6. Write the equation that represents the points in
the table in vertex form.
The vertex of the function is (0, 2).

X |. Y
-2.| 6
-1 |. 3
0. | 2
1. | 3
2. | 6

Answer:

6u+18

Step-by-step explanation:

6*u=6u and 6*3=18

For number 22:

7y=8x-14 ; y=6

Plugging in y, we get:

7*6 = 8x - 14

42 = 8x-14

56 = 8x

x = 7

Comparing answers, x is, indeed 7.

Answer:

25/64

Step-by-step explanation:

C=πd

find diameter:

small= 15 x 15= 225

large= 24 x 24= 576

multiply:

225 x 3.14= 706.5

576 x 3.14= 1808.64

ratio:

706.5/1808.64

reduce:

25/64

Length of the radius of the small pizza = 15 inches

Circumference of the small pizza :

\( =\tt 2\pi r\)

\( = \tt2 \times 3.14 \times 15\)

\( = \tt94.2 \: inches\)

Thus, the circumference of the small pizza = 94.2 inches

Length of the radius of the large pizza = 24 inches

Circumference of the large pizza :

\( = \tt2\pi r\)

\(\tt2 \times 3.14 \times 24\)

\( = \tt150.72\)

Thus, the circumference of the large pizza = 150.72 inches

Ratio of the circumferences of the two pizzas :

\( = 94.2 : 150.72\)

\( = \tt\frac{94.2 \times 100}{150.72 \times 100} \)

\( = \tt \frac{9420}{15072} \)

Let us simplify the fraction :

\( = \tt\frac{9420}{15072} \)

\( =\tt \frac{9420 \div 12}{15072 \div 12} \)

\( = \tt \frac{785}{1256} \)

\( = \tt\frac{785 \div 157}{1256 \div 157} \)

\( = \color{plum}{ \tt\frac{5}{8} }\)

Thus, the ratio of their circumferences = 5:8

Therefore, the ratio of the circumferences of the pizzas as a fraction \( = \color{plum}{ \tt\frac{5}{8} }\)

Answer:mean you have to switch define

1. Subtraction property of equality

2. Division property of equality

Step-by-step explanation:

Step-by-step explanation:

0.4x+3.9=5.78

0.4x=5.78-3.9

0.4x=1.88

x=1.88

0.4

x=4.7 ans

hope u want this.

The solution of the linear equation is d equals 1.

The linear equation is;

\(\rm d- 10-2d+7=8+d-10-3d\)

A linear equation is an equation for a straight line.

To determine the solution of the linear equation following all the steps given below.

The solution of the equation is;

\(\rm d- 10-2d+7=8+d-10-3d\\\\d-2d-10+7 = 8-10+d-3d\\\\-d-3=-2-2d\\\\-d+2d=-2+3\\\\d=1\)

Hence, the solution of the linear equation is d equals 1.

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The horizontal translations of exponential functions only affect the range of the function. The domain remains the same, and the asymptote is unaffected.

The domain of the function still persists as the same – all real numbers. When it comes to range, its variation may occur due to a horizontal shift. If C > 0, then the range will offset upwards by the value of C units, whereas if C < 0, then the range shifts downwards with the magnitude of the shift having no influence on the contour of the function.

Furthermore, exponential functions have a fixed horizontal asymptote at y =0, that is not affected by any horizontal translations and which overtly remains equal to its original function.

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There are 10,000 possibilities of creating a 4-digit pin with numbers 0-9 when repetition is allowed.

Every digit has ten possible values. Furthermore, any digit may follow a prior digit.

Therefore, there are 10⁴, or 10,000 possible 4-digit PINs.

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Answer:12x+2

Step-by-step explanation: the first step is to put g of x in f of x like this

3(4x)+2

As described in number system the of positive integers is 13

what is number system ?

A numeral system, also known as a mathematical notation, is a way of writing numbers that uses digits or other symbols to represent the numbers in a given set in a standardised way. In different numeral systems, the same set of symbols may represent various numbers.

