What is the equation of the line in slope-intercept form?

Answer:

c

Step-by-step explanation:

c Which system of linear inequalities has the point (2, 1) in its solution set? Which system of linear inequalities has the point (2, 1) in its solution set?

y less-than negative x + 3. y less-than-or-equal-to one-half x + 3 On a coordinate plane, 2 lines are shown. The first solid straight line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second dashed straight line has a negative slope and goes through (0, 3) and (3, 0). Everything to the left of the line is shaded.

y less-than negative one-half x + 3. y less-than one-half x. On a coordinate plane, 2 lines are shown. The first solid straight line has a negative slope and goes through (0, 3) and (4, 1). Everything below the line is shaded. The second dashed straight line has a positive slope and goes through (0, 0) and (2, 1). Everything below and to the right of the line is shaded.

y less-than-or-equal-to negative x + 3. y less-than-or-equal-to one-half x + 2 On a coordinate plane 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 4, 1) and (0, 3). Everything below the line is shaded. The second line has a negative slope and goes through (0, 3) and (3, 0). Everything below and to the left of the line is shaded.

y less-than one-half x. y less-than-or-equal-to negative one-half x + 2v

The system of linear inequalities x + 2y ≤ 4 and 2x - y > 0 has (2,1) in its solution set.

The solution set is given as:

\((x,y) = (2,1)\)

The above solution set is true for x + 2y ≤ 4 and 2x - y > 0, and the proof is as follows:

Substitute 2 for x and 1 for y in x + 2y ≤ 4 and 2x - y > 0.

So, we have:

\(\mathbf{2 + 2\times1 \le 4 }\)

\(\mathbf{2 + 2\le 4 }\)

\(\mathbf{4\le 4 }\) --- this is true, because 4 is less than or equal to 4

Also, we have:

\(\mathbf{2x - y > 0}\)

\(\mathbf{2 \times 2 - 1 > 0}\)

\(\mathbf{4 - 1 > 0}\)

\(\mathbf{3> 0}\) --- this is also true, because 3 is greater than 0

Hence, the system of linear inequalities x + 2y ≤ 4 and 2x - y > 0 has (2,1) in its solution set.

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By analyzing the degrees and leading coefficients, you can determine how the rational function behaves at the extreme ends of the x-axis.

To determine the end behavior of a rational function, you need to examine the degrees of the numerator and denominator polynomials. The end behavior refers to how the function behaves as the input (x-values) approaches positive or negative infinity.

Here are the steps to determine the end behavior of a rational function:

1. Identify the highest power of x in the numerator and denominator. Let's call them n and m, respectively.

2. If n < m, the degree of the denominator is greater than the numerator. In this case, the function's end behavior is determined by the degree of the denominator.

  - If m is even, the function approaches the horizontal axis (y = 0) as x approaches both positive and negative infinity.

  - If m is odd, the function approaches opposite infinities: positive infinity as x approaches negative infinity and negative infinity as x approaches positive infinity.

3. If n = m, the degree of the numerator is equal to the denominator. In this case, the leading coefficients of the numerator and denominator determine the end behavior.

  - The function approaches the ratio of the leading coefficients as x approaches both positive and negative infinity.

4. If n > m, the degree of the numerator is greater than the denominator. In this case, the function's end behavior is determined by the degree of the numerator.

  - If n is even, the function approaches positive infinity as x approaches both positive and negative infinity.

  - If n is odd, the function approaches opposite infinities: positive infinity as x approaches positive infinity and negative infinity as x approaches negative infinity.

By analyzing the degrees and leading coefficients, you can determine how the rational function behaves at the extreme ends of the x-axis.

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Answer:

The answer is the option C

Step-by-step explanation:

Hope it help

Answer:

c

Step-by-step explanation:

i took the quiz

An equation of the line that passes through the point (-8, 8), and has a slope of 3/4 is 3x - 4y = -56

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-8, 8), a linear equation of this line can be calculated in standard form as follows:

y - y₁ = m(x - x₁)

y - 8 = 3/4(x - (-8))

y = 3x/4 + 6 + 8

y = 3x/4 + 14

4y = 3x + 56

3x - 4y = -56

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Answer:

13 and 15

Step-by-step explanation:

13 and 15 are consecutive odd numbers and

13 + 15 = 28

The probability that the proportion of airborne viruses in a sample of 679 viruses would be greater than 8% is approximately 0.

To solve this problem,

Use the normal approximation to the binomial distribution.

We can assume that the sample proportion of airborne viruses follows a normal distribution with mean equal to the true proportion of 7% and standard deviation given by:

√(7%*(1-7%)/679) = 0.0155

Then, we want to calculate the probability that the sample proportion is greater than 8%.

Standardize the distribution as follows:

(z-score) = (sample proportion - true proportion) / std deviation (z-score)

              = (8% - 7%) / 0.0155

              = 64.52

Using a standard normal table, we can find the probability that a z-score is greater than 64.52, which is essentially 1.

