Transformation Question

Translate point (5, -6) based on vector V.
V:(-2,10)

Answer: 1898-1971

Step-by-step explanation: find the difference between the years and divide it over the change in cost

1. difference of yrs. : 1971-1898 = 73

2. difference of cost : 6-1 = 5

3. divide : 73/5 = 14.6 (avg)

avg for #1) 14.6

avg of #2) 1

avg of #3) 2.1

avg of #4) approx. 0.55

The area of an equilateral triangle having height 12 cm is 83.136 sq.cm.

An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It is sometimes referred to as a regular triangle because it is a regular polygon.

if height h is given in equilateral triangle then first we have to find the length of side which can be solve by this formula like a right angle triangle where side of equilateral triangle is a and another side is a/2 and next is height which is given 12 cm.

[tex]a^{2} -(a/2)^{2} = 12^{2}[/tex]

[tex](3/4)a^{2} = 144[/tex]

[tex]a^{2} = 192\\a = \sqrt{192}[/tex]

a = 13.85

area of equilateral triangle = [tex]((\sqrt{3})/ 4 )a^{2}[/tex]

= 1.732*192/4

83.136 sq.cm

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For the digits -5/4, -2 1/2, and -0.1, the correct inequality is -

Option D: -0.1 > -5/4 > -2 1/2

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The values for the inequality are -

A fractional number = -5/4

A mixed fractional number = -2 1/2

A decimal number -0.1

Convert the fraction number into decimal value using arithmetic operation of division -

-5/4 = -1.25

Convert the mixed fraction number into decimal value using arithmetic operation of multiplication and division -

-2 1/2 = -5/2 = -2.5

Here the greatest value is -0.1.

Then the second greatest value is -1.25 or -5/4.

The lowest value is -2.5 or -2 1/2.

So, the inequality obtained is = -0.1 > -5/4 > -2 1/2

Therefore, the inequality is -0.1 > -5/4 > -2 1/2.

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130 estimated to the nearest integer is 130 itself as 130 itself is an integer.

Integers are numbers which includes the set of natural numbers, 0 and the negatives of all those natural numbers.

Set of integers are usually denoted as Z.

A number is normally rounded to the nearest integer when it is decimal.

First we have to look at the tenths place.

When the digit in the tenths place is 5 or numbers greater than 5, then increase digit in the ones place by 1.

If the digit in tenths place is less than 5, then leave the ones place as such.

Suppose that the number is 1.30.

Then the digit in tenths place is 3, less than 5. So leave the digit in one place which is 1, as such.

So 1.30 rounded to the nearest integer is 1.

Here 130 itself is an integer.

Hence 130 rounded to nearest integer is 130.

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The ratio of employees who work in the office to employees who work in the warehouse is 5: 7

A ratio is a comparison of two quantities, and it is expressed as a fraction.

To find the ratio of employees who work in the office to employees who work in the warehouse, we need to first determine the total number of employees. In this case, we add the number of employees in the office (20) to the number of employees in the warehouse (28), which gives us a total of 48 employees.

Next, we can express the ratio of office employees to warehouse employees as a fraction by using the following formula:

Ratio = Quantity of First Term / Quantity of Second Term

In this case, the first term is the number of employees who work in the office (20) and the second term is the number of employees who work in the warehouse (28). So, the ratio of office employees to warehouse employees is:

Ratio = 20 / 28

Simplifying this fraction, we get:

Ratio = 5 / 7

This means that for every 5 employees who work in the office, there are 7 employees who work in the warehouse.

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Answer:

Below

Step-by-step explanation:

Go to   x = 1 on the x axis number line.....go UP to where the graph crosses x = 1  to find   y = 1    <====this is your answer for f(1)

for f(-)   go to x = 3 then go UP to the graph crossing at y = 1   <--answer

Answer:

Answer is Below ------v

1. clockwise

2. 3

1. (y, -x)

2. (3x,3y)

Dilation in coordinate geometry refers to the process of increasing or stretching the size of the originally drawn geometrical figure to a new figure by multiplying the co-ordinates of the original figure with a scale factor and obtain new co-ordinates to plot and form on the graph.

In the given figure, we observe that the original co-ordinates of the logo drew by Tyrone are:

A (-2,0) ; B (-2,3) ; C(2,2) ; D(2,-1)

From the graph, we see that the co-ordinates are multiplied by a scale factor of 5/2 and hence turn to new co-ordinates:

A'(-5,0) ; B'(-5, 15/2); C'(5,5) ; D'(5, -5/2)

Thus, we see that the rule followed to form the dilation of the logo on the coordinate plane was (5/2x, 5/2y).

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The circumference of a circle with a diameter of 11 inches using  π as 22/7 is 34.86 inches.

To find the circumference of a circle, we can use the formula:

C = πd

where C is the circumference, π is a mathematical constant (approximately 22/7), and d is the diameter of the circle.

The diameter of a circle is a straight line that passes through the center of the circle and touches two points on the edge of the circle. In this problem, we are given that the diameter of the circle is 11 inches.

To find the circumference, we can substitute this value for d in the formula:

C = πd = π(11 inches)

We can simplify this by using the approximation π ≈ 3.14 (or more precisely, π ≈ 22/7), to get:

C ≈ (3.14)(11 inches) = 34.54 inches

or

C ≈ (22/7)(11 inches) = 34.86 inches

So the circumference of the circle is approximately 34.54 inches or 34.86 inches, depending on which approximation of π is used.

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Answer:

31

Step-by-step explanation:

27.9/0.9 = 31

Last month 26 of the 280 students won a free lunch. The experimental probability of winning will be 13/140

Probability is the occurence of the events. Some of the events cannot be predicted with certainty. Probability of any event can be defined as P(A) , and there are many types of probability density functions.

Once a month, the cafeteria has each student pick a card from a standard deck of cards. From the deck of cards, each student has to pick a card for every one month.

Students who pick an ace get a free lunch

Given that,

Last month 26 of the 280 students won a free lunch and the percentage of winning is near to 9.2% approximately and it is very near to the 10%.

The experimental probability of winning is the ratio of number of possible outcomes to the total number of outcomes.

So, the experimental probability of winning is 26/280 = 13/140

Therefore, the  experimental probability of winning is 13/140

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Answer:

$115

Step-by-step explanation:

12 + 11 = 23

There are 23 students in the class.

Cost of supplies: $5 per student.

total cost = 23 × $5 = $115

The total cost to purchase the supplies is,

⇒ $115

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

There are 12 girls and 11 boys registered for the class.

And, You need to purchase supplies that will cost $5 per student.

Here, Total students = 12 + 11 = 23

Hence, The total cost to purchase the supplies is,

⇒ 23 x $5

⇒ $115

Thus, The total cost to purchase the supplies is,

⇒ $115

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Answer:

Step-by-step explanation:

Part A
First find the measure of angle C which is 52° due to it being next to angle D

Next add 52 to angle B to get 142

Subtract 142 from 180 to get 38°

Angle A is 38°

Part B

The fourth option is correct

Using the definition of congruent triangles, the missing values are:

x = 35

y = 30°

Given that the two triangles in the image above are congruent, it implies that all its corresponding angles and corresponding side lengths have equal measure.

Therefore, we have:

2x - 10 = x + 25

Solve for x:

2x - x = 10 + 25

x = 35

Plug in the value of x to find the missing angles:

y + 90 + (2x - 10) = 180 [triangle sum theorem]

y + 90 + (2(35) - 10) = 180

y + 90 + 60 = 180

y = 30°

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Answer:

slope = [tex]\frac{2}{5}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (5, 2) ← 2 points on the line

m = [tex]\frac{2-0}{5-0}[/tex] = [tex]\frac{2}{5}[/tex]

The length of the unknown side is 11.2ft

Using the Pythagorean theorem which states that the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

From the image shown,we have the parameters as;

Now, substitute the values, we have;

x² = 10² + 5²

Find the squares

x² = 100 + 25

Add the values

x ² = 125

Find the square root

x = 11.2 ft

Hence, the value is 11.2ft

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Answer:

y= 2200 (3/4)x

Step-by-step explanation:

You can model a real-world situation involving an initial value and a constant growth or decay factor with an exponential equation in the form y=a(b)x, where b>0 and b≠1.

