Similar figures review - Question 1

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{8}}} \implies \cfrac{-4 +4}{-6} \implies \cfrac{ 0 }{ -6 } \implies \text{\LARGE 0}[/tex]

Answer:

a = 191/81

Step-by-step explanation:

a+ 1 1/6 = 11 7/9

1 1/6 = 7/6

11 7/9 = 106/9

So, our equation is

a + 7/6 = 106/9

Subtract 7/6 from both sides

a = 191/81

So, the answer is

a = 191/81

Answer:

[tex]\dfrac{1}{2} z+5=57[/tex]

Subtract 5 from both sides:

[tex]\dfrac{1}{2} z+5-5=57-5[/tex]

[tex]\dfrac{1}{2} z=52[/tex]

Multiply both sides by 2:

[tex]2\times(\dfrac{1}{2} z)=2\times(52)[/tex]

[tex]\fbox{z = 104}[/tex]

Answer:

z=104

Step-by-step explanation:

1/2z=57-5

1/2z=52

1/2z*2=52*2

1z=104

1/1z=104/1

z=104

The value of b that needs to be simplified is indicated as 1.43. The correct response when the new population growth is specified is A.

A mathematical function known as an exponential function has the following formula: f (x) = an x, where x is a variable and an is a constant known as the function's base. The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base. Bacterial proliferation is an illustration of an exponential function. Some bacteria grow by twofolds per hour. After x hours, there will be twice as many germs present as there were when you started with just one. The formula for this is f(x) = 2x.

Given that,

When a fisherman unlawfully releases some fish into a pond, they immediately multiply (reproduce). P(x) = 6bx, where x is the number of weeks that have passed since the moment the fish was placed into the pond, and b is an unknown positive base, serves as a model for the population expansion of the new species.

According to the question,

P(x) = 6bˣ

Put p(x) = 51 and x = 6

51 = 6b⁶

17/2 = b⁶

b = [17/2]¹/⁶

b = 1.43

The b value that must be simplified is given as 1.43. A is the proper answer.

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On solving the provided question, we can say that - equation  at factors  x= -3 that value of a is = 33

A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.

4x^2 + 5x - 8

x = -3

36 + 15 -8

33

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The perimeter of each semicircular shape disc created by Amrita by dividing a circular disc of radius 7 cm into two equal parts is 44 cm. This is calculated by multiplying the circumference of the circle (2πr = 2 × 22/7 × 7 = 44 cm) by half.

Amrita divided a circular disc of radius 7 cm into two equal parts. This created two semicircular shape discs

Step 1: Calculate the circumference of the original circle.

Circumference of a circle = 2πr

Circumference of the circle with a radius of

7 cm = 2πr = 2 × 22/7 × 7 = 44 cm

Step 2: Calculate the perimeter of each semicircular shape disc.

The semicircular shape discs are created by dividing the original disc into two equal parts. Therefore, the perimeter of each semicircular shape disc is half of the circumference of the original circle.

Perimeter of each semicircular shape disc

= 44 cm/2

= 22 cm

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The actual dimensions are 9.75 feet and 7.5 feet. The area will be 73.125 square feet.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).  The scale factor is defined as the proportion of the new image's size to that of the previous image.

Here the scale factor for the given image is 2 inch = 3 ft.

The measure of the actual dimensions will be calculated as,

2 in = 3 ft

1 in = 3/2 ft

6.5 in = 6.5 x 3 / 2 = 9.75 ft

5 in = 5 x 3 / 2 = 7.5 ft

The actual area will be calculated as,

Area = 9.75 x 7.5

Area = 73.125 square feet

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The value of the expression using the distributive property is 5x + 50.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

5 (x - 10)

The distributive property of multiplication over addition states that,

a x (b +  c) = a x b + a x c

Now,

5 (x - 10)

= 5x + 5 x 10

= 5x + 50

Thus,

The expresssion is 5x + 10

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The number of possible different sequences of heads and tails is 1024.

