Given f(x) = x - 7 and g(x) = x2.
Find g(f(4)).

Answer:

The expression "5.25x + 1246x" is equivalent to "1771x"

The scale factor needed to form ΔA'B'C' from ΔABC is 1/2 or 0.5.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

The coordinate points of triangle ABC is -

A(2,6), B(2,2), and C(6,2)

The coordinate points of triangle A'B'C' is -

A'(1,3), B'(1,1), and C'(3,1)

Subtract the coordinate points of A'B'C' from ABC to find the scale factor -

A = (2 - 1, 6 - 3) = (1,3)

B = (2 - 1, 2 - 1) = (1,1)

B = (6 - 3, 2 - 1) = (3,1)

So, it can be seen that to form triangle ABC, the triangle A'B'C' is multiplied by the factor of 2.

A(2,6) = (x/2 , y/2) = A'(1,3)

B(2,2) = (x/2 , y/2) = B'(1,1)

C(6,2) = (x/2 , y/2) = C'(3,1)

Therefore, the scale factor is 1/2 or 0.5.

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If the sequence be 2, 9, 22, 45, 82, 137, 214 then the pattern be 6, 13, 23, 37, 55, 77.

The term "patterns" describes common, repeatable sorts of practices or regulations. To forecast what has happened or what might happen, patterns are helpful. come following a group of integers that are ordered specifically. Sequence describes this grouping of numbers.

Putting events or information in a precise order is referred to as sequencing. Higher-order thinking abilities—such as those for detecting patterns, figuring out causes and effects, and more—are necessary for sequencing. Sequencing aids students in both understanding and organizing the material they have learnt and in problem-solving.

Let the given sequence be 2, 9, 22, 45, 82, 137, 214

The differences to a pattern in the sequence be

= 9 - 2, 22 - 9, 45 - 22, 82 - 45, 137 - 82, 214 - 137

= 6, 13, 23, 37, 55, 77

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The grapefruit's volume in cubic centimeters to the nearest tenth is equal to 775.8 cubic centimeters.

Mathematically, the volume of a sphere can be calculated by using this mathematical expression:

Volume = 4/3 × πr³

Where:

r represents the radius.

Based on the information provided about the grapefruit, the diameter of the sphere is given by;

Diameter of sphere = 11.4 cm

Radius = diameter/2 = 11.4/2 = 5.7 cm.

Substituting the given points into the volume of a sphere formula, we have the following;

Volume of sphere = 4/3 × 3.142 × 5.7³

Volume of sphere = 775.8 cubic centimeters.

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Hey there!

Hope this helps!

Answer:

1224 cm²

Step-by-step explanation:

The picture is a rectangle with length 60 cm and width 30 cm.

area of rectangle = length × width

area of picture = 60 cm × 30 cm = 1800 cm²

Now we add the mat to the picture. The width of the mat is 6 cm, so when you add mat to two opposite sides, the total length of the picture and mat becomes 60 cm + 6 cm + 6 cm = 72 cm. When you add mat to the other two opposite sides, the total width of the picture and mat becomes 30 cm + 6 cm + 6 cm = 42 cm. Now we have a rectangle 72 cm by 42 cm.

area of picture and mat = 72 cm × 42 cm = 3024 cm²

The area of the mat is the difference in area between the picture with mat and the picture without mat.

area of mat = 3024 cm² - 1800 cm² = 1224 cm²

When there are 12 observations in a small sample, the median is calculated by: b. the average value of the sixth position and the seventh position of an ascending sorted.

In Mathematics, a median can be defined as the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.

First of all, we would sort the 12 observations from the least to greatest as follows:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

The median for 12 observations is the average of the 6th and 7th number:

Median = (6 + 7)/2

Median = 13/2

Median = 12.5.

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Answer:

Step-by-step explanation:

in the picture

Answer:

Jessica and some friends have ordered two pizzas. One is a medium sized pizza while the other is a large

Step-by-step explanation:

Jessica and some friends have ordered two pizzas. One is a medium sized pizza while the other is a large

Answer:

C. 25.12 inches

Step-by-step explanation:

radius = 4 inches

circumference = 2πr

circumference = 2 × 3.14 × 4 inches

circumference = 25.12 inches

Answer:c is correct 25.12

Step-by-step explanation:

Answer:

Step-by-step explanation:

First write down the decimal number divided by 1 like this:

0.607

1

As we have 3 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 103 = 1000, so that there is no decimal point in the numerator

0.607 × 1000

1 × 1000

=

607

1000

Therefore, 0.607 as a fraction is 607/1000

If two figures can be mapped onto one another or if all pairings of angles and side lengths are congruent, the figures are said to be congruent.

What is Triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

What is the condition to be congruent?

If two triangles are the same size and shape, they are said to be congruent. To establish that two triangles are congruent, not all six matching elements of either triangle must be located. There are five requirements for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.

Both triangles are said to be congruent if the three angles and three sides of one triangle match the corresponding angles and sides of the other triangle.

In Δ PQR and ΔXYZ, as shown in figure,

we can identify that PQ = XY, PR = XZ,

and QR = YZ

and ∠P = ∠X,

∠Q = ∠Y and ∠R = ∠Z.

Then we can say that Δ PQR ≅ ΔXYZ.

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Answer:

a) even

b) neither

c) odd

Step-by-step explanation:

A function is "even" when there is symmetry about the y-axis.

Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:

A function is "odd" when there is origin symmetry.

Functions are symmetric with respect to the origin if for every point (a, b) on the graph, there is also a point (-a, -b) on the graph:

From inspection of the graph, the curve appears to be symmetrical about the y-axis. Therefore, the function is even.

This is an absolute value function.  It has no symmetry about the y-axis or the origin.  Therefore, the function is neither.

From inspection of the graph, the curve appears to be symmetric with respect to the origin. Therefore, the function is odd.

The length of the missing side is 12cm.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. So if we know the lengths of two sides of a right triangle, we can use the theorem to find the length of the third side.

Given:

Base (b) = 16 cm

Hypotenuse (c) = 20 cm

We can use the Pythagorean theorem to find the length of the missing side (a), which is the side opposite the right angle and adjacent to the base.

c^2 = a^2 + b^2

20^2 = a^2 + 16^2

400 = a^2 + 256

144 = a^2

a = 12cm

once we have the length of the missing side, we can use the values of the base and hypotenuse to find the six trigonometric functions:

Therefore, the length of the missing side is 12cm.

The question is incomplete as it does not include the figure. Hence I have attached the figure for a complete understanding of the problem.

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The solution for the equation 3x²-4x-2=0 is 1.72076 and 0.387426.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

3x²-4x-2=0

Now, solving the above Quadratic Equation

D= √b² - 4ac

From the given equation

a= 3, b-4, c=-2

Then, D= √(-4)² - 4(3)(-2)

D= √16 +24

D = √40

Now, x= (-b ±D)/ 2a

x= -(-4) ± √40/ (6)

x= 4+ √40/6  or x= 4-√40/6

x = 1.72076 or x=−0.387426

Hence, the value of x is 1.72076 and 0.387426.

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Answer:

a. True

b. False

c. False

d. False

e. True

Step-by-step explanation:

a. True: The graph of f^-1(x) is a reflection of the graph of f(x) over the line y = x. This is because for any point (x,y) on the graph of f(x), the point (y,x) will be on the graph of f^-1(x), and vice versa.

b. False: The inverse function, f^-1(x) does not have to be always increasing. It depends on the original function, f(x) and its properties, A function could be increasing or decreasing, or it could be a combination of both, or none of them. A function which is strictly increasing is guaranteed to have a unique inverse, but that inverse function may or may not be increasing.

c.False: The function y = x^2 does not have an inverse function. Because it is not a one-to-one function. It is not injective, meaning that it maps multiple input values to the same output value, so it cannot be inverted.

d. False: If a function has a y-intercept, it does not mean that its inverse must also have a y-intercept. A y-intercept is a point at which a function crosses the y-axis, which corresponds to x = 0. However, the inverse function of a function will have its x and y coordinates swapped, so the inverse of a function that crosses the y-axis at a particular point will not cross the x-axis at the same point.

e. True: If a function has a y-intercept, it means that the function crosses the y-axis. But since the inverse function of a function will have its x and y coordinates swapped, the inverse of a function that crosses the y-axis at a particular point will cross the x-axis at the same point.

By calculating, The GCF of the given numbers 49 and 28 is 7.

What is Algebraic expression ?

An algebraic expression is an expression that consists of numbers, variables and operators such as addition, subtraction, multiplication and division. These expressions can be used to solve equations and other mathematical problems. Algebraic expressions can also be used to represent relationships between different variables. For example, the expression 4x + 2y can be used to represent the relationship between two variables, x and y.

So lets first find the prime factorization of 28

prime factorization of 28 = 2 × 2 × 7

So lets first find the prime factorization of 49

prime factorization of 49 = 7 × 7

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, The GCF  of the  given numbers 49 and 28 is 7.

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The algebraic expression will be Y=a+9

Where Y=number of cards Angelica has now, a=added movie cards,

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

As given

Angelica buys 3 packets of movie cards and 6 packets of cartoon cards

and and adds these to the 3 packets of movie cards she already has

Now let a=packets of movies she already has

and Y=number of cards Angelica has now

Therefore, The algebraic expression will be

             Y=a+3+6=a+9

            Y=a+9

             Where a=3

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A quadrilateral has diagonals that are perpendicular but not congruent

is a rhombus.

A quadrilateral with all equal sides is a rhombus. Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.

From the properties of a rhombus, we know,

A rhombus has an equal number of sides. In this case, ABCD equals DA.

At an angle of 90° divides each of the diagonals. In this instance, diagonals AC and BD split at a 90° angle.

A rhombus has parallel opposite sides. In this case, AB || CD and AD || BC.

In a rhombus, the opposite angles are equal. ∠A = ∠C, while ∠B = ∠D.

The sum of adjacent angles is 180°.

Diagonals of a rhombus bisect each other at the right angles but they are not congruent.

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Applying the properties of the diagonals of a square, the length of EG ≈ 8.5 units.

The diagonals of a square are line segments that connect opposite corners of the square. They have the following properties:

Therefore, each segment that is formed by the bisection of the diagonals would be equal to 6.

Applying Pythagorean theorem, we have:

EG = √(6² + 6²)

EG = √(36 + 36)

Length of EG ≈ 8.5 units.

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A significant number of accidents are caused by vehicle equipment failure such as the following except Operative lights.

Operative lights are also called Surgical lights which are medical equipment devices used to illuminate the operating field during surgery.

Surgical lights are referred to by many names: Operating lights, OR lights, operating room lights, surgical lamps, and surgical light heads.

The primary function of surgical lighting is to illuminate the operative site on and/or within a patient for ideal visualization by OR staff during a surgical procedure.

With proper lighting, operating room staff can achieve a higher level of efficacy during surgery and reduce the risk of complications.

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Any statistical relationship between two random variables or bivariate data, whether causal or not, is referred to as dependence or correlation.

The correlation between two variables A and B is exactly the same as the correlation between A and B, and it describes the strength of the association between the two.

A causal relationship exists when an alteration in one variable directly affects an alteration in the other variable. A causal generalization, such as the claim that smoking causes lung cancer, does not refer specifically to any one smoker but rather to the unique connection between the characteristic of smoking and the characteristic of developing lung cancer.

An overview was given as your information is incomplete and can't be found.

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Answer:

c) cryptography

Step-by-step explanation:

Cryptography is a mechanism used to encrypt and decrypt data.

The weighted average for A,B and C will be 0.333.

What is weighted average?

Weighted average is a mean calculated by giving values in a data set more influence according to some attribute of the data. It is an important section in CAT quantitative aptitude. Weighted average is an average in which each quantity to be averaged is assigned a weight, and these weightings determine the relative importance of each quantity on the average. Weightings are the equivalent of having that many like items with the same value involved in the average.

Now,

Given weight for A=0.5, B=0.1 and C=0.4

Weighted average=(A+B+C)/3

=(0.5+0.1+0.4)/3

=1/3

Weighted average=0.33

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The sides of the triangle ABC are 6, 10, and 8. The sides of the triangle LMN are 12, 20, and 16. The ratio of the respective sides is the same for the two triangles because they are comparable. Therefore, BC is 10 miles long.

Due to the equal ratio of their corresponding sides, the triangles ABC and LMN are comparable. This indicates that the lengths of the sides of LMN may be obtained by multiplying the lengths of the sides of ABC by the same factor. For instance, side AB in ABC is 6 inches long, whereas side LM in LMN is 12 inches long. The lengths are 6:12, or 1:2, apart. The ratio remains the same for all matching. We can examine the other two sides of ABC to verify this response. Ten is the length of AC, and twenty is the length of MN. These two sides must likewise be multiplied by the same factor (1/2), since the ratio of the corresponding sides is the same. This results in AC and MN having lengths of 10 and matching ABC's dimensions. This demonstrates that BC is eight miles long.

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the complete question is

triangles abc and lmn are similar with measurements as shown. what is the measurement of bc, rounded to an integer find BC?

The price of the ABC bond on the previous day is $104 3/4

From the question, we have the following parameters that can be used in our computation:

Rate = $10 per day

Current price = $114 3/4

Using the above as a guide, we have the following:

Previous price = Current price - Rate

Substitute the known values in the above equation, so, we have the following representation

Previous price = $114 3/4 = $10

Evaluate the difference

Previous price = $104 3/4

Hence, the previous price is $104 3/4

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Complete question

ABC bond increase by $10 everyday. If the price on a given is $114 3/4, what was the price of the ABC bond on the previous day?

The correct description of each function term is given as follows:

1. Input: A rule to determine the value of the output.

2. Output: The result of applying a function rule to the value of an input, and is the dependent variable.

3. Domain: the set of allowable inputs.

4. Range: The set of possible outputs.

5. Function: A relation in which each input has only one output.

A function has the notation y = f(x), in which.

Hence the input is applied to the function to obtain the output, and these concepts, along with domain and range, are presented in this problem.

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The garden can split into 20 plots.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

A community garden has an area of 10 square yards.

The community wants to divide it into plots that each have an area of 1/2 square yard.

The number of community garden,

= 10/(1/2)

= 20

Therefore, the number of required plots is 20.

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3/2 is a slope of a line perpendicular to the line whose equation of

2x+3y=-3 .

One specific example of the more broad mathematical concept of orthogonality is the concept of perpendicularity, which is the orthogonality of traditional geometric objects.

As a result, in higher mathematics, the term "perpendicular" is occasionally used to represent considerably more intricate geometric orthogonality criteria, like the relationship between a surface and its normal vector.

If two lines cross at a right angle, they are said to be perpendicular to one another.

A first line is explicitly said to be perpendicular to a second line if the two lines meet and the straight angle on one side of the first line is cut by the second line into two congruent angles at the point of junction.

This can be done by rearranging the equation into the slope intercept form.

2x +3y = -3

3y = -2x -3

y = -2/3x - 1

Thus, the slope of the given line is -2/3.

The slope of the perpendicular line is the negative reciprocal of the given line.

Slope of perpendicular line = 3/2

The slope-intercept form was:

(i) The reciprocal of m is 1/m.

(ii) The negative reciprocal of m is -1/m.

Negative reciprocal of -2/3

= -1 ÷ (- 2/3)

= -1 × (-3/2)

= 3/2

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The dimensions of the poster are given as (x^2 - 6) inches by (x^2 + 12) inches.

The area of the poster is given by the product of these two dimensions:

Area = (x^2 - 6) inches * (x^2 + 12) inches

Area = x^4 - 6x^2 + 12x^2 - 72

Area = x^4 + 6x^2 - 72 inches^2

So, the area of the poster is x^4 + 6x^2 - 72 inches^2.