A pair of linear equations is shown below: y = −3x + 5 y = x + 2 Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points) On a graph, find the point of intersection of two lines, the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1. On a graph, find the point of intersection of two lines, the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2. On a graph, find the point of intersection of two lines, the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1. On a graph, find the point of intersection of two lines, the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2.​

Marco's data points have a better line of best fit based on a comparison of Correlation coefficients.

Marco is incorrect in stating that his data points have a better line of best fit than Landon based solely on the comparison of correlation coefficients. The magnitude of the correlation coefficient alone does not determine the quality or strength of the line of best fit.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1. A positive correlation coefficient (such as 0.85) indicates a positive linear relationship, while a negative correlation coefficient (such as -0.85) indicates a negative linear relationship. The closer the correlation coefficient is to -1 or +1, the stronger the relationship. A correlation coefficient of 0 indicates no linear relationship.

In the case of Landon and Marco, both correlation coefficients have the same absolute value of 0.85, suggesting a strong linear relationship. However, the negative sign for Landon's correlation coefficient indicates a negative linear relationship, while the positive sign for Marco's correlation coefficient indicates a positive linear relationship.

The comparison between -0.85 and 0.85 should not be made in terms of greater or lesser quality of the line of best fit. The choice of a positive or negative correlation depends on the context and nature of the variables being analyzed.

The appropriateness of the line of best fit and the goodness-of-fit of the model should be evaluated based on additional factors such as the data points' distribution around the line, residuals, and the overall context of the analysis. These aspects provide more comprehensive insights into the quality of the fit and the reliability of the relationship being represented.

Therefore, Marco's data points have a better line of best fit solely based on a comparison of correlation coefficients. The interpretation of the correlation coefficient requires considering the nature of the variables and other factors influencing the analysis.

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Both options a. A = 129.9° and b. A = 53.1° are correct.

To find the possible values for angle A in triangle ABC, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Using the Law of Sines, we have sin(A)/a = sin(B)/b. Plugging in the given values, we get sin(A)/36 = sin(51°)/35.

To find the two possible values for angle A, we can solve the equation sin(A)/36 = sin(51°)/35. Taking the arcsine of both sides, we have A = arcsin((sin(51°)/35)*36).

Calculating this expression, we find two possible values for angle A:

A ≈ 53.1° (rounded to the nearest tenth)

A ≈ 129.9° (rounded to the nearest tenth)

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The two triangles therefore meet the Angle-Angle (AA) similarity criterion, which specifies that two angles of one triangle must be congruent with two angles .

Angles are typically modeled with a symbol that resembles a tiny arc between the angle's two sides, with a dot at the vertex. For illustration, angle BAC might be used to represent the angle created by the vectors AB and AC, with point A serving as the vertex. Calculus, geometry, trigonometry, and other branches of mathematics all depend on angles. They are used to calculate different quantities linked to angles and their trigonometry, to measure distances and areas, and to describe the shapes and sizes of objects.

given

Triangles ABD and ECD in the given figure are comparable triangles since they share the same shape and have equal corresponding angles. Angles ADB and CDE are equal because they are formed when parallel lines AB and CD are intersected by transversal BD, and angle BAD and angle EDC are also equal because they are formed when parallel lines AD and EC are intersected by transversal BD. In particular, angle ABD and angle ECD are both right angles (90 degrees).

The two triangles therefore meet the Angle-Angle (AA) similarity criterion, which specifies that two angles of one triangle must be congruent with two angles of another triangle in order for the triangles to be comparable.

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Answer:

1.  Y = -1/4x + 1

3. Y = 2/5x + 1

5. Y = 4/5x + 5

7. Y = -x + 5

9. Y = -5/2x - 16

Step-by-step explanation:

Find the slope using the formula

Use the slope and one of the points to find the y-intercept

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.

Answer:

\(x^{6} y^{4}\)

Step-by-step explanation:

\(( x^{3}*y^{2} )^{2}\)= \(x^{3} *x^{3} *y^{2}* y^{2}\)= \(x^{6} *y^{4}\)

The statement that could be true for g is g(-4) = -11.

