Solve -3+x=12 please answer this answer 15 points.

On soloing the provided question, we can say that an equation from the graphs for the function. 3x + 13.5y = 4.5 and x+1.5y = 2

Mathematicians use graphs to logically represent or chart facts or values. Typically, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, or vertices, and edges. The nodes, also known as vertices, should be joined with glue. This graph's vertices are 1, 2, 3, and 5, while its edges are 1, 2, 1, 3, 2, 4, and 2.5. (3.5). (4.5). Graphical depictions of exponential growth in statistical charts (bar charts, pie charts, line charts, etc.). triangle-shaped logarithmic graph.

an equation for the function.

3x + 13.5y = 4.5

and x+1.5y = 2

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Answer:

B

Step-by-step explanation:

Because two sides of the triangle are the same length

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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a) The probability that a single detection system will detect an attack is 0.84.

b) If two detection systems are installed in the same area and operate independently, the probability that at least one of the systems will detect the attack is 0.9736.

c) If three systems are installed, the probability that at least one of the systems will detect the attack is 0.9972.

d) Yes, I would recommend that multiple detection systems be used.

Explanation: Let p = 0.84 be the probability of detecting a missile attack. Since there are two outcomes, either the detection system detects the attack or it does not, the binomial distribution can be used.

The binomial probability mass function is:P (X = x) = nCx * p^x * (1-p)^(n-x), where X is the number of successful trials, n is the number of trials, p is the probability of success in a trial, (1-p) is the probability of failure in a trial, nCx is the number of combinations of n things taken x at a time.

In this case, since we are interested in detecting an attack, x = 1. Therefore, the probability that a single detection system will detect an attack is: P (X = 1) = 1C1 * 0.84^1 * (1-0.84)^(1-1) = 0.84.

As given, two detection systems are installed in the same area and operate independently. The probability that at least one of the systems will detect the attack is the probability of detecting the attack with one system plus the probability of detecting the attack with the other system plus the probability of detecting the attack with both systems.

P(at least one of the systems will detect the attack) = P(X = 1 with the first system) + P(X = 1 with the second system) + P(X = 2 with both systems)

P(X = 1 with the first system) = P(X = 1) = 0.84

P(X = 1 with the second system) = P(X = 1) = 0.84

P(X = 2 with both systems) = 0.84 * 0.84 = 0.7056

P(at least one of the systems will detect the attack) = 0.84 + 0.84 - 0.7056 = 0.9736.

Therefore, the probability that at least one of the systems will detect the attack is 0.9736 when two detection systems are installed in the same area and operate independently.

Let us compute the probability that at least one of the systems will detect the attack when three systems are installed.

P(at least one of the systems will detect the attack) = P(X = 1 with the first system) + P(X = 1 with the second system) + P(X = 1 with the third system) - P(X = 2 with the first two systems) - P(X = 2 with the first and third systems) - P(X = 2 with the second and third systems) + P(X = 3 with all three systems)

P(X = 1 with the first system) = P(X = 1) = 0.84P(X = 1 with the second system) = P(X = 1) = 0.84P(X = 1 with the third system) = P(X = 1) = 0.84

P(X = 2 with the first two systems) = 0.84 * 0.84 = 0.7056

P(X = 2 with the first and third systems) = 0.84 * 0.84 = 0.7056P(X = 2 with the second and third systems) = 0.84 * 0.84 = 0.7056

P(X = 3 with all three systems) = 0.84 * 0.84 * 0.84 = 0.592704

P(at least one of the systems will detect the attack) = 0.84 + 0.84 + 0.84 - 0.7056 - 0.7056 - 0.7056 + 0.592704 = 0.9972.

Therefore, the probability that at least one of the systems will detect the attack is 0.9972 when three systems are installed. We can observe that as the number of detection systems installed increases, the probability of detecting an attack increases. Therefore, it is recommended to use multiple detection systems.

