Given the functions, fx) = 3x-6 and g(x)= x² + 5x+7, perform the indicated operation. When applicable, state the
domain restriction.
f(g(x))

Answer:

2:9 or 2/9

Step-by-step explanation:

I guess this question asks the simplest form of ratio 4:18

so I divided it by two and since they cannot be divided further that's the answer

you can either choose to write it in ratio form or fraction form that's your choice good day.

Answer:

the technical number depends on what you are including to be algebraic identities.

There are multiple forms of most identities (pos. / neg.   and multiple ways of writing the same identity)

generally, you can consider there to be 10

Step-by-step explanation:

algebraic identity: an equality that holds true for any variable values

standard identities:

square of binomial:

(a+b)² = a² +2ab + b²

(a - b)² = a² - 2ab + b²

difference of squares:

(a + b)(a - b) = a² - b²

----

product of two binomials:

(x + a)(x + b) = x² + (a + b)x + ab

square of trinomial:

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

(x - y - z)² = x² + y² + z² -2(xy + yz - zx)

cube of binomial:

(x + y)³ = x³ + y³ + 3xy (x + y)

(x - y)³ = x³ + y³ - 3xy (x - y)

(a - b)³ = a³ - 3a²b + 3ab² - b³

sum of cubes:

a³ + b³ = (a + b)(a² - ab + b²)

x³ + y³ = (x + y)(x² - xy + y²)

x³ + y³ = (x - y)(x² + xy + y²)

difference of cubes:

a³ - b³ = (a - b)(a² + ab + b²)

x³ - y³ = (x - y)³ + 3xy(x - y)

--

x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)

                              = 1/2 (x + y + z) [(x -y)² + (y - z)² + (z - x)²]

(a + b + c)³ = a³ + b³ + c³ + 3(a + b)(b + c)(c + a)

--

and

if x + y + z = 0, then x³ + y³ + z³ = 3xyz

hope this helps!!

(this took me a while to write; there are also a few complicated identities also that I've left out)

[tex]( {a + b})^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \\ {a}^{2} - {b}^{2} = (a + b)(a - b) \\ \\ {a + b + c}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca \\ \\ {a + b}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ \\ {a - b}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b) \\ \\ {a}^{3} + {b}^{3} + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ca).[/tex]

The area of a triangle with vertices (-4,-5), (3,-3), and (3,-7) will be 7 square units.

The vertices of the triangle are (x₁, y₁), (x₂, y₂), and (x₃, y₃).

Then the area of the triangle will be

Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)]|

We have

(x₁, y₁) ⇒ (-4, -5)

(x₂, y₂) ⇒ (3, -3)

(x₃, y₃) ⇒ (3, -7)

Then the area will be

Area = 1/2[{(-4) x (-3) + (3) x (-7) + (3) x (-5)} – {(-5) x (3) + (-3) x (3) + (-7) x (-4)}]

Area = 1/2 [(12 – 9 – 21) – (- 15 – 9 + 28)]

Area = 1/2[-18 + 4]

Area = 1/2 × 14

Area = 7 square units

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N = 0

2(0)² + 4(0) = 0

0 + 0 = 0

Answer:

y=-x^2-4x-1

Step-by-step explanation:

when it is an arch like an upside down U then its

-x^2

it passes through the y axis at -1

its vertex or high point is -2,3 so its

-4x

Answer:

See below

Step-by-step explanation:

Dome shaped parabola      so   'a'  is negative

'c' is determined where x = 0

    this value is -1

Axis of symmetry is the x value of the vertex (which is the high point of the dome)

   x = -2

Answer:

F.  31.4 ft

Step-by-step explanation:

The distance around the edge of a circle is called the circumference.

Formula for the circumference of a circle

[tex]\sf Circumference\:of\:a\:circle=2 \pi r[/tex]

(where r is the radius)

Given values:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \sf circumference & = \sf 2 \cdot 3.14 \cdot 5\\ & = \sf 31.4\:ft \end{aligned}[/tex]

Therefore, the distance around the edge of the circular patio is 31.4 ft.

The distance around the edge of the patio is 31.4 feet, which is determined by the circumference of a circle. The correct answer is option (F).

To find the distance around the edge of the circular patio, we need to calculate the circumference of the circle.

The formula for the circumference of a circle is given by:

Circumference = 2 × π × radius

Given that the radius of the patio is 5 feet and using the approximate value of π as 3.14, we can now calculate the circumference:

Circumference = 2 × 3.14 × 5

Circumference = 31.4 feet

Therefore, the distance around the edge of the patio is 31.4 feet.

