How can you tell if a table or a set of ordered pairs can be modeled by a quadratic function?

Answer:

y = -3/4 x - 9

Step-by-step explanation:

Slope intercept form is

y = mx+b  where m is the slope and b is the y intercept

9x+ 12y = -108

Subtract 9x from each side

12y = -9x - 108

Divide by 12

12y/12 = -9x/12 -108/12

y = -9/12 x - 108/12

y = -3/4 x - 9

Answer:

y = (-3/4)x - 9

Step-by-step explanation:

Given equation,

→ 9x + 12y = -108

Now we have to,

→ convert into slope-intercept form.

Solving for the value of y,

→ 9x + 12y = -108

→ 12y = -9x - 108

→ y = (-9x - 108)/12

→ y = (-9/12)x - 9

→ y = (-3/4)x - 9

Hence, the form is y = (-3/4)x - 9.

Answer:

The answer would be y = 120.

Step-by-step explanation:

If x is always 1/4 of y, then if x equals 30, y would be 4 times the amount of x. I hope this helps you! :)

There are four significant figures in the number 1.032.

Significant figures are the digits in a number that carry meaningful information about its precision. To determine the significant figures in a number, follow these rules:

Non-zero digits are always significant. In this case, the digits 1, 0, 3, and 2 are non-zero.

Zeroes between non-zero digits are significant. In this case, the zero between 1 and 3 is significant.

Leading zeroes (zeros before the first non-zero digit) are not significant. In this case, there are no leading zeroes.

Trailing zeroes (zeros after the last non-zero digit) are significant only if there is a decimal point present. In this case, there is a trailing zero after the 2, and since there is a decimal point, it is significant.

By applying these rules, we find that the number 1.032 has four significant figures.

The number 1.032 has four significant figures.

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The flaw in reasoning is drawing a causal inference without considering confounding factors and relying solely on the total number of cases. Valid inferences require a comprehensive analysis, control of confounding variables, and consideration of multiple indicators of response effectiveness.

The flaw in reasoning in this scenario is that the blogger is drawing a causal inference without considering other factors that could affect the number of reported cases in each state, such as differences in testing availability and criteria, population density, and demographic characteristics.

The blogger is also assuming that the total number of cases accurately reflects the effectiveness of each state's response, without considering differences in testing and reporting delays.

To produce valid inferences, the blogger should have conducted a more comprehensive analysis, controlling for confounding variables and using appropriate statistical methods to compare the incidence rates or growth rates of COVID-19 cases in each state over time.

The blogger should also have consulted reliable sources of information, such as public health agencies and scientific studies, to evaluate the effectiveness of each state's response based on multiple indicators, including testing capacity, contact tracing, hospital capacity, and public compliance with guidelines and restrictions. Finally, the blogger should have acknowledged the complexity and uncertainty of the situation and avoided simplistic or divisive interpretations of the data.

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Answer:

x >-2

Step-by-step explanation:

-3 (x -3) > 5 - 5x

Distribute

-3x +9 > 5-5x

Add 5x to each side

-3x +9+5x > 5-5x+5x

2x +9> 5

Subtract 9 from each side

2x+9-9>5-9

2x > -4

Divide each side by 2

2x/2 >-4/2

x >-2

Answer:

A. x > -2.

Step-by-step explanation:

-3 (x -3) > 5 - 5x

-3x + 9 > 5 - 5x Subtract 9 from both sides and add 5x to both sides:

-3x + 5x = 5 - 9

2x > -4

x > -2.

We are given the function

we are to use remainders theorem to find p(3)

Therefore

Given p(3) then x = 3

Hence

Hence, p(3) = - 11

Therefore, the Remainder is - 11

Finding the quotient

Given

Therefore to find the quotient we will use long division method

This gives

Therefore, The quotient is

From the solution above

P(3) = - 11

As per the concept of unitary method, the another way to express 8 feet is 2 ²/₃ yards.

In math, unitary method is known as a way of finding out the solution of a problem by initially finding out the value of a single unit, and then finding out the essential value by multiplying the single unit value.

