Which of the following statements must be true about the diagram

The statements that are true regarding the area of circle D include the following:

A. The area of the circle depends on the square of the radius.

C. The area of circle D is 324π centimeters squared.

Mathematically, the area of a circle can be calculated by using this formula:

Area = πr²

Where:

r represents the radius of a circle.

In this context, we can reasonably infer and logically deduce that the area of any circle is directly proportional to the square of its radius.

Substituting the given radius into the formula for the area of a circle, we have the following;

Area of circle = π × 18²

Area of circle = 324π centimeters squared.

Based on the calculations, we can reasonably infer and logically conclude that the area of circle D in terms of pie (π) is equal to 324π centimeters squared.

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Which statements are true regarding the area of circle D? Select two options.

The area of the circle depends on the square of the radius.

The area of circle D is 36π centimeters squared.

The area of circle D is 324π centimeters squared

The area of the circle depends on the square of π.

The area of the circle depends on the central angle.

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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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.

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 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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Answer:

157.5 pounds

Step-by-step explanation:

11.25×12=135 then add 135 to 22.5

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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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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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 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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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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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 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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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:

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

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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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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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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angle of elevation = 17.5 degrees

shadow length = 4

To compute the tree height using the given formula, you would need to use the inverse tangent function (arctan) to find the angle of elevation in radians, and then multiply that value by the shadow length.

In this example:

angle of elevation = 17.5 degrees

shadow length = 4

tree height = tan⁻¹ (17.5) × 4

From this, the final output will be 7.398881327917831.

The formula states that the ratio of the tree's height to the shadow's length is equal to the tangent of the angle of elevation. So, by measuring the shadow length and the angle of elevation, we can use the tangent function to calculate the tree's height.

The inverse tangent function (arctan) is used to find the angle of elevation in radians, and then the result is multiplied by the shadow length to get the tree height.

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Answer: B $2:00

I Just took it

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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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).

JL has a length of 5.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees.

At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

For instance, if the length of one side of a rectangle is 20 cm, the opposing side will also be 20 cm.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.

It is also known as an equiangular quadrilateral for this reason.

Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.

According to our question-

3x + 4 = 4x - 1

-3x         -3x

4 = x - 1

+1      +1

5 = x

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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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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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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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Answer:

Step-by-step explanation:

40