Hence, the correct answer is option (F).

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Answer:

4^3 written in expanded form is 4*4*4

Mark as Brainliest please

Answer: 64

Step-by-step explanation:

Hii!

Do you need to know what 4^3 written in expanded form is? No problem!

4^3=4*4*4 (the ^3 tells us to multiply the base (which is 4 here) times 3)

The answer is 64.

Hope that this helped! Best wishes.

--

The  property that justifies the statement is the commutative law of addition

This law occurs if the same number or constant is added to both sides of an equation.

Given the equation

AB - BC = 12

Add BC to both sides

AB - BC + BC = 12 + Bc

AB = 12 + BC

Hence the  property that justifies the statement is the commutative law of addition

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You know that the sides of a square are increased by 2 inches: the expression should be written as (x+2)

The area is 25 square inches

The area of a square is s×s or s²

so it can be solved as:

(x+2)²=25

[tex](\sqrt{x+2})^{2} =\sqrt{25}[/tex]

x+2=5

x=3

The length of the original side is 3 inches

Hope it helps!

Answer:

-3

Step-by-step explanation:

/= negative slope; \= positive slope

The y-intercept is 2 because this is where it crosses the y-axis

Then you find the next point that touches the graph on an exact point which is (-2,-4)

So, your points are (0,2) and (-2,-4) then you do the slope formula of y2-y1 divided by x2-x1

-4-2/-2-0 = 3 and because the line is / then it is -3

The following statements accurately compare the three functions on the graph: option A and C.

In Geometry, the following statements are true about the graph of a function:

By critically observing the graph of a function, we can logically deduce that the following statements accurately compare the three functions on the graph:

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Answer:

let the no. be X

82% of X = 94.3

82/100 *X = 94.2

X = 94.2 *100/82

X = 94.2/0.82

X = 114.8

Answer:

115

Step-by-step explanation:

82% = 82/10 = 0.82

94.3 / 0.82 = 115

Hope this helps

Answer: 4.5

Step-by-step explanation:

[tex]\frac{6+3}{2}=\boxed{4.5}[/tex]

We want to find the median for the given density curve.

The value of the median is 4.5. ({3+6)/2}

Let's see how to solve this.

First, for a regular set {x₁, ..., xₙ} we define the median as the middle value.

The difference between a set and a density curve is that the density curve is continuous, so getting the exact middle value can be harder.

Here, we have a constant density curve that goes from 3 to 6.

Because it is constant, the median will just be equal to the mean, thus the median is the average between the two extreme values.

Remember that the average between two numbers a and b is given by:(a + b)/2

So we get: m = (6 + 3)/2 = 4.5

So we can conclude that the value of the median is 4.5, so the correct option is the second one, counting from the top.

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The domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) =  1/√x

m(x) = x² - 4

Domain of f(x)/m(x):

f(x)/m(x) = (1/√x)/(x² - 4)

f(x)/m(x) = 1/√x(x² - 4)

The denominator cannot be zero:

√x(x² - 4) ≠ 0

x(x - 2)(x+2) ≠ 0

x ≠ 0, 2, -2

and x > 0

Domain of f(x)/m(x) is:   (0, ∞) - {0, 2, -2} or [tex]\:\left(0,\:2\right)\cup \left(2,\:\infty \:\right)[/tex]

Domain of f(m(x)):

f(m(x)) = 1/√(x² - 4)

x² - 4 > 0

Domain: [tex]\rm \left(-\infty \:,\:-2\right)\cup \left(2,\:\infty \:\right)[/tex]

Domain of m(f(x)):

= ((1/√x)² - 4)

Domain: [tex]\:\left(0,\:\infty \:\right)[/tex]

Thus, the domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

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The equation is [tex]\boxed{y-2=6(x+9)}[/tex].

Answer:

1

Step-by-step explanation:

When you graph the functions they intersect at one point

(-3.368119, -31.10436)

Answer:

D) Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.

B) The slopes of EF and GH are both 5/8

Step-by-step explanation:

The following inference can be made about each answer choices:

For option A

A) The slope of EH is 3/2 and not -8/5

For EH, slope = (2--4)/(0--4) = 6/4 =3/2

For option B

B) The slopes of EF and GH are both 5/8

slope of a graph can be determined by change in y axis/ change in x axis

For EF, slope = (7-2)/(4--4) = 5/8

for GH, slope =  (1--4)/(8-0) = 5/8

For option C

C) FG is perpendicular to GH, its can't be determined since it is concluded that the quadrilateral is a parallelogram, therefore this option is wrong.