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The probability that at least one of the systems will detect the attack is 0.9959.

The probability that a single detection system will detect an attack is 0.84.

a. The probability that a single detection system will detect an attack can be calculated using the binomial probability formula:

P(X = 1) = nCk * p^k * (1 - p)^(n - k)

Here, n = 1 (number of trials), k = 1 (number of successes), and p = 0.84 (probability of success).

P(X = 1) = 1C1 * 0.84^1 * (1 - 0.84)^(1 - 1)

= 0.84

Therefore, the probability that a single detection system will detect an attack is 0.84.

b. If two detection systems are installed in the same area and operate independently, the probability that at least one of the systems will detect the attack can be calculated as the complement of the probability that both systems fail to detect the attack.

P(at least one system detects the attack) = 1 - P(both systems fail to detect the attack)

Since the systems operate independently, the probability that each system fails to detect the attack is (1 - 0.84) = 0.16.

P(both systems fail to detect the attack) = 0.16^2 = 0.0256

P(at least one system detects the attack) = 1 - 0.0256

= 0.9744 (rounded to 4 decimal places)

Therefore, the probability that at least one of the systems will detect the attack is 0.9744.

c. Similarly, if three systems are installed, the probability that at least one of the systems will detect the attack can be calculated as the complement of the probability that all three systems fail to detect the attack.

P(at least one system detects the attack) = 1 - P(all three systems fail to detect the attack)

P(all three systems fail to detect the attack) = (1 - 0.84)^3 = 0.004096

P(at least one system detects the attack) = 1 - 0.004096

= 0.9959 (rounded to 4 decimal places)

Therefore, the probability that at least one of the systems will detect the attack is 0.9959.

d. Based on the probabilities calculated, it is recommended to use multiple detection systems. The probability of detecting an attack increases significantly when multiple systems are installed. Having redundancy in the detection systems enhances the reliability and ensures a higher chance of detecting enemy attacks.

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Answer:

The first step in finding the equation for the line that passes through the points (5,-4) and (-1, 8) is to calculate the slope of the line:

(5,-4)(-1,8)=-2

-Therefore, the answer is A.

a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas (b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below. (c) The final total area is 2x² - 10x - 15.

An area model is a way to visualize multiplication by breaking up the larger rectangle into smaller rectangles whose areas represent the products of the terms being multiplied. To determine the correct rows and columns for the area model, we count the number of terms in each factor and use that as a guide. For example, if one factor has 3 terms and the other has 4 terms, we would use a 3x⁴ area model, with 3 rows and 4 columns.

a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.

b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.

   2x⁴ − 3x³ − 2x² − 4x − 1

 +---------------------------------------

x  |   2x⁵    -3x⁴    -2x³    -4x²   -x

 |

3  |   6x⁴    -9x³    -6x²    -12x    -3

 +---------------------------------------

c) To find the total area of a rectangle with length (x + 8) and width (x − 5), we can use an area model with 2 rows and 2 columns. The length (x + 8) corresponds to one dimension of the rectangle, while the width (x − 5) corresponds to the other dimension. The area of each smaller rectangle in the model represents the product of one term from each factor.

    x + 8      x - 5

 +--------------------

x  |  x² + 8x   x² - 5x

 |

-5 | -5x + -40   -5x + 25

 +--------------------

The final total area can be found by adding up the areas of the smaller rectangles:

Total area = x² + 8x + x² - 5x - 5x - 40 + 25

= 2x² - 10x - 15

= 2x² - 10x - 15.

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Answer:

Step-by-step explanation:

(-3, -3)

To determine which of the points (1, -2), (-3, -3), and (-2, -3) lie on the line 2x1 - 5x2 = 9, we need to substitute the x and y values of each point into the equation and see if the equation holds true. This is done as follows:

When x = 1 and y = -2,

2x1 - 5x2 = 2(1) - 5(-2) = 2 + 10 = 12 ≠ 9

This means that the point (1, -2) does not lie on the line 2x1 - 5x2 = 9.

