Cite an example from the leon to how that a mak could be ued for omething more complex than a "ceremonial" purpoe

Case 2

The quadratic equation x² - 14 · x + 48 = 0 have the following roots: x₁ = 6 and x₂ = 8. (Correct choice: B)

Case 3

We need to add + 64 to both sides. (Correct choice: B)

Case 4

We need to add + 16 to both sides. (Correct choice: C)

In this problem we find three cases of quadratic equation that are not perfect square trinomials, these equations can be rewritten partially in that form by algebra properties. Completing the square offers a quick method to determine the roots of quadratic equations with integer coefficients. Now we proceed to determine the solutions corresponding to each case:

Case 2

x² - 14 · x + 48 = 0

x² - 14 · x + 49 = 1

(x - 7)² = 1

x - 7 = ± 1

x = 7 ± 1

The roots of the quadratic equation x² - 14 · x + 48 = 0 are x₁ = 6 and x₂ = 8, respectively.

Case 3

x² - 16 · x = - 21

x² - 16 · x + 64 = 64 - 21

(x + 8)² = 43

The first step consists in adding both sides by + 64.

Case 4

x² - 8 · x = 0

x² - 8 · x + 16 = 16

(x - 4)² = 16

The first step consists in adding both sides by + 16.

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The hikers will be 8 miles apart after 2 hours of hiking.

The formula used to calculate the distance apart is the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the distance between the two hikers, and the other two sides are the distances each hiker has traveled in the two directions: 3 miles to the west, and 4 miles to the north. The formula is written as a^2 + b^2 = c^2, where a and b represent the side lengths, and c represents the hypotenuse. Plugging in the values, 3^2 + 4^2 = c^2, or 9 + 16 = c^2. Solving for c, c^2 = 25, so c = 5. Therefore, the distance between the two hikers is 5 miles after two hours of hiking.

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Therefore , the solution of the given problem of equation comes out to be the equation is: y = -700/9 * x + 700.

Equation construction is the process of connecting two expressions with the equivalent sign. An equation is, for illustration, 7x - 5 = 40. By solving this equation, we can determine that the value of the variable x is 6.

Here,

Given :

Regarding the details provided:

The formula is: y = -700/9 * x + 700

B) The slope represents the amount owned's rate of change.

c) Y-intercept represents the sum borrowed from his father.

thus , the solution is given above

Therefore , the solution of the given problem of equation comes out to be the equation is: y = -700/9 * x + 700.

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Answer:

i think 48.00

Step-by-step explanation:

10% of 50 is 5 while 6% of 50 is 3 so 50-5+3 is 48

The greatest possible weight of the large bag is 1.9n ounces.

Given:

Weight of 10 apples = n ounces

Weight of 1 apple = n/10 ounces

Weight of n apples = n²/10 ounces

It is given that a large bag of n of these apples weighs less than 40 ounces,

= n²/10 < 40

= n²< 400

= n < 20

So, the large bag contains at most 19 apples.

Hence, the weight of the large bag is at most 1.9n ounces, or (19/10)(n) ounces.

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The best equation that approximates the probability that at least 27 percent of the children in the sample live in households that are classified at a particular income level is [tex]p(z > \frac{0.27-0.22}{\frac{\sqrt{0.22*0.78} }{300} })[/tex] .

Given:

Probability of children who live in households with incomes that are classified at a particular income level,p = 22/100 = 0.22

Number of children in a simple random sample,n = 300

Probability of children who do not live in households with incomes that are classified at a particular income level, q = 1-p = 0.78

The probability of children in the sample living in households that are classified at a particular income level,p₁ = 27/100 = 0.27

Now, we know

[tex]p(z > \frac{p_{1} -p}{\frac{\sqrt{p.q} }{n} } )[/tex]

So,

[tex]p(z > \frac{0.27-0.22}{\frac{\sqrt{0.22*0.78} }{300} })[/tex]

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In order for the second plan to be preferable, a greater amount of 249.6 minutes would have to be used in one month.

