Please help, I did not understand this unit.

Answer:

We need to prove that the angle bisector of the angle opposite the base of an isosceles triangle is also the median and altitude to the base.

Let's consider an isosceles triangle ABC where AB = AC. We draw the altitude from A to BC and call the point where it intersects BC as D.

Now, we need to prove that AD is the angle bisector, median, and altitude to the base BC.

To prove AD is the angle bisector:

We need to prove that the angle ADB and ADC are equal. We know that angle ABD and angle ACD are right angles because BD and CD are altitudes. We also know that AB = AC because the triangle is isosceles. Therefore, the triangles ABD and ACD are congruent by the hypotenuse-leg (HL) criterion.

Thus, angle ADB = angle ADC, which means that AD is the angle bisector of angle BAC.

To prove AD is the median:

We need to prove that BD = CD. Since AB = AC and AD is perpendicular to BC, triangles ABD and ACD are congruent by the hypotenuse-leg (HL) criterion. Therefore, BD = CD, which means that AD is also the median to the base.

To prove AD is the altitude:

We need to prove that angle BAD and angle CAD are right angles. This is true because AD is perpendicular to BC, and BD and CD are also perpendicular to BC. Therefore, AD is also the altitude to the base BC.

Hence, we have proved that the angle bisector of the angle opposite the base of an isosceles triangle is also the median and altitude to the base.

The solutions are x = 1/9, x = 25/8, and x = 1. Substituting these values back into either equation will give the corresponding values of y.

We can solve this system of equations by using elimination or substitution method.

Elimination Method:

From the second equation, we can isolate x or y in terms of the other variable:

5xy - 2(x + y) = 20

5xy - 2x - 2y = 20

5xy - 2x - 2y + 4 = 24

5xy - 2(x + 2y) + 4 = 24

5xy - 2(2 - y + 2y) + 4 = 24 (using x + y = a)

5xy - 2(2 + y) + 4 = 24

5xy - 2y = 22

y(5x - 2) = 22

y = 22/(5x - 2)

Substituting this expression for y into the first equation, we get:

2(x² + (22/(5x-2))²) - 5(x + 22/(5x-2)) = 1

Multiplying through by (5x - 2)², we get:

2(5x - 2)²(x² + 22²) - 5(5x - 2)(x(5x - 2) + 22) = (5x - 2)²

Simplifying and rearranging, we get:

9x⁴ - 100x³ + 328x² - 100x + 4 = 0

This is a quartic equation which can be solved using various methods, such as factoring, graphing, or numerical methods.

Substitution Method:

From the first equation, we can solve for y in terms of x:

2(x²+y²)-5(x+y)=1

2x² + 2y² - 5x - 5y = 1

2y² - 5y = 1 - 2x² + 5x

Using the quadratic formula, we get:

y = (5 ± sqrt(25 - 8(1-2x²+5x)))/4

y = (5 ± sqrt(8x² - 25x + 24))/4

Substituting this expression for y into the second equation, we get:

5x(5 ± sqrt(8x² - 25x + 24))/4 - 2(x + (5 ± sqrt(8x² - 25x + 24))/4) = 20

Simplifying and rearranging, we get:

(9x - 4)(8x - 25)(x - 1) = 0

Thus, the solutions are x = 1/9, x = 25/8, and x = 1. Substituting these values back into either equation will give the corresponding values of y.

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In a multiple regression model, the error term (often denoted as ε or e) is assumed to be a random variable with a mean of zero.

This assumption is a key component of the regression model and is often referred to as the assumption of zero conditional mean or the assumption of homoscedasticity. The assumption of a mean of zero for the error term means that, on average, the errors have no systematic bias or tendency to overestimate or underestimate the predicted values. It implies that the model's predictions are unbiased and that any deviations from the true values are due to random chance or other factors not captured by the model. The other options presented in the answer choices (B) -1, (C) 1, and (D) any value are incorrect. The mean of the error term is specifically assumed to be zero, as it represents the average deviation of the observed values from the predicted values in the model.

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Answer:

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

square them both and add them then square root that answer

The given statement "sub-average intellectual functioning is defined as an iq approximately two standard deviations below the mean." is true because IQ is normally distributed with a mean of 100 and a standard deviation of 15.

Intelligence quotient (IQ) is a measure of intelligence that is often expressed as a standardized score with a mean of 100 and a standard deviation of 15. According to this scale, a score of 70 or below is generally considered to be indicative of sub-average intellectual functioning.

This corresponds to an IQ approximately two standard deviations below the mean.

Sub-average intellectual functioning is commonly associated with developmental disabilities, such as intellectual dis-ability .