The constant a represents the initial value. It is the y-value of the equation when x=0.

The constant b represents the growth or decay factor.

When the equation models exponential growth, b>1.

When the equation models exponential decay, 0<b<1.

An exponential equation in the form y=a(b)x can model the value of the machine, y, x years after purchase. To write the equation, first look for phrases in the problem that tell you about the initial value, a, and the growth or decay factor, b.

Tessa is opening Tessa's Terrific Tees, her own custom T-shirt business. She bought a T-shirt printing machine that is currently valued at $2,200. The machine loses  1/4 of its value every year.

The constant a is the initial value. The initial value of the machine is $2,200. So, a=2,200.

The constant b is the decay factor, since the value of the machine is decreasing. The machine loses 1/4 of its value each year. In other words, the value of the machine each year will be 1–1/4= 3/4

times the value the year before. So, b= 3/4.

The exponential equation y= 2200 (3/4)x models the value of the machine.

An exponential equation in the form y=a(b)x that can model the value of the machine, y, x years after purchase is y= 2200*14*x

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0. In mathematics, a linear equation is an equation that may be put in the form [tex]{\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0, } where x_{1}, \ldots, x_{n} are the variables, and {\displaystyle b, a_{1}, \ldots, a_{n}}[/tex] are the coefficients, which are often real numbers.

Given that;

The cost of tshirt printing machine= $2200.

The lose of machine= 14

Now,

Substituting all the values in equation y=a(b)x

a=2200

b=14

y=2200*14*x

Therefore, the linear equation of the question will be y=2200*14*x

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A 24.8% of babies have a head circumference greater than 14 inches.

The circumference of a circle is the length of the curved boundary or the perimeter of the circular shape. It is a measurement of the distance around the circle and is equal to the arc length of the circle if it were opened up and straightened out into a line segment. The circumference of a circle is related to its diameter by the formula: C = π * d

To calculate the percentage of babies with a head circumference greater than 14 inches, we need to find the area under the normal distribution curve to the right of 14 inches.

First, we need to convert 14 inches to the standard units (z-score). We can do that using the following formula:

z = (14 - 13.5) / 0.75 = 0.67

Next, we can use a standard normal distribution table to find the area to the right of z = 0.67. The value from the table is approximately 0.752.

Therefore, approximately 75.2% of babies have a head circumference less than or equal to 14 inches, and 24.8% of babies have a head circumference greater than 14 inches.

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The factored form of 8x^2+2x-3 is (8x-3)(x+1).

The factored form of 16x^2-1 is (4x+1)(4x-1). The expression 6x^2+1 cannot be factored further,

So the factored form of 36x^2+6 is 6(6x^2+1).

Factoring is a mathematical process that involves breaking down a complex expression into simpler terms that can be multiplied together to obtain the original word. In algebra, factoring is finding the factors or the prime numbers that multiply together to give the original polynomial.

For example, the expression x^2 + 5x + 6 can be factored as (x+2)(x+3). Factoring is a useful tool in solving equations and simplifying expressions, as it allows us to manipulate the original expression in a more manageable way. In addition, factoring is used in various fields such as cryptography, signal processing, and computer science. For instance, factoring large numbers is an important problem in cryptography and is used to secure data transmission.

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The probability of receiving two heads and one tail is 3/8, or 0.375.

One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.

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The point of symmetry on f⁻¹(x) is (4, 6) which is false.

The domain of f(x) is (-∞, 4) which is false.

The graphs of f(x) and f(x) are reflections across the x-axis which is also false.

The range of f⁻¹(x) is (- ∞, ∞) which is true.

Let the function f is given as

y = m(x + a) + c

Then the inverse function of the function f will be given by swapping x with y and y with x.

