The size of a television screen is measured by the length of the diagonal of the screen. What size is a television screen that is 4 feet tall and 6 feet wide

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: B.

Step-by-step explanation:

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

Answer:

the solution  is (1,-4)

Step-by-step explanation:

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:

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!

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.

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 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:

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

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:

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

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: 36

Step-by-step explanation:

[tex]g(2)=2^{2}=4\\g(3)=3^{2}=9\\g(2) \cdot g(3)=4 \cdot 9=\boxed{36}[/tex]

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

Using it's concept, it is found that the range of the function [tex]f(x) = 9^x[/tex] is given by:

all real numbers greater than 0.

It is the set that contains all possible output values for the function.

In this problem, the function is:

[tex]f(x) = 9^x[/tex]

For exponential functions without vertical shifts, as is the case in this problem, the range is given by:

all real numbers greater than 0.

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Answer:

The square root of 2 is 1.41421

Answer:

The square root of 2 is 1.414

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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[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]

Answer:

14

29  as a fraction

Step-by-step explanation:

Based on the given conditions, formulate:

14=19+14+6）

2 Calculate

14

9+14+6

Calculate

14

23+6

Calculate the sum or difference

14

29

X

Calculate the sum or difference

14

29

Alternative forms

~ 0.482759, ~ 48.275862%,

4.827586 × 10

Hope it help :)

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:

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

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

Answer: number 1 and number 2 and 4 and 5

Step-by-step explanation:

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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