuning fork = ?

The equation for a sine function is given by

f(t) = A sin(Bt + C) + D

here A is the maximum Displacement

When this equation is compared with the given equation

d = 0.4 sine (1760 pi t).

A = 0.4

The maximum displacement of the tuning fork is 0.4 mm

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Answer: number 1 and number 2 and 4 and 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Part A

Neighborhood A :

2, 2, 2, 4, 4, 5, 5, 5, 5

mean = [tex]\frac{2+2+2+4+4+5+5+5+5}{9}[/tex] = [tex]\frac{34}{9}[/tex] ≈ 3.8  

median = 4

mode = 5

range = 3

[tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 5 - 2 = 3

===================

Part B.

Neighborhood B :

1, 1, 2, 2, 3, 4, 5, 5, 12

mean = ( 1 + 1 + 2 + 2 + 3 + 4 + 5 + 5 + 12 ) ÷ 9 = [tex]\frac{35}{9}[/tex] ≈ 3.9

median = 3

mode = 1, 2, 5

range = 11

[tex]Q_{3}[/tex] - [tex]Q_{1}[/tex] = 5 - 1.5 = 3.5

Outlier = 12

Step-by-step explanation:

[tex] \frac{x}{6} = \frac{9}{20} \\ [/tex]

[tex]x \times 20 = 9 \times 6[/tex]

[tex]20x = 54[/tex]

[tex]x = \frac{54}{20} \\ [/tex]

[tex]x = 2.7[/tex]

Answer:

92 x 49 = 4,508

Step-by-step explanation:

According to the texts, she sold 92 blankets in her first month, bringing her total sales to 92, and each blanket cost $49.

Answer:

c

cuz it is

first of all 4,3 + 0,0 = 4,3

2,1+0,0 = 2,1

and which is the answer

Answer: B.

Step-by-step explanation:

   See attached. We examine the equation and decide which situation, or problem, models it correctly.