How was divison made?

Step-by-step explanation:

I hope this answer is helpful ):

The steps which you would take to determine if these figures are similar include the following:

2. Multiply the vertices of polygon ABCD by 1/2.

5. Reflect the intermediate image.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

By critically observing the graph representing polygon ABCD, we can logically deduce that a sequence of transformations that would polygon ABCD (pre-image) onto polygon A"B"C"D" (image) is a dilation by a scale factor of 1/2 and a reflection of intermediate image.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

E = {0, 1, 2, 3)

Step-by-step explanation:

E = {0, 1, 2, 3)

The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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Answer:

0.02

Step-by-step explanation:

Given a normal distribution :

Mean income (m) = 25000

Standard deviation of income (s) = 6000

X ≥ 12000

Using the relation to fund the standardized score :

Zscore =(x - m) / s

Zscore = ( 12000 - 25000) / 6000

Zscore = -13000 / 6000

Zscore = - 2.167

Using a z probability calculator :

P(Z ≤ - 2.167) = 0.015117

= 0.02

Julio will be 30 years old when his father is twice his age.

To determine the age at which Julio will be twice his father's age, we need to find the age difference between them and then add that difference to Julio's current age.

Currently, Julio is 12 years old, and his father is 42 years old. The age difference between them is 42 - 12 = 30 years.

For Julio to be twice his father's age, the age difference needs to remain the same as it is currently. Therefore, when Julio is x years old, his father will be x + 30 years old.

Setting up an equation to solve for x:

x + 30 = 2x

Simplifying the equation, we subtract x from both sides:

30 = x

Thus, when Julio is 30 years old, his father will be 30 + 30 = 60 years old. At this point, Julio will indeed be twice his father's age.

Therefore, Julio will be 30 years old when his father is twice his age.

Note : the translated question is Julio is 12 years old and his father is 42 years old. How old will Julio be when his father is twice his age?

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Answer:

Step-by-step explanation:

Either way works. It comes to the same thing.

(2x-5)(x+1)=9

F: 2x*x = 2x^2

O: 2x*1 = 2x

I: -5 * x = -5x

L: -5*1 = -5

2x^2 + 2x - 5x - 5 = 9    Subtract 9 from both sides

2x^2 - 3x - 14 =0            Divide by 2 (it makes life easier).

Factoring you get

(2x - 7)(x + 2)

2x - 7 = 0

2x = 7

x = 3.5

x + 2 = 0

x = -2

The x intercepts = (3.5,0) and (-2,0)

I've put a graph up for the given equation.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

8y + 16

Step 02:

factor:

8y + 16 = 8 (y + 2)

The answer is:

8 (y + 2)

Answer:

The coordinates of point B are (-3,-3).

Step-by-step explanation:

Let \(A(x,y) = (6,-6)\), \(C(x,y) = (-6,-2)\) and \(\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}\), then we have the following formula by vectorial definition of a line segment:

\(\overrightarrow{AB} = \frac{3}{4}\cdot \overrightarrow{AC}\)

\(B(x,y) -A(x,y) = \frac{3}{4}\cdot [C(x,y)-A(x,y)]\)

\(B(x,y) = \frac{3}{4}\cdot C(x,y) +\frac{1}{4}\cdot A(x,y)\)

\(B(x,y) = \frac{3}{4}\cdot (-6,-2)+\frac{1}{4}\cdot (6,-6)\)

\(B(x,y) = (-3, -3)\)

Answer:

-1/2y+1/2x

Step-by-step explanation:

Answer:

A. 0; 1

Step-by-step explanation:

Required

Mean and standard deviation of a standardized normal distribution

A standardized normal distribution is represented as:

\((\mu,\sigma) = (0,1)\)

This implies that:

\(\mu = 0\) -- mean

\(\sigma = 1\) --- standard deviation

Hence, (a) is true

Answer:

Andrew is correct because the Parallel lines always have the same slope.

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

A. The radius of a given circle is longer than its diameter.

False. The diameter is twice the radius.

B. The length of the radius is the same in all circles.

False. Since there are circles of many sizes, there are many different sizes of the radius.

C. The circumference is always twice the radius.

False. The circumference is 2π times the radius or π times the diameter.

D. All circles contain 360 degrees.

True.

The Length is 5 inches and the Breadth is 15 inches

What is Perimeter?

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.

Solution:

Perimeter of Rectangle = 2*(Length + Breadth)

According to the question

Breadth = 3*Length

Perimeter = 40

40 = 2*(Length + 3*Length)

20 = 4*Length

Length = 5 inch

Breadth = 15 inch

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Answer:

The answer is A

Its A.

Reasoning: Because I Took The Test

The transformation of f(x) to p(x) is that (a) the graph is reflected and shifted down

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

The functions f(x) and g(x)

In the function equations, we can see that

f(x) = x²

p(x) = -f(x) - 3

So, we have

Vertical Difference = 0 - 3

Evaluate

Vertical Difference = - 3

This means that the transformation of f(x) to p(x) is that f(x) is reflected and shifted down 3 units to p(x).

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Answer:

4.5

Step-by-step explanation:

Answer:

Look at Screenshot

The parabola that has the height and width similar to the Gateway arc, gives;

(a) The quadratic equation of the parabola is presented as follows;

\( f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot \)

(b) The completed table is presented as follows;

Width. Height

567. 63.12

478. 225.67

308. 459.2

The shape of a quadratic function is a parabola, which is either upward facing or downward facing

(a) The given dimensions of the arc are;

Height = 625

Width at the base = 598

The points on the parabola are therefore;

(0, 0), (598÷2, 625) = (299, 625), (598, 0)

The equation of the parabola is of the form;

f(x) = a•x² + b•x + c, which gives;

f(0) = 0 = a×0² + b×0 + c = c

c = 0

f(299) = 625 = a×299² + b×299 + 0...(1)

f(598) = 0 = a×598² + b×598...(2

(a×598² + b×598) - 2×(a×299² + b×299) = 0 - 2×625

a•178802 = -2×625

a = -2×625 ÷ 178802

a ≈ -6.991 × 10^(-3)

b ≈ 4.181.

