The equation y−k = a(x−h) ^2 has graph a parabola with vertex (h, k).

Suppose a > 0. A horizontal line 1 unit above the vertex intersects the

graph at two points. Find the distance between these two points.

The ratio of two polynomial functions with a non-zero denominator is known as a rational function. R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions, is the typical way to describe it. We studied the idea of the rational number in previous grades. It is the ratio or product of two integers with a non-zero denominator. As a result, the word ratio is where the name rational comes from.

a. A rational function with a hole at x = 1 and a vertical asymptote at x = -3 can be written as:

(x-1)/(x+3)

b. A rational function with a vertical asymptote at x = -2 and a horizontal asymptote at y = 3 can be written as:

(x+2)/(x+2) = 3

c. A rational function with an oblique asymptote y = x+1 but no vertical asymptote can be written as:

(x-1)/(x-1) = x+1

d. A rational function with a vertical asymptote at x = 3 and f(x) > 0 can be written as:

(x-3)/(x-3) > 0

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By the Application of Prime factorization method the value of x is 48

what is Prime factorization method?

Writing all numbers as the product of primes is a procedure known as prime factorization. Consider the case of the number 20, for instance. We can divide that into two elements. Well, that's four times five, we can say. Furthermore, 5 is a prime number.

Solution:

HCF = ( X, 54 ) = 6

LCM = ( X, 54 ) = 432

a = x  b = 54

using property

a * b = LCM * HCF

54a = 6 * 432

   a  = (6 * 432) / 54

   a = 48

Hence the value of x is 48.

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Answer:

coach seats is 310 and first class seats are 77

Step-by-step explanation:

x+4x+2=387

5x+2=387

5x=385

x=77

4x+2

4(77)+2=310

Answer:

There are 77 first-class seats. We can use this information to now define the number of seats in coach. And there are 310 seats in coach.

Step-by-step explanation:

The x and y values for the given equation are x= -20 and y=8

One of the fundamental operations defining a vector space in linear algebra in mathematics is scalar multiplication (or more generally, a module in abstract algebra). When a real Euclidean vector is multiplied scalarly by a positive real number, the direction of the vector remains unchanged, but the magnitude of the vector increases. A scalar is anything that scales vectors, which is how the word "scalar" itself came to be. It is important to distinguish between the inner product of two vectors and scalar multiplication, which is the multiplication of a vector by a scalar with a vector as the product.

Given,

-1/4[ x 12 -32 ] = [ 5  -3  y ]

[(-1/4)x    (-12/4)    (-32/-4)]=[5  -3  y]

-x/4=5

-x=20

x= -20

-32/-4=y

y=8

Therefore, the x and y values for the given equation are x= -20 and y=8

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deposited some money at 1.7​% annual​ interest, and two equal but larger amounts at 2.2​% and 24​%. The total amount invested was ​$26,000​ and the total annual interest earned was ​$574. How much was invested at each​ rate?

What is an investor?

An investor is an individual or an organization that gives money to A person or entity that invests in another with the hopes of making a profit in the future is known as an investor. According to the rules, anyone can invest: You are an investor if you put money into something.

Answer provided by our tutors

Let

x = the money invested at 1.7%

y = the money invested at 2.2%

y = the money invested at 24%

Since the total money invested was $26,000 we have:

x + 2y = 26000

The total annual interest was $574 means:

0.017x + 0.022y + 0.24y = 574

0.017x + 0.262y = 574

We have the following system of equations:

x + 2y = 26000

0.017x + 0.262y = 574

click here to see the system of equations solved for x and y

x = $24,842

y = $578

$24,842 was invested at 1.7%

$578 was invested at 2.2% and another $578 was invested at 24%.

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Answer:

1.6

Step-by-step explanation:

Firstly, we know the rate of change of volume [tex]v'=8[/tex].

The equation for surface area is: [tex]A = 4\pi r^2[/tex].

The derivative (rate of change) is then: [tex]A'=8\pi r*r'[/tex]

The equation of the volume of a sphere is: [tex]V=\frac{4}{3}\pi r^3[/tex].

The derivative (rate of change) is then: [tex]V' = 4\pi r^2 * r'[/tex].

This means that [tex]r'=\frac{V'}{4\pi r^2}[/tex].

We can then plug that into our equation for [tex]A'[/tex] and get:

[tex]A'=8\pi r*\frac{V'}{4\pi r^2}=2*\frac{V'}{r}[/tex]

After that, we can just plug in:

[tex]2*\frac{8}{10}=1.6[/tex]

67 books will fit on the shell.

