Find the value of c that makes DEF ~ XYZ

Answer:

Step-by-step explanation:

A teacher may receive funding from the school to buy arithmetic amount notebooks for the pupils in their class. Materials like notebooks, pens, calculators, and other essential items can be purchased with this money.

A teacher may receive funding from the school to buy arithmetic notebooks for the pupils in their class. Materials like notebooks, pens, calculators, and other essential items can be purchased with this money. It is crucial to provide each student with enough math notebooks so that they have enough supplies to work with. These notebooks can be used by the students to keep track of key information, practise equations and other mathematical ideas, and stay organised and study-focused. To make sure that kids have the resources they need to excel in the classroom, provide the instructor a budget to buy math notebooks.

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On solving the provided question, we can say that by percentage the proportion of pupils who participate in either cricket or volleyball.

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions.

In a study conducted at a school, 300 students preferred volleyball, 250 preferred cricket, and 110 preferred playing both sports. Calculate the following using a Venn diagram: a. the number of pupils who play cricket exclusively.

b. the proportion of pupils who participate in either cricket or volleyball.

After their SEE, a survey found that 120 students desired to be both an engineer and a doctor, while 190 students wanted to be both. Draw a Venn-diagram and count the number of students who said they wanted to be neither of them if 300 students were surveyed.

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It will take the painter a total of 5 minutes to paint this cone

Since the area of the base of the cone is doubled,

the new base area = 2 * 49π in² = 98π in².

The radius of the original cone can be found by using the formula for the area of a circle:

49π = πr^2

r = 7 in

The height of the new cone can be calculated using the same lateral height as the original cone:

h = 8 in

Using the formula for the volume of a cone, we can calculate the volume of the new cone:

V = (1/3)πr^2h = (1/3)π(7^2)(8) = (1/3)π(392)

The surface area of the original cone can be found using:

A = πr^2 + πrs

where s is the slant height of the cone.

s = √(r^2 + h^2) = √(7^2 + 8^2) = √(49 + 64) = √(113)

So, we have

A = πr^2 + πrs = π(7^2) + π(7)(√(113)) = 49π + 7π(√(113))

The surface area of the new cone can be found using the same formula:

A = πr^2 + πrs = π(7^2 * 2^2) + π(7 * 2)(√(113)) = 98π + 14π(√(113))

When the equations are compared, we have

2 * (49π + 7π(√(113))) = 98π + 14π(√(113))

i.e. the new cone has twice the surface area of the original cone

It will take 2.5 * 2 = 5 minutes to paint this cone.

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Let's call the number of small stuffed animals sold "x" and the number of large stuffed animals sold "y".

We know that:

x + y = 27 (the total number of stuffed animals sold)

13x + 12y = 350 (the total amount of money Aya earned)

We can use these two equations to solve for x and y. To do this, we'll use substitution:

x + y = 27

x = 27 - y

Now, we'll substitute this expression for x into the second equation:

13(27 - y) + 12y = 350

351 - 13y + 12y = 350

351 = 350

This equation is true for all y, which means that we cannot solve for y using these two equations. We need more information to determine the number of small and large stuffed animals sold.

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x + y = 27 (the total amount of stuffed creatures sold) (the total number of stuffed animals sold)

These two formulae can be used to find the answers to x and y. We'll use replacement to accomplish this:

x + y = 27

x = 27 - y

We will now change x in the second equation to the following expression:

13(27 - y) + 12y = 350

351 - 13y + 12y = 350

351 = 350

The height of the juice container with a base area of 100cm² is 15 cm

Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2

The base area of a cylinder is given by:

base area = π*r²

base area = 100 cm^2

100 = π * r^2

r^2 = 100 / π

r = √(100 / π)

The volume of a cylinder is given by:

volume = π*r²*h

1500 = π * [√(100 / π)]^2 * h

1500 = π* (100 / π) * h

1500 = 100h

Clearing the variable (h) height we have:

h = 1500 / 100

h = 15 cm

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If a fair coin is tossed 14 times then the probability that exactly three head occur is 0.023 .

The Binomial Probability formula is used to find the Probability of getting exactly 3 heads in 14 tosses of a fair coin .

The formula is:

⇒ P(X=k) = ⁿCₓ × pˣ ×  (1-p)ⁿ⁻ˣ  ;

where,

⇒ P(X=k) is the probability of getting exactly "x" heads in n tosses of coin ;

⇒ n (number of tosses) =  14

⇒ k (number of heads) = 3

⇒ p (probability of getting heads in a single toss) =  0.5 for a fair coin

Substituting  in the values, we get:

⇒ P(X = 3) = ¹⁴C₃ * (0.5)³ * (1 - 0.5)¹¹

⇒ P(X = 3) = ¹⁴C₃ * (0.5)³ * (0.5)¹¹

On simplifying further ,

we get ;

⇒ 0.02221679 ≈ 0.023 .

Therefore , the probability of getting exactly 3 heads 0.023 .

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Over the 0.33 and 0.375 range of values for the "bill passing" will country C remain optimal.

a. To calculate the estimated costs for each country, we must divide the cost by the likelihood of the bill being approved or rejected. Each country's expected cost is computed as follows:

Country A: 0.4 * 260 + 0.6 * 210 = 244

Country B: 0.4 * 320 + 0.6 * 160 = 256

Country C: 0.4 * 240 + 0.6 * 240 = 240

Country D: 0.4 * 275 + 0.6 * 210 = 250

Since country C has the lowest expected cost of $240,000, East West should choose this country for manufacturing.

b. Part a solution will continue to stay optimal as long as the estimated cost for country C is less than the estimated cost for the other countries. This means that if the "bill passing" range is such that country C still has the lowest estimated cost, the solution will remain optimal. To evaluate this range, we can find the "break-even points," which are the points at which the expected costs for country C equal the expected costs for countries A and D. The following is how these break-even points are calculated:

BE (country A) = (210 - 240) / (260 - 210) = 0.375

BE (country D) = (210 - 240) / (275 - 210) = 0.33

This means that as long as the probability of the bill passing is between 0.33 and 0.375, the solution of choosing country C will remain optimal.

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The total number of Cheeseburgers will be 263.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Cheese burgers= x

Hamburgers= y

y-x= 62

x+y = 588

we add both the equations we get 2y = 650

y=650/2

y= 325

x = 588-325= 263

Hence, The total number of Cheeseburgers will be 263.

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Solutions for the system of equations  2x −5y =1  , 4x −10y =3 has no solution as ( 2 /4 ) = (-5/-10) ≠ (1/3) .

Simplify the system of equations to get the solution of the system :

2x - 5y = 1

⇒ 2x = 1 + 5y

⇒ x = ( 1+ 5y ) / 2  __(1)

4x -10y = 3

⇒ 2 ( 2x - 5y ) = 3

⇒2x - 5y = 3/2  ___(2)

Standard form of the system of equations are :

a₁x + b₁y + c₁ = 0

a₂x + b₂y + c₂ = 0

Substitute the value of x from (1) into (2) we get,

2 ( 1 + 5y )/2  - 5y = 3/2

⇒1 + 5y -5y = 3/2

⇒1 = 3/2

⇒2 = 3 which is not true.

System of the equation has no solution.

Here, ( a₁ /a₂ ) = (b₁ /b₂) ≠ (c₁ /c₂ ) that is ( 2 /4 ) = (-5/-10) ≠ (1/3) .

Therefore, the system of equations has no solution.

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a) The experimental probability of both choosing a ball that is odd and drawing a car that is either a K or J is given as follows: 29/60.

b) The theoretical probability of both choosing a ball that is odd and drawing a car that is either a K or J is given as follows: 4/9.

c) With a small number of trials, it is not surprising when the experimental probability is much greater than the theoretical probability.

A probability is calculated via the division of the number of desired outcomes by the number of total outcomes.

An experimental probability, as the name says, is calculated considering previous experiments.

Out of 60 outcomes, the desired outcomes and their absolute frequencies are given as follows:

Hence the experimental probability is obtained as follows:

(8 + 4 + 10 + 7)/60 = 29/60.

For the theoretical probability, we have that:

Hence it is given as follows:

p = 2/3 x 2/3

p = 4/9.

For a small number of trials, there usually are differences between the experimental and the theoretical probabilities, but these probabilities get closer as the number of trials increase.

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a) The correct values is,

At x = - 1; y = 5

At x =  1; y = - 3

At x = 2; y = - 4

At x = 4; y = 0

b) The correct graph of equation y = x² - 4x is shown in graph by green curve.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

a) Complete table is find as;

The equation is,

⇒ y = x² - 4x

Hence, We get;

At x = - 1;

⇒ y = x² - 4x

⇒ y = (-1)² - 4 × - 1

⇒ y = 1 + 4

⇒ y = 5

At x = 1;

⇒ y = x² - 4x

⇒ y = (1)² - 4 × 1

⇒ y = 1 - 4

⇒ y = - 3

At x = 2;

⇒ y = x² - 4x

⇒ y = (2)² - 4 × 2

⇒ y = 4 - 8

⇒ y = - 4

At x = 4;

⇒ y = x² - 4x

⇒ y = (4)² - 4 × 4

⇒ y = 16 - 16

⇒ y = 0

b) The equation is,

⇒ y = x² - 4x

At x = 0;

⇒ y = 0

Hence, The correct graph of equation y = x² - 4x is shown in graph by green curve.

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The conditions that must be met for the results of an ANOVA test to be reliable are Independence , Random Sampling , Large Sample Size and Normality .

The ANOVA (Analysis of Variance) is defined as a statistical method that is used to determine if there are significant differences among the means of two or more groups.

For the results of an ANOVA test to be reliable, the conditions that must be met are :

(i) Independence: The observations within each group should be independent of each other.

(ii) Normality: The data within each group should be approximately normally distributed.

(iii) Random Sampling: The samples within each group should be selected randomly from the population.

(iv) Large Sample Size: The sample size within each group should be large enough to provide a robust estimate of the population mean.

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Population - - > Sampling Frame - - > Sample - - > Individual being surveyed is the order from largest to smallest.

The population is the largest as they include all units or subject of interest in a particular study or experiment.

Next is the sampling frame which is the list or compilation of all subjects which can form part of a sample. It is a compilation of all elements in the population from which the sample can be drawn.

The sample is a subset of the population of population, usually selected at random and it is representative of the population.

The individual surveyed represents a single subject or observation from the chosen sample.

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The display that correctly represents the sample space is an option(d) neither.

To determine this:

While both Chase and Emily have attempted to represent the sample space, neither of their displays accurately represents the sample space by randomly picking a height and color for the stools.

In Chase's display, he has repeated the same height and color combination multiple times, which is not correct as each combination should only appear once in the sample space.

In Emily's display, she has not explicitly listed all the possible height and color combinations. She has only listed 3 heights and 3 colors, but there are 9 possible combinations of height and color that should be included in the sample space.

The correct representation of the sample space would be a list of all 9 possible combinations, such as:

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The display that correctly represents the sample space is an option(d) neither.

To determine this:

While both Chase and Emily have attempted to represent the sample space, neither of their displays accurately represents the sample space by randomly picking a height and color for the stools.

In Chase's display, he has repeated the same height and color combination multiple times, which is not correct as each combination should only appear once in the sample space.

In Emily's display, she has not explicitly listed all the possible height and color combinations. She has only listed 3 heights and 3 colors, but there are 9 possible combinations of height and color that should be included in the sample space.

The correct representation of the sample space would be a list of all 9 possible combinations, such as:

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Sales tax is added to the price.

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

The statement is about sales tax

As a general rule

sales tax are added to the price of the item that is being bought

So, the complete statement is Sales tax is added to the price.

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The expression is not equal to the radicand.

What is Radical Index?

The root symbol nx. is known as a radical, and it is thus read "x radical n," or "the nth root of x." The horizontal line in the radical sign is known as the vinculum, the quantity under the vinculum is known as the radicand, and the quantity n written to the left is known as the index.

The radical is defined by the expression

[tex]\sqrt[n]{a}[/tex]

where a is radicand and n is index.

The index value of square roots is two. When there is no index provided for a radical, it is presumed to be an index of two, or a square root.

[tex]a^{1/2}[/tex] =[tex]\sqrt{a}[/tex]

Thus, the expression is not equal to the radicand.

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The expression is not equal to the radicand.

What is Radical Index?

The root symbol nx. is known as a radical, and it is thus read "x radical n," or "the nth root of x." The horizontal line in the radical sign is known as the vinculum, the quantity under the vinculum is known as the radicand, and the quantity n written to the left is known as the index.

The radical is defined by the expression

where a is radicand and n is an index.

The index value of square roots is two. When there is no index provided for a radical, it is presumed to be an index of two or a square root.

= a^(1/2)

Thus, the expression is not equal to the radicand.

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The graph representing the inequality x ≥ 12 is with a closed and shaded circle to the left.

What is inequality ?

An inequality is an expression that shows the non-equal comparison of the two or more numbers and variables. A number line can be used to represent numbers put on regular intervals. A number line is sometimes   used to represent an inequality.

The height of the water slide is = 56 feet

The graph representing the inequality x ≥ 12 is shown on the number line begining from 12 with a closed and shaded circle.

Therefore, The graph representing the inequality x ≥ 12 is with a closed and shaded circle to the left.

