A spherical ball of wax with a radius of 8 inches is melted and poured into a container shaped like a rectangular prism with a 14 inch x 16 inch base. What is the height of the melted wax in the new shape

Answer:

[tex]I'(-2,-4), J'(-4,4), K'(4,4)[/tex]

Step-by-step explanation:

Assuming the dilation is centered at the origin, it is known that for a dilation of scale factor [tex]k[/tex] centered at the origin, [tex](x,y) \to (kx,ky)[/tex].

Answer:

10

Step-by-step explanation:

using the distance formula

The right triangle in marked question number 3 have the value of u = 2 and v = √2 using the trigonometric ratio of sine and cosine of the angle 45°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

Considering the angle 45° for the right triangle, recall that sin 45° and cos 45° are generally both equal to √2/2

sin 45° = √2/u {opposite/hypotenuse}

√2/2 = √2/u

u = √2/√2 × 2 {cross multiplication}

u = 2

cos 45° = v/u {adjacent/hypotenuse}

√2/2 = v/2

v = 2/2 × √2

v = √2

Therefore, the value of u = 2 and that of n = 10, using the trigonometric ratio of sine and cosine of the angle 45° for the right triangle.

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Answer:

pro

Step-by-step explanation:

Answer:

A- NQ,

B- 24,

C- 14+10=24

The second coordinate in a two-dimensional coordinate system is the y-coordinate, which indicates the vertical distance from the origin point (0, 0).

Coordinate is a pair of numbers used to identify the position of a point in a plane or in space. It is mostly used in mathematics, science, and engineering. Coordinates are used to define locations on maps, to plot graphs, and to identify points on a two-dimensional plane. By knowing the coordinates of two points, one can calculate the distance between them.

The y-coordinate can be either positive, negative, or zero. The y-coordinate is also referred to as the “ordinate” or the “vertical coordinate”. The second coordinate is usually written as the number located at the top of the y-axis on a graph.

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Based on the definition of supplementary angles, the measures of the angles are:

Angle x = 122.5°

Angle y = 57.5°

When two angles gives a sum of 180 degrees when they are added together, then the two angles are referred to as supplementary angles.

For example, if angle x and angle y are supplementary angles, it means that:

Measure of angle x + measure of angle y = 180 degrees.'

Given the following:

The measure of angle x = x degrees

The measure of angle y = x - 65 degrees.

Therefore, we have:

x + x - 65 = 180

2x - 65 = 180

2x = 180 + 65

2x = 245

2x/2 = 245/2

x = 122.5

Thus:

Measure of angle x = 122.5°

Measure of angle y = 180 - 122.5 = 57.5°

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Answer:

A

Step-by-step explanation:

The cost price of large pizza is $12 and that of toppings is 0.75.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15. There are different types of equations like linear, quadratic, cubic, etc.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Let the cost of large pizza be x and that of toppings be y.

x + 2y = 13.50

x = 13.50 - 2y    - (1)

x + 5y = 15.75   - (2)

substitute equation (1) in equation (2),

13.50 - 2y + 5y = 15.75

3y = 15.75 - 13.50

3y = 2.25

y = 2.25 / 3

y = 0.75

now, put the value of y = 0.75 in equation (1),

x = 13.50 - 2 × 0.75

x = 13.50 - 1.5

x = 12

Therefore, the cost price of large pizza is $12 and that of toppings is 0.75.

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Answer: 64 miles per hour

Step-by-step explanation: 192 divided by 3= 64

Answer: $36

Step-by-step explanation:

Bill is $40, the 25% off coupon is used, and the 20% tip is left.

Step 1: Find 25% of 40

is/40=25/100 ------> 40(25)/100=10

Step 2: Find the new bill price after discount

40-10=30

Step 3: Find the 20% tip of 30

is/30=20/100 ---------> 30(20)/100=6

Step 4: Add the tip with the restaurant bill

30+6=$36

8.269 feet is the horizontal distance between the wall and the ladder's base.

Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.

The distance can refer to the physical length in physics or to an estimate based on other factors in ordinary language (e.g. "two counties over").