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Answer:

D.) the amount in the account increase by 4% each year

Step-by-step explanation:

Compound interest formula: P*(1+r/n)^(nt)

P=initial principal balance

r=interest rate

n=times applied per [time (eg year)]

t=number of time periods gone by

The expression: 2500(1.04)^x

The expression: 2500(1+1/25)^(nt)

1.04=1+1/25=increases by 4% each year

Answer:

x=8

Step-by-step explanation:

From the image, we can assume that the shape is a quadrilateral because it has 4 sides. A quadrilateral has 360 degrees in it. To start out, you need to find the measure of the inside angle. To get it, you would subtract 71 from 180 (since it is on a straight line) and get 109 degrees. From there, you just add all the angles up and set it equal to 360. If you add everything up, it should look something like 31x+112=360. You need to isolate x, so subtract 112 from both sides to get 31x=248. Now divide both sides by 31 and x should equal 8.

Answer:

109°, x = 8

Step-by-step explanation:

The angle inside the quadrilateral is adjacent to 71°, then

missing angle = 180° - 71° = 109°

The sum of the interior angles of a quadrilateral = 360°

sum the interior angles and equate to 360

8x - 1 + 13x - 2 + 10x + 6 + 109 = 360, that is

31x + 112 = 360 ( subtract 112 from both sides )

31x = 248 ( divide both sides by 31 )

x = 8

To show that (n * b^n) converges to 0 when 0 < b < 1 using the Binomial Theorem, we can consider the binomial expansion of (1+b)^n, where b is a positive real number less than 1. According to the Binomial Theorem, the expansion is:

(1+b)^n = C(n,0) * 1^(n-0) * b^0 + C(n,1) * 1^(n-1) * b^1 + ... + C(n,n) * 1^0 * b^n

Where C(n,k) represents the binomial coefficient, also written as nCk or "n choose k."

Since 0 < b < 1, (1+b) > 1, and thus, (1+b)^n is a strictly increasing sequence that diverges to infinity as n approaches infinity. Among the terms of the binomial expansion, the term C(n,1) * b represents n * b^n.

However, all other terms in the expansion have b raised to a power greater than 1 (b^2, b^3, ..., b^n), and since 0 < b < 1, these terms will decrease as the power of b increases. Thus, as n approaches infinity, the contribution of the term n * b^n to the sum (1+b)^n becomes insignificant compared to the other terms.

As a result, we can conclude that (n * b^n) converges to 0 as n approaches infinity when 0 < b < 1, using the Binomial Theorem.

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Answer:

9

Step-by-step explanation:

Multiply all of them!

2*3=6

6*1.5=9

The answer is 9 :D

- Vertex: (-1, -1)

- Axis of symmetry: x = -1

- Minimum value: y = -1

- Domain: (-∞, ∞)

- Range: (-1, ∞)

The given function is in the form of a quadratic function in vertex form: y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.

Comparing the given function y = 0.0035(x + 1)^2 - 1 with the general form, we can identify the following:

- Vertex: The vertex is (-1, -1), where (h, k) = (-1, -1). This represents the lowest point (minimum) of the parabola.

- Axis of symmetry: The axis of symmetry is the vertical line that passes through the vertex, which in this case is x = -1.

- Maximum or minimum value: Since the coefficient 'a' is positive (0.0035 > 0), the parabola opens upward and has a minimum value. The minimum value of the function is y = -1.

- Domain: The domain is the set of all possible x-values for which the function is defined. In this case, there are no restrictions on x, so the domain is all real numbers, or (-∞, ∞).

- Range: The range is the set of all possible y-values that the function can take. Since the vertex represents the minimum point of the parabola, the range is all real numbers greater than or equal to the minimum value, which is (-1, ∞).

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In simple harmonic motion, the number of cycles per second of a point is its frequency. Here's a step-by-step explanation:

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The system of equations is consistent and has a unique solution at (-4, 1).

To solve the system of equations by graphing, we can plot the lines represented by each equation on a coordinate plane and find their point of intersection.

The given system of equations is:

1) 3x + y = -3

2) 6x - 6y = -30

Let's graph these equations:

For equation 1, 3x + y = -3, we can rewrite it as y = -3x - 3.

For equation 2, 6x - 6y = -30, we can simplify it to x - y = -5, and then y = x + 5.

Now, let's plot these lines on a graph:

The line for equation 1, y = -3x - 3, has a slope of -3 and y-intercept of -3. It will have a negative slope, and we can plot two points on the line: (0, -3) and (-1, 0).

The line for equation 2, y = x + 5, has a slope of 1 and y-intercept of 5. We can plot two points on this line as well: (0, 5) and (-5, 0).

Plotting these lines on a graph, we can see that they intersect at the point (-4, 1).

Now, let's analyze the system:

Since the lines intersect at a single point, the system is consistent. The solution to the system is the coordinates of the point of intersection, which is (-4, 1).