When x = -3 and y = -3,

2x1 - 5x2 = 2(-3) - 5(-3) = -6 + 15 = 9

This means that the point (-3, -3) does lie on the line 2x1 - 5x2 = 9.

When x = -2 and y = -3,

2x1 - 5x2 = 2(-2) - 5(-3) = -4 + 15 = 11 ≠ 9

This means that the point (-2, -3) does not lie on the line 2x1 - 5x2 = 9.

Therefore, only the point (-3, -3) lies on the line 2x1 - 5x2 = 9.

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Based on the analysis of the data, the conclusions that can be reached are as follows: i) At the 0.01 level, subject visibility and test taker success are significant predictors of latency feedback. iii) At the 0.01 level, there is evidence to indicate that subject visibility and test taker success interact.

The table shows the results of the analysis, with the degrees of freedom (df), sums of squares (SS), mean squares (MS), and F-values for subject visibility, test taker success, error, and the total. The F-value indicates the significance of each factor in predicting latency to feedback.

To determine the conclusions, we look at the significance levels. At the 0.01 level of significance, which is a stringent criterion, we can conclude that subject visibility and test taker success are significant predictors of latency feedback. This means that these factors have a significant impact on the time it takes for subjects to provide percentile scores to the test taker.

Additionally, there is evidence of an interaction between subject visibility and test taker success. An interaction indicates that the effect of one factor depends on the level of the other factor. In this case, the interaction suggests that the impact of subject visibility on latency feedback depends on the success of the test taker, and vice versa.

Therefore, the correct conclusions are: i) At the 0.01 level, subject visibility and test taker success are significant predictors of latency feedback. iii) At the 0.01 level, there is evidence to indicate that subject visibility and test taker success interact.

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To determine whether there is enough evidence to reject the null hypothesis, we need to compare the computed test statistic to the critical value.

In this case, the computed test statistic is 2.50 and the critical value is 2.33. If the computed test statistic falls in the rejection region beyond the critical value, we can reject the null hypothesis. Conversely, if the computed test statistic falls within the non-rejection region, we fail to reject the null hypothesis.In this scenario, since the computed test statistic (2.50) is greater than the critical value (2.33), it falls in the rejection region. This means that the observed data is unlikely to occur if the null hypothesis were true.

Therefore, based on the given information, there is enough evidence for the emergency room nurse to reject the null hypothesis. This suggests that there is sufficient evidence to support the claim that the average number of cases of upper respiratory infections per day at the hospital is over 21 cases.

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There is enough evidence to reject the null hypothesis in this case because the computed test statistic (2.50) is higher than the critical value (2.33). This suggests the average number of daily respiratory infections exceeds 21, providing substantial evidence against the null hypothesis.

Yes, there is enough evidence for the emergency room nurse to reject the null hypothesis. The null hypothesis is typically a claim of no difference or no effect. In this case, the null hypothesis would be an average of 21 upper respiratory infections per day. The test statistic computed (2.50) exceeds the critical value (2.33). This suggests that the average daily cases indeed exceed 21, hence providing enough evidence to reject the null hypothesis.

It's crucial to understand that when the test statistic is larger than the critical value, we reject the null hypothesis because the observed sample is inconsistent with the null hypothesis. The statistical test indicated a significant difference, upheld by the test statistic value of 2.50. The significance level (alpha) of 0.05 is a commonly used threshold for significance in scientific studies. In this context, the finding suggests that the increase in respiratory infection cases is statistically significant, and the null hypothesis can be rejected.

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To calculate the standard deviation of the sampling distribution of p-hat, the answer will be 59 students.

By calculating,

600/10=60 and 59 students which is less than 10% of the population.

