Define functions f, g, h, all of which have R as their domain and R as their target. R is the domain of real number
f(x) = 3x + 1
g(x) = x2
h(x) = 2x
(1) What is (f ο g ο h)(-2)?
(2) What is (f o f-1 ) (2/3)?

The value of side AB is 6 units for parallelogram ABCD with perimeter is 22 units.

An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic

Parallelogram is a quadrilateral (four angles and sides) in which opposite sides are equal and parallel.

From the diagram:

AB = DC  (opposite sides are equal)

2y + 1 = 4 - 4w

2y + 4w = 3    (1)

AD = BC  (opposite sides are equal)

3x - 2 = x - w + 1

2x + w = 3    (2)

The perimeter of ABCD is 22:

2(AB + AD) = Perimeter

2(2y + 1 + 3 - 4w) = 22

2(2y - 4w + 4) = 22

4y - 8w + 8 = 22

4y - 8w = 14    (3)

From the three equations:

w = -0.5, x = 1.75, y = 2.5

AB = 2y + 1 = 2(2.5) + 1 = 6 units

The value of side AB is 6 units

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1. The function f(x) = (x+5)(x-9) in standard form is x²-4x-45.

2. The function f(x) = (x+4)² in standard form is x²+8x+16.

3. The function f(x) = (x+2)²-25 in standard form is x²+4x-21.

4. The function f(x) = 4(x-2)² in standard form is 4x²-16x+16.

5. The function f(x) = 6(2x+1)² in standard form is 24x²+24x+6.

6. The function f(x) = 3(x+4)(x-5) in standard form is 3x²-3x-60.

7. The function f(x) = (x+10)²-100 in standard form is x²+20x.

8. The function f(x) = 9-(x+1)² in standard form is -x²-2x-8.

9. The function f(x) = 2(x+5)²+10 in standard form is 2x²+20x+60.

What is the standard form?

A linear equation can also be written in standard form, slope intercept form, and point slope form.

The formula for standard form is Ax+By=C.

The first function is y = f(x) = (x+5)(x-9).

Simplifying the equation -

f(x) = (x+5)(x-9)

x(x-9)+5(x-9)

x²-9x+5x-45

x²-4x-45

Therefore, the standard form is x²-4x-45.

The second function is y = f(x) = (x+4)².

Simplifying the equation -

f(x) = (x+4)²

Follow the formula - (a+b)² = (a²+2ab+b²)

(x)²+2(x)(4)+(4)²

x²+8x+16

Therefore, the standard form is x²+8x+16.

The third function is y = f(x) = (x+2)²-25.

Simplifying the equation -

f(x) = (x+2)²-25

Follow the formula - (a+b)² = (a²+2ab+b²)

[(x)²+2(x)(2)+(2)²]-25

x²+4x+4-25

x²+4x-21

Therefore, the standard form is x²+4x-21.

The fourth function is y = f(x) = 4(x-2)².

Simplifying the equation -

f(x) = 4(x-2)²

Follow the formula - (a-b)² = (a²-2ab+b²)

4[(x)²-2(x)(2)+(2)²]

4[x²-4x+4]

4x²-16x+16

Therefore, the standard form is 4x²-16x+16.

The fifth function is y = f(x) = 6(2x+1)².

Simplifying the equation -

f(x) = 6(2x+1)²

Follow the formula - (a+b)² = (a²+2ab+b²)

6[(2x)²+2(2x)(1)+(1)²]

6[4x²+4x+1]

24x²+24x+6

Therefore, the standard form is 24x²+24x+6.

The sixth function is y = f(x) = 3(x+4)(x-5).

Simplifying the equation -

f(x) = 3(x+4)(x-5)

3[x(x-5)+4(x-5)]

3[x²-5x+4x-20]

3[x²-x-20]

3x²-3x-60

Therefore, the standard form is 3x²-3x-60.

The seventh function is y = f(x) = (x+10)²-100.

Simplifying the equation -

f(x) = (x+10)²-100

Follow the formula - (a+b)² = (a²+2ab+b²)

[(x)²+2(x)(10)+(10)²]-100

x²+20x+100-100

x²+20x

Therefore, the standard form is x²+20x.

The eighth function is y = f(x) = 9-(x+1)².

Simplifying the equation -

f(x) = 9-(x+1)²

Follow the formula - (a+b)² = (a²+2ab+b²)

9-[(x)²+2(x)(1)+(1)²]

9-x²-2x-1

-x²-2x-8

Therefore, the standard form is -x²-2x-8.

The ninth function is y = f(x) = 2(x+5)²+10.