Let

x -----> the number of minutes in a month

y ----> the charge  monthly

we know that

First Plan

y= 0.23 x ----> equation A

Second Plan

y= 0.12x+34.95 ----> equation B

Equate the equations A and B and solve for x

so x= 249.6

For x< 249.6  ----> is preferable the first plan

For  x> 249.6 ----> is preferable the second plan

therefore

In order for the second plan to be preferable, a greater amount of 249.6 minutes would have to be used in one month.

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The expression as a single real number is [tex]\frac{1-\sqrt{3} }{2}[/tex] .

What is trignomentry ?

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. It is used to study the properties of triangles and to solve problems involving angles and distances in two-dimensional space.

sin(π/6)cos(π/2) - cos(π/60)sin(π/2)

The first term in the expression, sin(π/6)cos(π/2), can be simplified as follows ,

sin(π/6) = √(3)/2, cos(π/2) = 0

so sin(π/6)cos(π/2) = (√(3)/2) * 0 = 0

The second term in the expression, -cos(π/60)sin(π/2) , can be simplified as follows ,

sin(π/2) = 1, cos(π/60) = sqrt(3)/2 - 1/2

so -cos(π/60)sin(π/2) = -(sqrt(3)/2 - 1/2) * 1 = -sqrt(3)/2 + 1/2

Now we can substitute the simplified values back into the original expression ,

0 - (-sqrt(3)/2 + 1/2)

and combining like terms, [tex]\frac{1-\sqrt{3} }{2}[/tex],

Hence ,  The expression as a single real number is [tex]\frac{1-\sqrt{3} }{2}[/tex] .

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According to the concept of probability, the smallest number of yellow marbles that Marcy could have is 24

The term probability is known as the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

Here we have given that all of Marcy's marbles are blue, red, green, or yellow. one third of her marbles are blue, one fourth of them are red, and six of them are green.

Here we know that the 6 green marbles and yellow marbles form is calculated as,

=> 1 - 1/3 - 1/4 = 5/12 of the total marbles.

Here let us consider that the total number of marbles is x.

And here we know the number of yellow marbles is is written as,

=> 5/12x - 6 and a positive integer.

Now, we have to divide 12 by x, then we get,

Then we get the value of x as 24.

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Answer:

There are 3! (3 factorial) ways for the toddler triplets to each choose a coat. However, we are only interested in the ways where exactly one of them ends up with their coat.

There are 3 ways for the first toddler to get their coat, 2 ways for the second toddler to get their coat, and 1 way for the third toddler to get their coat.

Therefore, there are 3*2*1 = 6 ways for exactly one of the toddler triplets to end up with their coat.

In other words, there are 6 possible scenarios in which exactly one of the toddler triplets get their coat.

For example, Red getting his coat, Green getting the wrong coat and Blue getting the wrong coat.

To steps to construct a line segment that is 1/2 the length of the given segment is:

Draw a line segment CD of any length.

Fix the compass's end on C and pencil on D. This gives the length of CD.

Now divide the length of CD by 2. That is the 1/2 the length of CD.

Draw a line 1. Mark a point A on line 1. Change compass's setting into 1/3 the length of CD, place the compass at A.

Make an arc on the line l which cuts l at B. Now, AB is a copy of CD which is 1/2 the length of CD.

What is line segment?

A line segment is bounded by two definite points on a line. We also can say a line segment is part of the line which connects two points. A line has no endpoints and extends immensely in both the direction but a line segment has two fixed or distinct endpoints.

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Answer:

w

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total points scored in the game is a sum of the points scored by both teams.Given that Eastern had double the score of Central before Central scored a three-pointer as the game ended, Eastern's score can be represented as 2c.So the total points scored in the game is:Central's score before the three-pointer + Eastern's score before the three-pointer + the points scored by Central in the last three-pointer.So the total points scored in the game can be represented as:c + 2c + 3 = 2c + 3So the correct answer is C) 2c +3

Peer-reviewed (refereed or scholarly) journals: Before an article is published in a journal, it is examined by a number of other experts in the subject to guarantee that it is of a high caliber. (The paper is more likely to be valid from a scientific standpoint, draw fair conclusions, etc.)

