Use the given information to complete parts I and II. In your final answer, include all calculations.

Planet Earth has an approximate diameter of 1.2742 · 10 10 millimeters. The sun has a diameter of 1.391 · 10 6 kilometers.

Part I: Given that for every one kilometer there are 1,000,000 millimeters, which unit of measurement should be used to best represent the lengths of the sun and Earth's diameters?

Part II: Approximate how many times greater the sun's diameter is than planet Earth's.

The weight of the brick that Sandra dropped is 40 N.

We must know that we can be able to define the density as the ratio of the mass to the volume of the object. We know that the density can be regarded as an intrinsic property of the substance.

We can see that;

Density = mass/volume

mass = Density * volume

Volume = 2 L or 2000 mL

Density = 2 grams per millimeters

Mass = 2 * 2000

Mass = 4000 g or 4 Kg

Weight = mass * acceleration due to gravity

Weight = 4 Kg * 10 m/s^2

Weight = 40 N

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The simplified expression of the ∛4x / 5 is ∛4x / ∛5

Index laws are the rules for simplifying expressions involving powers of the same base number, these laws are also called Laws of indices.

Laws of indices provide us with rules for simplifying calculations or expressions involving powers of the same base. The indices are also known as powers or exponents.

It is represented in the form:

am = a × a × a ×……× a (m times)

we have the  law of indices formula:

[tex]\sqrt[a]{b}=b^\frac{1}{a}[/tex]

∛4x / 5 = (4x/5)^1/3

Therefore,

∛4x / 5 = ∛4x / ∛5

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With a dilation factor of 1 / 4, Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) would be: A(-1, 1.5), B(-0.5 , 0.5), C(1, -0.5), D(1 , 1). Second option

The solution to the problem would be the solution that is gotten when we divide these points by 1/4. This is the dilation factor

we would have:

A(−4, 6), B(−2, 2), C(4, −2), D(4, 4)

= (-4 * 1/4, 6 * 1/4) , B(-2 * 1/4, 2 * 1/4), C(4 * 1/4, -2 * 1/4), D(4 * 1/4, 4 * 1/4)

= A(-1, 1.5), B(-0.5 , 0.5), C(1, -0.5), D(1 , 1)

Hence the second option is correct.

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Answer:A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1).

Step-by-step explanation:

To dilate a point using a scale factor, you multiply both the x-coordinate and the y-coordinate of the original point by the scale factor.

Given the original vertices of the polygon ABCD and a scale factor of one fourth (1/4), we can find the coordinates of the dilated vertices A', B', C', and D':

Original vertex A(-4, 6):

x-coordinate of A': -4 * 1/4 = -1

y-coordinate of A': 6 * 1/4 = 1.5

So, vertex A' is (-1, 1.5).

Original vertex B(-2, 2):

x-coordinate of B': -2 * 1/4 = -0.5

y-coordinate of B': 2 * 1/4 = 0.5

So, vertex B' is (-0.5, 0.5).

Original vertex C(4, -2):

x-coordinate of C': 4 * 1/4 = 1

y-coordinate of C': -2 * 1/4 = -0.5

So, vertex C' is (1, -0.5).

Original vertex D(4, 4):

x-coordinate of D': 4 * 1/4 = 1

y-coordinate of D': 4 * 1/4 = 1

So, vertex D' is (1, 1).

Comparing the calculated coordinates with the options given:

A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)

Among the given options, the correct vertices of polygon A′B′C′D′ are A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1).

The Kilograms of type B that are in one bag of the Latoya's Coffee shop blend would be = 3kg

What is a mixture?

A mixture is defined as the combination of two or more components which can or cannot be separated by ordinary methods.

The coffee blend of LaToya shop = Type A and B

A bag of the coffee blend = 6kg of Type A.

4 bags of coffee blend = 36kg

Therefore 4 bags of coffee blend contains = 6 see×4 = 24 kg of Type A

Type B in each bag = 36 - 24 = 12/4 = 3kg.

We are tasked with finding the amount in kilograms of type B coffee present in a bag of coffee.