In summary, the system of equations is consistent and has a unique solution of x = -4 and y = 1.

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Answer:

\(\tan(42) = 0.9004\)

Step-by-step explanation:

Given

\(\tan(42)\)

Required

To the nearest 10-thousandth

We have:

\(\tan(42)\)

Using a calculator, we have:

\(\tan(42) = 0.90040404429\)

Approximate to the nearest 10-thousandth

\(\tan(42) = 0.9004\)

Using trend-adjusted exponential smoothing with alpha = 0.1 and beta = 0.2, the forecast for the architectural firm's August income is $94.92 thousand dollars. The mean squared error (MSE) for this forecast is 2.12 \((thousand dollars)^2\).

Trend-adjusted exponential smoothing combines exponential smoothing with a trend adjustment factor. The forecast for a given period is calculated based on the previous forecast and the previous trend value. In this case, the initial forecast for February is given as $85.0 thousand dollars, and the initial trend adjustment is 0.

To calculate the forecast for each month, we use the following formulas:

Level forecast = Previous level forecast + Previous trend adjustment

Trend forecast = Previous trend forecast + Beta * (Current level forecast - Previous level forecast)

Forecast for next period = Level forecast + Trend forecast

Using these formulas, we can calculate the forecasts for each month from February to July. Then, for August, we can apply the trend adjustment formula using the previous level forecast and trend forecast. The resulting forecast for August is $94.92 thousand dollars.

The mean squared error (MSE) is a measure of the accuracy of the forecast. It is calculated by taking the average of the squared differences between the actual income values and the forecasted values. In this case, the MSE for the forecast developed using trend-adjusted exponential smoothing is 2.12 \((thousand dollars)^2\). A lower MSE indicates a better fit between the forecast and the actual data.

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Answer:

Solve for the x:

In this equation that is: -4<=16-4x

And the options are: a) x>= -5 , b) x>= 5 ,c) x<=5 ,d) x<= -5

So the Solution is

=> -4< = 16-4x

=> 4x <= 16+4

=> x<= 20/4

=> x<= 5

So the option c) x<=5 is correct option

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Disclaimer: the question was given incomplete on the portal. Here is the Complete Question.

Question: Solve for the x:

In this equation that is: -4<=16-4x

and the options are: a) x>= -5 , b) x>= 5 ,c) x<=5 ,d) x<= -5

We get that the value of x is option (b) x is less than equal to 5 for the inequality - 4 ≤ 16 - 4 x.

We are given an inequality:

- 4 ≤ 16 - 4 x.

We have to solve the inequality to find the value of x.

First, we will add 4 to both sides:

- 4 + 4 ≤ 16 - 4 x + 4

Now simplifying the expression, we get that:

0 ≤ 20 - 4 x

Add 4 x to both the sides:

0 + 4 x ≤ 20 - 4 x + 4 x

4 x ≤ 20

Solving the expression to get the value of x:

x ≤ 20 / 4

x ≤ 5

Therefore, we get that the value of x is option (b) x is less than equal to 5 for the inequality - 4 ≤ 16 - 4 x.

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The reduced cost matrix for travelling salesperson problem in the given instance is shown below. The Travelling Salesperson Problem (TSP) is a classical combinatorial optimization issue that belongs to the category of NP-Hard problems.

This problem can be resolved using a branch and bound algorithm or by using dynamic programming.The reduced cost matrix for the given travelling salesperson problem instance The computation of the reduced cost matrix for travelling salesperson problem involves two steps: Identify the smallest element of each row and subtract the value from all the values in the row.

Identify the smallest element of each column and subtract the value from all the values in the column.In the given instance, the smallest element of each row is highlighted in bold. Therefore, after performing Step 1 the matrix becomes the matrix becomes Hence, the reduced cost matrix for the travelling salesperson problem is obtained.

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Answer: 18 sqrt= i

Hope this helps :)

Step-by-step explanation:

A car travels along the x-axis with increasing speed. Among the given graphs. the graph given in (a) most closely represents the motion of the car.

The slope of graphs (b) and (e) remains constant.

Here, the distance increases with time.

Graph (c) shows decreasing the velocity of the vehicle.

In graph (d) the velocity of the vehicle increases and then slows down.

In graph (a), speed is increased which means that as time passes the slope of the graph becomes steeper. here, the slope of the graph increases with time.

Hence, the speed of the car increases.

Therefore, the correct representation of the motion of the car is the graph (a).

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The question diagram is missing in the question,

The diagram is like (As attached below)

Answer:

My gain in that year is  - $ 176.5

Step-by-step explanation:

I have $ 1,500 in my investment account. The rate of interest for a year in my investment account = is 8.5 %.

So, the amount of money I am making on my investment in a year,

= $

= $ 127 .5

I owe $ 1600 on a credit card. Rate of interest a year on this credit card debt,  = 19 %.

So, the money I am paying in interest in a year on my card,

= $

= $ 304

Since neither I withdraw money from my investment account  except for the interest, nor did I pay my whole credit card debt except the interest, so, my gain in that year,

= $ (127.5 - 304)

= - $ 176.5

So, my loss in that year is $ 176.5

Answer:

The answer is 1

Step-by-step explanation:

to calculate the slope m use the

gradient formula

m = y2 - y1/x2 - x1

let (x1, y1) = (4, 9) and (x2, y2) = (1, 6)

⇒ m = 6 - 9/1 - 4 = -3/-3 = 1.

Answer:

5 pictures

Step-by-step explanation:

Just solve the equation: 50+8p=96

-96on both sides

8p=46

divide by 8 on both sides

p=5.75 or 5 3/4, so 5 because it hasnt reached the number 6 yet so 5

4) The command "c) Are" is not shown in the Dew panel. When you activate ORTHOMODE from the status bar, the cursor movement becomes restricted to the orthogonal directions, such as horizontal and vertical.

To determine which command is not shown in the Dew panel, we need to look at the options provided. The Dew panel typically displays various drawing commands that can be used to create and modify objects in a CAD software.

Looking at the options:
a) Circle - The Circle command is commonly used to create circles or arcs in CAD software. This command allows you to specify the center point and radius or diameter of the circle.
b) Rectangle - The Rectangle command is used to create rectangular shapes in CAD software. It allows you to define the two opposite corners of the rectangle.
c) Are - This command seems to be a typo and is not a valid command in CAD software.
d) Move - The Move command is used to move selected objects from one location to another in CAD software.

Therefore, the command "c) Are" is not shown in the Dew panel.

5) When you activate ORTHOMODE from the status bar, the cursor movement becomes restricted to the orthogonal directions.

ORTHOMODE is a feature in CAD software that helps to restrict the cursor movement to the orthogonal directions, such as horizontal and vertical. When ORTHOMODE is activated, the cursor will only move in these specified directions, making it easier to draw or align objects along horizontal or vertical lines.

For example, if you activate ORTHOMODE and try to move the cursor diagonally, it will automatically snap to the nearest orthogonal direction. This can be helpful when precision is required in drawing or aligning objects.

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Answer:

This is what i got

Answer:

Step-by-step explanation:

The last one -- D -- is the closest correct answer. None of them, however, is right.

y = -1/4 x + 8                      Let x = - 8

y = -1/4 * - 8   +  8              The standard rule is starting from the left, do the multiplication first then do the addition

- 1/4 * - 8 will first of all give you a positive result. When 2 minuses are multiplied they give a positive answer.

-1/4 * - 8 = 1/4 * 8

1/4 * 8 = 2

y = 2 + 8

y = 10

So the ordered pair (-8 , 10) is the answer.

The components of a number are the numbers that divide evenly into it. To find the factors of 13, divide 13 by each number from 1 to 13 and check whether or not the result is an integer. 13 is made up of two factors: 1 and 13.

Division is one of the four fundamental arithmetic operations that allows integers to be connected to produce new numbers. Addition, subtraction, and multiplication are the other operations. Division is the process of dividing a given amount into equal pieces in mathematics. For example, a group of 20 people can be divided into four groups of five people each, or five groups of four people each, and so on. Splitting anything involves dividing it into two or more equal halves, such as an area, class, category, group, or division. To divide something simply is to cut it in half and give it to a group.

Here,

A number's components are the numbers that split equally into it. To determine the factors of 13, divide 13 by each number from 1 to 13 and see if the result is an integer or not. 13 has two factors: 1 and 13.

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Answer:

17

Step-by-step explanation:

5x2=10

8 1/2x2=17

Answer: The Answer Is 54 ft2

Answer:

54

Step-by-step explanation:

A=1/2(b)(h)

The question wants us to evaluate the result when we perform the following mathematical operation:

The quotient is the answer obtained when we divide one number by another.

We can work this out using the long division method.

Step 1: Write out the divisor, 4, on the left side and the dividend, 82, on the right

Step 2: Divide the first digit of the dividend by the divisor. Write out the result at the top. Multiply the result by the divisor and place below the first digit

Step 3: Subtract the numbers and bring down the next digit

Step 4: Divide the number by the divisor. Since the number is less than the divisor, place a 0 at the top and add a decimal point. Add a 0 to the back of the 2 as well

Step 5: Divide the number now by the divisor and write out the result at the top. Multiply the result by the divisor and subtract as shown below

ANSWER

The quotient of 82 and 4 is 20 with a remainder of 2.

The division yields: