For #5 - 7, using the given scale factor and center, dilate the following figures and state the new coordinates.

The first triangle is an Isosceles triangle:

2 equal sides

2 equal angles ( opposite to the sides)

The sum of all interior angles of a triangle is 180°

So, for the left triangle:

51+x+x2 = 180

x+x2 = 180-51

x+x2 = 129

Since both angles are equal:

129/2 = 64.5°

x= 64.5°

x+y = 90°

64.5 + y = 90

y= 90-64.5

y= 25.5°

Right triangle:

25.5+25.5 +z = 180

z= 180-25.5-25.5

z= 129°

we know that

In a paralleogram opposite angles are congruent and consecutive angles are supplementary angles

That means

and

so

substitute the given values

(3x+y)=5y+20

3x-4y=20 ------> equation 1

substitute

(3x+y)+(5x+10)=180

8x+y=170

y=170-8x ------> equation 2

solve the system

substitute equation 2 in equation 1

3x-4(170-8x)=20

solve for x

3x-680+32x=20

35x=20+680

35x=700

x=20

Find the value of y

y=170-8(20)

y=10

step 2

Find the measure of angle B

Answer:

D. 17.4 yards

Step-by-step explanation:

Since the area of the rectangle is 17.36 square yards, and the width is 3.1 yards, we set up and solve this equation to find the length:

17.36 = 3.1h, so h = 5.6 yards.

From this, the perimeter of the rectangle is 2(3.1 + 5.6) = 2(8.7) = 17.4 yards.

So D is the correct answer.

All the values are;

1) f (-4) = 16

2) f (1) = 1

3) f (5) = 10

4) f (7) = 14

5) f (9) = 50

What is substitution method?

Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The function is;

f (x) = { 4 - 3x ; if x ≤ 1

     = { 2x  ; if x > 1

     = { 5x + 5 ; if x ≥ 9

Now, Find all the values as;

Since - 4 is belong in x ≤ 1, so we get;

f (x) = 4 - 3x

f (-4) = 4 - 3 × -4

f (-4) = 4 + 12

f (-4) = 16

And, Number 1 is belong in x ≤ 1, so we get;

f (x) = 4 - 3x

f (1) = 4 - 3 × 1

f (1) = 4 - 3

f (1) = 1

And, Number 5 is belong in x > 1, so we get;

f (x) = 2x

f (5) = 2 × 5

f (5) = 10

And, Number 7 is belong in x > 1, so we get;

f (x) = 2x

f (7) = 2 × 7

f (7) = 14

And, Number 9 is belong in x ≥ 9, so we get;

f (x) = 5x + 5

f (9) = 5 × 9 + 5

f (9) = 50

Thus, All the values are;

1) f (-4) = 16

2) f (1) = 1

3) f (5) = 10

4) f (7) = 14

5) f (9) = 50

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Considering the parameters of the normal distribution for American men's heights, it is found that:

a) The percentage greater than 74 inches is: 2.5%.

b) The proportion between 64 and 71.5 inches is: 0.815.

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the following equation:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In the context of this problem, the mean and the standard deviation of the heights of American men are given as follows:

[tex]\mu = 69, \sigma = 2.5[/tex]

The proportion of heights that is greater than 74 inches is one subtracted by the p-value of Z when X = 74, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (74 - 69)/2.5

Z = 2.5

Z = 2.5 has a p-value of 0.9772.

1 - 0.9772 = 0.0228, hence the percentage is of 2.28%. Using the Empirical Rule, this percentage is rounded to 2.5%.

The proportion of heights between 64 inches and 71.5 inches is the p-value of Z when X = 71.5, subtracted by the p-value of Z when X = 64, hence:

X = 71.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (71.5 - 69)/2.5

Z = 1

Z = 1 has a p-value of 0.84. (rounded with the Empirical Rule).

X = 71.5:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (64 - 69)/2.5

Z = -2

Z = -2 has a p-value of 0.025. (rounded with the Empirical Rule).

Hence the proportion is:

0.84 - 0.025 = 0.815.

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Write a mathematical expression for the following statement: x is at least 19

this means that x > 19

in set builder notation: (19,∞)

ANSWER

The solution is: -3 < p < 3.8

EXPLANATION

When we have an absolute value inequality, to "eliminate" the absolute value we have to write the following:

To solve this we have to add 4 everywhere in the inequality:

And divide everything by 10:

To graph we have to draw a line from -3 to 3.8, with empty circles at the ends - because those values are not included in the solution.