The term is frequently used metaphorically to refer to a measurement of the difference between two common pieces (such as statistical distance between probabilistic or edit distance between strings of text) or a degree of separation, as spatial cognition is a rich source of conceptual metaphors in human thought (as exemplified by the distance between people in a social network).

So, using a right-angled triangle's trigonometry:

(x  = required distance)

cos 74 = x / 30      

x = 30 cos 74

x = 8.269 ft

Therefore, 8.269 feet is the horizontal distance between the wall and the ladder's base.

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Answer:

Step-by-step explanation:

Isosceles triangle (Same angle) means both sides are the same length, triangle is also right meaning you can plug values into Pythagorean theorem ([tex]a^2 + b^2 = c^2[/tex])

[tex]x^2+x^2 = 1^2\\2x^2=1\\x = \sqrt{\frac{1}{2} }\\x = 0.707...\\x=0.7[/tex]

Assuming all my math is right, this is your answer

The volume of top solid is 1570cm³, the volume of bottom solid is 157cm³and the total volume of toy is 1727cm³.

Solids or three-dimensional shapes are defined as any shape or figure with three dimensions or more. Solid geometry is the study of the characteristics, volume, and surface area of three-dimensional shapes.

The toy can be divided into two solids :

The top solid is a cone and the bottom solid is a cylinder.

The total volume of the toy can be found by adding the volumes of the cone and cylinder.

Volume of cone

Length of the cone l= 13cm

The radius of the base of the cone r = 5cm

Height of cone h =  = 12cm

Volume of cone =  =  = 1570 cm³

Volume of cylinder

Radius r = 5cm

Height h = 2cm

Volume of cylinder =  = 157cm³

Therefore the total volume of toy =  1570 + 157 = 1727 cm³

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Answer:

please name the chapter

Answer:

Pleae see the attached graph.

Step-by-step explanation:

The values of x are graphed for their respective valid regions, as defined in the question.

The figure is a regular polygon then the value of x is 21.

What is a regular polygon?

A regular polygon is a polygon that has all sides equal and each side subtends an equal interior angle at the center.

The sum of the interior angles of a polygon is

sum = 180° (n - 2)

n is the number of sides

Here n = 12, then

sum = 180° × 10 = 1800°

So the angle subtended by one side at the center is given as follows

Each of the 12 interior angles = 1800° ÷ 12 = 150

Then,

7x + 3 = 150

7x = 147

x = 21

Hence, If the figure is a regular polygon the value of x is 21.

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Answer: We can write a system of equations to model this scenario using the information given.

Let x represent the number of children who played minigolf that day, and let y represent the number of adults who played minigolf that day.

The first equation represents the total number of customers, which is the sum of the number of children and the number of adults.

x + y = 320

The second equation represents the total amount of money earned, which is the product of the number of children playing and the cost per child's game plus the product of the number of adults playing and the cost per adult's game.

7x + 10y = 2900

So the system of equations that models this scenario is:

x + y = 320

7x + 10y = 2900

We can use this system of equations to find the number of children and adults who played minigolf that day, given the total number of customers and total amount of money earned. By solving this system of equations we can find the values for x and y.

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

4 x 4 = 16

2 x 10 = 20

You would have to separate the square and the rectangle.

The way you do this is by cut of the number and subtracting them, like 6 and 2 to get the square.

Yes, an exponential function can have 1 as a base.

An exponential function is a function of the form f(x) = a^x, where a is the base and x is the exponent. The base can be any real number, including 1.

When the base is 1, the exponential function is defined as f(x) = 1^x = 1 for any value of x. This function is a constant function that always equals 1.

It is important to note that when the base of an exponential function is less than 0, the domain of the function is all real numbers except for certain values of x.

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The amount of money each of them spends on​ the wire will be $23.76 and $35.64, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Challenge Emily and Andy to each go to a home improvement shop to purchase wire. The table shows the expense y in dollars for x of the wire they need.

y = kx

9 = 100k

k = 0.09

Then the question is given as,

y = 0.09 · x

Emily needs 22 feet of wire. Then the cost is given as,

y = 0.09 · (22 × 12)

y = $23.76

Andy needs 11 yards of the wire. Then the cost is given as,

y = 0.09 · (11 × 3 × 12)

y = $35.64

The amount of money each of them spends on​ the wire will be $23.76 and $35.64, respectively.

