Properties of equality reference packet geometry

Answer:

To find what percent 120 is of 400, we can use either the percent proportion or the percent equation.

Using the percent proportion:

Let x be the percent we are looking for. Then we can write:

120/400 = x/100

Simplifying this equation, we get:

0.3 = x/100

Multiplying both sides by 100, we get:

x = 30

Therefore, 120 is 30% of 400.

Using the percent equation:

The percent equation states that:

part/whole = percent/100

In this case, the part is 120 and the whole is 400, so we can write:

120/400 = percent/100

Simplifying this equation, we get:

0.3 = percent/100

Multiplying both sides by 100, we get:

percent = 30

Therefore, 120 is 30% of 400.

Answer:

30%

Step-by-step explanation:

Write the expression:

x% of 400 = 120

Then solve:

x/100 x 400 = 120

4x = 120

x = 30%

Answer:

119

Step-by-step explanation:

divide the numbers needed until you get 119 then boom yo done brainest now!

The height needed to reach the desired volume, 30,875.88 in³, of a rectangular prism shaped sandbox is equals to 8.4 inches.

We have a family a family is building a sandbox for their yard that is shaped like a rectangular prism. Let the dimensions of rectangular prism be l, w and h inches.

Volume of box = 30,875.88 in³

Length of box , l = 62.3 inches

Width of box, w = 59 inches

We have to determine value of h.

The volume of shape is the space covered by the shape. The volume of rectangular prism, V = l× w×h

Substitute the known values in above formula, so, 30,875.88 in³ = 62.3 × 59 in² × h

=> 30,875.88 in³ = 3,675.7 in² × h

=> h = 30,875.88 in³/3,675.7 in²

=> h = 8.4 inches

Hence, required value of height, h is 8.4 inches.

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In the word problem , the number of days were in the "13-18" category is  C)4.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here the given data represent the numbers of loaves sold in the last 10 days is 5, 12, 8, 15, 18, 20, 3, 17, 14, 21.

Now number of loaves sold in last 10 days between from 13-18 is

=> 15,18,17,14

Hence the number of days were in the "13-18" category is  C)4.

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The provided information in the question is insufficient to accurately determine the hours for Lisa, David, and Sarah.   To determine how many hours should be assigned to each graphic designer, we need to first understand their individual work capacity, hourly rates, or the total workload available.  

However, we can help you calculate the total cost (in dollars) based on the given information. Here's a step-by-step explanation:
Identify the number of hours worked by each designer:
  - Lisa's hours: 26
  - David's hours: 39.6
  - Sarah's hours: 16.5
Determine the hourly rate for each designer:
  Since the hourly rates are not provided in the question, we cannot proceed with this step. Please provide the hourly rates for each graphic designer to help us calculate the total cost.
Once you have the hourly rates for each designer, you can calculate the total cost using the following formula:
Total Cost = (Lisa's hours * Lisa's hourly rate) + (David's hours * David's hourly rate) + (Sarah's hours * Sarah's hourly rate)

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Pour calculer 3/11 x 4/9, on multiplie les deux nombres ensemble en multipliant les numérateurs entre eux et les dénominateurs entre eux, ce qui donne :

3/11 x 4/9 = (3 x 4) / (11 x 9)

En simplifiant cette fraction, on peut diviser le numérateur et le dénominateur par leur plus grand diviseur commun, qui est 3 :

(3 x 4) / (11 x 9) = 12 / 99

La fraction 12/99 peut être simplifiée encore plus en divisant le numérateur et le dénominateur par 3 :

12 / 99 = 4 / 33

Ainsi, la forme la plus simple de 3/11 x 4/9 est 4/33.

Answer: umm please provide the answers you can chose then maybe i can help

Step-by-step explanation:

Constructing the foci of an ellipse using a compass works because the intersection of the arcs drawn with the compass is a point that is equidistant to the endpoints of the major or minor axis, which are precisely the foci of the ellipse.

Draw the major and minor axes of the ellipse.

Place the compass on one end of the major axis, and set the width of the compass to half the length of the major axis.

Draw an arc that intersects both the major and minor axes.

Repeat step 2 and 3 with the other end of the major axis.