A sampling distribution, also known as a finite-sample distribution, in statistics is the probability distribution of a given random-sample-based statistic. The sampling distribution is the probability distribution of the values that the statistic takes on if an arbitrarily large number of samples, each involving multiple observations (data points), were used separately to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample. Although only one sample is frequently observed, the theoretical sampling distribution can be determined.

Because they offer a significant simplification before drawing conclusions using statistics, sampling distributions are crucial in the field. They enable analytical decisions to be made based on the probability distribution of a statistic rather than the combined probability distribution of all the individual sample values

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the binary representation of 63.25 as 111111.01.

To convert the decimal number 63.25 to binary, we need to convert the integer part (63) and the fractional part (0.25) separately.

1. Converting the integer part (63):

  Divide 63 by 2, and keep track of the remainders:

  63 ÷ 2 = 31 (remainder 1)

  31 ÷ 2 = 15 (remainder 1)

  15 ÷ 2 = 7 (remainder 1)

  7 ÷ 2 = 3 (remainder 1)

  3 ÷ 2 = 1 (remainder 1)

  1 ÷ 2 = 0 (remainder 1)

  The remainders in reverse order give us the binary representation of the integer part: 111111.

2. Converting the fractional part (0.25):

  Multiply 0.25 by 2 and record the whole number part:

  0.25 × 2 = 0.5 (0)

  0.5 × 2 = 1.0 (1)

  The whole number parts give us the binary representation of the fractional part: 01.

Putting the integer and fractional parts together, we have the binary representation of 63.25 as 111111.01.

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The binary representation of the decimal number 63.25 is 111111.01.

To convert the decimal number 63.25 to binary, we need to separate the whole number part and the fractional part.

Whole Number Part:

Divide the whole number part (63) by 2:

Divide the quotient (31) by 2:

Divide the quotient (15) by 2:

Divide the quotient (7) by 2:

Divide the quotient (3) by 2:

Divide the quotient (1) by 2:

Reading the remainders in reverse order, the binary representation of the whole number part is 111111.

Fractional Part:

To convert the fractional part (0.25) to binary, we multiply the fractional part by 2 and note the whole number part of the result. Repeat this process until the fractional part becomes 0 or until the desired precision is achieved.

Multiply the fractional part (0.25) by 2:

Multiply the fractional part (0.5) by 2:

Since the fractional part becomes 0, we stop the process.

Reading the whole number parts in order, the binary representation of the fractional part is 01.

Combining the binary representation of the whole number part and the fractional part, the binary representation of the decimal number 63.25 is 111111.01.

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The points are K(0, 6), L(-8, 0), J(9, 4).

Given that is a coordinate plane with Points K, L, J we need to determine the location of the points,

So,

You require the point's coordinates, which are made up of an x-coordinate (horizontal) and a y-coordinate (vertical), in order to label it on a coordinate plane.

So, Point K is at 6 units upwards from the origin so the point (0, 6) the x-intercept is zero.

Point L is 8 units vertically left side so the point is (-8, 0) here the y-intercept is zero.

Point J is 9 units vertically right side and 4 units upwards so the point is (9, 4).

Hence the points are K(0, 6), L(-8, 0), J(9, 4).

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Answer:

10 I think

Step-by-step explanation:

well we add it all together 2+1+3+4

Answer:

9

Step-by-step explanation:

Split up the shape into 2 seperate shapes (I did a trapezoid and)

Rectangle:

1*4 = 4

Trapezoid:

3 - 1 = 2 (for trapezoid's height)

4 - 2 = 2 (for trapezoid's shorter base)

(3 * \(\frac{1}{2}\)) * (2 + 4) =

1.5 * 6 = 9

Answer:

the friend made more free throws

Step-by-step explanation:

17/20 = 85%

0.8 = 80

87.5% = 87.5

the friend has a bigger percentage. meaning she mad more free throws

The runner's average speed in kilometers per hour is 24.257 km.

The total distance covered by the runner is 1 mile. The relation between kilometers and miles is given as 1 km = 0.62 mi. Converting 1 mile to km by using the given relation, we get-

Distance = 1 mile

 = 1 mile × [1 km/0.62 mile]

= 1.6129 km

The time taken to complete a 1-mile run is 3 minutes and 59.37 seconds. The relation between hours and minutes is given below.

1 hour = 60 minutes ……(1)

Converting 3 minutes to hours using equation (1), we get-

3 minutes = 3 minutes × [1 hour/60 minutes]

= 0.05 hours

The relation between hours and seconds is given below.

1 hour = 3600 second …….(2)

Converting 59.37 seconds to hours using equation (2), we get-

59.37 seconds = 59.37 seconds × [1 hour/3600 seconds]

= 0.016492 hours

Total time to cover 1 mile = (0.05 + 0.016491) hours = 0.066492 hours

The average speed of the runner is calculated by the following relation-

Average Speed = Distance (km)/time (hours)

= 1.6129 km/0.066492 hours

= 24.257 km/hour

Therefore, the average speed in kilometers per hour is 24.257km.

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Answer:

\({\huge{\pink{\underline{\underline{Solution:}}}}}\)

As we know,sum of angles on a straight line is 180 degree..

(5z-4)+90+39=180

=>5z-4+90+39=180

=>5z-4+129=180

=>5z+125=180

=>5z=180-125

=>z=55÷5

Hence,the value of z=11 degree

Step-by-step explanation:

10 + 3x = 30 + 7x

collect terms that look alike on one side.

we can see that 3x & 7x have something in common which is x.

so move one of these to either of the equality's sides.

0 = 30 + 7x -10 - 3x

i changed the sign of 3x to -3x & 10 to -10 because we'll have to subtract 3x or 10 from the left side inorder for them to vanish & appear on the right hand side.

collect like terms.

0 = 30 - 10 + 7x - 3x

0 = 20 + 4x

take 20 to the left side to find x by dividing by 4.

20 = 4x

20 / 4 = x

5 = x

Answer:

Step-by-step explanation:

For the function (a) f(x, y) = xy - 2x - 2y:

To find the local maximum and minimum values and saddle point(s), we need to find the critical points by taking the partial derivatives with respect to x and y and setting them equal to zero.

∂f/∂x = y - 2 = 0

∂f/∂y = x - 2 = 0

From the first equation, we have y = 2, and from the second equation, we have x = 2. Therefore, the critical point is (2, 2).

To determine the nature of this critical point, we can use the second partial derivatives test. Calculate the second partial derivatives:

∂²f/∂x² = 0 (constant)

∂²f/∂y² = 0 (constant)

∂²f/∂x∂y = 1 (constant)

Since the second partial derivatives are constant and ∂²f/∂x² = ∂²f/∂y² = 0, we cannot determine the nature of the critical point based on the second partial derivatives.

To further analyze the critical point, we can observe the behavior of the function around this point. Calculating the value of f(x, y) at the critical point:

f(2, 2) = (2)(2) - 2(2) - 2(2) = 4 - 4 - 4 = -4

Therefore, the critical point (2, 2) is a saddle point since the function takes negative values around it.

For the function f(x, y) = 2:

To find the absolute maximum and minimum values of this constant function, we need to consider the given set. However, the set is not specified in the question. Please provide the set or any additional information about the domain of the function so that I can assist you further in finding the absolute maximum and minimum values.

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75% of the eruptions lasted between 1.77 and 4.93 minutes.

Chebyshev's Theorem calculates the proportion of observations that are within a given number of standard deviations of the mean. This theorem is applicable to many different probability distributions. Chebyshev's inequality is another name for Chebyshev's theorem.

According to Chebyshev’s theorem, the proportion of the data lying within k standard deviations of the mean is always at least 1 – 1/k^2, where k>1.

Given

Mean = 3.35

SD = 0.79

Mean – 1*SD = 3.35 – 1*0.79

= 3.35 – 0.79

= 2.56

Mean + 1*SD =3.35 + 1*0.79

= 3.35 + 0.79

= 4.14

Mean – 2*SD =3.35 – 2*0.79

= 3.35 – 1.58

= 1.77

Mean + 2*SD =3.35 + 2*0.79

= 3.35 + 1.58

= 4.93

Here, we have k = 2

For k = 2,

= 1- (1/k2)

= 1- (1/(2)2

= 1- ¼

= ¾

at least ¾ or 75% of all values lie within 2 standard deviations of the mean.

Therefore 75% of the eruptions lasted between 1.77 and 4.93 minutes.

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The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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The correct answer would be -3/8 or in decimal form -0.375 :)

Answer:

OOOOOOOOHHH SHUTE BROTHER SORRY WISHED I COULD HELP but im blonde so sowwy

Answer:

-3

Step-by-step explanation:

Pick two points on the graph, lets go with (0, 4) and (1, 1)

y = mx + b

m is the slope and to figure it out use below formula

m = (y₂ - y₁) / (x₂ - x₁)

  = (1 - 4) / (1 - 0)

  = -3 / 1

  = -3

Answer:

C. -3

Explanation:

Given problem;

 To solve for the slope of the line;

The slope of a line is the vertical distance to the horizontal displacement on a line.

  Slope  = \(\frac{Vertical distance}{horizontal displacement}\)

For lines such as this, we use the formula below;

                        Slope  = \(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

To find the slope reference the image attached;

     point 1 (0,4)      x₁  = 0   y₁  = 4

     point 2 (2,-2)    x₂  = 2   y₂  = -2

Now input the parameters and solve;

          Slope  = \(\frac{-2 - 4}{2 - (0)}\)   =    \(\frac{-6}{2}\)  

          Slope  = -3

The slope of the line is -3

The positive root of the equation \(4cos(x) - x^4\) using Newton's method is 0.866966.

We begin with an initial guess \(x_{0}=1\), and we can iteratively define the calculation using the formula:

\(x_{i+1}= x_{i} - \frac{ f(x_{i})}{f'(x_{i})}\)

where \(f(x)=4cos(x) - x^4\)and f'(x) is the derivative of f(x).

So, \(f'(x) = -4sin(x) - 4x^3.\)

We repeat this process, using the previous approximation to find the next one, until we reach the desired accuracy.

In each iteration, we substitute the current approximation into the formula to refine our estimate.

Iteration 1: \(x_{1}= x_{0}- f(x_{0})/f'(x_{0})= 1 - \frac{ (4cos(1) - 1^4)}{(-4sin(1) - 4(1)^3)}= 1.576\)

Iteration 2: \(x_{2}= x_{1} - f(x_{1})/f'(x_{1}) = 1.1576 - \frac{(4cos(1.1576) - 1.1576^4)}{(-4sin(1.1576) - 4(1.1576)^3)} = 1.2055\)

Iteration 3: \(x_{3}= x_{2} - f(x_{2})/f'(x_{2}) = 1.2055 - \frac{4cos(1.2055-(1.2055)^4)) }{(-4sin(1.2055) - 4(1.2055)^3)} = 1.2080\)

After several iterations, we get that the positive root of the equation \(4cos(x) - x^4\) is approximate x ≈ 0.866966, accurate to six decimal places.

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The correct option is (0, -4). The y-intercept of f(x+3) is -4.

Given that f(x) = -(2)^x + 4. We need to find the y-intercept of f(x+3).

The y-intercept of the given function is represented by f(0) as x = 0.

And the function is translated 3 units left for f(x+3) which means the y-intercept is still the same.

The y-intercept of the function f(x+3) is given by:

f(x+3) = -(2)^(x+3) + 4

f(0+3) = -(2)^(0+3) + 4

f(3) = -8 + 4

f(3) = -4

Thus, the y-intercept of f(x+3) is -4. Hence, the correct option is (0, -4).

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