A rigid motion maps each part of a figure to an______ part of its image

Answer:

44 ft

Step-by-step explanation:

To find the height of the tree, h, model the given scenario as a two right triangles and solve using the tan trigonometric ratio.

[tex]\boxed{\begin{minipage}{7 cm}\underline{Tan trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\end{minipage}}[/tex]

See attached for a diagram modelling the given information.

Create two tan ratios using the given information, and rearrange each equation to isolate x.

Equation 1

Given:

Therefore:

[tex]\begin{aligned}\implies \tan 42^{\circ}&=\dfrac{h}{x+12}\\\\ x+12&=\dfrac{h}{\tan 42^{\circ}}\\\\ x&=\dfrac{h}{\tan 42^{\circ}}-12\end{aligned}[/tex]

Equation 2

Given:

[tex]\begin{aligned}\implies \tan 50^{\circ}&=\dfrac{h}{x}\\\\ x&=\dfrac{h}{\tan 50^{\circ}}\end{aligned}[/tex]

To find the value of h, substitute equation 2 into equation 1 to eliminate x and solve for h:

[tex]\implies \dfrac{h}{\tan 50^{\circ}}=\dfrac{h}{\tan 42^{\circ}}-12[/tex]

[tex]\implies \dfrac{h}{\tan 50^{\circ}}-\dfrac{h}{\tan 42^{\circ}}=-12[/tex]

[tex]\implies \dfrac{h\tan 42^{\circ}-h\tan 50^{\circ}}{\tan 50^{\circ}\tan 42^{\circ}}=-12[/tex]

[tex]\implies \left(\dfrac{\tan 42^{\circ}-\tan 50^{\circ}}{\tan 50^{\circ}\tan 42^{\circ}}\right)h=-12[/tex]

[tex]\implies h=\dfrac{-12\tan 50^{\circ}\tan 42^{\circ}}{\tan 42^{\circ}-\tan 50^{\circ}}[/tex]

[tex]\implies h=44.1967977...[/tex]

Therefore, the approximate height of the tree to the nearest foot is 44 ft.

The difference of the numbers of cookies produced by production lines A and B in a day is 280 cookies.

When two algebraic expressions are equated, a mathematical statement is called an algebraic equation. P = 0 or P = Q, where P and Q are polynomials, are the generic forms of algebraic equations. One variable only algebraic equations are referred to as univariate equations, while multiple variable algebraic equations are referred to as multivariate equations. A balanced equation in algebra is a given. Because of this, the right side of the equation will equal the left side.

Let the cookies produced by production line A = x.

Let the cookies produced by production line B = y.

Given that, the two production lines produce 7280 cookies in total each day.

x + y = 7280

Also, production line A produces 8% more cookies than production line B.

x = y + y(8/100)

x = y + 0.08y

x = 1.08y

The system of equations thus are:

x = 1.08y

x + y = 7280

Substitute the value of x in equation 2:

x + y = 7280

1.08y + y = 7280

2.08y = 7280

y = 3500

Substitute the value of y in equation 2:

x + y = 7280

x + 3500 = 7280

x = 3780

The difference between the cookies produced is:

D = x - y

D = 3780 - 3500

D = 280

Hence, the difference of the numbers of cookies produced by production lines A and B in a day is 280 cookies.

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The term that describes a group of statements that executes as a single unit is a "block". A block of code is a program that is grouped together and treated as a single unit. So, the correct option is D.

In computer programming, a block is a group of statements or declarations that are enclosed within a set of curly braces ({ }). The block serves as a single unit that is executed together. Blocks are used to organize code and to apply control structures, such as loops and conditional statements, to multiple statements.

A block can contain any number of statements, which can include variable declarations, function calls, loops, conditional statements, and other constructs. The statements within a block are executed in sequence, one after another, unless a control statement is encountered that alters the normal sequence of execution.

For example, a while loop in Java consists of a block of code that is executed repeatedly while a certain condition is true:

while (condition) {

   // block of code to be executed while condition is true

}

In this example, the block of code inside the curly braces will be executed repeatedly while the condition specified in the while statement is true. The block can contain any number of statements, and these statements will be executed each time the loop iterates.