What is a function?

A function is a mathematical relationship between a set of inputs (called the domain) and a set of outputs (called the range), where each input has a unique output. In other words, for every value of x in the domain, there is exactly one corresponding value of g(x) in the range.

For the given function g, the domain is -20 ≤ x ≤ 5 and the range is -5 ≤ g(x) ≤ 45. We also know that g(0) = -2 and g(-9) = 6.

To determine which statement could be true for g, we can check each option against the given domain and range, as well as the known values of g(0) and g(-9):

g(7) = -1: This statement is not necessarily true, as g(7) may fall outside the given range of -5 ≤ g(x) ≤ 45.

g(-13) = 20: This statement is not necessarily true, as g(-13) may fall outside the given domain of -20 ≤ x ≤ 5.

g(-4) = -11: This statement could be true, as -20 ≤ -4 ≤ 5 and -5 ≤ -11 ≤ 45. However, we cannot confirm this without additional information.

g(0) = 2: This statement is not true, as g(0) is known to be -2.

Therefore, the statement that could be true for g is g(-4) = -11.

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The distance, y, in miles, covered by a car during a specific period, x, in hours and The distance, y, in miles, a car travels in a given period of time, x, in hours

The following graph displays the distance travelled as a linear function of time, D (in miles), and (in hours): To view a larger version of the graph, click on it.) Find AD and 4 values between the specified start and finish times for each interval: Fill in your responses in the appropriate columns in the table below: AD t =1tot=3.5, 0.5 to t =3.5, t=2tot=4, and AD t =3tot=4

b) In light of your findings in (a), it is evident that the average rate of change of D is constant. Decide on ALL that apply (more than one may apply) A It symbolises the car's velocity: B. The angle of the line's slope: C. The average speed of the car throughout the first two hours.

Therefore the correct answer is option A ) It travels for 3 hours, then stops for 2 hours, and finally travels again for 2 hours.

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Answer:

114.3

Step-by-step explanation:

multiple the length value by 2.54

Answer:

4x8-12

Step-by-step explanation:

If she had 4 trays and EACH had 8 muffins you would multiply. So 32 muffins in total, but when you take away which is subtraction, it would be the value of m which is 32-12 and you would get 20 muffins left.

The given differential form is examined to determine if it is exact and find the solution to the corresponding initial value problem. The differential form is y/t+1 dt + (ln(t + 1) + 3y²) dy = 0, with the initial condition y(0) = 1.

To check if the differential form is exact, we compute the partial derivatives of the terms with respect to y and t. Taking the partial derivative of y/t+1 with respect to y gives 0, and taking the partial derivative of (ln(t + 1) + 3y²) with respect to t gives 1/(t + 1). If these partial derivatives are equal, the differential form is exact.

Since the partial derivatives are not equal, the differential form is not exact. To find the solution to the corresponding initial value problem, we need to find an integrating factor. In this case, the integrating factor is given by the reciprocal of the coefficient of dy, which is 1/(ln(t + 1) + 3y²). Multiplying the entire equation by this integrating factor, we obtain the exact differential form:

(1/(ln(t + 1) + 3y²))(y/t+1) dt + (1/(ln(t + 1) + 3y²))(ln(t + 1) + 3y²) dy = 0.

By integrating both sides with respect to the respective variables, we can find the solution to the differential equation. The integration process involves simplifying the integrals and applying the initial condition y(0) = 1 to determine the constant of integration. Unfortunately, due to space limitations, I am unable to provide a detailed step-by-step solution here. However, using the integrating factor, you can solve the equation and find the solution to the initial value problem y(0) = 1.

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Answer:

Step-by-step explanation:

Answer:

10.9

Step-by-step explanation:

Your gonna use the Pythagorean theorem to find x

5^2+x^2=12^2

x^2= 12^2- 5^2

x^2= 144-25

x^2= 119

x= root 119 or 10.9

Speed is 22mph

Let x be the speed of the slow hiker.The other hiker's speed will be x + 1.1mph (as the hiker is walking 1.1 mph faster than the slower hiker). Also, Distance = rate × time (distance covered by both the hikers)55 = (x + x + 1.1) × 10. According to the above equation,55 = (2x + 1.1) × 10. Simplify the above equation:55 = 20x + 11. Divide both sides of the equation by 20:44 = 2x. So, x = 22 mph. Therefore, the speed of the slow hiker is 22 mph.