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Picture 1: w = 14 units

Picture 2: The angles are 30°, 60° and 90°

Picture 3: p = 22√2 units

Picture 4: The distance is 42 ft

Picture 5: The perimeter of the equilateral triangle is 30√3 m

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles

Picture 1

cos 30° = 7√3 / w

w cos 30° = 7√3

w  = 7√3 /(cos 30°)

w = 14 units

Picture 2

We have a right angle there already i.e. 90°. Let the two unknown angles be x and y.

sin x = (7√3) /(14√3)

sin x = 1/2

x = arcsin (1/2)

x = 30°

y = 90 - 30 = 60°

Thus, the angles are 30°, 60° and 90°

Picture 3

sin 45° = p/44

p = 44 * sin 45°

p = 44 * (√2)/2

p = 22√2 units

Picture 4

The distance from corner to corner is the length of the diagonal of the square.

Distance = √(30² + 30²) = 42 ft    (Pythagoras' theorem)

Picture 5

The perimeter of the equilateral triangle is the sum of all three sides.

Let's find the side x:

sin 60° = 15/x

x = 15/sin 60°

x = 10√3 m

perimeter = 3x = 3 * 10√3 = 30√3 m

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Answer:

Step-by-step explanation:

Angle ABD plus angle DBC = 90. That's what that little square in the corner there means...a right angle which is 90 degrees. Using substitution,

3x + 15 + 2x = 90 and

5x + 15 = 90 and

5x = 75 so

x = 15. Now we need to plug in 15 for x in 2x to get 2(15) which is 30. Second choice down.

The survey data collected by Account employees provides valuable insight into the amount of time executives spend on e-mails.

A survey was conducted by Account employees in 2001 to determine the amount of time executives spend each day reading and sending e-mails.

The results were recorded in minutes and analyzed to determine if the mean amount of time spent by all executives reading and sending e-mail daily differs from 60 minutes.

The survey data collected from the executives can be used to calculate the mean and standard deviation of the time spent on e-mails.

If the mean is significantly different from 60 minutes, it would suggest that the executives on average spend more or less time on e-mails compared to 60 minutes.

By conducting a statistical test, we can determine if the mean is significantly different from 60 minutes and make inferences about the e-mail habits of executives.

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The solution to the equations are given below.

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:

1. System A          System B

−12x+9y=7           −12x+9y=7

9x−12y=6             −9x+5y=9

Solving system A

x= -46/21 and y= -15/7

and, solving system B

x= -46/21 and y= -15/7

We can say that

Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 1/3 and adding to the first equation in system A.

2. -7 should be multiply the second equation by so that the sum of the x-coefficients is zero.

3. x−y=3

2x−3y=−1

Solving the above equation gives

x= 10 and y= 7.

The equation yields the same solution as above is

2x−2y=6

2x−3y=−1

4. Equation A: 5x+9y=12

Equation B: 4x−3y=8

Now, solving both equations we can proceed as Multiply equation B by 3 and add the result to equation A.

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Answer:

To determine which system of equations would have the same solution, we evaluate each system of equations.

System 1 4x − 5y = 2, 3x − y = 8

x = 38/11

y = 26/11

System 2 4x − 5y = 2, 3x − 2y = 1

x = 1/7

y = -2/7

System 3 4x − 5y = 2, 3x − 8y = 4

x = -4/17

y = -10/17

System 4 4x − 5y = 2, 10x − 9y = 4

x = 1/7

y = -2/7

Therefore, the correct answer is option 3. System 2 and system 4 are equal, because the second equation in system 4 is obtained by adding the first equation in system 2 to two times the second equation in system 2.

    4x− 5y = 2 2( 3x − 2y = 1)

-----------------------    10x - 9y = 4

Step-by-step explanation:

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tangential acceleration a in the form without finding t and n is |a|= T+ t N

The tangential acceleration is a measure of the rate of change in the magnitude of the velocity vector, i.e. speed, and the normal acceleration are a measure of the rate of change of the direction of the velocity vector.

r(t)=(cost+ t sin t )i +(  sin t−t cost)j

first find the particle's velocity.

[tex]v=dr/dt\\=(−sint+sint+tcost)i^+(cost−cost+tsint)j^\\\\ \\=(tcost)i^+(tsint)j^[/tex]

find the speed.

|v|=[tex]\sqrt{t^{2} cos^{2}t+ t^{2} sin^{2}t }[/tex]

    = √t^2

    =t

When  t>0 ,  |t| simply becomes  t .