Another common use of blocks is to define functions or methods. A function or method is a block of code that can be called from other parts of the program, and can take inputs (arguments) and return outputs. For example, in Python, a function can be defined as follows:

def function(argument1, argument2):

   # block of code to be executed in the function

   return result

In this example, the block of code enclosed within the function definition is executed when the function is called. The function can take inputs (argument1 and argument2), which can be used within the function, and it can return a result using the return statement.

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Expressing the given percentage as a fraction is; 1/10

To change a percent to a fraction, put the percentage over 100 (after removing the % sign) and simplify if necessary. For example, to convert 17% to a fraction, put 17 over 100, like this: 17/100.

Now, we are told that the largest Hmong population per capita in the United States is in St. Paul, Minnesota, where about 10% are Hmong Americans.

Thus, expressing this as a fraction gives us;

10/100 = 1/10

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Karen should order 41 square meters of carpet, and the cost will be $1,024.59 (taxes included).

An algebraic expression is a mathematical phrase that consists of variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. It is a combination of constants, variables, and operators that represent a value or a relationship between values.

For example, "3x + 5" is an algebraic expression where "3" and "5" are constants, "x" is a variable, and "+" is an operator. The expression can be evaluated by substituting a value for "x" and performing the necessary operations.

Algebraic expressions can also be simplified by combining like terms and using the rules of arithmetic to simplify the expression. For instance, the expression "2x + 3x" can be simplified to "5x" by adding the coefficients of the like terms "x".

Algebraic expressions are used extensively in algebra to represent equations and relationships between variables. They are also used in a wide range of mathematical and scientific applications, including physics, engineering, and finance.

To calculate the amount of carpet Karen needs to order, we first need to convert the measurements of her living room from feet to meters:

Length: 18 feet = 5.4864 meters (rounded to four decimal places)

Width: 24 feet = 7.3152 meters (rounded to four decimal places)

To find the area of the living room in square meters, we multiply these two values:

Area: 5.4864 meters x 7.3152 meters = 40.0637 square meters (rounded to four decimal places)

Since Karen can only order full square meters of carpet, she should order 41 square meters (to be safe).

To calculate the cost of the carpet, we simply multiply the area by the cost per square meter:

Cost: 41 square meters x $24.99/square meter = $1,024.59

So Karen should order 41 square meters of carpet, and the cost will be $1,024.59 (taxes included).

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The zeroes of the equation is  0, 1 and 9.

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:

w³ -w² + 9w= 9

Now. solving for 'w'

w(w² - w + 9)=9

so, either w= 9 or w² - w + 9 = 9

w= 9 or w² - w = 0

w= 9 or w(w-1) = 0

w= 9 or w= 0, w= 1

So, the zeroes are 0, 1 and 9.

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Answer:

Step-by-step explanation:

There are several ways to find the center of a triangle:

The Centroid: The centroid is a point that divides each median of the triangle into two equal parts. It is the average of the vertices of the triangle. To find the centroid, you simply average the x-coordinates and the y-coordinates of the vertices:

G = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3

where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices of the triangle.

The Circumcenter: The circumcenter is the center of the circle that passes through all three vertices of the triangle. To find the circumcenter, you need to find the midpoint of each side of the triangle and then draw perpendicular bisectors to each side. The point where the perpendicular bisectors intersect is the circumcenter.

The Orthocenter: The orthocenter is the point where the altitudes of the triangle intersect. The altitudes are the perpendicular lines from each vertex to the line that contains the opposite side. To find the orthocenter, you need to find the equations of the altitudes and then solve for the point where they intersect.

Note: If the triangle is an equilateral triangle, then the circumcenter and the centroid are the same. If the triangle is a right triangle, then the orthocenter and the circumcenter are the same.