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On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -

1 - A

2 - C

3 - B

4 - D

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Work Shown:

-7/2 = -3.5

The two given points are (-2,-3.5) and (4,-4)

Let's use the slope formula.

\((x_1,y_1) = (-2,-3.5) \text{ and } (x_2,y_2) = (4,-4)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-4 - (-3.5)}{4 - (-2)}\\\\m = \frac{-4 + 3.5}{4 + 2}\\\\m = \frac{-0.5}{6}\\\\m = \frac{-1/2}{6}\\\\m = \frac{-1/2}{6/1}\\\\m = \frac{-1}{2}\div\frac{6}{1}\\\\m = \frac{-1}{2}*\frac{1}{6}\\\\m = -\frac{1}{12}\)

The slope is -1/12

It means "go down 1 unit, then go to the right 12 units".

You can use a tool like GeoGebra to confirm the answer is correct.

The point estimate of the population standard deviation is the sample standard deviation, calculated from a sample of the population.

The score estimate is a single value given as an estimate of the population parameter. This is the value that best represents the population parameter based on a sample of the population. For example, the point estimate of the population mean is the sample mean, calculated from a sample of the population. Similarly, the point estimate of the population standard deviation is the sample standard deviation, calculated from a sample of the population. The sample standard deviation is calculated by taking the square root of the sum of the squares of the difference between each data point and the sample mean, divided by the sample size minus 1. It is a measure of data prevalence. The sample standard deviation can provide a good estimate of the population's standard deviation, but it's important to remember that it is an estimate and may not be completely accurate. 

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Answer:

Initial Question: How to find percent of a number?

What I know: Percents can be written as decimals.

Points of confusions: What do I do next after turning the percent into a decimal?

Steps: *Example* What is 60% of 30:

60% = .60

.60 x 30 = 18

Step-by-step explanation:

Hope this helps.

1

Explanation:

7/7 - 2/5

Using compatible numbers:

7/7 = 1 as it is closer and equal to 1

so we have: 1 - 2/5

2/5 is approximately 0 as it is closer to 0 than 1

= 1 - 0 = 1

7/7 - 2/5 using compatible number = 1

Answer:

1

Step-by-step explanation:

Given,

Mass ( m ) = 500 g

Volume ( V ) = 500 ml

To find : Density ( D ) = ?

Formula : -

D = m / V

D = 500 / 500

D = 1 g/ml

Hence,

1 g/ml is the density of a substance that has a mass of 500 g and a volume of 500mL.

Answer:

180

Step-by-step explanation:

2 squared is 4

3 squared is 9

4 x 9 x 5 = 180

Answer:

A. 11

Step-by-step explanation:

Since the angles are vertical angles (share a vertex) they are equal in measure.

160 = 10x + 50

subtract 50 from both sides

110 = 10x

divide both sides by 10

x = 11

Answer:

x = 6

y = -9

Step-by-step explanation:

Here, we want to solve the simultaneous equation using the substitution method

from the first equation;

x = -3-y

Put this in the second equation

-3-y + 2y = -12

-3 + y = -12

y = -12 + 3

y = -9

Recall;

x = -3-y

x = -3-(-9)

x = -3 + 9

x = 6

Given:

The lengths, in inches, of each fish are listed:

9, 13, 9, 21, 18

To find:

The statement that best represents the meaning of the range for these data.

Solution:

The given data values are:

9, 13, 9, 21, 18

Arrange the data values in ascending order.

9, 9, 13, 18, 21

Here, the maximum value is 21 and the minimum value is 9.

We know that,

\(\text{Range}=\text{Maximum value}-\text{Minimum value}\)

\(\text{Range}=21-9\)

\(\text{Range}=12\)

The range of the data set is 12. Therefore, the difference between the shortest and longest fish is 12 inches.

Answer:

36

Step-by-step explanation:

Substitute n for 7 to give you:

\(4(7)+8 = 28+8 = 36\)

Answer 36

step 4(7)+8=28+8=36

The variance of the given data set is 5.5. None of the options provided (a) 2.87, (b) 8.25, (c) 8.30, or (d) 68.75 match the correct variance calculation.

To find the variance of a data set, we need to follow a specific formula. Given that the sum of the numbers is 55 and the sum of their squares is 385, we can calculate the variance as follows:

Find the mean of the data set by dividing the sum of the numbers by the total count. In this case, the mean would be 55/10 = 5.5.

Calculate the squared deviation of each number from the mean. This is done by subtracting the mean from each number, squaring the result, and summing up the squared deviations.

(1-5.5)^2 + (2-5.5)^2 + ... + (10-5.5)^2 = 6.25 + 9.00 + ... + 6.25 = 55

Finally, divide the sum of squared deviations by the count of numbers to obtain the variance:

Variance = 55/10 = 5.5

Therefore, the variance of the given data set is 5.5. None of the options provided (a) 2.87, (b) 8.25, (c) 8.30, or (d) 68.75 match the correct variance calculation.

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This question is incomplete

Complete Question

Joe needs to transfer 28 quarts of oil into gallons containers joe calculated that he needs 112 containers but he made a mistake in his calculations identify and correct his error

Joe's error:

28 quarts × 4 quarts/ 1 gallon

= 28 quarts/1 × 4 quarts/ 1 gallon

= (28 × 4)/ ( 1 × 1) = 112 gallons

Answer:

7 gallons is the correct answer

Joe needs to transfer 28 quarts of oil into 7 gallons

Step-by-step explanation:

Joe's error:

28 quarts × 4 quarts/ 1 gallon

= 28 quarts/1 × 4 quarts/ 1 gallon

= (28 × 4)/ ( 1 × 1) = 112 gallons

Correcting Joe's error, we have:

4 quarts = 1 gallon

28 quarts = x

Cross Multiply

4 quarts × x = 28 quarts × 1 gallon

x = 28 quarts × 1 gallon/ 4 quarts

x = 7 gallons

= 28 quarts/x gallons × 1 gallon/4 quarts

= (28 × x)/ ( 1 /4) = 7 gallons

Therefore, Joe needs to transfer 28 quarts of oil into 7 gallons

Answer:

0.00497512437

Step-by-step explanation:

calcuator

Answer: 0.00497512437

Step-by-step explanation:

To divide a decimal number by a whole number, long divide as you would with two whole numbers, but put the decimal point in the answer at the same place it is at in the dividend. If it does not divide evenly, add a 0 to the end of the dividend and continue dividing until there is no remainder.

a) The regression equation for the given output is:
log(Income) = 0.5445 + 0.1000 * log(Lag Income)
b) The slope coefficient of 0.1 represents the change in the natural logarithm of income for a one-unit increase in the natural logarithm of lagged income. In other words, it indicates the elasticity of income with respect to its lagged value. A slope coefficient greater than one indicates that income is very sensitive to its past values, while a slope coefficient less than one indicates that income is less sensitive to its past values.

c) The model seems to be appropriate for forecasting based on the high value of the adjusted R-squared (0.843), which indicates that 84.3% of the variation in income can be explained by the lagged income variable. However, it is important to note that there may be other factors influencing income that are not included in the model, and that past performance may not necessarily be a good predictor of future income.
d) The coefficient of the dummy variable for gender (male=1, female=0) is 0.1. This means that, all else being equal, being male is associated with a 10% increase in income compared to being female. It is important to note that this interpretation assumes that all other variables in the model are held constant.


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Answer:

All you have to do is find the diameter and divide it by 2. I'm sorry if I can't give you a direct answer because I cannot see the diagram.

Step-by-step explanation:

Answer:

7=2.75

8=18

9=3.625

10=29

Step-by-step explanation: