5. Given no other restrictions, what are the domain and range of the following function?
f(x) = x2 – 2x + 2
OD= all real numbers
R = {yl y> 1}
OD = {xx> 1}
R= all real numbers
OD = all real numbers
R= {yly<1}
OD = {x|x>0}
=
R = all real numbers

Answer:

The value of the notebook at the end of 2013 is $980

Step-by-step explanation:

First, find 30% of 2,000. To do so you need to convert 30% into a decimal by dividing it by 100.

30% ⇒ 0.30

Now multiply 0.30 by 2,000 to find 30% of 2,000.

2,000 × 0.30 = 600

Subtract 600 from 2,000 to find the price of the notebook in 2013.

2,000 - 600 = 1,400

Now find 30% of 1,400 using the same process.

1,400 × 0.30 = 420

Subtract 420 from 1,400 to find the price of the notebook in 2014.

1,400 - 420 = 980

Of 103 people that are considered to use two facilities, only 14 use all three. In this case, we must make a percentage of this information.

This is roughly 14.5%, meaning there is only a 14.5% chance someone will use all three facilities if they are known to use two.

The probability that a randomly selected person uses at least two facilities is 103/135 and the probability that the selected people uses all the three facilities is 14/103.

Probability is the likeliness of an event to happen, it has a range from 0 to 1.

The number of people using the facilities are

73 people use the gym.

73 people use the swimming pool.

67 people use the track.

36 people use the gym and the pool.

35 people use the pool and the track.

32 people use the gym and the track.

14 people use all three facilities.

The total people using two facilities is = (36+32+35 ) = 103

Total number of people is 135

The probability that a randomly selected person uses at least two facilities is 103/135.

The probability that the selected people uses all the three facilities is 14/103.

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Answer:

um

Step-by-step explanation:

Hope you could get an idea from here.

Doubt clarification - use comment section

Hey there! I'm happy to help!

Since we are using graphs, we will do not need to algebraically solve this system of equations.

When you graph a system of equations, the solution is always the point at which the two lines intersect.

Here is our system of equations graphed. We see that the lines intersect at about (1 1/3, 2 1/3). Therefore, the correct answer is C. x=1 1/3, y=2 1/3

Have a wonderful day! :D

Answer:

A.) 4/5

Step-by-step explanation:

Another fraction that's not on there that is correct is 8/10

384 +37289 x 638203

then you will get the calculation

Answer:

its option c i believe

Answer: C

Step-by-step explanation: The range of a function is all the outputs, or in this case all the values on the right side of the function. Therefore, we just look at what numbers are there and we find the range

Answer:

A. x = 4

B. RQ = 6

C. 48 square units

Step-by-step explanation:

A. 3x - 2 = 10

3x = 12

x = 12/3

B. a^2 + b^2 = c^2

8^2 + b^2 = 10^2

64 + b^2 = 100

b = sqrt (100 - 64

b = 6

C. Area of a triangle = (b*h)/2

b = (2)(6) = 12

Area = (12 * 8)/2 = 48 square units

Answer:

[tex]f(x)\div g(x)=x-10[/tex]

Step-by-step explanation:

[tex]\frac{x^2-19x+90}{x-9}[/tex]

[tex]\frac{(x-10)(x-9)}{x-9}[/tex]

[tex]x-10[/tex]

Answer:

[tex]f(x)\div g(x)=-10[/tex]

Step-by-step explanation:

Solve [tex]f(x)[/tex]

[tex]f(x)=x^2-19x+90[/tex]

[tex]x^2-19x+90[/tex]

[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]

[tex]\left(x^2-9x\right)+\left(-10x+90\right)[/tex]

[tex]\mathrm{Factor\:out\:}x\mathrm{\:from\:}x^2-9x[/tex]

[tex]=x(x-9)[/tex]

[tex]\mathrm{Factor\:out\:-10\;from}\:\:-10x+90[/tex]

[tex]=-10(x-9)[/tex]

[tex]=x\left(x-9\right)-10\left(x-9\right)[/tex]

[tex]\mathrm{Factor\:out\:common\:term\:}x-9[/tex]

[tex]\bold{\left(x-9\right)\left(x-10\right)}[/tex]

Solve [tex]g(x)[/tex]

[tex]g(x)=x-9[/tex]

[tex]\bold{x-9}[/tex]

[tex](x-9\right)\left(x-10)}\div \:x-9[/tex]

Now, solve:

[tex](x-9\right)\left(x-10)}\div \:x-9[/tex]

[tex]=\frac{(x-9)\left(x-10)}{:x-9}[/tex]

[tex]= -10[/tex]

Therefore, [tex]f(x)\div g(x)=-10[/tex]

The function of the polynomial is (b) [tex]f(x) = (x + 2) ^ 2 * (x - 3) * (x + 1)[/tex]

From the graph, we have the following highlights

The above highlights mean that:

So, the function of the polynomial is:

[tex]f(x) =a(x + 2)^2(x + 1)(x - 3)[/tex]

Assume a = 1.

So, we have:

[tex]f(x) =1(x + 2)^2(x + 1)(x - 3)[/tex]

Multiply

[tex]f(x) =(x + 2)^2(x + 1)(x - 3)[/tex]

Hence, the function of the polynomial is (b) [tex]f(x) = (x + 2) ^ 2 * (x - 3) * (x + 1)[/tex]

Read more about polynomial graphs at:

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Answer:

y=10x+10

Step-by-step explanation:

Answer:

  x = {-2 5/6, +2}

Step-by-step explanation:

To use the quadratic formula, it is helpful to write the equation in standard form.

  (2x +1)(3x +1) = 35

  6x^2 +5x -34 = 0 . . . . . . . subtract 35 and simplify. a=6, b=5, c=-34

The quadratic formula tells you the values of x are ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-5\pm\sqrt{5^2-4(6)(-34)}}{2(6)}\\\\=\dfrac{-5\pm\sqrt{841}}{12}=\dfrac{-5\pm29}{12}\\\\\boxed{x=\left\{-\dfrac{17}{6},2\right\}}[/tex]

Answer:

y = 7x -26

Step-by-step explanation:

[tex]y-9=7(x-5)[/tex]

[tex]y=7x-35+9[/tex]

[tex]y=7x-26[/tex]

Hope this helps

Answer:

96

Step-by-step explanation:

C=πd

C=?

π=3

d=32

C=3×32

Therefore C=96

Answer:

7 ^2 ⋅ 7 ^4 = 49^6

Step-by-step explanation:

7² / 7 ⁻⁴

= 7²⁻⁽⁻⁴⁾

= 7 ⁽²⁺⁴⁾

= 7⁶

= 117649

Remember :-

xᵃ / xᵇ = xᵃ⁻ᵇ

___

Hope it helps ⚜

⁽

Answer: The equation is not an identity

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

Explanation:

We'll expand out the right hand side to see if we can simplify it to the left hand side. The stuff on the left will stay the same for each step.

I'll use  c = a+b as a way to help distribute.

[tex]a^4 + b^4 = (a+b)(a^3 - a^2b-ab^2 + b^3)\\\\a^4 + b^4 = c(a^3 - a^2b-ab^2 + b^3)\\\\a^4 + b^4 = a^3c - a^2bc-ab^2c + b^3c\\\\a^4 + b^4 = a^3(c) - a^2b(c)-ab^2(c) + b^3(c)\\\\a^4 + b^4 = a^3(a+b) - a^2b(a+b)-ab^2(a+b) + b^3(a+b)\\\\a^4 + b^4 = a^4+a^3b - a^3b-a^2b^2-a^2b^2-ab^3 + ab^3+b^4\\\\a^4 + b^4 = a^4+(a^3b - a^3b)+(-a^2b^2-a^2b^2)+(-ab^3 + ab^3)+b^4\\\\a^4 + b^4 = a^4-2a^2b^2+b^4\\\\[/tex]

Unfortunately, we can't go any further. We have a^4 and b^4 on the right hand side, but we also have the term -2a^2b^2 that didn't cancel out. Therefore, the original equation is not an identity.

----------------

Here's another way you can see that we don't have an identity.

Let's say we fixed 'a' to be equal to 1.

That means the equation

[tex]a^4 + b^4 = (a+b)(a^3 - a^2b-ab^2 + b^3)[/tex]

would turn into

[tex]1^4 + b^4 = (1+b)(1^3 - 1^2b-1b^2 + b^3)[/tex]

and simplify to

[tex]1 + b^4 = (1+b)(1 - b-b^2 + b^3)[/tex]

Now replace b with x and you'll have the two equations to represent the left and right hand sides

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

which you can graph on the same xy axis. You should note that the two equations produce different curves. The curves would need to be identical if we wanted an identity to happen.

Side note: you can pick other values for 'a' instead of just 1.

Answer:

3/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

9h + 24 = 60

Answer:

Step-by-step explanation:

A( - 1 , - 3 ) ------> A' ( - 2 , - 1 )

B( 4 , - 3 ) ------> B' ( 8 , - 1 )

C( 4 , 3 ) ------> C' ( 8 , 1 )

D ( - 1 , 3 ) ------> D' ( - 2 , 1 )

Answer:

-4/3

Step-by-step explanation:

(-4 + 2) • (-5 + 3)/-3

=> -2 • (-2)/-3

=> -2 • 2/3

=> -4/3

Therefore, -4/3 is your answer.

Hoped this helped.

Answer:

The answer is -4/3.

Step-by-step explanation:

(-4+2) = -2

x (-5+3) = -2

-2 x -2 = 4.

=-4/3

The multiplication property of equality states that if [tex]x=y[/tex] is true, then [tex]xz=yz[/tex] must also be true.

The property of equality illustrated by the statement "if x = y, then -2x = -2y" is the: Multiplication Property of Equality.

The properties of equality describe the relation between the two sides of an equation and state that the two sides remain equal even after applying the same arithmetic operation on each side.

The property of equality illustrated by the statement "if x = y, then -2x = -2y" is the Multiplication Property of Equality.

This property states that if you multiply both sides of an equation by the same nonzero number, the equality still holds true.

In this question, both sides of the equation are multiplied by -2, maintaining the equality between the expressions.

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Using proportions, it is found that $147.8 billion was spent on television advertising in the previous year.

This year spending's is of 141.7 billion, hence, the equation is:

[tex]0.959x = 141.7[/tex]

[tex]x = \frac{141.7}{0.959}[/tex]

[tex]x = 147.8[/tex]

$147.8 billion was spent on television advertising in the previous year.

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Answer:

4:1

Step-by-step explanation:

Answer:

edge of cube = 20 cm

volume of cube = 20x20x20

volume of each small cube = 5x5x5

number of cubes

= (20x20x20)/(5x5x5)

=64

Step-by-step explanation:

I believe that is the answer im sorry in advanced if its not.

Listamos los lados faltantes a continuación:

El teorema de Pitágoras establece que la medida de la hipotenusa ([tex]c[/tex]), en centímetros, de un triángulo rectángulo es igual a la raíz cuadrada de la suma de los cuadrados de los catetos ([tex]a,b[/tex]), en centímetros. La fórmula se encuentra expresada a continuación:

[tex]c^{2} = a^{2}+b^{2}[/tex] (1)

La hipotenusa es el lado de mayor longitud del triángulo, los catetos son los dos lados restantes.

A continuación, procedemos a resolver cada caso:

1) [tex]a = 3\,cm[/tex], [tex]b = 5\,cm[/tex]

[tex]c = \sqrt{a^{2}+b^{2}}[/tex]

[tex]c = \sqrt{(3\,cm)^{2}+(5\,cm)^{2}}[/tex]

[tex]c \approx \sqrt{34}\,cm[/tex]

2) [tex]x = 6.8\,cm[/tex], [tex]y = 4.5\,cm[/tex]

[tex]z = \sqrt{x^{2}-y^{2}}[/tex]

[tex]z = \sqrt{(6.8\,cm)^{2}-(4.5\,cm)^{2}}[/tex]

[tex]z \approx 5.098\,cm[/tex]

3) [tex]n = 13\,cm[/tex], [tex]m = 12\,cm[/tex]

[tex]p = \sqrt{n^{2}-m^{2}}[/tex]

[tex]p = \sqrt{(13\,cm)^{2}-(12\,cm)^{2}}[/tex]

[tex]p = 5\,cm[/tex]

4) [tex]m = 2.7\,cm[/tex], [tex]s = 2.5\,cm[/tex]

[tex]l = \sqrt{m^{2}+s^{2}}[/tex]

[tex]l = \sqrt{(2.7\,cm)^{2}+(2.5\,cm)^{2}}[/tex]

[tex]l\approx 3.680\,cm[/tex]

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From the computation done, the linear equation that represents the information given will be A. y = -2x + 30.

From the information given, we're told that Yuson must complete 30 hours of community service and that she does 2 hours each day.

Therefore, the linear equation that represents the hours Yuson has left after x days will be represented thus:

y = 30 - (2 × x)

y = 30 - 2x

y = -2x + 30

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Answer: Start off and multiply 12x30=360

Step-by-step explanation: He will recieve 360$