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The complete question is given below.

Therefore , the solution of the given problem of triangle comes out to be the measure of each angle is  36,54 and 90.

A triangle is a three-sided polygon in geometry that has three edges and three vertices. The fact that the internal angles of a triangle add up to 180 degrees is the most crucial aspect of triangles. Angle sum property of a triangle is the name of this property.

Here,

Using the angle sum property of triangle,

90+4x-16+3x+15=180.( Since its a right angle triangle)

7x+89=180

7x=91

x=13

Therefore, ∠G=4X-16=36 and ∠H=3x+15=54.

Hence, the measure of each angle is triangle is 36,54 and 90.

Therefore , the solution of the given problem of triangle comes out to be the measure of each angle is  36,54 and 90.

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The shifted coordinates for each of the following are (20,-11) and (6,2).

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).

Given, (x,y) → (x + 10, y - 6)

a)  when the input is (10,-5) -

10 + 10 = 20

- 5 - 6 = - 11

(20,-11)

b) when the input is (-4,8) -

-4 + 10 = 6

8 - 6 = 2

(6,2)

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The coordinates of M´ would be : (4, 1) after reflection across the line y = x.

The coordinates of J'' would be : (3, -1) after counterclockwise about the origin.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The quadrilateral JKLM is shown in the given figure.

As per the given graph, we can see that

The coordinates of M would be : (4, 1)

Suppose quadrilateral J´K´L´M´ is a reflection of JKLM in the line y = x.

Then the coordinates of M´ would be : (4, 1)

The coordinates of J would be : (1, 3)

Suppose quadrilateral J''K''L''M'' is a rotation of JKLM 90° counterclockwise about the origin.

Under a counterclockwise rotation about the origin of  90 degrees

A coordinate ( x, y ) → ( y, - x ),

The coordinate J is (1, 3) and is translated using the rule

Then simply plug in the values of x and y which are x = 1 and y = 3

Thus (1, 3) → (3, -1)

Thus, the coordinates of J'' would be : (3, -1)

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Answer:

2/3

Step-by-step explanation:

Choose any of the similar sides and set up the ratio, then reduce to the simplest fraction:

12/18 = 4/6 = 2/3

8/12 = 4/6 = 2/3

10/5 = 2/3

By solving these equations, Cole is currently 27 years old, and Anya is 30 years old.

A person's date of birth is compared to the date on which their age needs to be calculated as part of the age calculation process. The person's age is determined by deducting the person's birthdate from the given date. Age equals Given Date - Birthdate

Let x stand in for Anya's current age and y for Cole's present age.

Cole's older brother, Anya, is three years older. Hence:

x = y + 3

x - y = 3 (1) (1)

The total of their ages will be 79 in 11 years. Hence:

(x + 11) + (y + 11) = 79

x + y = 57 (2) (2)

Equations 1 and 2 are simultaneously solved to produce:

x = 30, y = 27

Cole is currently 27 years old, and Anya is 30 years old.

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The math word problems with the given words is A has 52 marbles, B has 105 marbles, find the difference between the number of marbles between A and B.

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."

1. A has 52 marbles, B has 105 marbles, find the difference between the number of marbles between A and B.

2. The temperature of city A is 35 degrees, on the second day the temperature decreased to 15 degrees. How much did the dropped (temp)?

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Answer: It is True

Step-by-step explanation:

The increase in thermal energy allows molecules to decrease their density and escape the liquid state to become gas molecules.

Yes, the mentioned sides of triangle will be right angles triangle because they follow Pythagoras theorem.

A right angled triangle is characterized by presence of hypotenuse, perpendicular and base. The sides of right angled triangle are related through Pythagoras theorem, which is -

Perpendicular² = Base² + Hypotenuse²

As we know that hypotenuse is the longest side of triangle, hence, will be the 13 cm.

So, keeping the values in formula -

13² = 5² + 12²

Taking square on both the sides of equation

169 = 25 + 144

Performing addition on Right Hand Side of the equation

169 = 169

Since, LHS is equal to RHS, hence, it is right angled triangle.

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