The intersection of the two arcs is one of the foci of the ellipse.

To find the other focus, repeat the above steps using the minor axis instead of the major axis.

Now, let's justify why this method works. Recall that an ellipse is defined as the set of all points such that the sum of their distances to the foci is constant. This means that the foci play a fundamental role in defining the shape of the ellipse.

When we draw the arcs using the compass, we are essentially finding all the points that are equidistant to the two endpoints of the major or minor axis. The intersection of these arcs is a point that is equidistant to both endpoints of the major or minor axis, which means it lies on the ellipse.

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well, first off, hmmm let's find their slopes in the first place

[tex]p=\stackrel{\stackrel{m}{\downarrow }}{2}n+5\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad {\Large \begin{array}{llll} \boxed{x=2} \end{array}}[/tex]

now,  to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below for BrandY[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 6 } \implies {\Large \begin{array}{llll} 1=Y \end{array}}[/tex]

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above for BrandZ

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{9}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{9}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ 6 }{ 4 } \implies {\Large \begin{array}{llll} \cfrac{3 }{ 2 }=Z \end{array}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{X}{2} ~~ > ~~ \stackrel{Y}{1}\hspace{5em}\stackrel{X}{2}~~ > ~~ \stackrel{Z}{\frac{3}{2}}~\hfill[/tex]

Answer:

the inequality can be written as -5

Answer:

Step-by-step explanation:

(A) and (B)

Not much explanation can be given as these are basically just following  definitions

The exact value of cos H from the right triangle is cos(H) = 0.98

From the question, we have the following parameters that can be used in our computation:

The right triangle

The exact value of cos H can be calculated as

cos(H) = HI/HJ

Where

HI = 40 and HJ = 41

So, we have

cos(H) = 40/41

Evaluate

cos(H) = 0.98

Hence, the value is 0.98

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Answer:

If the circular track has a circumference of 0.5 mile, then its circumference in feet is:

0.5 mile x 5,280 feet/mile = 2,640 feet

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference and r is the radius of the circle. Substituting the values we have:

2,640 = 2 x 3.14 x r

Solving for r, we get:

r = 2,640 / (2 x 3.14) = 420.38 feet

Therefore, the radius of the circular track, in feet, is approximately 420.38 feet. Rounded to the nearest hundredth, the answer is 420.38 feet, which corresponds to the third option.

Answer: 3 days

Step-by-step explanation:

Answer:

I agree with 3 days

Step-by-step explanation:

1) Ratio for laps to meters to days

1 lap: 400 meters -> 10 laps: 400 meters = 1 day

OK, 1 kilometer is 1,000 meters. Keep that in mind.

*12 kilometers is the equivalent to 12000 meters*

2) Ratio problem and cross multiply

10:400 = 1 day so x laps :12000 meters

HOW MANY TIMES DOES 400 GO INTO 12000? 30 times

30 is the amount of laps ran.

If you multiply 10:400 by 3 it will equal 30:12000.

3 is your answer

Answer: x=14.75

2(2x+2)=3(21)

   4x+4 = 63

       4x = 63-4

          x = 59÷4

          x = 14.75

Check:  2(2*14.75+2)=3(21)

                             63 = 63

Answer: 63

Step-by-step explanation: It's stated that it equals 3(21) and that's 63.

The expected value in the game of mentioned probability is $-5.26.

Expected value can be calculated by the formula -

Expected value = (probability × winning amount) + (probability × (- losing amount))

Keep the values in formula to find the expected value -

Expected value = (1/42 × 67) + (41/42 × -7)

Performing multiplication in the brackets on Right Hand Side of the equation

Expected value = 1.57 - 6.83

Performing subtraction on Right Hand Side

Expected value = $-5.26

Hence, the expected value is $-5.26.

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Any value of x that is less than 400 dollars will satisfy this inequality and will represent the amount of money Ron can spend on the rental car.

An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).

The inequality that models the amount of money Ron can spend on the rental car is:

x < 400

This inequality means that the value of x (the amount of money Ron can spend) is less than 400 dollars. The symbol "<" indicates that the value of x must be less than 400, which means that Ron cannot spend more than 400 dollars on the rental car.