Peer review has been conducted on the publications in a refereed journal. The papers were evaluated for quality by reputable academics or subject-matter experts before being approved for publication, so this tells us that they are of a high caliber. Also known as "scholarly" or "peer-reviewed," these pieces are published in journals.

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The yellow mark is 1 foot above the water level.

This question can be answered using the concept of trigonometry.

According to the given question

radius of the waterwheel r= 4 feet

let OD is the part of the waterwheel that is submerged in the water and its value is to be determined.

From the figure we can see that

OA=OC=radius= 4 feet

Now

In triangle OAB

cos 60= [tex]\frac{OB}{OA}[/tex]

[tex]\frac{1}{2}= \frac{OB}{OA}[/tex]

OB= 2 feet

which means the length of the yellow mark above water is given by

OB-OD= 2-1= 1 feet.

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Answer:

To find out how much money is allotted for each of these items, we can multiply the percentage of the income allocated to each item by the total income.

Food: 20% of $25,000 = $25,000 x 0.20 = $5000

Shelter: 25% of $25,000 = $25,000 x 0.25 = $6250

Clothing: 15% of $25,000 = $25,000 x 0.15 = $3750

So the family has $5000 for food, $6250 for shelter and $3750 for clothing.

The value x-coordinates which is required is found out to be as Q = -19.41 and +19.41.

The given values are,

radius , r = 35 feet

speed of ball = 11 ft./sec

location of the cup =  (0, 0)

starting location the ball = (-40. -50)

In order to find the possible x-coordinates of Q,

The coordinates of the rightmost edge of the golf course = (35, 0)

slope = m = ( y2 - y1)/ ( x2 - x1)

now , the equation for a circle is known as , (x - h)² + (y - k)² = r²

and the center of the course is given as ,  (h, k) = (0, 0)

Therefore the equation becomes (x - 0)² + (y - 0)² = x² + y² = 35²

equation of tangent , y = -3x/2

putting this value in the tangent = x² + ( -3x/2 )²  = 35²

13x² /4 = 35²

x = √ ( 35²  x 4 )/ 4 = 35²

x = 70/13√ 13 = 19.41

Therefore, the  coordinates of Q are found out to be as  -19.41 and +19.41

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The angle of rotations are 90° , 180° and 270° counterclockwise

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the point be represented as A

Now , the value of A is

a)

Let the coordinates of the point be A = A ( 4 , 1 )

Now , the rotation angles are 90° , 180° and 270° counterclockwise

90° counterclockwise = A' ( -1 , 4 )

180° counterclockwise  = A'' ( -4 , -1 )

270° counterclockwise = A''' ( 1 , -4 )

b)

Let the coordinates of the point be A = A ( 0 , -7 )

Now , the rotation angles are 90° , 180° and 270° counterclockwise

90° counterclockwise = A' ( 7 , 0 )

180° counterclockwise  = A'' ( 0 , 7 )

270° counterclockwise = A''' ( -7 , 0 )

c)

Let the coordinates of the point be A = A ( -2 , 9 )

Now , the rotation angles are 90° , 180° and 270° counterclockwise

90° counterclockwise = A' ( -9 , -2 )

180° counterclockwise  = A'' ( 2 , -9 )

270° counterclockwise = A''' ( 9 , 2 )

d)

Let the coordinates of the point be A = A ( -12 , -4 )

Now , the rotation angles are 90° , 180° and 270° counterclockwise

90° counterclockwise = A' ( 4 , -12 )

180° counterclockwise  = A'' ( 12 , 4 )

270° counterclockwise = A''' ( -4 , 12 )

Hence , the rotation of coordinates are solved

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The given system of equation has no solution.

What is elimination method?

The elimination method is a way to get rid of one of the variables in a system of linear equations by using multiplication or division of the variable coefficients along with addition or subtraction of the variables and their coefficients.

Substitution, elimination, and augmented matrices are the three approaches that are most frequently used to solve equation systems.

Consider, the given system of equations

7x - 12y = -3       ..(1)

-7x + 12y = 2      ..(2)

Adding equation (1) and (2).

       7x - 12y = -3

 +   -7x + 12y = 2

___________________

                0 = -1

0 = -1 is false.

Hence, the given system of equation has no solution.

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According to the round off rule, the resulting value of the total distance is  135,000

As we al know that if the rounded number increases then the given number is said to be rounded up on the other hand if the rounded number decreases then it is said to be rounded down.

Here we have given the details about the race is made up of 4 separate stages.

Now, we need to find the total distance, that can be calculated by adding all the given distance, then we get,

=> 30,060 + 21,111 + 33,501 + 49,840

=> 134512.

Now, we have to round off the value to the nearest thousandth term, then it can be written as,

Here we need rounded to the nearest thousands place. The 4 in the thousands place rounds up to 5 because the digit to the right in the hundreds place is 5.

=> 135,000

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The length of the piece of clothing decreased by 16% after washing.

What is the percentage decrease?

To compute a percentage drop, first determine the difference (decrease) between the two values being compared. Then, divide the reduction by the original number and multiply the result by 100. The percentage change is expressed as a result of the alteration.

The percentage decrease in length of the piece of clothing can be calculated as follows:

Percentage decrease = (original length - new length) / original length * 100

Percentage decrease = (5 - 4.2) / 5 * 100

Percentage decrease = 0.8 / 5 * 100

Percentage decrease = 16%

Hence, the length of the piece of clothing decreased by 16% after washing.

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Answer:

0.7

Step-by-step explanation:

if we set the total race of win and lose is 1

then we use 1-0.3=0.7

It is not possible to construct a triangle with 2cm, 3cm, and 7cm.

The sides measure 2 cm, 3 cm, and 7 cm in length.

Only when the third side is greater than the sum of any two sides can a triangle be drawn. This the condition.

Let's verify the rule now.

2 + 3 > 7        Not true

2 + 7 > 3        True

3 + 7 > 2        True

As 2 + 3 > 7 does not satisfy the condition.

Hence, it is not possible to construct a triangle having 2cm, 3cm, and 7cm in length.

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Answer:

-4190

Step-by-step explanation:

910-5100

Answer: 16 Teaspoons

Hope this helps! :)

Step-by-step explanation:

1 Tablespoon= 3 Teaspoons

6 Tablespoons= (6*3) 18 Teaspoons

18 - 2= 16 tsp

Answer: C and D

Step-by-step explanation:

Plug in the X and Y from the coordinates into each equation. If both sides are equivalent, that means that the line passes through.

The correct statements are given below.

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here: The graph of two functions plotting distance vs time of two Alberto and Bianca

1) Early in the race Alberto runs faster.

2) Alberto maintains a contain speed of 20 km/hr

3) Meanwhile Bianca's Speed is 8.33 km/hr

4) The first person to cross the finish line is Bianca.

Hence, Bianca reached the finished line before Alberto.

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Zero is not a real number that is positive. Because it lies between positive and negative real numbers. Therefore, it is considered neither a positive nor negative real number.

Real numbers are founded on the idea of the number line: the positive numbers to the right of zero and the negative numbers to the left of zero. Any number that fits on this number line can be considered real.

All numbers that are either rational or irrational are also referred to as real numbers. A real number that is positive and bigger than zero is known as a positive real number. Any real number that is not a positive integer is either zero or negative. Therefore, 0 is neither positive nor negative.

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The probability you'll see one over half an hour is 0.26

The term probability in math is defined as  the possibility of the outcome of any random event

Here we have given that the probability you'll see a falling star in the sky over the course of one hour is 0.44.

Then in an hour can be taken as two half hours so we can write the probability to see a falling star as

Then it can be written as,

=> (1-P)*(1-P) = 1 - 0.44

When we simplify this one then we get

=> (1 - P)² = 0.56

Here we need to value of p then it can be written as,

=> 1 - P = √0.56

Then the value of P is calculated as,

=> -P = 0.74 - 1

=> P = 0.26

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