One foot has 12 inches (in) (ft). In the US customary and imperial measurement systems, both feet and inches are units of length. The foot has had many different definitions throughout history, but since 1959, it has been defined as exactly 0.3048 meters, and the inch as 2.52 centimeters. The meter is the International System of Units' base unit of length (SI).

In the given question,

Then the number of books

= 42 / (5/8)

= 42 (8/5)

= 336/5

= 67 1/5

Finally, we round 67.2 to the nearest LESSER integer number and obtain

67.

Hence, 67 books will fit on the shell.

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Answer:

x = 6 ans y=4

Step-by-step explanation:

The number of free throws made = x

The number of three points shots made = y

We can make an equation

x+y= total shots made

x+y= 10

So if we want "x",

x=10-y (First equation)

x is one point

y is three point

We can make another equation on how much points gained

(1)x + 3(y) = total points gained

x + 3y =18

If we want "x" ,

x =18-3y (second equation).

Now that we got two equation solve the question with simultaneous equations

x=10-y

x=18-3y

Substitute "x=18-3y" into equation 1

18-3y=10-y

10-y=18-3y

3y-y=18-10

2y=8

y=4 (Three points shots)

x=10-y

x=10-4

x=6 (Free throws made)

Therefore , x=6 and y=4

Answer: 1/4,2/5,3/10

Step-by-step explanation:

The fourth proportional {x} between a, b, and c can be written as {x} = (ac/b).

Given are three length parameters as [a], [b] and [c].

For the fourth proportional {x}, the relationship can be written as -

a/x = b/c = k  {constant}

x = (ac/b) = k  {constant}

Therefore, the fourth proportional {x} between a, b, and c can be written as {x} = (ac/b).

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Based on Simple Interest, 8125 was invested at the rate 1.7%.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

Although some mortgages employ this calculation approach, this kind of interest typically relates to auto loans or short-term loans.

> The daily interest rate, the principle, and the number of days between payments are multiplied to determine simple interest.

> Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest.

> Simple interest loans are frequently used for auto loans and short-term personal loans.

Let the amount at 1.7% be x. Then:

[tex]0.017x+0.023(\frac{(25000-x)}{2}) +0.024(\frac{(25000-x)}{2})=535[/tex]

[tex]0.023+0.024 = 0.047 \\\frac{0.047}{2} = 0.0235[/tex]

Now we got rid of the two divisions. Rewrite the equation:

[tex]0.017x+0.0235(25000-x) = 535[/tex]

[tex]0.017x+587.5-0.0235x = 535[/tex]

[tex]-0.006x = -52.5[/tex] Divide both sides by -0.006 and remember -/- = +

x = 8750

This is how much was invested at 1.7% The rest, the problem says, was invested in equal amounts:

[tex]25000-8750 = 16250[/tex]; [tex]\frac{16250}{2}=8125[/tex] So, 8125 was invested each at 2.3% and 2.4%

Based on Simple Interest, 8125 was invested at the rate 1.7%.

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Answer:

7x ( - x + 5 )

Step-by-step explanation:

- 7x² = 7x × - x

35x = 7x × 5

- 7x² + 35x = 7x ( - x + 5 )

Therefore, In  Optimistic Criterion  decision of cases : 300 and in Pessimistic Criterion decision of cases : 200

Probabilities can be written as percentages with a 0%–100% range or proportions with a 0–1 range. An event's probability is measured from 0 to 1, with 0 being the most unlikely scenario and 1 being the most likely. When an event's probability is 0.45 (45%), there are 45 percent (100) odds that it will happen.

Here,

a) Optimistic Criterion

Demand/#of  No. of cases

cases

100      $1,000 $900 $800

200     $800 $2,000 $1,900

300     $600 $1,800 $3,000

Maximum of

Column    $1,000 $2,000  $3,000

Maximum

Decision: 300 cases

b) Pessimistic Criterion

Demand/#of   No. of cases

cases

100      $1,000 $900 $800

200     $800 $2,000 $1,900

300     $600 $1,800 $3,000

Minimum Of

Column    $600  $900  $800

Maximin

Decision: 200 cases

Therefore in  Optimistic Criterion  decision of cases : 300 and in Pessimistic Criterion decision of cases : 200

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An invalid speculation is a sort of measurable theory that suggests that no factual importance exists in a bunch of offered viewpoints.

Speculation testing is utilized to evaluate the validity of a speculation by utilizing test information. It is represented as H0, and it is sometimes referred to as the "null."

Give the null hypotheses a name.