Simplifying the equation -

f(x) = 2(x+5)²+10

Follow the formula - (a+b)² = (a²+2ab+b²)

2[(x)²+2(x)(5)+(5)²]+10

2[x²+10x+25]+10

2x²+20x+50+10

2x²+20x+60

Therefore, the standard form is 2x²+20x+60.

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Answer:

1,400

Step-by-step explanation:

y=mx+b

plug in 460 for b

y=mx+460

plug 20 for m

y=20x+460

and when graphed on a graph you would see the answer

The number that would complete the square is 1.

We know that the method of completing the square would involve a quadratic equation that does have the general form;

ax^2 + bx + c =0

We have to note that the number that is going to complete the square is the number that is going to correspond to 1/2(b).

This implies that we have to look at the b term in the equation and we b = 2.

Thus;

1/2(2) = 1

Hence, we have found that the square can be completed by 1.

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A polygon having seven sides and seven angles is called a heptagon. Seven straight sides and seven corners, or vertices, make up a heptagon. It's also referred to as a "septagon" at times.

A seven-sided polygon is called a heptagon. A closed figure with seven vertices, it is. Another name for a heptagon is a septagon.

There are various sorts of hexagons, depending on the angles and diagonals.

Regular and Irregular Heptagons

Concave and Convex Heptagon

The following are some heptagon's characteristics:

(1) The inner angles of a heptagon add up to 900 degrees.

(2) A heptagon's outside angles add up to 360 degrees.

(3) The internal angle of a normal heptagon measures approximately 128.57 degrees.

(4) The size of a typical heptagon's central angle is roughly 51.43 degrees.

(5) There are fourteen diagonals in a heptagon.

(6) Convex heptagons are another name for regular heptagons.

(7) A heptagon has a total of five triangles.

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Translation type of transformation can be defined as moving a figure to a new location with no change to the size or shape of the figure.

Now, According to the question:

Type of Transformation:

There are four types of transformation in geometry, namely translation, reflection, rotation, and dilation. In translation, it slides the figure in any direction while in reflection, it flips the figure over a point or a line. Also, in rotation the figure turns, while in dilation the figure is either enlarged or reduced.

The type of transformation can be defined as moving a figure to a new location, without any change in the figure's size or shape being called translation. In translation, the figure merely slides or moves in the same direction and distance.

Therefore, the answer is Translation.

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The equation m = 4w + 3 shows the number of days in January.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A pattern shown in the image.

Let m is the number of days in a month.

And w represents the number of days in the weeks.

So, algebraic equation,

m = 4w + 3.

Therefore, the equation is m = 4w + 3.

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when graphing inequalities, we use an open  point when the sign is greater or less than  when the sign is ,and a closed point when the sign is greater or less than or equal to

Graph following inequalities.

1) x≥3

2) x<-2

3) x< 7

4) x ≤ -4

explanation

To find the equation of a linear function from its graph:

Find the slope by finding the rise and run.

Find the y-intercept (the point where the line crosses the y-axis)

Substitute the value into the function f(x)= mx+b .

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Answer: You can make more bracelets than necklaces. ✅

Step-by-step explanation:

You have 2.88 meters of copper wire and 5.85 meters of aluminum wire.

With 2.88 meters of copper wire, you can make 12 bracelets because each bracelet needs 0.24 meters of copper wire.

With 5.85 meters of aluminum wire, you can make 9 necklaces because each necklace needs 0.65 meters of aluminum wire.

So you can make 12 bracelets and 9 necklaces.

Therefore you can make more bracelets than necklaces.

One solution exists for the given equation.A linear equation with one variable has only ever one solution.

A linear equation with one variable has only ever one solution. The unique solution of a linear equation is the location at which LHS and RHS are identical when substituted.

The solution must be an ordered pair when there are two linear equations operating simultaneously (x, y). In this case, the ordered pair will fulfill the set of equations.

Given:

2x + 5y = 4

-4x - 13y = 9

Now,

a 1 = 2,  b1 = 5 , = -4

a2 = -4 , b2 = -13, = 9

Now,  = 2 / -4

= 5 / -13

As, a1/ a2 = 2/-4

b1 / b2 = 5 /-13

Thus, the relationship mentioned above reflects intersecting lines.

So, there is only one solution to the given problem.

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Answer:

x = 92

y = 92

Step-by-step explanation:

164 + 102 + 90 + x + x = 540

2x + 356 = 540

2x = 184

x = 92

When t = 3, the exponential function has a value of 59.375.