So, any value of x that is less than 400 dollars will satisfy this inequality and will represent the amount of money Ron can spend on the rental car. For example, if Ron decides to spend $350, then the value of x would be 350, which is less than 400 and satisfies the inequality.

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Emerson needs 3 bags in total to hold all of her snack mix .  

To determine the number of plastic bags that Emerson needs, we have to divide the total amount of snack mix by the amount of snack mix in each bag.      

Emerson made 8 cups of snack mix, and she puts 3 1/2 cups of mix into each bag. We can write this as a mixed number: 3 1/2 = 7/2. So Emerson puts 7/2 cups of mix into each bag.    

To find out how many bags Emerson needs, we divide the total amount of mix by the amount of mix in each bag:    

8 cups ÷ (7/2 cups per bag) = 16/7 bags

We can simplify 16/7 by dividing the numerator and denominator by 1 (the greatest common factor of 16 and 7)

16/7 ÷ 1/1 = 16/7 x 1/1 = 16/7

So Emerson needs 16/7, or approximately 2.29, bags. Since she can't use a fraction of a bag, she will need to round up to the nearest whole bag. Therefore, Emerson needs 3 bags in total to hold all of her snack mix.

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To find the first four terms of the sequence given by the formula aₙ=43-4(n-1), we substitute n=1, 2, 3, and 4 in the formula and simplify.

a₁=43-4(1-1)=43-4(0)=43-0=43

a₂=43-4(2-1)=43-4(1)=39

a₃=43-4(3-1)=43-4(2)=35

a₄=43-4(4-1)=43-4(3)=31

Therefore, the first four terms of the sequence are 43, 39, 35, and 31

The coordinates of the endpoints of the image A''B'', following the rotation and reflection transformation are are;

A''(-5, 2), and B''(1, -1)

A reflection transformation is a type of transformation that takes each point on a figure and flips or reflects it across a line known as the line of reflection to create a mirror image.

What is a rotation transformation?

A rotation transformation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees about a specified point.

The transformations in the question are a reflection and a rotation

The coordinates of the point (x, y) on the coordinate plane, following a reflection across the y-axis is; (-x, y)

The coordinate of the point (x, y) following a rotation of 90° counterclockwise about the origin is; (-y, x)

Therefore, the coordinates of the image of points A and B following a reflection across the y-axis are;

A(-2, 5) → A'(2, 5)

B(1, -1) → B'(-1, -1)

The coordinates of the image of points A' and B' following a rotation of 90° counterclockwise about the origin are;

A'(2, 5) → A''(-5, 2)

B'(-1, -1) →  B''(1, -1)

The coordinates of the endpoints of the image, A''B'' are therefore;

A''(-5, 2) and B''(1, -1)

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According to the given information we have that (a) Linear (b) = Non-linear

(c) Linear (d) Non Linear.

What about linear graph?

A linear graph is a graph of a linear equation, which is an equation that represents a straight line when plotted on a coordinate plane. The standard form of a linear equation in two variables x and y is:

ax + by = c

where a, b, and c are constants. When this equation is graphed, it produces a straight line with a constant slope (a/b) and y-intercept (c/b). Linear graphs are used to represent relationships between two variables that change at a constant rate.

Define non linear graph:

A non-linear graph is a graph that does not represent a straight line when plotted on a coordinate plane. A non-linear graph can represent a wide variety of mathematical functions, including exponential functions, power functions, trigonometric functions, and logarithmic functions. Non-linear graphs are often used to model complex real-world phenomena that do not follow a simple linear pattern.

The shape of a non-linear graph depends on the specific equation or function being graphed, and it may have one or more curves, bends, or peaks. The slope and y-intercept of a non-linear graph are not constant and can change at different points along the curve. Non-linear graphs can be analyzed using calculus and other advanced mathematical techniques to understand the behavior and properties of the underlying function.

According to the given information:

(a) The equation given in the question follow the property of linear graph that it create a straight line in constant way .

(b) Non -linear not follow the condition.

(c) It is also linear in nature form a straight line with constant approch.

(d) The given coordinate form non-linear graph.

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The answer is Positive Linear Correlation.

A scatter plot is a graphical representation of data points where each point represents two variables, typically plotted on the horizontal and vertical axes.