The area of the triangle is given by Heron's formula A = 269.99 units² which is approximately 270 units²

Heron's formula is used to calculate the area of a triangle in terms of the lengths of its sides. If a, b, and c are the lengths of the sides, then the area of the triangle is

Area of Triangle A = √ [ s(s - a) (s - b) (s - c) ]

where s is half the perimeter, or (a + b + c) / 2

Given data ,

Let the triangle be represented as ΔKLM

Now , the measure of side KL , a = 30

The measure of side KM , b = 25

The measure of side LM , c = 22

From Heron's formula , the half the perimeter s = (a + b + c) / 2

Substituting the values in the equation , we get

s = ( 30 + 25 + 22 ) / 2

s = 38.5

Now , Area of Triangle A = √ [ s(s - a) (s - b) (s - c) ]

Substituting the values in the equation , we get

Area of Triangle A = √ [ 38.5 ( 38.5 - 30 ) ( 38.5 - 25 ) ( 38.5 - 22 ) ]

On simplifying the equation , we get

Area of Triangle A = √ [ 38.5 ( 8.5 ) ( 13.5 ) ( 16.5 ) ]

Area of Triangle A = √ ( 72,894.9375 )

On further simplification , we get

Area of Triangle A = 269.99 units² ≈ 270 units²

Hence , the area of triangle is 270 units²

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Answer:

3x+4=6

Step-by-step explanation:

Answer:false

Step-by-step explanation:

Answer:

y ≥ 9

Step-by-step explanation:

−2(4y+4)+5y ≤ −35

-8y - 8 + 5y ≤ -35

-3y - 8 ≤ -35

-3y ≤ -27

y ≥ 9

[tex] \sf 36 \degree = 3x[/tex]

[tex] \sf36 \div 3 = 3x \div 3 \\ \tt \: x = 12[/tex]

Answer:

Step-by-step explanation:

The equation h = -0.0159d² + 290 models the curve of the natural stone bridge, where h is the height of the curve in feet and d is the width of the curve in feet.

To find the vertex of the curve, we need to use the formula x = -b / 2a, where x represents the x-coordinate of the vertex and a and b are coefficients of the quadratic equation. In this case, the quadratic equation is h = -0.0159d² + 290, so a = -0.0159 and b = 0. To find the vertex, we plug these values into the formula:

x = -b / 2a = 0 / (2 * (-0.0159)) = 0

So the x-coordinate of the vertex is 0, which means the vertex is at the point (0, 290).

The vertex tells us that the highest point of the bridge (the vertex) is at a width of 0 feet. This means that the bridge is tallest at its center, and the height decreases as the width increases in either direction. Additionally, since the coefficient of the squared term is negative, the parabolic curve is downward-facing, which indicates that the bridge curves downward as it extends outward.

To find the span of the rainbow bridge, we need to find the width of the bridge where the height is 0. This represents the point where the bridge intersects with the river. To do this, we set h = 0 and solve for d:

0 = -0.0159d² + 290

0.0159d² = 290

d² = 290 / 0.0159

d ≈ 77.36

So the width of the bridge where the height is 0 is approximately 77.36 feet. Therefore, the span of the rainbow bridge is approximately 154.72 feet (twice the width at the point where the height is 0).

After multiplying and adding given equations, new equations are
3x² + 2xy - 8y² = -273 and 4x - 2y = -32 respectively.

Solutions of the equations are x = -5 and y = 6.

A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. where x is a variable, A is a coefficient, and B is a constant.  

Given equations,

a) x + 2y = 7

b) 3x - 4y = -39

Multiplying both equations

(x + 2y)(3x - 4y) = (7)(-39)

Using Foil method (a+b)(c+d) = ac + ad + bc + bd

3x² - 4xy + 6xy - 8y² = -273

3x² + 2xy - 8y² = -273

Which is a new equation.

Adding both equations

(x + 2y)+(3x - 4y) = (7)+(-39)

Adding like terms, we get

4x - 2y = -32

Solving the equations (a) and (b)

a) x + 2y = 7

x = 7 - 2y

Substituting x in terms of y in equation (b)

b) 3x - 4y = -39

3(7 - 2y) - 4y = -39

21 - 6y - 4y = -39

-10y = -60

y = 6

then x = 7 - 2(6)

⇒ x = - 5

Hence, x = -5 and y = 6 are solutions of given equations.