Therefore, the probability of the sample proportion being greater than 8% is approximately 0.

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The rate at which the end of the person's shadow is moving from the lamppost is 4ft/sec.

Let us consider the the distance of the person from the bottom of the lamppost is = xft

therefore the length of shadow is = yft

then the formula is

x + y/15 = y/6

or, 6(x + y) = 15y

=> 6x + 6y = 15y

=> 9y = 6x

therefore, y = 2x/3

Differentiation of both sides w.r.t t

dy/dt = 2/3 × dx/dt

we know that,

dx/dt = 6 ft/sec

then,

dy/dt = 2/3 × 6 => 4 ft/sec

The rate at which the end of the person's shadow is moving from the lamppost is 4ft/sec.

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Answer:

B

Step-by-step explanation:

No these triangles are not congruent.

Left triangle

Shortest side = 6 cm

Longest side = 13 cm

3rd side = unknown but < 13

Right triangle

Shortest side = 6 cm

Longest side = unknown but > 13

3rd side = 13 cm

Although the shortest side of both triangles is 6 cm, the longest side of the left triangle is 13 cm, whereas the longest side of the right triangle is unknown but will be more than 13 cm.

We do not know if any of the angles are congruent.  If they were congruent, we would expect to see this marked by the same angle line(s) on each triangle.

A common rule of thumb for determining the number of classes to use when developing a frequency distribution with classes is the square root of the total number of observations.

Frequency distribution with classes are formed from frequency tables that are used to represent the distribution of data. The number of classes in a frequency distribution will depend on the data set size and should reflect the number of observations, in order to provide the best representation of the data.

A rule of thumb for determining how many classes to use when developing a frequency distribution with classes is the square root of the total number of observations in the data set. This is also known as the square root rule. This rule is not a hard-and-fast rule, but rather a useful guide that should be adjusted if necessary based on the distribution of the data.

Therefore, it is important to take the size of data set and the shape of the data distribution into account when deciding the number of classes to use for a frequency distribution.

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The largest number common to both sequences is 67.

The arithmetic sequence with first term 1 has a common difference of 6 is given by:-

1,7,13,19, 25, 31, 37, 43, 49, 55, 61, 67, 73, 79, 85, 91, and 97

The arithmetic sequence with first term 4 has a common difference of 7 is given by:-

4,11, 18, 25, 32, 39, 46, 53, 60, 67, 74, 81, 88, and 95.

I have written the sequence until 100 only.

Hence, the numbers common to both the arithmetic sequences are :-

25 and 67

Hence, the largest number common to both sequences is 67.

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Answer:

(x-3) (x-2)

Step-by-step explanation:

\(x^{2}\) - 5x + 6

How to break down the equation and factorise it:

-3 x -2 = 6

-3 + -2 = -5

Final Answer:

(x-3) (x-2)

Answer:

100

Step-by-step explanation:

If we divide the circle into 12 equal parts, each sector would have an angle of π/12 radians. By using the formula, we can calculate that the area of one sector would be (2π/3) square units.

To find the area of a sector, you can use the formula A = (θ/2) * r^2, where θ is the angle in radians and r is the radius.

To give you an example, let's say we have a circle with a radius of 4 units. In this case, the given angle is 0 = π/12 radians and the radius is 4. Let's substitute these values into the formula:

A = (π/12 / 2) * 4^2

Simplifying the expression inside the parentheses:

A = (π/24) * 16

Now, we can simplify further:

A = (π/24) * 16
A = (π/3) * 2
A = (2π/3)

Therefore, the area of the sector is (2π/3) square units.

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Answer:

C 50 grams

Step-by-step explanation:

The y-intercept is (0, 50), meaning that when the experiment first began, the sample was 50 grams.

Have the day you deserve :)

Answer:

0 - $45

1 - $42

2 - $39

3 - $36

3(a)=45

with 2 more cups it there would be $30 left

Step-by-step explanation:

Answer:

Step-by-step explanation:

A = 45 - 3x ;

(0, 45);

(1, 42);

(2, 39);

(3, 36)

Answer:

Yes, True

Step-by-step explanation:

The reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself

Answer:

5

Step-by-step explanation:

$82.50 divided by $16.50 is five so there must be five people, so four friends plus mohammad?

9514 1404 393

Answer:

  C  log3(√((x -4)/x)

Step-by-step explanation:

The applicable rules of logarithms are ...

  log(a/b) = log(a) -log(b)

  log(a^n) = n·log(a)

The base is irrelevant, as long as all logs are to the same base.

__

  \(\dfrac{1}{2}(\log_3{(x-4)}-\log_3{(x)})=\dfrac{1}{2}\log_3(\dfrac{x-4}{x})=\boxed{\log_3\left(\sqrt{\dfrac{x-4}{x}}\right)}\)

any cylindrical shape that has the r²h equal to 160 will have an equal volume.

Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.

Given, Right circular cylinder A has a volume of $160pi cubic feet.

The product of a cylinder's base area and height provides the formula for calculating the cylinder's volume. A cylinder's volume is equal to πr²h cubic units.

Where r is the radius

and h is the height

In our case volume = 160 * pi

By comparing,

r²h = 160

So we can state that any cylindrical shape that has the r²h equal to 160 will have an equal volume.

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The main answer to this question is that there could be several reasons why an experiment may not produce significant results even if the research hypothesis is true.

One possible explanation could be that the sample size used in the experiment was too small, which could have resulted in insufficient statistical power to detect the true effect of the independent variable on the dependent variable. Another explanation could be that there were extraneous variables that were not controlled for in the experiment, which could have influenced the results and made it difficult to detect the true effect of the independent variable.

it is important to consider all possible factors that may affect the results of an experiment and to take steps to minimize their impact. This includes ensuring that the sample size is appropriate, controlling for extraneous variables, and using appropriate statistical tests to analyze the data. By doing so, researchers can increase the likelihood of obtaining significant results that accurately reflect the effects of the independent variable on the dependent variable.

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Answer:

1.75

Step-by-step explanation:

Given that:

Tyler tried to solve an equation step by step as:

\(\qquad\begin{aligned} 3(x+4)&=-18\\3x+12&=-18&\green{\text{Step } 1}\\ 3x&=-30&\blue{\text{Step } 2} \\ x&=-10&\purple{\text{Step } 3}\end{aligned}\)

To find: Consider we need to find Tyler mistake (if any) and property used for each step.

Solution:

In the given steps, all steps are correct.

In Step 1, Distributive property is used.

In Step 2, Subtraction property of equality is used.

In Step 3, Division property of equality is used.

Answer:

No mistakes

Step-by-step explanation:

I promise

Khan

The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.

To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.

On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.

Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.

Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.

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The equation relating x, y, and z is:

z = 0.5 * x * y.

In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.

To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.

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Answer:

yes it is rotated

Step-by-step explanation:

since it was already dilated (widened), it was the rotated to create the way that it is now

In statistics the sampling method is collecting data based on sample of people who represent a population, whereas the census method involves studying each and every member of the population.

What is statistics?

The gathering, characterization, analysis, and drawing of inferences from quantitative data are all tasks that fall under the purview of statistics, a subfield of applied mathematics. Probability theory, linear algebra, and differential and integral calculus play major roles in the mathematical theories underlying statistics.

The differences between census and sampling method is -

The investigator gathers data using the census method, which asks questions about every component of the population.

The investigator gathers data using the sampling method by selecting a sample of the objects that represent the entire population.

The Census Method of Collecting Data is appropriate when the area under inquiry is rather small. The sampling method is preferred when the investigation region is large.

The Census Method requires more time to gather data. The sampling method requires less time to gather data.

Generally speaking, the Census Method is more accurate than the Sampling Method. This accuracy can be attributed to the Census Method's inclusion of a study of every component of the population. The sampling approach has a lower level of accuracy because it examines a smaller sample of the population. However, since there are fewer elements in the sampling method, errors are simple to find and eliminate. Consequently, if that's the case, the sampling method gives more accuracy than census method.

Therefore, the differences for census and sampling method are pointed out.

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What is the difference between census method and sampling method in statistics?

Answer:

a. geometric

b. an =  2(2)^n-1 or an = 2^n

c. an+1 = an x 2

Step-by-step explanation:

The sequence, 2, 4, 8, 16, 32,...

a. The sequence is geometric because there is a common ratio in the numbers of the sequence. Each number is made by multiplying the common ratio and the previous number.

b. The explicit formula that can be used to find any term is an =  2(2)^n-1 or an = 2^n

Note: the variable n and number 1 is written in italics to show that it should be in subscript

an = a1 (r)n-1

With the common ratio of n being 2 and first number being 2, we have:

an =  2(2)^n-1

or

an = 2^n

c. The recursive formula for the sequence is an+1 = an x 2

an+1 = an x r

Plugging in the values, we have

an+1 = an x 2

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Answer:

y = -5.2

Step-by-step explanation:

To solve this problem use inverse operations,

-5 ( y + 0.2 ) = 25

/-5                   /-5

y + 0.2 = -5

   -0.2     -0.2

y = -5.2

Answer:

y = -5.2

Step-by-step explanation:

Simplify this equation by dividing both sides by -5.  We get:

y + 0.2 = -5.  Subtracting 0.2 from both sides:  y = -5.2

Answer:

4

Step-by-step explanation:

3 (week), 12 (inches)

(3,12) = (1,4)

(x,y)

x=1

y=4

Ans- y=4