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise indicated, the word refers to a positive-valued function of a real variable, however it can be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras. A mathematical function of the following type is an exponential function: f (x) = an x, where x is a variable and an is a constant known as the function's basis. The transcendental number e, which is about 2.71828, is the most often encountered exponential-function base.

Here,

Given the exponential function h (t) = 475(0.5)^t

When t = 3

h(3) = 475(0.5)^3

h(3) =59.375

h(3) = 59.375

The exponential function when the value of t is 3 is 59.375.

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The coefficient of x²y in the product ( 7x²-5y) ( x²+3y) is 16.

The coefficient of x²y in the product (7x²-5y) (x²+3y) is the numerical factor that is multiplied to x²y when the two polynomials (7x²-5y) and (x²+3y) are multiplied together.

To find the coefficient of x²y in the product, you can use the distributive property of multiplication over addition, also called the FOIL method, which states that to multiply two binomials, you must multiply the first term of the first binomial by the first term of the second binomial, the first term of the first binomial by the second term of the second binomial, the second term of the first binomial by the first term of the second binomial, and the second term of the first binomial by the second term of the second binomial.

The product of (7x²-5y) (x²+3y) can be expanded as follows:

(7x²-5y) (x²+3y) = 7x²x² + 7x²3y -5yx² -5y3y

=7x⁴ + 21x²y -5x²y - 15y²

= 7x⁴ + 16x²y - 15y²

So, the coefficient of x²y in the product ( 7x²-5y) ( x²+3y) is 16.

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Step-by-step explanation:

Today, we are going to be talking about the three-way principle of mathematics. Basically, there are three ways to solve a problem in math: verbally, graphically, or by example. In this lesson, we will discuss each of these principles by solving sample problems using each type.

The triangles QRS and TUV are similar. They are similar as ΔTUV = 3ΔQRS.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

There are two similar looking triangles, ΔQRS and ΔTUV.

In ΔQRS, the measure of line segment QR = 9 units

In ΔQRS, the measure of line segment RS = 10 units

In ΔQRS, the measure of line segment QS = 11 units

In ΔTUV, the measure of line segment TU = 27 units

In ΔTUV, the measure of line segment UV = 30 units

In ΔTUV, the measure of line segment TV = 33 units

The pattern here can be seen that -

For the line segment TU -

3 (QR) = TU

3 (9) = 27

Similarly, for the line segment UV -

3 (RS) = UV

3 (10) = 30

Similarly, for the line segment TV -

3 (QS) = TV

3 (11) = 33

Therefore, the triangle TUV is three times scaled version of triangle QRS.

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The number of people visited the zoo from the state is  200

Number deals with quantity of people that came to the zoo from the state over the period.  These people must be from the state.

The given parameters that will help us to solve the question are:

The ratio is approximately 7 to 3.

The number of people = 2000

The sum of the ratios is equal to 7+3 = 10

This is to say that 10% of the people visited the zoo

10/100*2000/1

Therefore about 200 people visited the zoo

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The linear equation for a line made of points  (r,5) and (6,r) has slope = 5/8 so r=5.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

As slope (m)=(y2-y1)/(x2-x1)

and m=5/8, (x1,y1) and (x2,y2) are (r,5) and (6,r)

Therefore, 5/8=(r-5)/(6-r) --> 5(6-r)=8(r-5)--->13r=70-->r=5

Hence,

         r=5

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The maximum number of drinks Liam can buy is 4 without over exceeding his price.

Unitary method:

The unit method is a method of obtaining a single-unit value from a multiple-unit value and obtaining a multiple-unit value from a single-unit value. This is the method used for most calculations in mathematics. This method is useful when solving problems involving proportions and proportions, algebra, geometry, and more.

The unit method allows us to find missing values. For example, if a pack of juice costs $5. Then you can easily see that the cost is 5 packages, or $25.

According to the Question:

If Liam has $30 to spend and he must buy at least 9 drinks and tacos altogether, it means that,

$3.50 for 5 tacos

⇒ 3.50 x 5 =  $17.50

Now,

9 - 5 tacos = 4 drinks

Cost of 4 drinks x $2 = $8

The total price :

$17.50 + $8 = $25.50 out of $30 price limit

Thus, the number of drinks that she could buy is 4.

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Answer:

Step-by-step explanation:

0.25

Yes, the square of any number like X² is always positive.

Example:

If we calculate the square of a negative number, let's say -x, where x > 0, then (-x) (-x) = x².

Here, x² > 0.

Hence, the square of any number like X² is always positive.

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Answer:

The total number count we are looking at from the numbers 30 to 65 is 36. So that is a total of 72 digits making up this numbers from 30 to 65. Also, we can see that the whole range of numbers 0 to 9 is being used for this range

Answer:

271.2

Step-by-step explanation:

Write it down and remove the decimals and do long multiplication. After that, count the decimal points and add them back ro the answer

Answer:

271.2

Step-by-step explanation:

move the decimal point 2 places to the right in the two numbers and multiple

[tex]2825 \times 960 = 2712000 [/tex]

and then move you decimal point 4 places to the left so your finally answer should be 271.2

Answer:

[tex]y= \frac{x}{2x−1}[/tex]

Step-by-step explanation:

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: y=x/2x−1 becomes x=y/2y−1.

Now, solve the equation x=y/2y−1 for y.

y=x/2x−1

The price of the adult ticket is $9

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Set up equations to represent the problem.

Let the A and S represent the prices of adult and student ticket respectively. So we can write:

4A + 10S = 106 --- (1)

4A + 9S = 99  --- (2)

Subtracting (2) from (1) will give:

S = 7

Put S = 7 into (1):

4A + 10S = 106

4A + 10(7) = 106

4A + 70 = 106

4A = 106 - 70

4A = 36

A = 36/4

A = 9

Thus, the price of the adult ticket is $9

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The quadratic equation written in the vertex form is:

f(x) = 2*(x - 2)^2 - 8

We know that for any parabola whose vertex is (h, k) and the leading coefficient is a, can be written in the vertex-form as:

f(x) = a*(x - h)^2 + k

In this particular case, we know that the vertex of the parabola is the point (2, -8), replacing that in the quadratic equation above we will get:

f(x) = a*(x - 2)^2  - 8

Now we also know that our parabola passes through the point (0, 0), then if we replace these values in the equation we will get:

f(0) = 0 = a*(0 - 2)^2 - 8

        0 = a*4 - 8

        8 = a*4

        8/4 = a

          2 = a

Then the quadratic equation in the vertex form is:

f(x) = 2*(x - 2)^2 - 8

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A constant polynomial is a polynomial with a degree of 0, meaning it has no variable terms. The only possible constant polynomial is the term with a coefficient of 3, which is 3.

This can be seen by looking at the formula for a polynomial, which is:

P(x) = a0 + a1x + a2x2 + ... + anxn,

where a0 is the constant term, a1 is the linear term, a2 is the quadratic term, and so on. Since this polynomial has no variable terms (x = 0), the only possible constant polynomial is the term with a coefficient of 3.

To calculate the value of a constant polynomial, you simply substitute 0 for x in the equation above. For example, in the polynomial 3, the value would be 3 when x = 0.

P(0) = 3

Therefore, the answer is option b, 3.

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The area of rectangle is found to be 117 sq. yd.

Let the length of rectangle be L:

The, the width is W + 4 = L

Perimeter = 2(length + width)

P = 2(L + B)

P = 2(W + 4 + W)

P = 2(2W + 4)

40 = 4W + 4

4W =36

W = 9

The, L = 9 + 4 = 13 yd.

Area = length * width

Area = 9*13

Area = 117

Thus, the area of rectangle is found to be 117 sq. yd.

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Answer:

Step-by-step explanation:

The perimeter of a rectangle is the total circumference of the rectangle.

Perimeter=2(Length + breadth)

Perimeter=40yd

Length=x+4 and breadth=x

40=2(x+x+4);

40=4x+8;

4x=32 and x=8yd

So, length=12yd and breadth=8yd.

Area = length*breadth

So Area = 12*8= 96ydsq

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The height of the tailgate (from the ground), holding the 8 ft ramp inclined at 35° with the ground, found using trigonometric ratios is about 4.59 ft

A trigonometric ratio (trig ratio) specifies the relationship between an angle in a right triangle and two sides of the right triangle.

The length of the ramp = 8 ft

The angle the ramp forms with the ground = 35°

The ramp leads from the ground to the tailgate of the truck

The height of the tailgate from the ground can therefore be found using trigonometric ratios as follows;

The trigonometric ratio for the sine of an angle, θ, using SOH CAH TOA therefore is; sin(θ) = Opposite side

Where;

θ = 35°

The opposite side to the angle θ = Height of the tailgate from the ground = h

The hypotenuse side of the right triangle formed by the ramp = The length of the ramp = 8 ft. We get;

sin(35°) = (Height of the tailgate from ground, )/(Length of the ramp)

Therefore;

sin(35°) = h/8

h/8 = sin(35°)

h = 8 × sin(35°) ≈ 4.59

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