3x² + 2xy - 8y² = -273 is the equation, after multiplying both equations.

4x - 2y = -32 is equation after both equations are added.

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Let's start by substituting the right-hand side of the equation into the left-hand side:

What does the math equation mean?

Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

4y - 3 = 4(y + 1)

4y - 3 = 4y + 4

Now, we can isolate y by subtracting 4y from both sides:

0 = y + 4

-4 = y

So, there is a solution to the equation: y = -4. This means that Dawson is incorrect in saying that the equation has no solution.

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If you are told that a 20 kilogram object is raised by 10 meters, you know that (b) the mass of the object is 20 kilograms.

The force of gravity, also known as gravitational force, is the force that attracts two objects with mass towards each other.

AS we all know that Mass refers to the amount of matter an object contains, and is measured in kilograms. Weight, on the other hand, refers to the force of gravity on an object, and is measured in newtons.

Now, let's look at the options provided.

Option b states that the mass of the object is 20 kilograms, which is correct. This means that the object contains 20 kilograms of matter, regardless of its location or gravitational force acting on it.

In conclusion, we can determine from the given information that the mass of the object is 20 kilograms. However, we cannot determine the force of gravity acting on the object without additional information.

To calculate the force of gravity on an object, we can use the formula

Fg = mg,

where Fg is the force of gravity, m is the mass of the object, and g is the acceleration due to gravity (approximately 9.81 m/s² on Earth).

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Monica's age is 20 years and her father's age is 52

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.

Represent Monica's age by x and her father's age by y

y -x = 32 equation 1

y-16= 9(x-16)

= y-16 = 9x -144

y-9x = -144+16

y - 9x = -128 equation 2

subtract equation 2 from 1

-x-( -9x )= 32-(-128)

8x = 160

x = 160/8

x = 20

substitute 20 for x in equation 1

y = 32+x

y = 32+20

y = 52

Therefore Monica's age is 20 and her father's age is 52

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Answer:

y=4x-30

Step-by-step explanation:

Answer: To find the solution to the equation 21/2 + x = 31/2, we need to isolate x on one side of the equation. Subtracting 21/2 from both sides gives us:

x = 31/2 - 21/2

Combining the fractions on the right side gives us:

x = 10/2

Dividing the numerator by the denominator gives us:

x = 5

So the solution to the equation 21/2 + x = 31/2 is x = 5. To fill in the bubbles on the grid, you would need to write the number 5 in the appropriate row and fill in the corresponding bubbles to indicate the digits of the number.

Step-by-step explanation:

The angle 'b' measure 120 degrees from the diagram.

The given diagram is a circle geometry. Given the following parameters

x= 44° and;

a = 32°

In order to determine the measure of angles 'b'. we will use the expression below;

x = 1/2(b + a)

44 = 1/2 (b- 32)
88 = b - 32

b = 88 + 32

b = 120 degrees

Hence the measure of the angle 'b' from the diagram is 120 degrees.

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Expression is equivalent to ³√27x + ³√x, if x # 0, The correct answer is A. 4³√x.

To find the equivalent expression, we can factor out the common term of ³√x from both terms in the original expression:

³√27x + ³√x = ³√x(³√27 + 1)

Next, we can simplify the term ³√27 by finding the cube root of 27, which is 3:

³√x(3 + 1) = ³√x(4)

Finally, we can simplify the expression by multiplying ³√x and 4:

³√x(4) = 4³√x

Therefore, the equivalent expression is 4³√x, or answer choice A.

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The equivalent fraction to the given fraction is 1/2. Therefore, option C is the correct answer.

Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.

On the number line, the fraction marked is 3/6.

Here, divide both numerator and denominator by 3

We get (3÷3)/(6÷3)

= 1/2

Therefore, option C is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

Johnny found a fraction equivalent to the one shown by the point on the number line.  Which fraction could he have found?