The diagram of the solid is shown below:

The surface area ould be the sum of the area of each face

The area of the first rectangular face = 1.5 * 3.3 = 4.95 cm^2

The area of the middle rectangular face = 2.5 * 3.3 = 8.25 cm^2

The area of the third rectangular face = 2.0 * 3.3 = 6.6 cm^2

Area of each triangle is 1/2 * base * height = 1/2 * 2 * 1.5 = 1.5

Since the faces are 2, area of both triangular faces = 1.5 * 2 = 3 cm^2

Total surface area of the solid is

4.95 + 8.25 + 6.6 + 3 = 22.8 cm^2

X' is the set of blood types that type AB- cannot donate blood to

Y is the set of blood types that type AB+ can donate blood to

From the table, AB- cannot donate blood to:

(This is all the blood types minus the ones that can receive from AB-)

U - {AB+, AB-} = {A+, B+, A-, B-, O+, O-} = X'

Y = {AB+}

So the negations:

X = {AB+, AB-}

Y' = {A+, B+, AB-, A-, B-, O+, O-}

And this is our final answer

Lauren can add $30 each month to her savings account

Income made by Lauren from part-time job = $185

Money sent to Lauren by her parents = $120

Total income of Lauren  = Money from job+ money received from parents = 120+185 = $305

Let her total expenses be x

Substituting the values in the formula we get:

Sum of Lauren's paycheck + Money she gets from her parents = Total expenses+ 11% more than her total expenses

185 + 120 = x+11% of x

305=x+11/100*x

305 = 1.11x

x=274.77 or 275

Money she can add in her savings account each month = Total money received - Expenses = 305 - 275 = $30

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Relation 1:

It is a function because one point of its range (axis y) have two points in the domain (axis x).

Relation 2:

It is not a function because one point in the domain have two points in the range:

Relation 3:

It is a function because each point in the domain have a different point in the range.

Relation 4:

It is not a function because the point -7 in the domain have three values for the range:

The answer is, the relations: 2,4 are not functions and the functions 1, 3 are functions.

The percent tip paid on the Ai Mi's $9 dinner is 31%.

Tip increases the price paid for a service rendered. Percentage is the rate of amount that is expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to change a number to percentage, multiply the number by 100.

The first step is to determine the tip paid : $11,79 - $9 = $2.79

Now, express the tip as a ratio of the cost of the dinner and multiply by 100

(2.79 / $9) x 100 = 31%

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Hi there. To solve this question, we'll have to remember some properties about parabolas and its roots.

Given the function:

that models the height of the football Armando kicked from the ground, in feet, with respect to time x in seconds, we have to determine:

The time it takes for the ball to return to the ground after being kicked.

Let's suppose that the ball was kicked from x = 0, since the times x is given in seconds and we can't have negative time.

Before supposing it, in fact we have to determine which moments the ball was at the ground, that is, f(x) = 0. We're finding the roots of the function:

To solve this quadratic equation, remember the general solution to a quadratic equation

Is given by the formula:

Plugging a = -7, b = 38 and c = 0.22, we get:

Multiply the values, square the number and add inside the radical.

Separing the solutions and calculating their values, we get

In this case, we before had supposed the ball started from x = 0. This is not really necessary because we found that the roots of this functions are contained in the positive x-axis.

To find the time for the ball to return to the ground, we make:

Or 5.42 seconds.

Graphically, what we have is:

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Describe the first experiment

Two slips were drawn simultaneously, this means that the outcome of the first slip drawn will be multiplied by the outcome of the second slip drawn. The probability will follow the "and rule of probability".

STEP 2: Describe the second experiment

Since one slip is drawn and then put back into the box before a second slip is drawn, this is a PROBABILITY WITH REPLACEMENT. The outcome of the first event will not affect the outcome of the second event since the paper slips are replaced hence not reduced.

STEP 3: Describe the third experiment

Since one slip is drawn and not put back into the box before a second slip is drawn, this is a PROBABILITY WITHOUT REPLACEMENT. The outcome of the first event will affect the outcome of the second event since the paper slips reduce.

Difference between b and c is that b is with replacement and the total outcomes does not change while c is without replacement and the total outcomes change(reduce) after the first slip is drawn.

It is an Irrational number.

Mathematics Number Types

The numbers are divided into many sorts based on their characteristics and how they are shown on a number line. To help readers comprehend each kind of number, descriptions, features, and examples are included. Here are the many kinds of numbers:

Natural Numbers

Natural numbers, which include the range of positive integers from 1 to infinity, are sometimes known as "counting numbers." The letter "N" stands for the set of natural numbers. The definition of the natural number set is:

N = {1, 2, 3, 4, 5, ……….}

For instance, 35, 59, 110, etc.

Natural Numbers' Characteristics

Natural number addition is commutative, associative, and closed.

Multiplication of Natural Numbers is closed, associative, and commutative.

Zero is the identity component of a natural number when added.

A natural number's identity component under multiplication is one.

Complete numbers

Natural numbers with a zero are another name for whole numbers. The set is made up of non-negative integers without any fractional or decimal parts. The entire set of numbers is "W" which stands for the concept. The definition of the natural number set is:

W = {0,1, 2, 3, 4, 5, ……….}

For instance, 67, 0, 49, 52, etc.

Whole-number properties:

Under addition and multiplication, whole numbers are closed.

The identity component of the whole numbers that are additive is zero.

The multiplicative identity element is 1, which.

It complies with addition and multiplication's commutative and associative properties.

The distributive property that favors multiplication over addition and vice versa is satisfied.

Here is further information about the entire numbers.

The set of all whole numbers with a negative set of natural numbers is known as an integer. The letter "Z" stands for the integer set. The definition of the set of integers is:

Z = {-3, -2, -1, 0, 1, 2, 3}

For instance: -52, 0, -1, 16, 82, etc.

Characteristics of integers

For addition, subtraction, and multiplication, integers are closed.

For integer addition and multiplication, the commutative property is met.

It abides by the addition and multiplication operations' associative feature.

For addition and multiplication, it abides by the distributive property.

The integers' additive identity is 0.

Integers have a multiplicative identity of 1.

Actual Figures

Real numbers are any number, including positive and negative integers, fractional and decimal numbers, and quantities without imaginary numbers. The letter "R" is used to signify it.

Examples are 34, 0.333, 2, 0, -10, 20.

Real Numbers' Characteristics

Under addition and multiplication, Real Numbers are commutative, associative, and distributive.

The opposite property applies to real numbers.

Real numbers have identity elements that are 0 and 1, respectively, for addition and multiplication.

Rational  Numbers

Any integer that can be expressed as p/q, or as a ratio of one number to another, is referred to be a rational number. The letter "Q" can be used to signify a rational number.

Examples include 7/1, 10/2, 1/1, and 0/1.

Rational number properties include:

Addition, subtraction, multiplication, and division all result in closed rational numbers.

With regard to addition and multiplication, it meets the commutative and associative properties.

For addition and subtraction, it abides by the distributive property.

Unrealistic Numbers

The amount that cannot be represented by p/q. It denotes a number as being irrational if it cannot be expressed as a ratio of one to another. The letter "P" is used to signify it.

Examples include 2 and Euler's constant.

Irrational number characteristics include:

Irrational numbers do not meet the property of closure.

Under addition and multiplication, it complies with the commutative and associative properties.

Irrational numbers can be added to and subtracted from in distributive ways.

Large Numbers

Complex numbers are those that take the form a+bi, where a and b should be real values, and I should be an imaginary number.

Examples are 1 + 2i, -2 + 3i, and 4 + 4i.

Complex number properties include:

The complex numbers have the following characteristics:

a characteristic of addition and multiplication that is associated.

Commutative addition and multiplication properties.

Multiplication's distributive advantage over addition.

Unreal Numbers

The complex numbers category includes imaginary numbers. It is the result of adding actual numbers with the hypothetical unit "i." It defines the imaginary portion of complex numbers.

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Answer:

506.40

Step-by-step explanation:

.

Using unitary method, it is better to buy 18 ounce of rice for $6.30

There are three types of rice

Rice 1

The cost of 18 ounce of rice = $6.30

Here we have to use the unitary method

The cost of 1 ounce of rice = 6.30/18

= $0.35

Rice 2

The cost of 12 ounce of rice = $4.56

Apply unitary method

The cost of 1 ounce of rice = 4.56/12

= $0.38

Rice 3

The cost of 7 ounce of rice = $2.59

Apply unitary method

The cost of 1 ounce of rice = 2.59/7

= $0.37

So It is better to buy rice 1

Hence, unitary method, it is better to buy 18 ounce of rice for $6.30

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Step-by-step explanation:

[tex]\sqrt[3]{t^{2} } + 4\sqrt{t^{3} } \\=t^{\frac{2}{3} } + 4t^{\frac{3}{2} }\\\\then, \\u` = \frac{2}{3}t^{-\frac{1}{3}} + 6t^{\frac{1}{2} }[/tex]

The expression equivalent to 3(−4.5b − 2.1) − (6b + 0.6) is -19.5b - 6.9.

Given expression:

3(−4.5b − 2.1) − (6b + 0.6)

To simplify the expression open the brackets and multiply the terms,

-13.5b − 6.3 − 6b - 0.6

Now, combine the like terms together and add them,placing a negative sign in front of the terms

-13.5b − 6b - 0.6 - 6.3

-19.5b - 6.9

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Answer: 600

Step-by-step explanation:

I did not check your work from parts a and b.

Assuming they are correct,

You have found the total amount after the first year and the total amount after the first two years.

To find the total amount for only the second year,

you subtract the second year totals from the first year totals.

So,

(b) - (a) = 1000 - 400 = 600

Answer:

Step-by-step explanation:

Angles A and B, same as angles C and D are vertical angles and have equal measure according to definition of vertical angles:

Find the measure of angles C and D.

∠C and ∠D are supplementary with ∠A or ∠B, so the pair sums to 180°.

So the angle measures are:

Given:

Initial amount (Base) = 15, 757

Rate of increase = 3.5% or 0.035 in decimal form

Find: new price and the price increase

Solution:

To be able to get the new price, we need to solve for the price increase first. To do that, we need to know what is 3.5% of the old price 15, 757. To calculate that, we will multiply 0.035 by 15,757.

3.5% of 15, 757 is 551.50. This is the price increase of the car next year.

Hence, by next year, the new price will now be 15,757 + 551.50 = 16, 308.50.

The Quadrilateral can best be described as a trapezoid with it's two parallel sides and two non- parallel sides.

A Quadrilateral is a type of polygon that is known to have four sides from which the name is being derived.

Examples of quadrilateral include the following:

The quadrilateral represented in the coordinate grid is a trapezoid because it has two parallel sides which are AB and DC and two non parallel sides such as AD and CB.

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The proportional relationship graph that represents the table of values given would look like the graph shown below.

A proportional relationship graph always passes through the point of origin, (0, 0). The slope of the graph of a proportional relationship is also called the constant of proportionality, k, which can be calculated by using the coordinates of any point on the line, (x, y).

Constant of proportionality, k = y/x.

The equation for a proportional relationship is given as y = kx.

Given the table of values above which represents a proportional relationship, the graph of the table of values will go through the points below:

(0, 0)

(14, 7)

(6, 3)

(26, 13)

Therefore, the graph of the proportional relationship would look like the graph attached below which passes through:

B. (0, 0) and continues through the point (14, 7).

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The possibles values of d i.e., the distance between Berlin and Budapest will be as follows

200 miles < d < 458 miles

The triangle inequality theorem explains the connection between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side.

Case 1

129 miles + d > 329 miles

⇒ d > 200 miles

Case 2

129 miles + 329 miles > d

⇒ 458 miles > d

From Case 1 and Case 2, for d we can say

200 miles < d < 458 miles

Therefore, The possibles values of d i.e., the distance between Berlin and Budapest will be as follows

200 miles < d < 458 miles

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(a) Josh would pay $592.48 for the television at the department store.

(b) Josh would pay $634.8 for the television at the superstore.

(c) Josh would pay less for the television at the department store.

Given:

Wholesale price of television = $529

(a) In the department store,

Television wholesale price is marked up by 40%.

Discount = 20%

Marked price = 529 × ( 1 + 40%)

                      = 529 × (140/100)

                      = $740.6

Selling price = 740.6 × (1 - 20%)

                     = 740.6 × (80/100)

                     = $592.48

(b) In the superstore,

Television wholesale price is marked up by 20%.

Marked price = 529 × ( 1 + 20%)

                       = 529 × (120/100)

                      = $634.8

He must pay the full in-store price.

Selling price = $634.8

Ignoring the tax, he must pay the full price at the superstore which is $634.8.

(c) As the selling price in the department store is less than in the superstore, $592.48 < $634.8.

So, Josh would pay less for the television at the department store.

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The ladder leaning on the house formed a right angled triangle

Using an illustration from the diagram given:

To get the height the house makes with the ladder, we will apply pythagoras' theorem:

Hypotenuse² = opposite² + adjacent²

Answer:

To solve this problem you will have to use PEMDAS (parenthesis, exponents, multiplication, division, addition, and subtraction).