For option D

D) Quadrilateral EFGH is a parallelogram because both pairs of opposite sides are parallel.

Slope of a graph can be determined by rise divided by run change in y axis/ change in x axis

For EF, slope = (7-2)/(4--4) = 5/8

for GH, slope =  (1--4)/(8-0) = 5/8

For EH, slope = (2--4)/(0--4) = 6/4 =3/2

for FG, slope =  (7-1)/(8-4) = 6/4 =3/2

EF and GH give the same slope, likewise EH and FG and they are opposite to each other, this make them parallel. Therefore, EFGH is a parallelogram.

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The vertex form of the quadratic function f(x) = x² + 2x + 3 is given as follows:

f(x) = (x + 1)² + 2

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the function is:

f(x) = x² + 2x + 3

Completing the squares, we find the equation in vertex form, as follows:

f(x) = (x + 1)² + 2

As (x + 1)² = x² + 2x + 1, hence 2 has to be added to find the equivalent function.

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Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at  (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].

Given, that a hyperbola centred at the origin has vertices at (0, ±9)  and foci at  (0, ±10).

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

The formula for a hyperbola centred at the origin is [tex]\frac{(x-h)^{2} }{a^{2} } -\frac{(y-k)^{2} }{b^{2} } =1[/tex]

Where (h, k) is the center = (0, 0)

Distance from centre to vertices a = 9 ⇒ a² = 81

Distance from centre to vertices which is given from the foci c = 10

⇒ c² = 100

Using the Pythagorean formula, c²= a²+ b²

Substituting the values 100 = 81 + b²

So we get, b²= 100 - 81 = 19

Substituting the values in the standard form [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].

Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at  (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].

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Answer:

26.85%

Step-by-step explanation:

first you find the difference in price increase

633-499=134

*percentage increase=increase value/original value x100

so;=134/499x100=28.85%

hope it helps you.please don't forget to give me a thanks

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Answer:  [tex]\textsf{Option B, 81}\pi\textsf{ in}^2[/tex]

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

Given: [tex]\textsf{Circumference = 18}\pi[/tex]

Find:  [tex]\textsf{The area of the circle}[/tex]

Solution:  We need to first determine the radius using the circumference formula and once we get the radius then we can plug in the value into the area formula and get our final answer.

Determine the radius

Determine the area

Therefore, the correct answer would be option B, 81π in2.

Answer:

48/49

Step-by-step explanation:

divison and multiplcation

Step-by-step explanation:

[tex]f(x) = 5x - 1[/tex]

[tex] \: [/tex]

[tex]y = 5x - 1[/tex]

[tex]5y - 1 = x[/tex]

[tex]5y = x + 1[/tex]

[tex]y = \frac{x + 1}{5} [/tex]

[tex] {f}^{ - 1} (x) = \frac{x + 1}{5} [/tex]

Answer:

x = ±5

Step-by-step explanation:

x² - 25 = 0

x² = 25

√x² = √25

x = ±5

Check:

5² - 25 = 0

-5² - 25 = 0

25 - 25 = 0

Answer:

D, E, F is the answer.

Step-by-step explanation:

From the diagram:-

Therefore, D, E, F.

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

Answer:

Area of the minor segment = 2.505324230749 cm²

Step-by-step explanation:

Area of the minor segment

= Area of the sector ABC - Area of the triangle ABC

……………………………………………………………………………………

• Area of the sector ABC

= Area of the whole circle ÷ 8

= (π×8²) ÷ 8

= 8π

______

•• Area of the triangle ABC

= (1÷2) × CA × CB × sin(45)

= (1÷2) × 8 × 8 × (√2/2)

= 16√2

______

Thus

Area of the minor segment

= 8π - 16√2

= 2.505324230749

Based on my experiences so far, the approach to geometry that I prefer is: Euclidean Geometry. This is because the problems are easy to visualize since they are restricted to two-dimensional planes.

The approach that is easier to extend beyond two dimensions is Euclidean Geometry. Again, this is because of how it deals with shapes and visualization of the same.

Take for instance a triangle; it is easy to go from a two-dimensional equilateral triangle  to a square pyramid.

Analytical geometry is a superior technique for discovering objects (points, curves, and planes) based on their qualities in some situations than Euclidean geometry is in others (for example, when employing topography or building charts).

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Answer:

The answer is y = -4x+11