To construct a scatter plot, we need two sets of data:

one for the x-axis and one for the y-axis.

The data points are then plotted on the graph with the x-value along the horizontal axis and the y-value along the vertical axis.
To answer your question, I need to know what data you have to construct the scatter plot.

Once you provide me with the data, I can help you create the scatter plot and answer any questions you may have about it.
In general, scatter plots are used to identify any patterns or trends in the data.

By visually examining the scatter plot, we can determine whether the data points are positively or negatively correlated, or if there is no correlation between the two variables.

To determine the type of correlation, we can visually inspect the scatter plot. We see that as x increases, y tends to increase as well, indicating a positive linear correlation.

This can help us make predictions or draw conclusions about the relationship between the variables.
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Total service hours are what the y-intercept is referring to in the graph of linear equation. representing the hours Yuson left after x days.

A straight line's general equation is -

[y] = [m]x + [c]

where -

The rate at which [y] varies in respect to [x] is shown by the slope of the line, [m].

The y-intercept, or the place where the graph crosses the [y] axis, is represented by [c].

The equation of a straight line can also be written as -

Ax + By + C = 0

By = - Ax - C

y = (A/B - B/C)x - A/C

Presented is Yuson, who must perform 30 hours of volunteer work.

After [x] days, Yuson's hours of service are represented by the equation:

y = 30 - 2x

OR

y = - 2x + 30

Please see the following graph.

Therefore, the y intercept here is the total hours of service.

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The complete question and graph has been attached below.

A) Quartile 1 (Q1): 2, Quartile 2 (Q2): 6, Quartile 3 (Q3): 7, Decile 1 (D1): 1, Decile 2 (D2): 2, Decile 3 (D3): 3, Decile 4 (D4): 7
B) Quartile 1 (Q1): 11, Quartile 2 (Q2): 14, Quartile 3 (Q3): 16, Decile 1 (D1): 11, Decile 2 (D2): 12, Decile 3 (D3): 14, Decile 4 (D4): 17
C) Quartile 1 (Q1): 77, Quartile 2 (Q2): 85, Quartile 3 (Q3): 94, Decile 1 (D1): 71, Decile 2 (D2): 81, Decile 3 (D3): 87, Decile 4 (D4): 98
D) Quartile 1 (Q1): 42, Quartile 2 (Q2): 66, Quartile 3 (Q3): 86, Decile 1 (D1): 28, Decile 2 (D2): 42, Decile 3 (D3): 57, Decile 4 (D4): 98
E) Quartile 1 (Q1): 100, Quartile 2 (Q2): 117, Quartile 3 (Q3): 133, Decile 1 (D1): 33, Decile 2 (D2): 100, Decile 3 (D3): 111, Decile 4 (D4): 147
F) Quartile 1 (Q1): 113, Quartile 2 (Q2): 126, Quartile 3 (Q3): 146, Decile 1 (D1): 110, Decile 2 (D2): 113, Decile 3 (D3): 121, Decile 4 (D4): 848

Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be used in many different forms. It can be represented by symbols such as 1, 2, 3, or 4, or by words such as one, two, three, or four. It is also used to represent quantities, distances, and other measurements. Number is an important part of mathematics, and it is used in virtually every aspect of life.

A)
Quartile 1 (Q1): 2
Quartile 2 (Q2): 5
Quartile 3 (Q3): 7
Interquartile Range (IQR): 5
Decile 1 (D1): 2
Decile 2 (D2): 2.6
Decile 3 (D3): 3.4
Decile 4 (D4): 6

B)
Quartile 1 (Q1): 12
Quartile 2 (Q2): 14.5
Quartile 3 (Q3): 16
Interquartile Range (IQR): 3.5
Decile 1 (D1): 11.1
Decile 2 (D2): 12.9
Decile 3 (D3): 14.7
Decile 4 (D4): 16.4

C)
Quartile 1 (Q1): 77
Quartile 2 (Q2): 85
Quartile 3 (Q3): 92
Interquartile Range (IQR): 15
Decile 1 (D1): 77
Decile 2 (D2): 81
Decile 3 (D3): 85.8
Decile 4 (D4): 92

D)
Quartile 1 (Q1): 42
Quartile 2 (Q2): 63
Quartile 3 (Q3): 86
Interquartile Range (IQR): 44
Decile 1 (D1): 42
Decile 2 (D2): 52.8
Decile 3 (D3): 66.2
Decile 4 (D4): 86

E)
Quartile 1 (Q1): 100
Quartile 2 (Q2): 117
Quartile 3 (Q3): 133
Interquartile Range (IQR): 33
Decile 1 (D1): 100
Decile 2 (D2): 107
Decile 3 (D3): 116
Decile 4 (D4): 133

F)
Quartile 1 (Q1): 110
Quartile 2 (Q2): 121
Quartile 3 (Q3): 136
Interquartile Range (IQR): 26
Decile 1 (D1): 110
Decile 2 (D2): 113
Decile 3 (D3): 117.8
Decile 4 (D4): 136

From the calculated values above, it can be seen that the quartiles and deciles of each set of data differ. This is due to the different values of the data sets and the number of data points in each set. The quartiles and deciles show different ranges and values which indicate the spread of the data. The quartiles and deciles are an important measure of the spread of the data and can help to identify any outliers. The quartiles and deciles also help to identify any skewness in the data.

In conclusion, the quartiles and deciles of each set of data differ due to the different values and the number of data points in each set. The quartiles and deciles provide an important measure of the spread of the data, helping to identify any outliers or skewness.

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The TWO given model statements that are true for the given model are A and D.

The given passage describes a model that predicts the number of pounds of trash an apartment building needs to dispose of each week based on the number of tenants in the building.

The model is y = 6.4x + 13.9, where y is the number of pounds of trash, and x is the number of tenants in the building. The task is to select the TWO given model statements that are true for the given model. Let's analyze each statement:

A. For each additional tenant in the building, the amount of trash that needs to be disposed each week increases by 6.4 pounds.

This statement is true according to the given model equation, where the coefficient of x is 6.4. Therefore, for each additional tenant, the amount of trash that needs to be disposed of increases by 6.4 pounds.

B. When no tenants are in the building, other activities would require the disposal of 6.4 pounds of trash each week.

This statement is not true because the intercept of the model equation is 13.9, not 6.4. Therefore, when there are no tenants in the building, the amount of trash that needs to be disposed of is 13.9 pounds, not 6.4 pounds.

C. For each additional tenant in the building, the amount of trash that needs to be disposed each week increases by 13.9 pounds.

This statement is not true according to the given model equation, where the coefficient of x is 6.4, not 13.9. Therefore, for each additional tenant, the amount of trash that needs to be disposed of increases by 6.4 pounds, not 13.9 pounds.

D. When no tenants are in the building, other activities would require the disposal of 13.9 pounds of trash each week.

This statement is true according to the given model equation, where the intercept is 13.9. Therefore, when there are no tenants in the building, the amount of trash that needs to be disposed of is 13.9 pounds.

E. For each day, the building, the amount of trash that needs to be disposed each week increases by 20.3 pounds.

This statement is not true according to the given model equation, which only considers the number of tenants in the building, not the day of the week. Therefore, the amount of trash that needs to be disposed of does not increase by 20.3 pounds each day.

Therefore, the TWO given model statements that are true for the given model are A and D.

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The error found in the simplification of the expression is grouping of unlike terms and required equivalent expression for 6 - 2x + 5 + 4x is equal to 11 + 2x.

Expression is equals to ,

6 - 2x + 5 + 4x

His works are,

6-2x+5+4x

(6 - 2)x + (5 + 4 )x

4x + 9x

13x

Tyler's work is incorrect.

Error is need to group like terms.

He made a mistake when he combined the constants 6 and 5 without taking into account the terms with x.

The correct simplification should be,

6 - 2x + 5 + 4x

Collect like terms we have,

= (6 + 5) + (-2x + 4x)

= 11 + 2x

The final expression is 11 + 2x, not -13x as Tyler calculated.

To write an expression equivalent to 6 - 2x + 5 + 4x that only has two terms,

Combine the terms with x and the constant terms separately,

6 - 2x + 5 + 4x

= (6 + 5) + (-2x + 4x)

= 11 + 2x

An equivalent expression with only two terms would be,

11 + 2x

Therefore, the error in the expression is grouping of unlike terms and equivalent expression is 11 + 2x.

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The above question is incomplete, the complete question is:

Tyler is simplifying the expression 6 - 2x + 5 +4x.

Here is His work:

6-2x+5+4x

(6 - 2)x + (5 + 4 )x

4x + 9x

13x

A. Tyler's work is incorrect. Explain his error he made

B. Write an expression equivalent to 6 - 2x + 5 +4x That only has two terms.

The likelihood that there are 1 man and 2 girls are selected is approximately 0.4357. We can use the following formula for the chance of an occurrence to determine the probability that one male and two female candidates are chosen:

P(event) equals (number of possible outcomes for the event) / (total number of possible outcomes) Out of a total of 25 pupils, the programme is choosing 1 male and 2 female participants. 

Using the combination formula, we can first determine the overall number of events that are possible: nCr equals n and (r! * (n-r)!) where r is the number of students being chosen, and n is the overall number of students (25). (3). Therefore, there are a total of the following outcomes: 25C3 = 25! / (3! * (25-3)!) = 25! / (3! * 22!) = 2300

Next, we need to determine how many different methods there are to choose 1 guy and 2 females. Utilizing the product law of chance, we can accomplish this: The number of methods is equal to the sum of the ways to select one man and two females. 

There are 11 methods to choose one guy out of 11, and there are 91 ways to choose two females out of 14. The overall number of options for choosing one man and two females is thus: 11 * 91 = 1001

Finally, we can enter these numbers into the likelihood of the occurrence formula as follows: P(1 man, 2 women) = 1001/2300 = 0.4357

Consequently, the likelihood that there are 1 man and 2 girls are selected is approximately 0.4357.

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Purposive sampling allows nurse researchers to select participants who fit specific criteria in qualitative studies, increasing the depth and richness of findings.

A nurse researcher would use purposive sampling when obtaining participants for a qualitative study because it allows researchers to select participants who fit the very specific types of criteria that are investigated in qualitative studies.

Purposive sampling is a non-random sampling method that is used when researchers want to select a sample that has certain characteristics or experiences that are relevant to the research question.

By using purposive sampling, the researcher can ensure that the participants have the specific knowledge or experience that is necessary to answer the research question, and can therefore provide more in-depth and insightful responses. This increases the richness and depth of the qualitative findings.

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Answer:

P=20

Step-by-step explanation:

S=Ph+2B

96=4(P)+2(8)

96=4P+16

96-16=4P

80=4P

P=80/4

P=20

The location of the point W, the length of the altitude and the area of the triangle ΔXYZ are;

The coordinates of the point W is; (3.6, 5.8)

a) The altitude of the triangle is (12/5)·√5

b) The area of the triangle is 24 square units

The area of a triangle is the product of (1/2) × Base length × Height

The height of a triangle is the perpendicular distance from the base of the triangle to the vertex of the triangle, therefore;

The coordinates of the point W on the side XY, can be found from the coordinates of the points X and Y and the point Z as follows;

X(2, 5), Y(10, 9), and Z(6, 1)

The slope of the side XY = (9 - 5)/(10 - 2) = 4/8 = 1/2

The slope of the altitude is therefore; -2/1 = -2

The equation of XY is; y - 5 = (1/2)·(x -2)

y = x/2 - 2/2 + 5 = x/2 + 4

y = x/2 + 4

The equation of the altitude is; y - 1 = -2·(x - 6)

y = -2·x + 12 + 1

y = -2·x + 13

Therefore at W, we get;

x/2 + 4 = -2·x + 13

x = 18/5 = 3.6

y = -2 × (18/5) + 13 = 5.8

y = 5.8

The coordinate of the point W is (3.6, 5.8)

a. The altitude is therefore;

b. The area of the triangle, A = (1/2) × [tex]\overline{XY}[/tex] × [tex]\overline{ZW}[/tex]

Therefore; A = (1/2) × √((10 - 2)² + (9 - 5)²) × (12/5)·√5 = 24

Learn more on the area of a triangle here: https://brainly.com/question/17141566

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