The function is given below.

f(x) = 5(x - 6)³ + 4

The inverse function of the function f(x) is given as,

x = 5(y - 6)³ + 4

y = ∛[(x - 4) / 5] + 6

f⁻¹(x) = ∛[(x - 4) / 5] + 6

The graph of the function and inverse function is given below.

The point of symmetry on f⁻¹(x) is (4, 6) which is false.

The domain of f(x) is (-∞, 4) which is false.

The graphs of f(x) and f(x) are reflections across the x-axis which is also false.

The range of f⁻¹(x) is (- ∞, ∞) which is true.

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Answer:

you took shorter time to complete by 2minutes

Step-by-step explanation:

30 minutes till 8.00 pm

plus

52 minutes

so

30+52=82 minutes

my homeworks

20 minutes till 9.00 pm

plus 1 hour or 60 minutes till 10.00 pm

20+60=80 minutes

80<82

so I took shorter time to complete the homework

The appropriate response will be (A). The first equation of motion gives the link between "velocity and time."

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

An equation is a mathematical representation of two equal objects, one on each side of a "equals" sign. We can solve challenges in our daily lives with the aid of equations. Most of the time, we look for help with pre algebra to resolve problems in real life. Pre-algebra concepts contain the fundamentals of mathematics.

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Answer:

Second string, first fret.

Step-by-step explanation:

Option D (x, y)→ (-2x, 2y) is the transformation that maps triangle UVW to triangle EFG.

In mathematics, a transformation refers to a process of changing the position, size, or orientation of a geometric shape. It is a fundamental concept in geometry, algebra, and other branches of mathematics that studies the properties of objects and their relationship with space.

Transformations can be classified into two main types: rigid and non-rigid transformations. Rigid transformations preserve the size and shape of the object while changing its position and orientation. Common examples of rigid transformations are translations, rotations, and reflections. Non-rigid transformations, on the other hand, change the size and shape of the object as well as its position and orientation.

Transformations are used in various areas of mathematics and science, such as computer graphics, physics, and engineering. They are also important in real-world applications, such as in designing and modeling objects, analyzing data, and solving practical problems.

The transformation involves a reflection across the y-axis (multiplication by -1 on the x-coordinate) and a dilation by a factor of 2 in the y-direction (multiplication by 2 on the y-coordinate).

Applying this transformation to the coordinates of triangle UVW:

(0, -2) -> (0, -4)

(2, 0) -> (-4, 0)

(-2, 2) -> (4, 4)

These transformed coordinates match the coordinates of triangle EFG, so option D is the correct answer.

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The percent error in a measure is given by the formula:

P = 100%*|real value - measure|/real value

Here we know that:

real value = 20.8 cm

measure = 20cm

Replacing that in the formula we will get:

P = 100%*|20.8 cm - 20cm|/20.8cm = 3.8%

That is the percent error.

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Complete question:

Jayden measured a pen to be 20 cm long the actual length of the pen is 20.8 cm, then what is the percentage error?.

Type A: 5.45 per pound, Type B: 4.35 per pound. This month's mixture: We know that an is 5.45 per pound, so we divide  total cost  401.65 by 5.45 to get a result of 73.69 LB of Type A. 2B + A = 410.35 2(4.35) = 8.70 A + 8.70 = 410.35 A = 401.65.

Total cost is a term used in economics to describe the least expensive way to produce a specific amount of a good (TC). Fixed costs, which are unaffected by the quantity of a good produced and include inputs like buildings and machinery, possibly including sunk costs, and variable costs, which change with the quantity of a good produced and include inputs like labor and raw materials, make up the total economic cost of production. Economics considers the total potential cost of each manufacturing item as one of the total cost's fixed or variable costs.

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The account that will yield the greatest future value is the first IRA. The difference in value would be $3,403.07.

The formula for calculating future value = annuity factor x monthly payments

Annuity factor = {[(1+r)^n] - 1} / r

Where:

Future value with monthly compounding: $416.66 x [{1.00208^360] - 1 }/0.00208] = $222,916.59

Future value with annual compounding: 5000 x [{1.025^30) - 1} / 0.0205] = $219,513.52

Difference in values = $222,916.59 - $219,513.52 = $3,403.07

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