Negative hypothesis:

H. There is no correlation between gender and election participation.

Other possibilities:

H: Gender and participation in the most recent election are linked.

Rule of rejection:

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Answer:

25

Step-by-step explanation:

1: Add up the ratio then divide by the number of students.

3+5=8

40/8=5

2: Each count is equal to 5 students.

3: Multiply the ratio of students who stay after soccer practice by Each count

5*5=25

Answer 34

...................................................................................

The probability of getting heads on the a coin and a number less than 3 on cube is given as 1/6.

In order to find the probability take the ratio of the favorable outcome to the total possible outcome.

The set of total possible outcomes is known as sample space.

The number of elements in the sample space is given as,

Possible outcomes for coin × Possible outcomes for cube

= 2 × 6 = 12

The given two events flipping of coin and rolling of cube are mutually independent.

Which implies it is not the case of conditional probability.

The favorable number of outcomes are as below,

Number of head × Number of numbers less than 3

= 1 × 2 = 2

Now, the probability is given as,

P(getting head on coin and less than 3 on cube) = 2/12 = 1/6

Hence, the probability of getting the required outcome is given as 1/6.

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The measure of exterior angle to ∠X is 79.38°. So, option 4 is correct.

Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.

In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.

Given,

In ΔXYZ, m∠Y=71.02° and m∠Z=29.6°

We know that,

The angles sum in a triangle is 180°.

m∠X+m∠Y+m∠Z=180°

m∠X+71.02°+29.6°=180°

m∠X=180°-100.62°

m∠X=79.38°

Therefore, the measure of exterior angle to ∠X is 79.38°.

So, option 4 is correct.

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An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function

This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous.

At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.

The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.

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Step-by-step explanation:

always remember that 100% is the whole.

so, 15% means 15/100 of the whole.

1/5 = 0.2 = 20/100 of the whole.

so, Target is taking 15/100 off the price.

Walmart is taking 20/100 off the price.

20/100 is bigger than 15/100, so Walmart deducts more off the price, and has therefore the lower and therefore better sale price.

Target sale price :

100/100 - 15/100 = 85/100 × 80 = $68

in short

80 × (1 - 0.15) = 80 × 0.85 = $68

Walmart sale price :

100/100 - 20/100 = 80/100 × 80 = $64

in short

80 × (1 - 0.20) = 80 × 0.80 = $64

The values of x, y and z are 24, 10 and 17 using the similar triangles properties and triangles sum properties.

A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Given that ΔHPS≅ΔCNF.

We can see that angle H in triangle HPS is obtuse whereas angle N in triangle CNF is obtuse so comparing this we get,

6x - 29 = 115

6x = 144

x = 24

Comparing angle C and angle P we get

4z - 32 = 36

4z = 68

z = 17

Now the remaining angle in trinagle CNF is angle F which is 3y - 1 as we know that sum of angles in a triangle is 180 and the angle C and N are 36 and 115 we can say that F  is  29

Now to find y we equalise it to 29

3y - 1 = 29

3y = 30

y = 10.

The values of x, y and z are 24, 10 and 17 using the similar triangles properties and triangles sum properties.

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The area of the shape as shown in the diagram is 11.25 cm².

Area is the region occuppied by a plane shape.

To calculate the area of the shape, we use the formula below.

Formula:

Where:

From the diagram,

Given:

Substitute these question into equation 1

Hence, the area of the shape is 11.25 cm².

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The interval containing the rational zero of f(x) = 3x³ - 5x² + 5x + 7 is given as follows:

-1 < x < 0.

To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.

The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.

The parameters for this function are given as follows:

The factors are given as follows:

Hence the possible zeros are given as follows:

±1/3, ±1, ±7/3, ±7.

The numeric values for the function are these points are of:

This means that there is a zero between -7/3 and -1/3, as the function changes from negative to positive, hence the interval is given as follows:

-1 < x < 0.

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The equation for the relationship between the number of cans of paint, x, and the total weight of the cans, y, in slope-intercept form is y = 6x + 0. This equation can be derived from the formula for the slope-intercept form of a line, y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, since the weight of each can of paint is 6 pounds and there is no y-intercept (the line passes through the origin), the slope of the line is 6 and the y-intercept is 0.

A table of possible values for the number of cans of paint, x, and the total weight of the cans, y, based on this equation is shown below:

x (number of cans of paint) y (total weight of cans)

1 6

2 12

3 18

4 24

5 30

As the table shows, for each additional can of paint, the total weight of the cans increases by 6 pounds. This is because each can of paint weighs 6 pounds, and the weight of the cans is equal to the number of cans multiplied by the weight of each can.

Answer: y = 6x

Step-by-step explanation:

       For each can of paint (x) 6 pounds is added. This is represented as;

         y = 6x

       For the table of possible values, we will plug a value in for x, and then evaluate the function for y. See attached.

y = 6(1) = 6

y = 6(2) = 12

y = 6(3) = 18

Answer:

304

Step-by-step explanation:

To find the surface area of a rectangular prism with length 4, width 10, and height 8, you can use the formula 2 * (length * width + width * height + height * length).

Plugging in the given values, the surface area is equal to 2 * (4 * 10 + 10 * 8 + 8 * 4) = 2 * (40 + 80 + 32) = 2 * 152 = 304.

Answer: 304

Step-by-step explanation:

It will take approximately 7.66 years for the amount of Americium-241 remaining to reach 6 kg, assuming that the initial amount was 10 kg. We can use formula Q(t) = Pe^(rt) to calculate half-life of Americium-241.

To construct a function that will model the amount of Americium-241 remaining after t years from an initial amount of 10 kg, we can use the formula:

Q(t) = Pe^(rt)

where Q(t) is the amount of Americium-241 remaining after t years, P is the initial quantity (10 kg in this case), r is the decay rate (the negative of the half-life of Americium-241, which is -432.2 years), and e is the mathematical constant approximately equal to 2.71828.

Plugging in the values, we get:

Q(t) = 10 * e^(-432.2t)

This is the function that will model the amount of Americium-241 remaining after t years from an initial quantity of 10 kg.

To find out how long it will take for the amount of Americium-241 remaining to reach 6 kg, we can solve the equation Q(t) = 6 for t.

[tex]Q(t) = 6\\6 = 10 * e^(-432.2t)\\0.6 = e^(-432.2t)\\ln(0.6) = -432.2t\\t = ln(0.6) / -432.2\\[/tex]

t = approximately 7.66 years

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Arun sold 41 pound of raspberries and 25 pound of grapes.

What is a linear equation?

The equations with one, zero, or an infinite number of solutions are known as linear equations with two variables. Each of the two variables in these equations has the largest exponent order of 1. A two-variable linear equation has the conventional form axe + by + c = 0, where x and y are the two variables. The answers can also be expressed as ordered pairs, such as (x, y).

Given that the cost of 1 pound of raspberries is $1.50 and 1 pound of grapes is $2.75.

Arun sells 66 pounds with cost $130.25.

Assume that Arun sells x pound of raspberries and y pound of grapes.

Therefore,

x + y = 66   ......(i)

The cost of x pound of raspberries and y pound of grapes is 1.50x + 2.75y.

1.50x + 2.75y = 130.25  .....(ii)

Solving equation (i) and (ii) by using elimination method.

Multiply equation (i) by 1.5

1.50x + 1.50y = 99 ....(iii)

Subtract equation (iii) from (ii)

1.50x + 2.75y = 130.25

1.50x + 1.50y  = 99

(-)      (-)             (-)

________________

              1.25 y = 31.25

                     y  = 25

Putting y = 25 in equation (i)

x + 25 = 66

x = 41

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Step-by-step explanation:

the slope-intercept form is

y = ax + b

a being the slope, b being the y-intercept (the y-value when x = 0), which we get from (0, 3) : 3.

the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.

we got 2 points, so, let's use them :

(-4, 0) and (0, 3)

x changes by +4 (from -4 to 0).

y charges by +3 (from 0 to +3).

so, the slope is +3/+4 = 3/4.

therefore, our equation is

y = f(x) = (3/4)x + 3

The difference between the number of miles travelled on train and car is 110 miles

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

The difference between the distance covered can be calculated as

Distance difference = The difference of the product of speed and time

Substitute the known values in the above equation, so, we have the following representation

Distance difference = 70 * 3 - 50 * 2

Evaluate the products

This gives

Distance difference = 210 - 100

Evaluate the

Distance difference = 110 miles

Hence, the distance difference is 110 miles

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The cleveland cavaliers and of the golden state warriors in game 7 of the 2016 nba finals the player are 8.

A scatter plot is a hard and fast of factors plotted on a horizontal and vertical axes. Scatter plots are essential in facts due to the fact they could display the quantity of correlation, if any, among the values of determined portions or phenomena (referred to as variables).

Scatter plots are used to plan facts factors on a horizontal and a vertical axis withinside the strive to expose how a great deal one variable is laid low with another. Each row withinside the facts desk is represented through a marker whose role relies upon on its values withinside the columns set at the X and Y axes.

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