We already know that in a bag , there are 4kg of type A coffee. Hence, in 6 bags, what we will be having would be 6 * 4kg = 24kg of type A coffee

The total kilograms of coffee in 6 bags of coffee is 48kg. Now we know we have 24kg of type A, the amount of type B coffee present is thus 48kg -24kg = 24kg

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The value of x and y in the equation is (x,y) = (68,2) (optionA)

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

x= 60+4y equation 1

7x + 12y = 500 equation 2

rearranging the equation

x- 4y = 60

7x+12y = 500

using elimination method

7x-28y = 420 equation 3

7x+12y = 500 equation 4

subtract equation 4 from 3

-40y = -80

divide both sides by -40

y = -80/-40

y= 2

substitute 3 for y in equation 1

x = 60+4(2)

x= 60+8

x= 68

Therefore the value of x and y is 68 and 2 respectively.

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Three images are formed when two plane mirrors are placed at 120.

assuming an angle of x between the mirror and the object. The previous graphic makes it evident that, regardless of the value of x assumed, the angle of the fourth picture will be more than 180 degrees. A mirror's reflection of the object in question produces a mirror image. The mirror image is what an object seems to be when it is placed in front of a mirror. The reality is quite different from what appears to be the case. No, some messages contain both mirror images and real photographs.

We know that angle = 120

number of images = 360/120

number of images = 3.

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Answer:

157.5 pounds

Step-by-step explanation:

11.25×12=135 then add 135 to 22.5

Talking about the 4:12 and 5:15 can be written in the form of 1:3

What do you mean by ratios?

Mathematical ratios show how many times one number appears in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a fruit plate. The ratio of lemons to oranges is 6:8, while the ratio of oranges to the total amount of fruit is 8:14.

How to address a ratio issue

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The expression is equivalent to the given expression is 5x²+12x-7: Option C

You should understand that  simplification means making an expression more simpler for better understanding

The given expression is

-2x²+8x-9+4x+7x²+2

The first thing to do is to rearrange the expression in the following ways by collecting the like terms

7x²-2x²+8x+4x-9+2

This implies that

5x²+12x-7

Conclusively the simplest form of the expression is 5x²+12x-7

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The equation will be [tex]x-3.2=18.2[/tex] by simple calculation.

An algebraic equation that only requires one step to solve is known as a one-step equation. Once you've figured it out, you'll know what the variable's value is that makes the equation true. In order to obtain the variable by itself when solving one-step equations, we perform the inverse (opposite) of the operation that is being applied to the variable.

An equation that must be solved in two steps is referred to as a two-step equation. Any constant that is on the same side as the variable must be removed first. To solve, isolate the variable on its own using inverse operations. Keep in mind that anything you do to one side must also be done to the other.

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In ΔOPQ, o = 10 cm, p = 67 cm, ∠Q=24,∠P=152.

A triangle in geometry is a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.

This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.

In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.

The vertex is the intersection of two straight lines. The triangle therefore has three vertices.

Hence, In ΔOPQ, o = 10 cm, p = 67 cm, ∠Q=24,∠P=152.

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The amount charged by the boutique for each item is given as follows:

The price of each item is obtained considering a system of equations, for which the variables are given as follows:

From the description, the equations are given as follows:

Simplifying the first equation by 11, we have that:

3.272727x + y = 299.5454

y = 299.5454 - 3.272727x

Replacing on the second equation, the cost of a wallet is given as follows:

91x + 10(299.5454 - 3.272727x) = 7599

58.2728x = 4603.5455

x = 4603.5455/58.2728

x = 79.

Then the cost of a belt is obtained as follows:

y = 299.5454 - 3.272727(79)

y = $41.

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Answer:

79 degree

Step-by-step explanation:

A triangle is 180 degrees

We know that angle D and F is equal to each other

180 - 22 = 158 degree

158 / 2 = 79 degree

So, m<F = 79 degree

Finding a number's square root is the equivalent as squaring it, or the opposite process. When you multiply the square root of a given integer by itself, you get the original number. Since 8 x 8 equals 64, as fact, 8 is the square root of 64.

It is possible to multiply an integer by its square root in order to obtain the original value. Square root of, end square root is the symbol for this mathematical concept. Contrary to squaring, finding a number's square root is the reverse.

For instance, 3 is squared at 9, 32, and its square root at 9, which is 9, is equal to 3. It is simple to multiply by 9 since it is a perfect square.

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The equation of the line with points (0.0) and (-3,-7) is y = 7/3 * x

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.

The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.

The points are (0,0) and (-3, - 7)

The equation of the line will be

y - 0 = (-7 - 0)/(-3-0) * (x - 0)

⇒y = 7/3 * x

The equation of the line with points (0.0) and (-3,-7) is y = 7/3 * x

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Answer:

21. 41,281

22. 17,401

23. 682,198

24. 1,795,329

29. 360

30. 335

31. 5,992

25. 78,461

26. 2158

27. 3167029

28. 5955748

32. 1452

33. 612

34. 7141

Your welcome

We can define a function f(x) with a domain of all real numbers (−[infinity],[infinity]) and a range of [-11,3].

Let's start by defining our function f(x):

f(x) = [-11,3]

Now, let's define our new function g(x):

g(x) = f(6x) + 1

This means that the range of g(x) is the range of f(x) plus 1, so the range of g(x) is [-67, 19]. In interval notation, this can be expressed as [-67, 19].

We can define a function f(x) with a domain of all real numbers (−[infinity],[infinity]) and a range of [-11,3]. To generate a new function, g(x), we can define it by g(x) = f(6x) +1. This means that the range of g(x) is the range of f(x) plus 1, so the range of g(x) is [-67, 19]. To express this in interval notation, we can write [-67, 19]. This means that the output of g(x) lies between the values -67 and 19. This new range can be found by multiplying each value in the range of f(x) by 6 and then adding 1 to each value. Therefore, the range of g(x) is [-67, 19] in interval notation.

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The points A(3,-2), B(-3, 8), C(-5, -1) and D(2,16) would form a parallelogram.

How to plot points on graph?

In mathematics, points on a graph are typically plotted on a coordinate plane. The x-coordinate and y-coordinate of each point determine its location on the plane. To plot a point, you will need to know its coordinates (x, y).

To plot the points A(3,-2), B(-3, 8), C(-5, -1) on the coordinate axes, we can start by drawing the x-axis and y-axis, where the x-axis is the horizontal line and y-axis is the vertical line.

We can then locate point A by starting at the origin (0,0) and moving 3 units to the right on the x-axis and 2 units down on the y-axis. Point B can be located by starting at the origin and moving 3 units to the left on the x-axis and 8 units up on the y-axis. Point C can be located by starting at the origin and moving 5 units to the left on the x-axis and 1 unit down on the y-axis.

To form a parallelogram, point D must be opposite of point B and have the same distance from point C and point A. Since a translation of a vector is a linear transformation, D is the translation of vector AB to point C.

The coordinates of point D would be (2,16), which is the translation of point B by the vector (2,8) to point C.

So the points A(3,-2), B(-3, 8), C(-5, -1) and D(2,16) would form a parallelogram.

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The slope-intercept form of the given linear equation 2x + y = 10 is y = -2x + 10.

If we draw the graph of the linear equation y = mx + c. The result is a line with m as the slope, and c as the y-intercept. This form of the linear equation y = mx + c is called the slope-intercept form, and the values of m and c are real numbers.

The slope, m, of the line represents the steepness of a line. This is also termed a gradient, sometimes. The y-intercept, c, represents the y-coordinate of the point where the graph of the line intersects the y-axis.

Now, change the given equation to slope-intercept form, y = mx + c, where m is the slope and c is the y-intercept.

2x + y = 10

Subtract 2x from both sides of the above equation, we get

y = -2x + 10

This is the required slope-intercept form of the given linear equation.

-- The given question is incorrect, the correct form of equation is

"What is the slope-intercept form the linear equation  2x + y = 10?" --

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Answer:

Step-by-step explanation:

40

The statements and reasons that are true and can be used in a proof that m∠8  <  m∠6 are:

A) m∠6+m∠2+ m∠3 = 180° because the sum of the measures of the interior angles of a triangle is 180°.

C) m∠8+m∠1+m∠2+m∠3+m∠4 = 180° because the sum of the measures of the interior angles of a triangle is 180°.

Interior angles can be created in geometry in two different ways. In one, parallel lines are cut by a transversal, and in the other, they are inside a polygon. Depending on how large they are, angles are divided into various types. Other angles fall into the category of pair angles because they need to be present in pairs in order to display a particular characteristic. One type of these is interior angles.

Interior angles can be outlined in two different ways:

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When the input x is -18, the output h is 14. The answer is obtained using substitution method.

What is substitution method?

One of the algebraic techniques for solving simultaneous linear equations is the substitution approach. It entails changing any variable's value from one equation to the other by substituting it in. In this manner, a pair of linear equations are combined into a single, simple linear equation with just one variable.

Now, we are given h = 17+x/6

So, when the input x is -18, using substitution method,

h=17+(-18/6)

=17+(-3)

=17-3

=14

Hence, when the input x is -18, the output h is 14.

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27.5 hrs are  long did she walk take to cover distance .

In math, what is a distance?

The length of the segment of the line that connects the supplied two points determines the distance between them.

                    The shortest segment of a line connecting a point to a line will have a length equal to the distance between them.

Distance covered by Alliosn =  1/2 km

Time taken by Alliosn  = 1/5hr

Hence,

speed of peter = Distance/time

= (1/2)/(1/5) km/hr

= 1/10 km/hr

Distance travelled by Alliosn = 1  1/4 km

=  11/4km

Speed = distance/time

1/10 = (11/4) / time

i.e.

Time = 11 * 10/4

       = 27.5 hrs

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So the value of integral [tex]\int\limits^4_1 {\frac{x}{x^2+13} } \, dx[/tex] is 0.51

An integral is a mathematical concept used to calculate area or change over an interval, represented by ∫. It is opposite of derivative, with two types: definite and indefinite. Used in many areas of mathematics and physics.

The integral of x/(x^2+13) from x=1 to x=4 can be evaluated using the method of substitution.

Let u = x^2+13, then du/dx = 2x dx

so x dx = du/2

now the integral becomes 1/2 * integral (1/u) du

so intergral is 1/2* [tex]\int\limits {\frac{1}{u} } \, du[/tex]

=> 1/2 [tex]\left \{ {{x=4} \atop {x=1}} \right.[/tex] ln([tex]x^2[/tex]+13)

=> 0.5 ( ln(39)-ln(14))

=>0.51

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Complete question:

evalute integral [tex]\int\limits^4_1 {\frac{x}{x^2+13} } \, dx[/tex]

Answer: To use the elimination method to solve the system of equations, we'll try to eliminate one of the variables by adding or subtracting the equations.

We have:

4x+y=8

3x-2y=6

multiplying the first equation by -2:

-8x-2y=-16

and adding it to the second equation:

3x-2y+(-8x-2y)=6+(-16)

-5x = -10

x = 2

substituting x=2 in the first equation:

4(2)+y = 8

8+y = 8

y = 0

So the solution is x=2 and y=0, that corresponds to the option B.

The center of a transformation refers to the fixed point through which the transformation takes place.

The center of a transformation can be found by the following methods:

Translation: The center of a translation is the point that remains fixed during the transformation.

Rotation: The center of rotation is the point around which the object rotates.

Reflection: The center of reflection is the line of reflection or the point of symmetry.

Dilation: The center of dilation is the point that remains fixed during the transformation and all the distances from it are multiplied by a scale factor.

Combination of Translations, Rotation, Reflection, and Dilation: The center of transformation will be the point of intersection of all the fixed points of above mentioned four transformations.

It is important to note that not all transformations have a center, and some may have multiple centers.

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The ratio of the area of a circle to the area of a square with sides of length equal to the circle's diameter is π/4.

This can be expressed mathematically as A_circle/A_square = π/4, where A_circle is the area of the circle and A_square is the area of the square.

To calculate the area of the circle, use the formula A_circle = πr^2, where r is the radius of the circle. To calculate the area of the square, use the formula A_square = (d^2)/4, where d is the diameter of the circle. Therefore, the ratio of the area of the circle to the area of the square is A_circle/A_square = πr^2/(d^2/4) = 4πr^2/d^2.

For example, if the radius of the circle is 4 cm, then the diameter is 8 cm, and the ratio of the area of the circle to the area of the square is A_circle/A_square = 4π(4^2)/(8^2) = 16π/64 = π/4.

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