Here we have given that a clothesline rope is 8 feet long.

Now we need to find another way to express 8 feet.

We know that the formula to convert the measurement it to divide the length by the conversion ratio.

As we know that one yard is equal to 3 feet, then we can use this simple formula to convert is written as

=> yards = feet ÷ 3

Here the equivalent yard measurement is written as,

=> yards = 8 ÷ 3

Then we have to convert the improper fraction into mixed fraction form, then we get,

=> 2 ²/₃ yards.

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If the population grew to 35203 by the year 2019 , then the equation to model this situation is y = 1174x + 29333 .

We use the given data points to create a linear equation to model the population growth over the years.

Let , x₁ = 0 represents the year 2014

⇒ y₁ = 29333 represents the population in the year 2014

⇒ x₂ = 5 represents the year 2019

⇒ y₂ = 35203 represents the population in the year 2019

Using these variables, we can find the slope of the line that represents the population growth:

So , slope = (y₂ - y₁)/(x₂ - x₁)

⇒ slope = (35203 - 29333)/(5 - 0)   ;

⇒ slope = 5870/5 = 1174  ;

Now , by using the point-slope form of a linear equation

we get ;

⇒ y - y₁ = m(x - x₁)  ;

⇒ y - 29333 = 1174(x - 0)  ;

Simplifying this equation ;

we get ;

⇒ y = 1174x + 29333 ;

Therefore, the equation for the model is y = 1174x + 29333, where y represents the population and x represents the number of years since 2014.

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The given question is incomplete , the complete question is

The population in a small us city has been increasing linearly. in 2014, the population of this town was 29333. and by the year 2019, it grew to 35,203. Find the equation for this model ?

After answering the question provided, we can predict that the result will be as by equation As a result, the correct response is: Minimum: 41.64; Maximum: 62.76.

A mathematical equation is a process that links two statements and indicates equality using the equals sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula may be used to understand the link between the two sentences that are written on opposite sides of a letter. Frequently, the logo and the particular software are identical. like in 2x - 4 = 2, for example.

A binomial distribution with the specified values of n and p has a mean of = np and a standard deviation of = sqrt(np(1-p)).

Inputting n = 261 and p = 1/5 results in:

μ = np = 261 × 1/5 = 52.2

5.28 is equal to sqrt(np(1-p)) = sqrt(261 1/5 4/5)

Calculating the minimal typical value of 2 is as follows:

μ − 2σ = 52.2 − 2 × 5.28 ≈ 41.64

The calculation for the maximum typical value + 2 is as follows:

μ + 2σ = 52.2 + 2 × 5.28 ≈ 62.76

These values are rounded to the nearest hundredth, giving us:

The range is 41.64 to 62.76.

As a result, the correct response is: Minimum: 41.64; Maximum: 62.76.

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Answer:

Minimum: 39.28; maximum: 65.12

The coordinates of point P along the directed line segment AB is (8, 10).

The coordinates of point P along the directed line segment AB so that AP to PB is the given ratio 1: 4 is calculated as follows;

We will use the following formula;

P(x, y) = ((mx₂) + (nx₁))/(m + n), ((my₂) + (ny₁))/(m + n)

Where;

The coordinates of point P along the directed line segment AB is;

Px = ( 1 x 16   +  4x6 ) / (1 + 4) = 8

Py = ( 1 x 14  +  4 x 9) / (1 + 4) = 10

(Px, Py) = (8, 10)

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Answer:490

Step-by-step explanation:15 times 22 +120=490

The statements that apply to the relative use of dot plots and histograms are Dot plots show the relative frequency of data values and Dot plots are most useful for small data sets.


1. Dot plots are a graphical representation of data that show the relative frequency of data values. Each dot in a dot plot represents one data point, and the position of the dot on the axis represents the value of the data point. Histograms, on the other hand, show the frequency distribution of data values in a bar graph format.

2. Dot plots are most useful for small data sets because they allow for the easy visualization of individual data points and their distribution. Histograms, on the other hand, are more useful for large data sets as they provide a summary of the data distribution in a more concise manner. Dot plots can become cluttered and difficult to read when used with large data sets.

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The value of trigonometric ratio tan A= 12/5.

We have,

Adjacent side= 5

Opposite side= 12

Hypotenuse= 13

We know, The tangent (tan) is a trigonometric ratio that relates the angle of a right triangle to the ratio of the length of the side opposite the angle to the length of the adjacent side.

In a right triangle, if one of the acute angles is denoted as θ, then the tangent of θ is defined as:

tan(θ) = opposite/adjacent

So, tan A = 12/5

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We have explained all the steps to solve an infinite arithmetic sequence.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term is the sum of the previous term and a constant called the common difference.

When it comes to solving an infinite arithmetic sequence, you can use the following formulas:

The n-th term of an arithmetic sequence can be represented as a+(n-1)d, where "a" is the first term, "d" is a common difference, and "n" is the position of the term in the sequence.

The sum of the first n terms of an arithmetic sequence is represented as S_n = n/2(2a + (n-1)d), where "a" is the first term, "d" is a common difference, and "n" is the number of terms.

If a sequence is infinite, the sum of all terms can be represented as S_inf = a/(1-r) where "a" is the first term and "r" is the common ratio (r=1+d)

Hence, we have explained all the steps to solve an infinite arithmetic sequence.

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Answer:

  A.  50°

Step-by-step explanation:

The external angle ACB created by tangents CA and CB is the supplement of arc AB it intercepts.

  ∠ACB = 180° -AB

  ∠ACB = 180° -130°

  ∠ACB = 50°

The particular solution to the differential equation in de initial condition y() = 3 is:

 y(x) = 3sin(x) - ∫e^(xy) dx + 3

The given differential equation with the initial condition y(0) = 3. Here's a step-by-step explanation:

1. Identify the differential equation: dy/dx = 3cos(x) - e^(xy)

2. Integrate both sides of the equation with respect to x to find y(x):

  ∫(dy/dx) dx = ∫(3cos(x) - e^(xy)) dx

  y(x) = 3∫cos(x) dx - ∫e^(xy) dx + C

3. Solve the integrals:

  For ∫cos(x) dx, the antiderivative is sin(x), so 3∫cos(x) dx = 3sin(x)

  For ∫e^(xy) dx, we cannot directly integrate with respect to x since there is a term involving y. We can leave this term as an indefinite integral: ∫e^(xy) dx

  Therefore, y(x) = 3sin(x) - ∫e^(xy) dx + C

4. Apply the initial condition y(0) = 3:

  3 = 3sin(0) - ∫e^(0*y) dx + C

  3 = 0 - ∫1 dx + C

5. Solve for C:

  C = 3

6. Write the particular solution:

  y(x) = 3sin(x) - ∫e^(xy) dx + 3

Note that the term ∫e^(xy) dx is left as an indefinite integral because it cannot be directly integrated in terms of elementary functions.

The answer represents a family of particular solutions, with the specific function for ∫e^(xy) dx depending on the context of the problem.

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The direction of the resultant vector is approximately -68.75°.

To find the direction of the resultant vector, we can use the formula:

θ = arctan(Vy/Vx)

where Vy is the vertical component (y-coordinate) of the vector and Vx is the horizontal component (x-coordinate) of the vector.

In this case, we have a resultant vector with components Vx = -6 and Vy = 16.

θ = arctan(16/-6)

Using a calculator or trigonometric table, we can find the arctan of -16/6 to determine the angle in radians.

θ ≈ -1.2039 radians

To convert the angle from radians to degrees, we multiply by 180/π (approximately 57.2958).

θ ≈ -1.2039 * 180/π ≈ -68.7548°

Rounding to the nearest hundredth, the direction of the resultant vector is approximately -68.75°.

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Answer:

yes they can

Step-by-step explanation:

To find the probability of the event "the first die is 6 or the sum is 8," we need to count the number of outcomes that satisfy this event and divide it by the total number of possible outcomes.

To find the probability of the event "the first die is 6 or the sum is 8," we need to consider the total possible outcomes when rolling two dice and the favorable outcomes for this event.

Total possible outcomes: 6 sides on each die, so there are 6 x 6 = 36 possible outcomes.

Favorable outcomes:
1. First die is 6: There are 6 possible outcomes (6,1), (6,2), (6,3), (6,4), (6,5), and (6,6).
2. Sum is 8: There are 5 possible outcomes (2,6), (3,5), (4,4), (5,3), and (6,2).

However, (6,2) is counted twice, so we should subtract 1 from the total favorable outcomes: 6 + 5 - 1 = 10.

Probability = Favorable outcomes / Total possible outcomes = 10/36. Simplifying the fraction gives 5/18.

So, the probability of the event "the first die is 6 or the sum is 8" is 5/18.

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Answer:

m=-9

Step-by-step explanation:

If the side length of the pentagon is 19.27 centimeters. Then the area of the pentagon will be 337.225 square cm.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The apothem of the pentagon is 7 cm.

Then the area of the pentagon will be

\(\rm Area = 5 \times \dfrac{1}{2} \times apothem \times side \ length\)

The side length of the pentagon will be

\(\rm Side \ length = 2 \times 7 \tan 54^o \\\\Side \ length = 19.27\ cm\)

Then the area will be

\(\rm Area = 5 \times \dfrac{1}{2} \times 7\times 19.27\\\\Area = 337.225\)

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Answer:

degree 61 minute 24 second 36.00 (I might be wrong lol)

Step-by-step explanation:

1 degree (°) = 60 arc minutes and 1 arc minute = 60 arc seconds. We denote a an angle given in DMS form using a°b'c''.

Now,

0.41° × (60' / 1°) = 24.6'

and

0.6' × (60'' / 1') = 36''

so that

61.41° = 61° 24' 36''

As we know that

♦ Area of rectangle = Length × breadth

Substituting known values ,

⇒ 144x⁴ = 12x ( Length )

⇒ 144x⁴ / 12x = Length

⇒ 12x³ = Length

⇒ Length = 12 x³

Step-by-step explanation:

U = (x - 5)

V = y^3

because we follow the rule

(U+V)^2 = U^2 + 2UV + V^2

factor the expression will be

\(((x - 5) + {y}^{3} )((x - 5) + {y}^{3} )\)

Answer: Y=-5/2x+5(Idk i'm doing it off of my head)

Answer:

y=5/2x -5 slope is 5/2

Step-by-step explanation:

parallel lines have the same slope

Answer:

x would be equal to 70 grades

Step-by-step explanation:

The angle QRS is equal to 180 - 130 = 50 grades.

We add up that with the other 60 grades on the left, and we encounter ourselves with a simple equation:

60 + x + 50 = 180

x = 70

Hope this was helpful

The ramp must be 72 feet long for the slope to meet the regulation of 1 inch of rise for every 1 foot of run. The length of the ramp is 72 feet.

To calculate the length of the ramp, we can use the formula: length = height / slope.

Let's denote the length of the ramp as "L" in feet.

Since the regulation is 1 inch of rise for every 1 foot of run, the slope would be 1/12 (1 inch divided by 12 inches).

Given that the entrance is 6 feet above ground level, the length of the ramp would be:

length = 6 / (1/12) = 6 * 12 = 72 feet.

Therefore, the ramp must be 72 feet long for the slope to meet the regulation of 1 inch of rise for every 1 foot of run.

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Answer:

\(V =33.5\ inches\)

Step-by-step explanation:

Step 1:  Find the volume of the sphere

Formula for the volume of a sphere:  \(V=\frac{4}{3}\pi r^{3}\)

\(Radius = Diameter / 2\)

\(Radius = 4 / 2\)

\(Radius = 2\)

\(V=\frac{4}{3}(3.14) (2)^{3}\)

\(V =33.5\ inches\)

Answer:  \(V =33.5\ inches\)