A) 1/4

B) 1/3

C) 1/2

D) 2/3

The total cost of wax to cover the floor is

The area for of the floor is calculated and multiplied by the unit cost $1.38 to get the total cost

The floor is segmented and the area calculated and added together at last

1. Area of rectangle joining the right triangle

= 15 * (30 - 20)

= 150 square feet

2. Area of right triangle

= 1/2 * 15 * (35 - 10)

= 187.5 square feet

3. Area of the large rectangle

= 40 * 20

= 800 square feet

total area = 800 + 187.5 + 150 = 1137.5

cost of wax to cover the floor

= total area * unit cost

= 1137.5 * 1.35

= $1569.75

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complete question: image is attached

Answer:

The correct answer is B.

Step-by-step explanation:

I literally just took the test.

The age of the mother and the daughter currently would be = 30 and 6 years respectively.

The previous age of the mother(M) = 5D

Where D = daughter

Let the current age of the mother after 6 years ;

M + 6 = 3( D+6)

substitute 5D for M

5D + 6 = 3( D+6)

5D + 6 = 3D+ 18

5D-3D = 18-6

2D = 12

D= 12/2

D = 6 years

Therefore the current age of the mother= 5×6= 30 years

and daughter = 6 years.

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The pair of measurements that is not equivalent is 25 g and 25,000 kg. Option A.

Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.

Here,

The pair of measurements that is not equivalent is 25 g and 25,000 kg.
25 g is a relatively small amount of mass, while 25,000 kg is a very large amount of mass. Therefore, these two measurements are not equivalent.

The other pairs of measurements are equivalent because they involve conversions between different units of the same base unit. For example:

16 g and 16,000 mg,  1 g = 1,000 mg, so 16 g = 16,000 mg

140 mg and 0.14 g, 1 g = 1,000 mg, so 0.14 g = 140 mg

5 kg and 5,000 g,  1 kg = 1,000 g, so 5 kg = 5,000 g

Thus, the pair of measurements that is not equivalent is 25 g and 25,000 kg. Option A.

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The probability that the number is either even or a perfect square is [tex]\frac{3}{5}[/tex]

Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability is a concept in mathematics that helps predict the likelihood of certain events. Probability generally refers to the degree to which something is likely to occur..we will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.

Total Number of Outcome = 100

Number of even numbers = 50

Number of perfect square = 10

[tex]Probability \:=\:\frac{Number\: of\: favourable\:outcome\:}{Number\: of\: total\:outcome\:}[/tex]

[tex]Probability=\frac{50}{100} +\frac{10}{100} = \frac{60}{100} =\frac{3}{5}[/tex]

Therefore,  the probability that the number is either even or a perfect square is [tex]\frac{3}{5}[/tex]

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Using the cosine ratio, the value of x, to the nearest tenth, is: 39.3°.

The cosine ratio is part of the trigonometric ratios, which is given as:

cos ∅ = length of adjacent side / length of hypotenuse.

Given the following:

Length of adjacent side = 6.5

Length of hypotenuse = 8.4

Reference angle (∅) = x

Plug in the values:

cos x = 6.5/8.4

x = cos^(-1)(6.5/8.4)

x = 39.3°

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The required probability of the randomly selected households either having internet access or cable television is equal to 0.85.

Let us consider 'A' represents the number of house hold has internet access.

And 'B' represents the number of house hold has cable television.

P(A) = 75%

      = 0.75

P(B) = 80%

       = 0.80

Number of household has both internet access and cable television

= P( A∩B)

= 70%

= 0.70

Probability of randomly selected household either with internet access or cable are P( A∪B) :

P( A∪B) = P(A) + P(B) - P( A∩B)

Substitute the value we get,

⇒  P( A∪B) = 0.75 + 0.80 - 0.70

⇒  P( A∪B) =  0.85

Therefore, the probability of household having either internet access or cable television is equal to 0.85.

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Answer:123 degrees west

Step-by-step explanation: ngl i need them points but the degrees add up to 123 sine the is a prime number