The equation is therefore;

\( f(x) = -6.991 \times 10^{-3} \cdot x^2 + 4.181 \cdot \)

(b)

The table of values is completed as follows;

When the width is 567 feet, x = 299 - 567÷2 = 15.5

\( \displaystyle{f(15.5) = -6.991 × 10^{-3} \times 15.5² + 4.181 \times 15.5 approx 63.12} \)

When the width is 478 feet, x = 299 - 478÷2 = 60

\( \displaystyle{f(60) = -6.991 × 10^{-3} \times 60² + 4.181 \times 60 approx 225.67} \)

When the width is 308 feet, x = 299 - 308÷2 = 145

\( \displaystyle{f(145) = -6.991 × 10^{-3} \times 145² + 4.181 \times 145 approx 459.2} \)

The table is therefore presented as follows;

Width. Height

567. 63.12

478. 225.67

308. 459.2

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Answer:

2001.19

Step-by-step explanation:

V=πr^2h

π×7^2×13=2001.19

\( \{ \: \alpha \: , \: \beta , \: a, \: b \}\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{n} \)

where, n denotes to number of elements in set .

Since, given set contains 4 elements .

Thus , 2⁴ {2 raise to power 4} .

\( \sf \longrightarrow \: No. \: of \: \: subsets = {2}^{4} \)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 2 \times 2 \times 2 \times 2\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 4 \times 4\)

\( \sf \longrightarrow \: No. \: of \: \: subsets = 16\)

Therefore, Required subsets are 16.

They are , Namely;

\( \sf \longrightarrow \: subsets \: = \phi \: \{ \alpha \} \{ \beta \} \{ a\} \{ b\} \: \{ \alpha \beta \} \{ \alpha a\} \{ \alpha b\} \{ \beta a\} \{ \beta b\} \: .....\)

_____________________________

If n is the number of elements in the set then,

No. of subsets possible for this subset is 2^n that's the (2 raise to the power n).

Let's take another example, {1,2}

Here, n = 2

subsets =2^2 =4

Subsets = ϕ, {1}, {2},{1,2}

Note :- every set is a subset of itself i.e. {1,2} and ϕ is a subset of every set

Hey there!☺

\(Answer:\boxed{6}\)

\(Explanation:\)

If x is equal to 4, then you will have to multiply 6 by x which is 4.

\(6*4=24\)

Now subtract 18 from 24.

\(24-18=6\)

\(6x-18=6\)

6 is your answer.

Hope this helps!☺

The volume of a solid formed by revolving the region bounded above by the line is (932π/15)

To use the disk method, we need to integrate over the axis of revolution, which is the y-axis in this case. We can break the solid into vertical disks of thickness dy.

The radius of each disk is given by the distance between the y-axis and the curve \(x = y^2 - 1\). So the radius is:

\(r = y^2 - 1\)

The height of each disk is the difference between the y-coordinate of the top curve y = 3 and the y-coordinate of the bottom curve y = 1. So the height is:

h = 3 - 1 = 2

The volume of each disk is then:

\(dV = \pi r^2h dy\)

Substituting r and h, we have:

\(dV = \pi (y^2 - 1)^2 (2) dy\)

To find the total volume, we integrate over the range of y from 1 to 3:

\(V = \int_{1}^{3} \pi(y^2 - 1)^2 (2) dy\)

This integral can be simplified by expanding the squared term:

\(V = \int_{1}^{3} \pi (y^4 - 2y^2 + 1) (2) dyV = 2\pi \int_{1}^{3}(y^4 - 2y^2 + 1) dyV = 2\pi [(1/5)y^5 - (2/3)y^3 + y]^3_1\)

V = \(2\pi [(1/5)(3^5 - 1^5) - (2/3)(3^3 - 1^3) + (3 - 1)]\)

V = 2π [(1/5)(242) - (2/3)(26) + 2]

V = 2π [(242/5) - (52/3) + 2]

V = 2π [(726/15) - (260/15) + 30/15]

V = 2π [(466/15)]

V = (932π/15)

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Note: The full question is

Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = 1, y = 3, x = y^2 - 1.

The missing fourth vertex needed to create a rectangle is (25, 3) option D.

Vertices (singular: vertex) are the corners or points where two or more lines, edges, or curves intersect and form an angle.

Here, the width of one side of the rectangle;

⇒ +3 - (-6) = 9 unit                (left side y-coordinates)

Similarly the length of the rectangle;

⇒ 25 - (-15) = 40 unit             (up-side x-coordinates)

Since a rectangular shape has two sets of equal sides of equivalent width (y-coordinates) and length (x-coordinates), we realize that the missing fourth vertex should be 9 units and 40 units over the point (25, -6). and (-15, 3)

So, we add 9 to the y-coordinate of (25, -6) and add 40 to the x-coordinate of (-15, 3) to get the missing vertex:

⇒ (25, -6+9) = (25, 3)

⇒ (-15+40, 3) = (25, 3)

Therefore, the missing fourth vertex is (25, 3)

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Answer:

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

Given:

Set equation and solve for x, the missing number: