Find the least common denominator of 1/2x-6 and 2x/7x-21.

Y = 2(x-2)²+2 is the equation used to model the bird's vertex form journey.

A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices. For instance, the points A, B, C, D, and E in the aforementioned figures are vertices.

Formula for the general vertex form: f(x) = a(x − h) ² + k

where the vertex is (h,k).

This equation can be used to represent a bird's flight path:

y = 2x² - 8x+10

Vertex form equation conversion

Filling in the square:

y = 2(x² - 4x+5)

y=2

(x²-4x+5+ (2)2- (2)2)

y=2(x²-4x+5+ (2)²-4) y=2((x-2)2-4+5)

y=2((x-2)²+1)

y = 2(x-2) (x-2)²+2

Where:

(h,k)=(2,2)

a=2

Consequently, the vertex form equation for the bird's journey is Y = 2(x-2)²+2

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Complete Question -

Flight Path of a Bird

In this activity, you'll use quadratic equations to model situations and interpret the solutions to the equation

The flight path of a bird can be represented by this equation, where x represents the horizontal distance, in feet, from a tree

branch and y represents the height, in feet, relative to the ground.

y = 2x2 - 8x + 10

Part A

Question

Rewrite the equation modeling the path of the bird in vertex form by completing the square,

Substitute the values of a, h, and k to complete the equation.

[tex]t+7.87 > 9.87[/tex]

Subtract 7.87 from both sides:

[tex]t+7.87-7.87 > 9.87-7.87[/tex]

Answer:

[tex]t > 2[/tex]

Answer:

[tex] \sf \: t > 2[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of t.

The inequation is,

→ t + 7.87 > 9.87

Then the value of t will be,

→ t + 7.87 > 9.87

→ t > 9.87 - 7.87

→ [ t > 2 ]

Hence, the value of t is 2.

Answer:

The answer is 0.165 inches.

Step-by-step explanation:

The volume of a rectangular pool can be calculated as the product of its length, width, and depth. To find out how much the water level increased, we'll calculate the volume of one quart of water and compare it to the volume of the pool.

One quart is equivalent to 0.946 liters, and 1 liter of water has a volume of 1000 cubic centimeters. Therefore, one quart of water has a volume of 0.946 liters x 1000 cubic centimeters/liter = 946 cubic centimeters.

Since 1 cubic foot is equivalent to approximately 28,317 cubic centimeters, the volume of one quart of water in cubic feet is:

946 cubic centimeters / 28,317 cubic centimeters/cubic foot = 0.033 cubic feet.

The volume of the pool can be calculated as:

12 ft x 20 ft x depth (in feet) = 240 cubic feet

So, if the pool is 12 ft x 20 ft, the water level increased by:

0.033 cubic feet / 240 cubic feet = 0.0001375 feet = 0.165 inches.

Therefore, the water level in the pool increased by approximately 0.165 inches.

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Answer:

Step-by-step explanation:

a/sin A=b/sin B

20/sin90⁰=x/sin60⁰

cross multiply

20sin60⁰=xsin90⁰

17.32=

area=1/2a/bsin∅

=1/2×17.32×20 sin30⁰

86.6square

Answer:

n(A) = 6

n(B) = 4

Step-by-step explanation:

The integers greater than -9 but less than -2 are

-8, -7, -6, -5, -4, -3

There are 6 integers and the set A = {-8, -7, -6, -5, -4, -3}

Cardinality of a set is the number of elements in that set

n(A) = 6

n(B) = 4 since there are 4 elements - this seems to have been answered

Answer:Taking into account that X + Y = X + X + B = A, one can obtain the following formulas for finding X and Y:

X = (A – B) / 2.

Y = X + B = (A + B) / 2.

Step-by-step explanation:

If the ratio of their corresponding sides are identical, then the triangles are similar to each other. Triangle ABC, GHI and JKL have similar ratio of their corresponding sides. Thus, Triangle ABC,JKL and GHI are similar to each other.

It is not necesary that sides are equal in similar triangles but it is mandatory to have all the angles are identical in similar triangles.

If the length of corresponding sides of the triangle are in the same proportion then the triangles are similar to each other.

Therefore,

Sides of the triangle ABC and triangle GHI are in proportion, hence both the triangles are similar to each other.

Sides of the triangle ABC and triangle JKL are in proportion, hence both are similar to each other.