A list of numbers (or other components) that follow a specific pattern is called a sequence. An arithmetic progression is one of the common examples of sequence and series.

A sequence can be arranged in either ascending or descending order.

Each flip has two outcomes H or T, so in ten flips you can get a sequence like HTHHTHTTTH

The number of possible different sequences is simply 2*2*2*2*2*2*2*2*2*2 = 2^10 = 1024

Thus, The number of possible different sequences of heads and tails is 1024.

Complete question:

If you flip a coin ten times, how many different sequences of heads and tails are possible?

a. 2° = 512

b. 10 = 100

C. 102 = 1024

d. 210 = 1024

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The inequality that represents the situation is 45x + 1240 ≥ 6000

There are 45 members overall.

If one individual contributes $x, then

The sum that 45 individuals together raised is then equal to 45x.

$6000 is the bare minimum necessary to enter the competition.

$1240 is the amount they already have.

Therefore, the amount they need to raise is $6000 minus $1240.

Inequality can be displayed as:

45x ≥ 6000 - 1240

This demonstrates that the total amount raised by 45 individuals (45x) should be equal to or more than the sum they need to raise ($6,000 - $1240).

change the equation's order;

45x + 1240 ≥ 6000

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No. the sum of any two lengths of the triangle is greater than the third length.

Option (A) is correct.

A triangle is a polygon with three edges and three vertices. In Euclidean geometry, a triangle is completely determined by the three points that make up its vertices.

Kathy wants to place a printer 9ft from the filing cabinet. Can the other two distances are shown to be 7ft and 2ft.

No the sum of any two lengths of the triangle should be greater than the third side.

but 7 + 2 = 9, so the condition for a triangle is false.

Hence, the correct explanation would be "No. the sum of any two lengths of the triangle is greater than the third length."

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Kathy wants to place a printer 9ft from the filing cabinet. Can the other two distances shown be 7ft and 2ft? Identify the answer with the correct explanation. Printer Desk Filing Cabinet

O Yes; the sum of any two lengths is greater than the third length.

O No; the sum of any two lengths is not greater than the third length.

O Yes; the sum of any two lengths is equal to the third length.

O No; the sum of any two lengths is greater than the third length

Answer:

No; The sum of any two lengths is NOT greater than the third length

Step-by-step explanation:

It is given that three objects, a desk, a filing cabinet, and a printer, form a triangle.

Use the Triangle Inequality Theorem to determine whether the given distances can be the lengths of the sides of a triangle.

9+7=16>2

9+2=11>7

7+2=9=9

The sum of one pair of lengths is equal to the third length. Therefore, the distances between the desk, the printer, and the desk and the filing cabinet cannot be 7ft and 2ft since 7+2 equals 9.

The odds against Arjun taking the longest trail are 4 : 9 .

The probability that when Arjun is hiking from the mountain lodge to the nearby summit, he takes the longest trail, is 5 / 9.

This means that the odds that Arjun will not take the longest trail, or rather, the odds against him taking the longest trail, will be the difference between 1 and the probability that he takes the longest trail:

= 1 - 5 / 9

= 4 / 9

When given as a ratio, this would be:

=  4 : 9

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The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
A) "Individuals are carefully observed in their natural environments" is a description of participant observation, which is a type of qualitative research method. In this method, researchers observe and interact with individuals in their natural environments in order to understand their behaviours and attitudes in context. This method is often used in fields such as anthropology, sociology, and psychology.

B) "A representative, random sample of individuals are questioned regarding their attitudes or behaviours" describes a survey, which is a quantitative research method. Surveys are used to gather information from a representative sample of individuals in order to make inferences about a larger population. Surveys can be conducted in various ways, such as through phone calls, mail or online and can be used to study the attitudes, behaviours, and characteristics of a population.

C) "An individual is studied in great depth" is a description of a case study, which is a qualitative research method. In this method, a researcher closely examines an individual or a small group of individuals in order to gain a detailed understanding of their experiences, behaviours, and attitudes. Case studies are often used in fields such as psychology, sociology, and anthropology.

D) "An investigator determines the extent to which two variables influence each other" is a description of a correlation study, which is a quantitative research method. In this method, the researcher examines the relationship between two or more variables. The researcher measures the values of the variables for a sample of individuals, and then uses statistical methods to determine the degree of association between the variables, and if there is a causal relationship or not.

Thus, The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)

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the answer would be -144

you would have to multiply 3 by square 2, then multiply them which would be 3*4=12 and then you would square that which is 144 and because it is negative it would be -144

A linear equation in two variables has only 1 solution.

Now, According to the question:

Let's know:

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2. Whereas if we speak about linear equation in two variables, it has two solutions.

An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0.

A linear equation in two variables has only 1 solution.

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9 non-congruent squares can be drawn.

Non-congruent squares are two squares with different side lengths. These two squares can be drawn separately and still have four right angles and four equal sides, but the lengths of the sides are not the same. Non-congruent squares are a type of quadrilateral and have both diagonals and parallel sides. These shapes can be used to create a variety of geometric designs and patterns, and often appear in art and architecture.

Each of the four corners of the 5 by 5 grid can be the vertices of a square, and the middle of each side of the 5 by 5 grid can be the vertices of a square. This makes eight non-congruent squares in total. Additionally, the center point can be the vertex of another non-congruent square, making nine in total. All of these squares are constructed from lattice points, and none of them are congruent to each other.

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The population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235

A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours.

Given that,

P_t = P_0 * 2^(t/d) , which refers to the formula for the calculation of the number of bacterial cell in a population.

In the given formula, P_t is the population after t hours, P_0 is the initial population, t is the time in hours and d is the doubling time in hours,

Therefore,

P_0 = 7100

d = 2

t = 15

so,

P_15 = 7100 * 2^(15/2) = 7100 * 181.019= 1285234.9 which is nearly equal to 1285235

A culture of bacteria has an initial population of 7100 bacteria and doubles every 2 hours, the population of bacteria in the culture after 15 hours, to the nearest whole number would be 1285235

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The length of PG if PG' is 0.5 units is; 3 units.

The act or action of enlarging, expanding, or widening : the state of being dilated: such as. : the act or process of expanding (such as in extent or volume)

Here, given that,

Dilation is simply defined as the shrinking or enlarging of an object by a scale factor.

Now, we are told that Line HG is dilated to form a shorter line H'G'.

We are told that the scale factor is 1/6.

Point P is the center of dilation and if PG' is 0.5 units, then we can write the relation as follows;

Length of PG'/Length of PG = 1/6

Thus;

0.5/length of PG = 1/6

Length of PG = 0.5/(1/6)

Length of PG = 4 units

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Really sorry, misunderstood the equation. This is the answer though.

Answer:

24

Step-by-step explanation:

We have our function g(x) = [tex]x^{3}[/tex] - x

Now, we will substitute 3 in for x, giving us:

[tex]3^{3} - 3[/tex]

Now, we will simplify our exponent, giving us:

27 - 3 = 24

So your answer is 24.

Hope this helped!

Two slopes can be compared on a graph by analyzing the steepness of the lines and their direction (positive or negative).

The steepness of a line on a graph is determined by its slope, which is the ratio of the change in y to the change in x (rise over run). A steep line has a large slope, meaning that for a small change in x, there is a large change in y. A shallow line has a small slope, meaning that for a small change in x, there is a small change in y. To compare two slopes, one can compare the steepness of the lines by comparing the absolute value of the slopes.

If one line has a larger absolute value than the other, it is steeper. Additionally, one can also compare the direction of the slope, which is determined by the sign of the slope. A positive slope indicates that the line is increasing and a negative slope indicates that the line is decreasing. By comparing the steepness and direction of the slopes, one can determine whether the two lines are parallel or not, and whether they are going in the same direction or not.

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Answer:

The answer to this question is x= 51/4

Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.

Food items manufactured from (or containing) milk are referred to as dairy products or milk products (also known as lacticinia).

The cow, water buffalo, nanny goat, and ewe are the most popular dairy animals.

Dairy products include staples from Western grocery stores including yogurt, cheese, and butter.

A dairy is a place where dairy products are made .Various amounts of dairy products are consumed worldwide (see consumption patterns worldwide) .

After standardizing the fat content and optional homogenization or pasteurization, milk is produced in a variety of grades with the potential addition of the microorganisms Streptococcus lactis and Leuconostoc citrovorum.

Based on the type of product generated, milk can be divided into a number of distinct categories, including cream, butter, cheese, newborn formula, and yogurt.

Hence, Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.

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Answer:

(r + 7)(r - 4) = 0

Step-by-step explanation:

r² + 3r - 28 = 0

(r + 7)(r - 4) = 0

r = -7, 4

Hello there!

Answer:

$400'000

Step-by-step explanation:

Estate -- $2.4 million or $2'400'000

Springfield University will receive: 10% * $2'400'000 = 0.1 * $2'400'000 = $240'000

First Church of Springfield will receive: 15% * $2'400'000 = 0.15 * $2'400'000 = $360'000

Wife will receive $600'000

Total: $240'000 + $360'000 + $600'000 = $1'200'000

Children will receive at total: $2'400'000 - $1'200'000 = $1'200'000

So each child will receive: $1'200'000 / 3 = $400'000

Answer: Each child of Homer Simpson gets $400000.

Step-by-step explanation:

Homer Simpson left 10% of his estate, or (10/100)  x $2.4 million

= $ (10/100)x2400000= $240000

$240,000 to Springfield University.

He left 15% of his estate, or (15/100) x $2.4 million = $(15/100)2400000

= $360000

So 360,000 to the First Church of Springfield.

So in total, he left $240,000 + $360,000 + $600,000 = $(240000+360000+600000)

=$1200000

 $1,200,000 to organizations and his wife.

That means the remainder of the estate, $2.4 million - $1,200,000

= $2400000-1200000

= $1200000

1,200,000, was divided among his three children. So each child received $1,200,000 / 3 = $1200000/3

=$400000

Answer: $400000.

the middle value in a data set when the values are put in order

For example, the set {3,1,2} sorts to {1,2,3} where the median is 2.

Another example: The set {1,2,3,4} has 2 and 3 tied for the middle most position. The midpoint is (2+3)/2 = 5/2 = 2.5 which is the median.

Answer:

0.28

Step-by-step explanation:

1% = 0.01

0.01 × 28 = 0.28

It depends on your personal financial situation and goals. Generally, it is important to save for major purchases such as a house, car, and vacations, as well as setting aside money for retirement. Additionally, you may want to consider investing in stocks, bonds, or mutual funds to achieve your long-term financial goals.

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{13}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{6}}}{\underset{\textit{\large run}} {\underset{x_2}{13}-\underset{x_1}{1}}} \implies \cfrac{ -4 }{ 12 } \implies {\Large \begin{array}{llll} - \cfrac{1 }{ 3 } \end{array}}[/tex]

One would earn more if one apprenticed for Sara as a professional artist as evident judging from the current sales ratio and commission rates.

As evident in the task content; the current ratio of Sara's sales to Ravi's sale is 100 : 2.

Since Sara's pieces of art sell for $25, the total earnings is; 25 × 100 = $2500.

Hence, since the commission rate is 60%, it follows that the commission earned on sales of Sara's pieces is; 60% of 2500 = 0.6 × 2500 = $1500.

Also, since Ravi's pieces each cost $2000, it follows that for 2 pieces, the total earnings is; 2 × $2000 = $4,000.

Hence, since the commission rate for Ravi's pieces is 25%, the commission earned is therefore; 25% of 4000 = 0.25 × 4000 = $1000.

Ultimately, one would earn more if one apprenticed for Sara.

Complete question; Sara's pieces of art sell for $25 each your commission is 60%.

Ravi's pieces of art sell for $2000 each and your commission is 25%.

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