Solve the right triangle shown in the figure, given the following measures. Remember, exact lengths can be approximated on a calculator. For example, StartRoot 2 EndRoot almost-equals 1.414. Angle A = 45 degrees, side A B = 12 StartRoot 2 EndRoot centimeters, Angle C = 90 degrees a. Side B C = 6 StartRoot 3 EndRoot centimeters, angle B = 45 degrees, Side A C = 6 StartRoot 3 EndRoot centimeters b. Side B C = 6 StartRoot 2 EndRoot centimeters, angle B = 45 degrees, Side A C = 6 StartRoot 2 EndRoot centimeters c. Side B C = 24 centimeters, angle B = 45 degrees, Side A C = 24 centimeters

Using the roots of the quadratic equation the equation is solved to be

Information from the problem include

The quadratic function f(x) has roots of −2 and 3 and point (2, −4) lies on f(x)

from the roots

x = -2 and x = 3

x + 2 = 0 and x - 3 = 0

(x + 2)(x - 3)

passing through points (2 , -4)

y = a(x + 2)(x - 3)

-4 = a(2 + 2)(2 - 3)

-4 = a * 4 * -1

-4 = -4a

a = 1

the quadratic  equation is f(x) = (x + 2)(x − 3)

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The symbol that represents an expression in statistics are That is option A , B and C.

Statistics is defined as the area of study that is concerned with the collection, organization, analysis, interpretation, and presentation of data.

The importance of statistics is that it helps in conducting research, evaluating results, developing critical thinking and making informed decisions.

The various symbols use in statistics include the following:

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Answer:

Step-by-step explanation:

You want the measures of the numbered angles in the figure comprised of overlapping right triangles.

The acute angles in a right triangle are complementary, as are the two angles into which a right angle is divided.

  ∠1 +35° = 90°   ⇒   ∠1 = 55°

  ∠3 +35° = 90°   ⇒   ∠3 = 55°

The angle marked 70° is exterior to the bottom right triangle, so is equal to the sum of angles 3 and 4.

  ∠3 +∠4 = 70°

  55° +∠4 = 70°   ⇒   ∠4 = 15°

Angle 2 is the other acute angle in the bottom right triangle, so ...

  ∠2 = 90° -∠4 = 90° -15°

  ∠2 = 75°

If the value x =12 then 2x - 5 = 19 the statement is true if 2x -5 = 19 then x = 12. The correct options are A and D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the statements are:-

x = 12, then 2x - 5 = 19.

2x - 5 = 19

(2 x 12 ) - 5 = 19

24 - 5 = 19

19 = 19

If 2x - 5 = 19, then x = 12. The value of x will be calculated as,

2x - 5 = 19

2x = 19 + 5

2x = 24

x = 24 / 2

x = 12

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The real-life measurement, if the scale factor is 2, is 4, 4, 1, 18 for the second table.

A scale factor, also known as a conversion factor, is a number that is used to increase or decrease the size of a figure without changing its shape. It is used to modify an object's size.

Given:

Scale factor = 2

Calculate the actual measurements as shown below,

[tex]Actual \ measure = Scale \ factor \times Scale \ measurement\ on\ paper[/tex]

Actual measurement = 2 × 2 = 4

Actual measurement = 2 × 2 = 4

Actual measurement = 2 × 0.5 = 1

Actual measurement = 2 × 9 = 18

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The factors of  2x² - 7x - 15 are (2x + 3) and (x - 5).

By splitting the middle term and factoring the polynomial,

2x² - 7x - 15

= 2x² - 10x + 3x - 15

= 2x(x - 5) + 3(x - 5)

= (2x + 3)(x - 5)

The factors of  2x² - 7x - 15 are (2x + 3) and (x - 5).

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From the concept of algebra of venn diagram we obtain that
P(A or B) = 0.75.

A set is a collection of well-defined objects.

A subset contains all the elements or few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

From set theory, we know that N(A∪B) = N(A) + N(B) - N(A∩B).

It states that N(A) or N(B) is the sum of N(A) and N(B) minus the common intersecting region N(A∩B) as we have already considered the region in the sum of N(A) and N(B) twice.

Similarly, P(A or B) = P(A) + P(B) - P(A∩B)>

Therefore, P(A or B) = 0.50 + 0.40 - 0.15.

P(A or B) = 0.90 - 0.15.

P(A or B) = 0.75.

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When the mean is 6, the mean deviation of a given collection of data is 2.4.

The deviation is a metric used in statistics and mathematics to discover the difference between the actual and predicted values of a variable. The deviation is just the distance from the central point. The mean deviation is a statistical metric that computes the average departure from the mean value of a given data collection. Using the following approach, you can simply determine the mean deviation of the data values. We categorize the data and describe the frequency distribution of each group to provide it in a more concise way. These are referred to as class intervals.

Here,

To find out the mean deviation, just follow the steps given below.

Step 1: Find the mean for the given set of values

Step 2: Find the distance. (i.e) Subtract the mean value from each given values, and ignore minus symbol if any

Step 3: Finally, find the mean of the obtained distance, which is called the mean deviation.

=(2+4+6+8+10)/5

=6

mean deviation,

=(4+2+0+2+4)/5

=2.4

The mean deviation of given set of values is 2.4 when mean is 6.

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By using the concept of conjugate, it can be calculated that

Conjugate of [tex]x + \sqrt{y}[/tex] is [tex]x - \sqrt{y}[/tex]

What is conjugate?

Conjugating is the process of changing a verb in a sentence to match the person, number, gender, tense, mood, and voice of the subject. For example, the verb "to walk" changes to "walked" when conjugated in the past tense. Conjugation is important in many languages, including English, as it helps to make communication more precise. Conjugation involves making changes to the base form of the verb, such as adding suffixes or prefixes, or changing the spelling of the word. Different languages have different rules for conjugating verbs, so it is important to understand the language’s system of conjugation before attempting to use it.

Here the expression is [tex]x + \sqrt{y}[/tex]

Conjugate of [tex]x + \sqrt{y}[/tex] is [tex]x - \sqrt{y}[/tex]

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Answer:

  1/2

Step-by-step explanation:

Given right triangle ABC with right angle A and tan(B) = 1, you want the value of the expression tan(C) -sin(B)cos(C).

Angle A is given as 90°.

Angle B is found from ...

  tan(B) = 1   ⇒   B = arctan(1) = 45°

Angle C is its complement:

  C = 90° -B = 45°

The relevant trig functions are ...

  tan(C) = tan(45°) = 1

  sin(B) = sin(45°) = 1/√2

  cos(C) = cos(45°) = 1/√2

Then the value of the expression is ...

  tan(C) -sin(B)cos(C)

  = 1 -(1/√2)(1/√2) = 1 -1/2

  = 1/2

Counting to 100 frequently and accurately can be mastered between the ages of three and a half and five and a half, but no later than the age of six.

The series of physical, language, mental, and emotional changes that occur in a kid from birth to the beginning of maturity is referred to as child development. During this phase, a kid moves from being dependent on their parents/guardians to be more self-sufficient.

Most parents will notice their children can count to 100 without any assistance around this age.

So it was apparent that they had a lot of practice time and focused specifically on counting to 100. The average age of parents in the discussion cable ranged from tardily 5 to early 6 years old.

Some parents expressed concern about their children not being able to count to 100 by the age of six, but they were apathetic because it was apparent their child was capable of other developmental goals.

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(i) Large Table Required are 3 and Small Table required are 8

(ii) Price of Student Ticket is $5.5 and Adult Ticket is $7.5

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

(i)

Seats in Large Table = 12

Cost of Large Table = $50

Seats in Small Table = 8

Cost of Small Table = $25

Let, Number of Large Tables = x

Number of Small Tables = y

According to the Question:

12x + 8y = 100

50x + 25y = 350

x = 3, y = 8 (refer graph 1)

(ii)

Cost of Student Ticket = x

Cost of Adult Ticket  = y

According to the Question:

16x + 3y = 110.5

12x + 4y = 96

x = $5.5, y = $7.5 (refer graph 2)

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Answer: The answer is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The second tile represents the missing alternatives.

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters

Given is a square array of tiles as shown in the image attached.

The tile given at the second number is the missing tile of the given alternatives.

Therefore, the second tile represents the missing alternatives.

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The multiplicity of a number is the number of times a number is a factor of another number.

In general, the multiplicity of a number can be determined by dividing the number by the factor. If the result is a whole number, then the multiplicity of the factor is equal to the result of the division. If the result is a decimal or fraction, then the multiplicity of the factor is 0.

For example, if we wanted to find the multiplicity of 5 in 25, we would divide 25 by 5: 25/5 = 5. This means that the multiplicity of 5 in 25 is 5.

The multiplicity of 5 can also be determined by finding the prime factorization of the number. For example, if we wanted to find the multiplicity of 5 in 30, we would factorize 30: 30 = 2 x 3 x 5. This means that the multiplicity of 5 in 30 is 1, because there is only one 5 in the prime factorization of 30.

In summary, the multiplicity of a number is the number of times a number is a factor of another number. The multiplicity of a number can be found by dividing the number by the factor, or by finding the prime factorization of the number.

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Hannah's thought that the original photo is congruent and similar to the final image is false

From the question, we have the following parameters that can be used in our computation:

Translation creates congruent and similar shapes

However, dilation only create similar shapes,  but not congruent shapes

This means that the shapes are similar, but not congruent

Hence. Hannah is incorrect

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56.6 years  is the mean of the modes of the given set of numbers.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

The mean is calculated by adding together all the values

                 =  (54+54+54+55+56+57+57+58+58+60+60

                  = 623

                  =  56.6 years.

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Answer:

(D) 1/9

Step-by-step explanation:

9x-2=-3

9x=1

x=1/9

Answer:

1/ simplify polynomial is x^3 y^2 - x^2 y^3 + xy

2/ Answer is -86

Step-by-step explanation:

x²yxy-xy²xy +xy

Simplify each term, and I get

x^3 y^2 - x^2 y^3 + xy

I may be wrong!

Now let's put -3 in for x and 2 in y and evaluate

(-3)^3  (2)^2 -  (-3)^2  (2)^3  +  (-3 times 2)

(27) (4) - (9) (8) - 6

-86

I may be wrong, but I tried my best to help you since this question has been on for a long time, but no one answered. If I am wrong, I am sorry!

Answer: X=20 Y=70

Step-by-step explanation:

There’s no labels so it might be hard to explain this one otherwise

-We’ll call the point at the top left with y°: A

-the bottom right point with x°: C

-the point in between them with 40°: B

-the bottom left point with the right angle: D

angle DBC = 140° because angles on a straight line sum to 180°

so x must equal 20 because the other angles in an isosceles triangle are equal and 180-140=40 and 40/2=20

90-20=70 so angle ADB=70

meaning that y must equal 70 because 70+40=110 and 180-110=70

By assuming that both tests measure the same kind of ability, Bob did better in terms of the standardized Z-score.

We have provide a data about two major math's tests.

First Major test : SAT math score normally distributed with

Mean , μ = 516 and

Standard deviations, σ = 115

Second Major test: ACT math score normally distributed with

Mean, μ = 22

Standard deviations, σ = 5

Anna scores in SAT test 650

i.e x = 650

Using Z-Score formula,

Z = (x - μ)/σ

Z = (650 - 516)/115 = 154/115 = 1.17

Also, Bob score on ACT math test is 29 i.e x = 29

Z-Score = (x - μ)/σ

=> Z = (29 - 22)/5 = 7/5

=> Z = 1.4

Since, Z-Score for Bob's ACT math test is high as compared to Anna's SAT math test.

So, Bob did better in terms of the standardized z-score.

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Answer:

Greg is correct

Step-by-step explanation:

To determine which of them is experiencing warmer weather, you need to compare the temperatures in the same unit of measurement. 77°F is equivalent to 25°C, while 30°C is equivalent to 86°F. Therefore, Greg is experiencing warmer weather than Josh.

The difference in the temperatures they reported is due to the fact that they are using different temperature scales. The Fahrenheit scale is used in the United States, while the Celsius scale is used in most other countries. The two scales are related by the equation:

C = (F - 32) / 1.8

To convert from Fahrenheit to Celsius, you can use this equation to determine the temperature in Celsius. To convert from Celsius to Fahrenheit, you can use the equation:

F = C * 1.8 + 32

Using these equations, you can compare temperatures in different scales to determine which is warmer.

The parallel marks the northern limit of the Southern Ocean (though some organisations and countries, notably Australia, have other definitions) and of the Antarctic Treaty System.

Parallel lines are straight lines that never meet each other no matter how long we extend them

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are additional, others are congruent (equal).

The fundamental characteristics listed below make it simple to recognise parallel lines.

Parallel lines are defined as straight lines that are always the same distance apart.

No matter how far apart they are from one another, parallel lines can never intersect.

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We will write greater than 20 using Inequality sign as ( > 20).

The first number in every inequality sign tells us how the first and second numbers relate to one another, so  > 20 means "A number is greater than 20."

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than symbol (>) is used when the first number exceeds the second number. The less than symbol (<) is used when the first number is less than the second number.

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The rule is that words, not numerals, should be used to represent numbers and ordered events that are less than 10 in total.

An arithmetic value known as a number is used to calculate and represent a quantity. Numerical writings, such as the letter "3," are used to represent numbers. A number system is a way of writing numbers that uses logical symbols or digits to represent them.

here

There are occasional exceptions, but generally speaking, numbers and ordered events that are less than 10 in total should be expressed as words.

Except for when they are the first digit of a phrase, numbers with two or more digits should be written as numerals.

The rule is that words, not numerals, should be used to represent numbers and ordered events that are less than 10 in total.

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Therefore, we can construct the only one quadrilateral can I construct with the following data quadrilateral  PQ 4.5 cm angle P 70 ∘ angle Q 100 ∘ angle r 80 ∘ and angle S 110  with the above diagram.

An example of a closed quadrilateral is a polygon, which has four sides, four vertices, and four angles. It has four non-collinear points that are joined together. The interior angles of quadrilaterals are all sums of 360 degrees.

Here,

the following construction steps:

I Build a line segment with a QR of 4.5 cm.

(ii) Create a ray QX with an angle of 80 degrees and cut off QP = 4 cm at the point Q.

(iii) Create a ray at the point R that forms an angle of 110 degrees, and then cut it off at RS = 4.5 cm.

Now join PS. (iv)

PQRS is hence the necessary quadrilateral.

Therefore, we can construct the quadrilateral can I construct with the following data quadrilateral  PQ 4.5 cm angle P 70 ∘ angle Q 100 ∘ angle r 80 ∘ and angle S 110  with the above diagram.

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Omar would most likely use a line graph to show changes in water depth. A line graph would allow him to plot the water depth readings against a timeline and visualize how the depth changes over the duration of the drought.

A line graph is the most appropriate method of displaying data to show changes in water depth over the duration of the drought. A line graph is a type of chart that plots data points on a two-dimensional coordinate system. It is used to show how one set of data changes over a period of time. Omar would plot the water depth readings along the vertical y-axis and the days of the drought along the horizontal x-axis. A line would then be drawn to connect the data points, depicting the changes in water depth over the period of the drought. Additionally, the data points can also be labeled to provide more detailed information about the water depth readings at each point. This would allow Omar to compare the readings over time and monitor the effects of the drought on the water depth.

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