Solution:

we want the integers b such that

2013 = 3 ( modb)

=> b is a factor of 2010

since 2010 has 2 * 3 * 5* 67 it has

(1+1)(1+1)(1+1)(1+1) = 16 factors

since b cannot equal to 1, 2, or 3, as these cannot have 3 in there base representation, our answer is 16 - 3 =13.

therefore the number of positive integers is 13

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In order to show that 6x2 + 3x + 4 is O(22), we need to find suitable values for c and k in the definition of big-O.  Recall that a function f(x) is O(g(x)) if there exist positive constants c and k such that |f(x)| ≤ c|g(x)| for all x ≥ k.

Looking at the options given, we can see that the value of c must be greater than or equal to 1, since we are looking for an upper bound for the function.

Option a, where c = 100 and k = 1, is not a suitable choice because it is too large of a value for c. Similarly, option e, where c = 7 and k = 87, is not a suitable choice because it is too large of a value for k.

Option b, where c = 13 and k = 1, is a possible choice. To show this, we need to prove that there exist constants c = 13 and k = 1 such that:

\(|6x2 + 3x + 4| ≤ 13|22| for all x ≥ 1.\)

Note that |22| = 22 and |6x2 + 3x + 4| ≤ 6x2 + 3x + 4.

Thus, we need to show that:

6x2 + 3x + 4 ≤ 13(22) for all x ≥ 1.

Simplifying the inequality, we get:

6x2 + 3x + 4 ≤ 286

This inequality holds for all x ≥ 1, since the left-hand side is a quadratic function that is increasing for x ≥ 0. Therefore, option b is a suitable choice.

Option c, where c = 1 and k = 87, is not a suitable choice because it is too small of a value for c.

Option d, where c = 10 and k = 2, is not a suitable choice because it is too small of a value for k.

Option f, where c = 7 and k = 1, is also a possible choice. To show this, we need to prove that there exist constants c = 7 and k = 1 such that:

\(|6x2 + 3x + 4| ≤ 7|22| for all x ≥ 1.\)

Note that |22| = 22 and |6x2 + 3x + 4| ≤ 6x2 + 3x + 4.

Thus, we need to show that:

6x2 + 3x + 4 ≤ 154 for all x ≥ 1.

This inequality holds for all x ≥ 1, since the left-hand side is a quadratic function that is increasing for x ≥ 0. Therefore, option f is also a suitable choice.

In summary, options b and f are both suitable choices for c and k in the definition of big-O to show that 6x2 + 3x + 4 is O(22).

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The equation that expresses the relationship between the two variables is 6x = y.

Let's assume that Chad runs 'x' laps, then Kyle runs 6 times as many laps as Chad, which means Kyle runs 6x laps. Therefore, the equation expressing the relationship between Chad's laps and Kyle's laps can be written as:

Kyle's laps = 6 times Chad's laps

or                              

6x = the number of laps Kyle runs

So, the equation is: 6x = y, where 'x' represents the number of laps Chad runs i.e. he ran six times more, and 'y' represents the number of laps Kyle runs i.e. he ran six times lesser than Chad.

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James should set up the refreshment stand on the incentre of the obtuse triangle.

The incentre of a triangle is defined as the intersection between the angle bisectors of a triangle. The inradius is the line segments from the incenter of the triangle to each of the three sides of the triangle which are all equal.

The inradius is defined as the radius of an inscribed circle in the triangle. Therefore, the required shortest equal distance from his stand to each road so that the stand is at the same distance for all three roads is on the incentre.

Hence, the correct option is C.

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The bar showing the spending for the chamber of commerce makes comparisons with the other groups more difficult.

The structured presentation is a well known visual device for showing information and making correlations between various classifications or gatherings. Nonetheless, certain elements of the information can utilize a visual chart less supportive for correlations. For this situation, the bar showing the spending for the office of trade makes correlations with different gatherings more troublesome on the grounds that it is altogether bigger than different bars, which can make it harder to analyze the general sizes of different bars precisely.

Furthermore, the information would preferable fit a flat rather over an upward show, as this would consider a more clear representation of the information and more precise correlations between the various classifications.