Similarly, triangle JKL and GHI both are similar to each other.

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Number of pages needed to read per day = 22.5 pages.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Given,

No. of chapters in book = 15

No. of pages per chapter = 7 1/2 = 15/2 pages

Total pages in book = 15 × 15/2 = 225/2 pages

There are 5 days in Monday to Friday,

So, No. of pages read per day = 225/2×5 = 22.5

No. of chapters in included in 22.5 pages = 22.5/7.5 = 3

Hence, 22.5 pages or 3 chapters will be needed to read everyday.

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Therefore , the solution of the given problem of expression comes out to be √15 -4 < √15 -7  and so on.

Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.

Here,

Given :

to find which is greatest expression among them

=> √15 -4 < √15 -7

=> 2√18  < 2√21

=>-³√30  > -3

=>√8 + 1 < √17 -2

Therefore , the solution of the given problem of expression comes out to be √15 -4 < √15 -7  and so on.

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Since the data has only numerical values and deals with only one attribute, that is age, we can say that the given data is numerical as well as univariate.

In statistics, univariate data is the kind of data which consists of observation which only deals with one kind of trait or characteristic. In the given data, age is the only characteristic which the observations represent and hence we can say that the given set of data is univariate.

Numerical data in statistics is the data in which the observations are just in number forms and are not in a descriptive form or in a language. The set of data given to us has only numerical values so we can say that the data is numerical.

--The given question is incomplete, the complete question is

The display shows musicians' ages in a community orchestra.

1 79

2 0446

3 23557

4 2489

5 12

6 5

Key 17 = 17

Which of the following describes this data set?"--

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Answer:

<

Step-by-step explanation:

-3 is greater than -7 since its more closer to the 0 then -7.

Based on the definition of complementary angles, he measure of each of the angles are: 10.4 degrees and 79.6 degrees.

Complementary angles are defined as any two angles whose sum will be equal to 90 degrees when added together.

Therefore, let x be the measure of the angle.

According to the problem statement, the angle measures 69.2° less than the measure of its complementary angle.

So we have x + (x + 69.2) = 90

By simplifying the equation:

2x + 69.2 = 90

2x = 90 - 69.2

2x = 20.8

x = 20.8/2 = 10.4

So the angle measures 10.4 and the complement of angle is (10.4 + 69.2) = 79.6.

Thus, the measure of each of the angles are: 10.4 degrees and 79.6 degrees.

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0.17 acres can be planted per pound of seed.

What is Ratio ?

In mathematics, the term "ratio" is used to compare two or more numbers. It is used to show how big or little an amount is in relation to another. Two quantities are compared using division for calculating a ratio.

Given, It takes 29 pounds of seed to completely plant a 5-acre field.

So, Acres per pound of seed = 5 Acres ÷ 29 pounds of seed

                                                = 0.17 acres (approx).

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According to the given statement,  0.17 acres can be planted per pound of seed.

In mathematics, the term "ratio" is used to compare two or more numbers. It is used to show how big or little an amount is in relation to another. Two quantities are compared using division for calculating a ratio.Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were going to compare one piece of data (A) to some other data point (B).

Given, It takes 29 pounds of seed to completely plant a 5-acre field.

So, Acres per pound of seed = 5 Acres ÷ 29 pounds of seed

= 0.17 acres (approx).

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Answer:

14 rows.

Step-by-step explanation:

It could be any amount, but there is a clear pattern that follows "-3". Starting from 51 and ending at 12, let's subtract by 3.

51, 48, 45, 42, 39, 36, 33, 30, 27, 24, 21, 18, 15, and 12.

There are 14 numbers; therefore, there are 14 rows.

Step-by-step explanation:

-1/5x - 2 > 4

-1/5x - 2 + 2> 4 +2

first you subtract 2. The two cancels out into 0 making the equation this

↓

-1/5x x -1/5> 6 x -1/5

you multiply both sides by the -1/5 and if you divide or multiply a number over the inequality you must change the sign to the opposite one.

ANSWER:

x< -30

Answer:

x < -30

Step-by-step explanation:

-1 / 5 * x – 2 > 4
-1 / 5 * x > 6

We divide both parts of the inequality by (-1 / 5). It must be remembered that when dividing or multiplying both sides of the inequality by a negative number, the sign changes to the opposite:

x < 6 / (-1 / 5)
x < 6 * 5 / -1
x < -30

Сheck:

for -29 (> then -30):
-1 / 5 * -29 – 2 > 4
3.8 > 4? - No

for -31 (< then -30):
-1 / 5 * -31 – 2 > 4
4.2 > 4? – Yes

The solution is right!

The possible values for each expression are given as follows:

1. 8 ≤ a+b ≤ 16

2. -6 ≤ a - b ≤ 2

3. 15 ≤ ab ≤ 63

4. 1/3 ≤ a/b ≤ 7/5.

For the sum we have that:

For the subtraction, we have that:

For the multiplication we have that:

For the division, we have that:

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For n = 8, the sum of squares from 1 to 8 would be:

Σ i² = 8(8 + 1)(2(8) + 1) / 6 = 204.

The act of adding anything up is called summarizing. To produce an action potential in the nervous system, numerous stimuli that are each individually subthreshold must be combined to reach a suprathreshold level (a response). Usually, a sum of numerous terms is indicated by the symbol "sigma." To include all terms that must be taken into account when computing the sum, this symbol is typically followed by an index that varies.

The summation notation "Σ" is used to represent the sum of a sequence of numbers. The expression "Σ i²" means the sum of the squares of the numbers from i=1 to i=8.

The formula to find the sum of the squares from 1 to n is given by:

Σ i² = n(n + 1)(2n + 1) / 6

So, for n = 8, the sum of squares from 1 to 8 would be:

Σ i² = 8(8 + 1)(2(8) + 1) / 6 = 204.

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Answer:

(A)
Domain: [tex]\mathbf {(-\infty, \infty)}[/tex]
Range : [tex]\mathbf {(-\infty, \infty)}[/tex]

(B)
[tex](-2\sqrt{2} , 0) \;and\; (2\sqrt{2} , 0)[/tex]

(C)
(- ∞, -2] and [ 0, 2 ]

(D)

(- ∞, -2] and [ 0, 2 ]

(E)

[-2, 0 ] and [2, ∞ )

(F)

There is no interval where the function is constant

(G)

The graph is symmetric about the y-axis

(H)
This is an even function

Step-by-step explanation:

Warning!!
Pay careful attention to the use of two different brackets when using interval notation. A square bracket means the value next to it is included in that interval, a regular bracket indicates it is excluded

For example: [2, 4) means 2 is included but not 4

Pay careful attention to which bracket is being used where in my explanation and answers. You could lose points if you use the wrong brackets

(A)

Domain is the set of all x values that yield a real and defined value for y

Since the graph continues forever, the range of x values is -∞ to +∞

This is written as - ∞ < x < ∞ or, in interval notation as [tex]\mathbf {(-\infty, \infty)}[/tex]

Range is the set of y values for the given domain. Since the graph goes on forever, the range of y is - ∞ < y < ∞. Interval notation: [tex]\mathbf {(-\infty, \infty)}[/tex]

(B)

The x-intercepts are where the function graph crosses the x-axis. Mathematically, it is the value of x at y =

There are two x-intercepts:

[tex](-2\sqrt{2} , 0) \;and\; (2\sqrt{2} , 0)[/tex]

(C)
y-intercept is where the graph intersects the y-axis. Here the graph touches the y-axis at (0, 0).So y-intercept = (0,0)

(D)
The function is increasing in the intervals (- ∞, -2] and [ 0, 2 ]

(E)
The function decreases in the following intervals for values of x
[-2, 0 ] and [2, ∞ )

(F)

There is no interval where the function is constant

(G)
The graph is symmetric about the y-axis as you see visually. Mathematically, a graph is symmetric about the y axis if f(-x) = f(x)
Here we see that  f(2) = 16 and f(-2) = 16 so there is y-axis symmetry

There is no symmetry about the x axis

To see if there is symmetry about the origin, replace any(x, y) with (-x, -y) and see if it is valid. (2, 16) replaced with (-2, -16) is not a point on the graph hence no symmetry about origin

(H)
This is an even function since it is symmetric about the y-axis

The point where x = -1 is the location of a relative maximum.

What is the critical point?

The concept of "critical point" is used in a lot of different ways, particularly, the most common way in which it is used is to describe the points where the slope of the tangent line is zero in continuous functions.

A critical point is a point where the first derivative of a function is equal to zero or is undefined.

A relative maximum occurs when the first derivative is zero and the second derivative is negative, while a relative minimum occurs when the first derivative is zero and the second derivative is positive.

The given information tells us that f'(x) is positive in the interval x < -1, negative in the interval -1 < x < 0, and positive in the interval x > 0.

This means that f'(x) is increasing in the interval x < -1, decreasing in the interval -1 < x < 0, and increasing in the interval x > 0. Therefore, at the critical point x = -1, f'(x) is zero and f''(x) is negative.

This means that the function changes from an increasing function to a decreasing function, indicating that the point where x = -1 is the location of a relative maximum.

Hence, the point where x = -1 is the location of a relative maximum.

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In both cases, the probability would be 0.0045%.

What is Poisson's distribution?

The Poisson distribution is used to model the number of times an event occurs within a given time interval with a known average rate of occurrence. The probability of exactly k occurrences in a Poisson process is given by the equation:

P(k; λ) = (λ^k * e^-λ) / k!

Where λ is the average rate of occurrences and k is the number of occurrences.

a. In this case, the average rate of arrivals is alpha = 10 per hour, and the probability of no equipment violations is 0.5. The probability that exactly ten vehicles arrive during the hour and all ten have no violations is:

P(10; 10) * (0.5)^10 = 0.000045 or 0.0045%

b. The probability that ten "no-violation" cars arrive during the next hour is:

(10 * 0.5)^10 * e^(-10*0.5) / 10! = 0.000045 or 0.0045%

This probability is the same as in a. because it's the probability of exactly ten "no-violation" cars arriving during the next hour given that the number of cars arriving follows a Poisson distribution with an average rate of arrival of 10 per hour.

Hence, in both cases, the probability would be 0.0045%.

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Answer: 2.7*10^7

Step-by-step explanation:

due to the rules of exponents you would multiply 10^2 times the 3 making it 10^6. 3^3 is 27 but scientific notation numbers cannot be more than ten. so you add a decimal in-between making 2.7 for and you would add the one 10 to the original exponents making it 10^7.  

Therefore , the solution of the given problem of percentage comes out to be the sum of money needed to complete the transaction is $7,722.

A percentage is mathematics is a figure or number that is stated as a proportion of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. However, the symbol "%" used to denote it is frequently used. The percentage amount is flat; there are no dimensions. Given that their numerator is 100, percentages are basically fractions.

Here,

According to the clauses 1/10, n/30, the buyer would receive a 1% reduction if the discount was applied within 10 days.

The consumer would be required to pay the whole amount in 30 days if the payment was not completed within this time frame.

Considering this and the fact that Nieman invoiced $2,400 for the returned goods, you must deduct this sum from their original purchase:

=> $12,200-$2,400= $7,800

Then, you must figure out the discount at 1% of $7,800 and deduct it from $7,800:

=> $7,800*1%= $78

=> $7,800-$78= $7,722

This means that, in the event Nieman Company settles the invoice during in the buy the product, the sum of money needed to complete the transaction is $7,722.

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The area of a large circle contains six small circles (radius = 4cm ) each of which is tangent to the two other small circles and the large circle is  [tex]452.2[/tex] [tex]cm^{2}[/tex].

Given,

      A large circle contains six circles having tangents with a large circle and two small circles as shown in the attached figure.

          The radius of a small circle = 4cm

we know that,

         The radius of a large circle [tex]= \frac{8+8+8}{2}[/tex]

                                                       [tex]= \frac{24}{2}[/tex]

                                                       [tex]= 12 cm[/tex]

            Area of Large circle [tex]= \pi R^{2}[/tex]

                                              [tex]= 3.14* 12^{2}[/tex]

                                              [tex]= 3.14 * 144[/tex]

                                              [tex]= 452.2[/tex]

Therefore, the Area of the large circle is approx [tex]452.2[/tex] [tex]cm^{2}[/tex] .

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A subgroup of index p must contain all elements of g, hence it is normal. Therefore, every group of order p2 has a normal subgroup of order p.

Let p be a prime and g be a group of order p a for some a ∈ Z.

First, we prove that every subgroup of index p is normal in g.

Since the order of g is p a , and the index of a subgroup of g is p, the subgroup must contain all elements of g. Thus, the subgroup is normal in g.

We can now deduce that every group of order p2 has a normal subgroup of order p.

Since the order of a group of order p2 is p2, we can divide it into two subgroups: one of order p, and one of order p. Since the subgroup of order p has an index of p, it must be normal in the group of order p2. Therefore, every group of order p2 has a normal subgroup of order p. Every group of order p2 has a normal subgroup of order p due to the fact that a subgroup of index p must contain all elements of g.

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The sample size for part(A)=318  and part(B) is 423 and the difference of samples is 105.

PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 75% of Italians can taste PTC, for example. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC.

Part(A)

it is given in the question that.

margin of error E=0.04

guessed value p=75%=0.75

confidence interval =90%=0.90

now to find the sample size,

[tex]n=\frac{{[z_{a/2}}]^2p(1-p) }{E^{2}}[/tex]

[tex]n=\frac{1.645^2(0.75)(.25)}{0.04^2} \\\\n=318[/tex]

therefore, the sample size is 318.

Part(B)

find the new sample size by the above formula.

p=0.5

so, n'=423.

thus, the new sample size is 423.

for the difference between the two sample sizes.

N=105.

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1) The Roman military was directed by consuls

2) Senate, a body where plebians chose the leaders.

3) a patrician-only ruling body known as the Assemblies.

The highest ranked magistrate in the Roman Republic was known as a consul (consul in Latin). Two consuls, who were responsible for overseeing the state and, in particular, the army in the field, were chosen annually from among citizens over the age of forty-two for the office, which was annual and collegiate. The consuls, however, held relatively little power and influence during the foundation of the Empire because the emperor assumed the role of supreme leader, serving solely as a symbol of Republican Rome's past.

The Senate, also known as Senatus, de senex, elder, was one of the components of Ancient Rome's government. It was made up of 300 members drawn from the ancient magistrates during the most of the Republic, yet following Sila's dictatorship and during the imperial era, that number rose to 900. It was responsible for approving the laws chosen by the electorate, giving magistrates advice, and managing foreign policy, finances, and religion.

The complete question is :

Insert a picture below

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The number of kilograms of each must be woven together to make 75 kg of cloth which is 94% silk is:

30 kg of pure silk thread and 45 kg of some thread.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

The amount of pure silk thread= x

The amount of some thread = y

The amount of silk pure silk thread= 100%

The amount of silk in some thread = 85%

Now,

Two equations are:

x + y = 75 _____(1)

x = 75 - y _____(2)

x + 0.85y = 0.94 x 75 _____(3)

Substituing (2) in (3)

75 - y + 0.85y = 70.5

75 - 70.5 = y - 0.85y

4.5 = 0.15y

y = 30

Now,

x = 75 - 30

x = 45

Thus,

30 kg of pure silk thread and 45 kg of some thread.

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Answer:

2^1 = 2 -> last digit is 2

2^2 = 4 -> last digit is 4

2^3 = 8 -> last digit is 8

2^4 = 16 -> last digit is 6

2^5 = 32 -> last digit is 2

2^6 = 64 -> last digit is 4

2^7 = 128 -> last digit is 8

We can observe that the last digit follows a pattern of 2,4,8,6,2,4,8 and repeat.

Therefore, 2 to the power of 47 will have the same last digit as 2 to the power of (47 modulo 4) + 3

(47 mod 4) + 3 = 51 mod 4 = 3

The last digit of 2 to the power of 3 is 8

Therefore, the last digit of 2 to the power of 47 is 8.

The number of boxes that he can put into the truck will be 12.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

From the information, the moving truck can carry no more than 1,480 pounds of cargo. Brian loaded x640 pounds into the truck already. He is loading boxes that weigh 70 pounds.

Let the number of boxes that he can put into the truck will be represented as x.

640 + 70x = 1480

Collect the like terms

70x = 1480 - 640

70x = 840

Divide

x = 12

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The equation represents the relation between s and t is s = 9t

This question is an example of Direct Variation, which is a type of proportional relationship between two variables. In direct variation when one variable increases, so does the other, and when one variable decreases, so does the other.

This relationship can be expressed mathematically by the equation

y = k x

where k is the constant of variation. In the given problems is the dependent variable, and t is the independent variable.

Since we know that when t = 4, s = 9, we can substitute these values into the equation and solve for k.

9 = k(4)

k = 9/4

Therefore, the equation for this direct variation is s = (9/4)t.

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