We know that  a T= [tex]\frac{d}{dt}[/tex]|v|

, which we can use to find that  [tex]\frac{d}{dt}[/tex](t)=1

Now that we know  a T , we can use it to find  a N

a=(cost−t sin t ) i+(sin t +t cos t)j

|a|^2=t^2+1

a N=√(t^2+1) -1

     = t

By substituting this back into the original definition, we find that

|a|=(1)T+(t)N=T+ t N

a in the form without finding t and n is |a|= T+ t N

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The surface area of the prism is 456cm² and the volume is 408cm³

A prism is a solid shape that is bound on all its sides by plane faces. There are two types of faces in a prism. The top and bottom faces are identical and are called bases. A prism is named after the shape of these bases. For example, if a prism has a triangular base it is called a triangular prism.

The formula for the surface area of a prism is SA=2B+ph, where B, again, stands for the area of the base, p represents the perimeter of the base, and h stands for the height of the prism.

Base area = 1/2× 8× 6

= 4×6 = 24 cm²

perimeter of the base = 6+8+10 = 24cm²

therefore SA = 2(24)+24×17

= 48+408

= 456cm²

Volume of the prism = base area × height

= 24 × 17

= 408cm³

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Myers' taxable income of $49,000 was located on the tax schedule. He then added the base amount of $4,386 to the amount over $31,850 multiplied by 25%, totaling $8,673.50 in taxes.

To figure out the taxes due on Myers' taxable income of $49,000, he first located his earned income level on the tax schedule. The base amount was then calculated by entering the base amount of $4,386. Next, he found the amount over $31,850 and multiplied it by 25%, which was $7,025.00. Finally, he added the base amount and the multiplied amount over 31,850 together to get a total of $8,673.50 in taxes due. Therefore, Myers' taxable income of $49,000 was located on the tax schedule. He then added the base amount of $4,386 to the amount over $31,850 multiplied by 25%, totaling $8,673.50 in taxes.

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The measure of the angle X for the trigonometric ratio of sine X equal to 0.7547 is 49° to the nearest degree.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

For the sine of X equal to 0.7547, we can make x the subject by finding the sine inverse of 0.7547 as follows:

sin X = 0.7547

X = sin⁻¹(0.7547)

X = 48.9992

Therefore, the measure of the angle X for the trigonometric ratio of sine X equal to 0.7547 is 49° to the nearest degree.

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The C++ or Python code for the given problem is float ballRadius = ballHeight / 2.0;

To assign the value of ballRadius with ballHeight divided by 2.0, you can write the following code in a programming language such as C++ or Python:

float ballRadius;

float ballHeight = [some value];

ballRadius = ballHeight / 2.0;

This code uses the division operator (/) to divide ballHeight by 2.0, which results in a floating-point value. This value is then assigned to the variable ballRadius. By dividing ballHeight directly by 2.0, we are not using the fraction 1.0 / 2.0.

In detail, the operation ballHeight / 2.0 performs floating-point division, which means that the result will be a floating-point value with decimal places. The value of ballHeight is divided by 2.0, which is a floating-point constant. The result of this division is assigned to the variable ballRadius, which is also a floating-point value.

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Answer:

3 ways

Step-by-step explanation:

Let us take boat A and Boat B

Boat A - 6 people

Boat B - 4 people

1st way - In Boat A 4 people and in Boat B 4 people

2nd way - In Boat A 5 people and in Boat B 3 people

3rd way - In Boat A 6 people and in Boat B 2 people

Answer: The given expression is already in the vertex form:

y = 2(x-3)² - 1

It is the standard form of a parabolic equation with the vertex at (3, -1) and opens upwards.

Step-by-step explanation:

Answer:

[tex]y=2(x-3)^2-2[/tex]

Step-by-step explanation:

[tex]y=2(x-4)(x-2)\\y=2(x^2-6x+8)\\y+2(1)=2(x^2-6x+8+1)\\y+2=2(x^2-6x+9)\\y+2=2(x-3)^2\\y=2(x-3)^2-2[/tex]

All the missing reasons are given below.

A parallelogram is a two-dimensional shape with four sides and opposite sides that are parallel and equal in length. It can be defined as a quadrilateral with two pairs of parallel sides. In other words, opposite sides of a parallelogram are parallel and equal in length. The opposite angles of a parallelogram are equal and its diagonals bisect each other. A rectangle and a rhombus are both examples of parallelograms. The properties of parallelograms are important in geometry, trigonometry, and linear algebra.

The missing reasons for steps 3 and 4 are:

So the complete proof would be:

Given: ABCD with diagonal BD

Prove: ABD = CDB

Statements:

Reasons:

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