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The question to be solved is;

From the steps shown in the question, it was glaring Ravis made a mistake from the onset.

The proper solution and the right approach to the question is shown below;

I'm assuming you want to answer problem 5.

If so, then the answer is A = 84 degrees

==========================================================

Explanation:

Minor arc BC is 96 degrees. This is the measure along the edge of the curve from B to C, following the shorter path. You correctly identified that the central angle BKC is also congruent to this arc measure, since the central angle cuts off this arc.

Because segments AB and AC are tangents to the circle, this makes the segments to be perpendicular to the radii that meet at the point of tangency. In other words, AB is perpendicular to BK, and AC is perpendicular to CK.

Ignore line BC. Focus on quadrilateral ABKC. So far we know that

The only thing missing is angle A, which is what we're after. Recall that for any quadrilateral, the four interior angles always add to 360 degrees.

So,

A+B+K+C = 360

A+90+96+90 = 360

A+276 = 360

A = 360-276

A = 84

-----------------------

Or as a shortcut, you can use the property that because B and C are right angles, this means we have 360-B-C = 360-90-90 = 180 degrees left for angles A and K to add to. This makes angle A and angle K to be supplementary.

So,

A+K = 180

A+96 = 180

A = 180-96

A = 84

A symbol that completes the inequality 6x - 3y ___ -12 is: C. ≥.

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Next, we would evaluate the inequality by using specific ordered pairs (x, y) as follows;

(0, 0)

6(0) - 3(0) ? -12

0 ≥ -12

(1, 2)

6(1) - 3(2) ? -12

0 ≥ -12

(-1, 2)

6(-1) - 3(2) ? -12

-12 ≥ -12

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The average daily balance at the end of the month will be $1,000.00 (option C).

To calculate the average daily balance, we need to determine the total balance over the 30-day period and divide it by the number of days (30) to get the average.

The daily balance for the first 10 days is $500, for the next 10 days is $1,000, and for the last 10 days is $1,500.

To find the total balance, we can multiply each daily balance by the number of days it was held:

Total balance = (10 days * $500) + (10 days * $1,000) + (10 days * $1,500)

Total balance = $5,000 + $10,000 + $15,000

Total balance = $30,000

Now we divide the total balance by the number of days (30) to find the average daily balance:

Average daily balance = Total balance / Number of days

Average daily balance = $30,000 / 30

Average daily balance = $1,000

Therefore, the average daily balance at the end of the month will be $1,000.00 (option C).

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The  product of prime polynomials which is equivalent to 30x3 – 5x2 – 60x is option C) 5x(2x – 3)(3x + 4).

We have 30x³ - 5x² - 60x

We take common value out so

5x(6x² - x - 12)

By following the factorization method we get,

6x² - x - 12

b²-4ac = -1² - 4x6x(-12)

= 289

x = -b ± √289/2a

= 1 ± 17/-2

x = 3/2 or x = -4/3

So,

6x² - x - 12

6(x-3/2)(x-(-4/3))

(2x-3) (3x+4)

Therefore,

30x³ - 5x² - 60x = 5x(6x² - x - 12)

= 5x (2x-3) (3x+4)

The  product of prime polynomials is equivalent to 30x3 – 5x2 – 60x is 5x(2x – 3)(3x + 4).

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True. Since the square matrix that represents the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same. This property is a fundamental characteristic of orthogonal matrices and holds true for all orthogonal matrices.

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False While it is true that the square matrix that represents the DCT coefficient is orthogonal, it does not mean that its inverse and transpose are the same.

the inverse of an orthogonal matrix is its transpose. However, the transpose of the matrix does not necessarily mean that it is the same as the inverse of the matrix. In the statement is false because the inverse and transpose of an orthogonal matrix are not always the same.


The Discrete Cosine Transform (DCT) coefficient matrix is an orthogonal matrix. In the case of orthogonal matrices, the inverse matrix is indeed equal to the transpose of the original matrix. This is because the product of an orthogonal matrix and its transpose results in the identity matrix.

Since the square matrix representing the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same.

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Answer:

C

Step-by-step explanation:

You are correct

*Per something means multiplication*

20 per 4 weeks = 20 × 4

write the given equation in a standard form

3x + 4y = 6

4y = 6 - 3x

4y = - 3x + 6

divided by 4 in both sides

y = - 4/3x + 3/2

standard form of a linear equation is

y = mx +c

therefore m for gradient is -4/3

the product of the gradient of the lines that are perpendicular to each other is -1

- 4/3 × mx = -1

mx = 3/4

y = mx + c

-5 = 3/4(2) + c

-5 = 3/2 + c

c = -13/2

therefore your equation is

y = 3/4x - 13/2

The linear function rule that models the cost y of a package containing any number x of comic books is y = 5.50 + 0.50x.

To find the linear function rule that models the cost of a package containing any number of comic books, we need to determine the equation based on the given information.

Let's denote the cost of the poster as p and the cost of each comic book as c. We can write two equations based on the given information:

Equation 1: p + 2c = 7.50

Equation 2: p + 11c = 16.50

To find the linear function rule, we need to solve these two equations simultaneously. Let's use the method of elimination:

Multiply Equation 1 by 11 to eliminate p:

11p + 22c = 82.50

Now, subtract Equation 2 from the above equation to eliminate p:

11p + 22c - (p + 11c) = 82.50 - 16.50

10p + 11c = 66

Next, rearrange this equation to solve for c in terms of p:

10p = 66 - 11c

10p = 66 - 11c

c = (66 - 10p) / 11

Now, we can substitute this value of c into Equation 1 and solve for p:

p + 2((66 - 10p) / 11) = 7.50

11p + 2(66 - 10p) = 7.50 * 11

11p + 132 - 20p = 82.50

-9p = -49.50

p = 49.50 / 9

p = 5.50

Now that we have the values of p and c, we can write the linear function rule for the cost y of a package containing any number x of comic books:

y = 5.50 + 0.50x

Therefore, the linear function rule that models the cost y of a package containing any number x of comic books is y = 5.50 + 0.50x.

To compare the deals between the two stores, we need to consider the initial value (y-intercept) of each linear function. The first store's deal has an initial value of $5.50, while the second store's deal has an initial value of $5.75. Since a lower initial value indicates a better deal, the first store offers a better deal. Customers will pay less for the same number of comic books in the first store.

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a) The sales 2 months after the end of the campaign will be $29,600. b)  it will take 10 months (round up to the nearest whole number) for sales to drop below $1,000, if no new campaign is initiated.

The sales 2 months after the end of the campaign can be found by plugging x = 2 into the equation:
S = 80,000e-0.5x
S = 80,000e-0.5*2
S = 80,000e-1
S = 80,000 * 0.37
S = 29,600

Therefore, the sales 2 months after the end of the campaign will be $29,600.

We can solve this by setting the equation equal to 1000 and solving for x:
1000 = 80,000e-0.5x
1000/80,000 = e-0.5x
0.0125 = e-0.5x
ln(0.0125) = ln(e-0.5x)
-4.81 = -0.5x
x = 9.62

Therefore, it will take 10 months (round up to the nearest whole number) for sales to drop below $1,000, if no new campaign is initiated.

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Answer:

59.40 or 59.4 dollars

Step-by-step explanation:

First, we need to find how many hours she worked to earn $46.20. She worked from 8 am to 1:15 pm, which is 5 hours and 15 minutes. We can write that number in terms of hours as 5.25 hours.

Now that we know how many hours she worked to earn $46.20, we can divide the money by the hours to find out how much she makes per hour.

46.20 dollars / 5.25 hours = 8.8 dollars per hour

Now that we know she earns 8.8 dollars per hour, we can calculate how much she would earn if she worked from 8 am to 2:45 pm. To do that, we need to find out how many hours is from 8 am to 2:45 pm (Hopefully that makes sense.)

From 8 am to 2:45 pm is 6.75 hours. Now that we know the time, we should multiply the money she earns per hour by the hours she should work.

8.8 dollars per hour * 6.75 hours = $59.4

Thus, the answer is 59.40 or 59.4 dollars.

1. In the context of spacetime, the locus of points equidistant from the origin of a spacetime plane is a hyperbola.

In Euclidean space, the distance between two points is given by the Pythagorean theorem, which only considers spatial dimensions. However, in spacetime, the concept of distance is extended to include both spatial and temporal components. The spacetime distance, also known as the interval, is given by the Minkowski metric:

ds^2 = -c^2*dt^2 + dx^2 + dy^2 + dz^2,

where c is the speed of light, dt represents the temporal component, and dx, dy, dz represent the spatial components.

To determine the locus of points equidistant from the origin, we need to find the set of points where the spacetime interval from the origin is constant. Setting ds^2 equal to a constant value, say k^2, we have:

-c^2*dt^2 + dx^2 + dy^2 + dz^2 = k^2.

If we focus on a spacetime plane where dy = dz = 0, the equation simplifies to:

-c^2*dt^2 + dx^2 = k^2.

This equation represents a hyperbola in the spacetime plane. It differs from a circle in Euclidean space due to the presence of the negative sign in front of the temporal component, which introduces a difference in the geometry.

Therefore, the locus of points equidistant from the origin in a spacetime plane is a hyperbola.

(Note: The explanation provided assumes a flat spacetime geometry described by the Minkowski metric. In the case of a curved spacetime, such as that described by general relativity, the shape of the locus of equidistant points would be more complex and depend on the specific curvature of spacetime.)

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Answer:

8 units

Step-by-step explanation:

The line segment is 8 units long just by looking at the graph. You can also calculate this by looking at the y values and doing 5--3 or 5+3 which equals 8.

The expected value is $3, we can conclude that the expected gain from playing this game is $3.

Expected value of the carnival game: The expected value of the carnival game to you can be calculated by adding the products of the probability of each event occurring and the monetary gain/loss of that event.

It is given that there are 100 plastic fish circulating in the pond and their prizes are given as follows: 10 red fish with a $10 prize20 blue fish with a $5 prize30 green fish with a $2 prize40 orange fish with a $1 prize

Probability of catching a red fish: P(red) = 10/100 = 1/10

Probability of catching a blue fish: P(blue) = 20/100 = 1/5

Probability of catching a green fish:P(green) = 30/100 = 3/10

Probability of catching an orange fish:P(orange) = 40/100 = 2/5

Let us calculate the expected value:

Expected value = (P(red) × $10) + (P(blue) × $5) + (P(green) × $2) + (P(orange) × $1)Expected value = [(1/10) × $10] + [(1/5) × $5] + [(3/10) × $2] + [(2/5) × $1]

Expected value = $1 + $1 + $0.60 + $0.40

Expected value = $3 Let X be the monetary gain/loss of playing this game. Since the expected value is $3, we can conclude that the expected gain from playing this game is $3.

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The maximum distance Frank can travel would be 10 miles.

What is maximum distance?

For maximum distance that is maximum range of a projectile, the angle of projectile should be 45°.

From given question,

taxicabs charge for first mile = $1.00

for each additional mile = $0.30

The cost for the first mile is $1, and for each additional mile it's $0.30, so for 10 miles it would be $1 + 9 * $0.30 = $4.70. Since Frank has only $3.50, he can travel a maximum of 10 miles.

Therefore, The maximum distance Frank can travel would be 10 miles.

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1 is returned by the peek operation on the following priority queue.

The smallest value in a min-heap is returned by peak operation.

Heap:

By creating a min-heap or max-heap using the elements of the supplied array, the elements of a heap sort are processed. The root component or element of an array's sequence, which reflects the array's minimal or maximal element, can be described using either of the heaps (max or min). We will study more about heap sort algorithms in this article. When it comes to the heap sort, the elements are primarily sorted in the following two steps: To construct a heap, the array's elements must first be changed. Next, move the heap's root component to the end of the array and hold the heap structure with the left components while continually removing it.

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