we should expect 4 white horses among the next 20 horses that come to board. we can solve by equation .
what is equation ?
An equation is a mathematical statement that uses symbols and variables to show that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables, constants, and mathematical operations such as addition
In the given question,
Out of the 15 horses currently boarded, 3 are white. This means that the proportion of white horses among the currently boarded horses is:
3 / 15 = 0.2 or 20%
Therefore, if we assume that the next 20 horses that come to board will have a similar distribution of coat colors, we can expect approximately 20% of them to be white.
So, the expected number of white horses among the next 20 horses that come to board is:
20 x 0.2 = 4
Therefore, we should expect 4 white horses among the next 20 horses that come to board.
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Mia is designing a cake for a birthday party. She plans for a total of 20 guests, each of whom may eat a piece of cake that has a volume of 8 cubic inches. Which of the following cakes would provide enough cake for each guest to have one piece of cake, with the least amount left over?
The square cake can be distributed in such a way that each person out of 15 guest may get 8 , with the least amount left over .
The Correct option is (1).
What is Volume of any shape?
The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms ofof cubic units.
First find the volume of square cake,
Volume = l x b x h
= 8 x 8 x 2
=128
Now there are total 15 guests, Each of get
=
= 8.533
2.Volume of round cake (d= 6 inch, r=3 inch, h= 3 inch)
Volume=
=
=
=28.26
Now there are total 15 guests, Each of get
=
= 1.884
3.Volume of round cake (d= 8 inch, r=4inch, h= 3 inch)
Volume=
=
=
=50.24
Now there are total 15 guests, Each of get
=
= 3.349
4. Volume = l x b x h
= 6 x 9 x 2
=108
Now there are total 15 guests, Each of get
=
= 7.2
According to question each person may get 8 .
Only the square cake can be distributed in such a way that each person may get 8 , with the least amount left over .
Saloni computed in a two-way table the relative frequencies of boys and girls participation in school sports at her school which statement best describes the relationship between the two variables
The statement that best describes the relationship between the two variables is "There is an association because the relative frequencies by column are different, and the relative frequencies by row are also different." (option a).
To understand the relationship between these two variables, we need to analyze the frequencies by row and by column. The rows represent one variable (in this case, gender), and the columns represent the other variable (participation in school sports).
If we look at the relative frequencies by row, we see that the percentage of girls participating in school sports is higher in the fall (63%) than in the spring (43%), while for boys, the opposite is true. This indicates an association between gender and participation in school sports, as the relative frequencies vary by row.
Alternatively, if we look at the relative frequencies by column, we see that the percentage of boys participating in school sports is higher in the spring (57%) than in the fall (37%), while for girls, the opposite is true. This also indicates an association between gender and participation in school sports, as the relative frequencies vary by column.
Therefore, we can conclude that the best statement to describe the relationship between the two variables is option A: "There is an association because the relative frequencies by column are different, and the relative frequencies by row are also different."
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Complete Question:
Siloni computed in a two-way table the relative frequencies of boys’ and girls’ participation in school sports at her school.
School Sports Participation by Gender Fall Spring
Boys 37% 57%
Girls 63% 43%
Which statement best describes the relationship between the two variables?
a) There is an association because the relative frequencies by column are different.
b) There is an association because the relative frequencies by row are different.
c) There is no association because the relative frequencies by column are different.
d) There is no association because the relative frequencies by row are different.
Identify an equation in standard form for ellipse with its center at the origin, a vertex at (3, 0), and a focus at (1, 0). HELP ASAP! This is due in 15 minutes!!
Answer:
Step-by-step explanation:
The standard form equation for an ellipse with center at the origin is:
x^2/a^2 + y^2/b^2 = 1
where 'a' is the distance from the center to the vertices along the x-axis and 'b' is the distance from the center to the vertices along the y-axis.
In this case, the center is at the origin, and a vertex is at (3, 0). So, we know that 'a' = 3.
We also know that the distance from the center to the focus is 'c', and that:
c^2 = a^2 - b^2
Since the center is at the origin, 'c' is the distance from the focus (1, 0) to the origin, which is 1. So, we can solve for 'b' as:
c^2 = a^2 - b^2
1^2 = 3^2 - b^2
b^2 = 3^2 - 1^2
b^2 = 8
b = sqrt(8) = 2sqrt(2)
Substituting these values into the standard form equation, we get:
x^2/3^2 + y^2/(2sqrt(2))^2 = 1
Simplifying:
x^2/9 + y^2/8 = 1
So, the equation in standard form for the given ellipse is:
9x^2 + 8y^2 = 72
The figure on the right is a scaled copy of the figure on the left
Which side in the figure on the right corresponds to segment UV?
What is the scale factor
The side that corresponds to uv is LK
The scale factor is 3 : 1
How to solve for the scale factorTo solve for the scale factor between two geometric figures, follow these steps:
Identify corresponding sides or corresponding lengths between the two figures.
Choose one pair of corresponding sides and write a proportion using the lengths of those sides.
Solve for the scale factor by simplifying the proportion.
The shape in UV occupies the space of 6 boxes
The space in LK is made of 2 boxes
Hence we have 6 : 2
= 3 : 1
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What kind of geometric transformation is shown in the line of music?
•
reflection
translation
glide reflection
Answer:
translation
hope this helps:) !!
Find the distance between the zeros of the (2x-8)^2-4=12
The distance between the zeros of the equation [tex](2x-8)^{2}[/tex] - 4 = 12 is 4 units.
First, we can simplify the equation [tex](2x-8)^{2}[/tex] - 4 = 12 by adding 4 to both sides:
[tex](2x-8)^{2}[/tex] = 16
Next, we can take the square root of both sides:
2x-8 = ±4
Solving for x in each case, we get:
2x-8 = 4: 2x = 12 → x = 6
2x-8 = -4: 2x = 4 → x = 2
So the zeros of the equation are x=6 and x=2. The distance between them is:
distance = |6 - 2| = 4
As a result, there are 4 units between zeros of the equation [tex](2x-8)^{2}[/tex] - 4 = 12.
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[tex]y=2cos^{2}(x) , y=2e^{-x}+2x-2[/tex]
(a) Write an equation whose solutions are the points of intersection of the graphs.
(b) Use the intersect feature of the graphing utility to find the points of intersection (to four decimal places). (Enter the point of intersection whose x-coordinate is within the interval [0, 2). If there is no solution, enter NO SOLUTION.)
a. The equation whose solutions are the points of intersection of the graphs is y = -0.14x + 0.80.
b. The points of intersection are (-0.827, 0.918) and (0.951, 0.675).
The solution has been obtained using the slope - intercept form.
What is the slope - intercept form?
When you are aware of the slope of the line being investigated and the given point is also the y intercept, use the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is represented by the symbol b in the equation.
a. From the graph, we have two points of intersection.
Using this, we get the slope as;
m = -0.14
Now, using the slope intercept form, we get the intercept as
b = 0.80
So, the equation comes out to be
y = -0.14x + 0.80
b. The graph of the equations have been attached below.
From the graph, we get the points of intersection as (-0.827, 0.918) and (0.951, 0.675). Both the points have their x-coordinate within the interval [0, 2).
Hence, the required solutions have been obtained.
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need answer for this +explanation
______________________________
A = L × B × H = 2 × 2 × 5= 20in²______________________________
You are asked to advise Alpha Tire Co. on the feasibility of offering a 35,000-mile warranty on their tires. At this time Alpha Tire believes the mean time to failure is 40,000 miles
µ
with standard deviation of miles to failure at 3700 or
. If a free replacement warranty is offered, promising that the tires will last for at least 35,000 miles, what proportion of tires would qualify for the free replacement because they are expected to fail while they were still covered by the warranty? In light of your finding, what advice would you give to Alpha Tires about a warranty for a free tire replacement if the tires fail before 35,000.
Where the above conditions exist, the probability is that about 41.19% of tires woudl be eligible for free replacement.
Why is this so ?Using a standard normal distribution table or calculator, we can find the z scores corresponding to 35,000 miles and 40,000 miles...
z 1 = ( 35,000 - 40,000) / 3,700 = -1.35
z 2 = (40,000 - 40,000) / 3,700 = 0
Then, we can find the area between these z scores, which represents the proportion of tires that would fail before 40,000 miles and qualify for a free replacement:
P( -1.35 < Z < 0) = 0.4119 or 41.19%
What it means is that , about 41.19% of the tires would qualify for a free replacement.
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A prisms base is a hexagon of a side length 10 The height of the prism is 14 Find the volume of the prism
Answer: The volume of the prism is 4200 cubic units.
Explanation:
The volume of a prism is given by the formula V = Bh, where B is the area of the base and h is the height. For a hexagonal base with a side length of 10, we can divide it into six equilateral triangles with side lengths of 10. Each equilateral triangle has an area of (1/2)bh, where b is the base and h is the height. Since the base of each equilateral triangle is also 10, we have:
Area of one equilateral triangle = (1/2)(10)(10√3/2) = 50√3
Area of the hexagonal base = 6 times the area of one equilateral triangle = 6(50√3) = 300√3
Now we can use the formula for the volume of a prism:
V = Bh = (300√3)(14) = 4200 cubic units.
Therefore, the volume of the prism is 4200 cubic units.
Simplify. Simplify. Express your answer as a single term, without a denominator.
pls helpppppp
Simplifying further, you can move any negative exponents to the denominator by changing their sign:
t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)
what is denominator ?
In a fraction, the denominator is the bottom number that represents the total number of equal parts into which the whole is divided. For example, in the fraction 3/4, the denominator is 4, which indicates that the whole has been divided into four equal parts.
In the given question,
When multiplying two terms with the same base, you can add their exponents, so:
t⁻¹ u v⁴* t⁻¹ u⁻⁷ v⁰ = t⁻² u⁻⁶ v⁴
Simplifying further, you can move any negative exponents to the denominator by changing their sign:
t⁻² u⁻⁶ v⁴ = v⁴ / (t² u⁶)
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Please help me this is so hard. Please if you help i give you 60 points. This is really hard for me and i dont get this.
Answer:
The discriminant is:
(-3)^2 - 4(1)(18) = 9 - 72 = -63
Since this discriminant is negative, f(x) does not have any real number solutions.
Madison tossed a paper cup and records wether it lands on its side. In 20 trails the cup lands on its side 19 times. In 90 trials the cup lands on its side 81 times
Answer:90% probability
Step-by-step explanation:
To calculate the experimental probability of the cup landing on its side, we can use the formula:
experimental probability = number of times the cup landed on its side / total number of trials
For the first set of trials, the experimental probability is:
experimental probability = 19/20 = 0.95
For the second set of trials, the experimental probability is:
experimental probability = 81/90 = 0.9
So the experimental probability of the cup landing on its side for the first set of trials is higher than for the second set of trials. However, since the number of trials is relatively small, it is possible that this difference is due to chance and does not reflect a real difference in the probability of the cup landing on its side. To determine this with more confidence, we would need to conduct more trials and perform statistical tests to determine whether the difference is statistically significant.
Which one of the following examples represents a proper
fraction?
A. 15/22
B. 12/9
C. 3/2
O D. 8/8
A.15/22 is the correct answer.
The correct answer is:
A. 15/22, represents a proper fraction.
Here, we have,
A proper fraction is a fraction where the numerator (the top number) is smaller than the denominator (the bottom number).
Out of the given options, only option A,
15/22, represents a proper fraction because 15 is smaller than 22.
Therefore, the correct answer is:
A. 15/22, represents a proper fraction.
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Select all equations that have infinitely many solutions
Answer:
2 and 4
Step-by-step explanation:
1)
14x+6=2(5x+3)
14x+6=10x+6
No Solutions
2)
3(x-5)+6=x-(9-2x)
3x-9=3x-9
Infinitely Many
3)
2+5x-9=3x+2(x-7)
5x-7=5x-14
No Solutions
4)
3(4x-6)+2=-4(4-3x)
12x-16=12x-16
Infinitely Many
Find the area of the regular polygons and degree of central angle when given either the apothem or side length.
The length of the apothem is 10. 99cm
How to determine the valuesTo determine the apothem of a polygon, we have to use the formula;
a = s/2 tan (180/n)
Such that the parameters are;
a is the length of the apothem.s is the side length of the polygonn is the number of sides of the polygonNow, substitute the values, we have;
a = 8/2tan(180/9)
divide the values
a = 8/2tan 20
Find the values
a = 8/0. 7279
Divide the values
a = 10. 99cm
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Which scenario can be represented using the inequalities below?
1.25 < x < 1.5
A container of milk costs at least $1.25 but less than $1.50.
A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework.
A tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%.
The point value of a test item is more than 1.25 points and less than 1.5 points.
The scenario that can be represented by the inequalities 1.25 < x < 1.5 is: A. A container of milk costs at least $1.25 but less than $1.50
How to Represent a Scenario Using Inequalities?The inequality 1.25 < x < 1.5 represents a range of values between 1.25 and 1.5, where x falls within that range.
Option A, which states that a container of milk costs at least $1.25 but less than $1.50, fits this range.
Option B, which states that a student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework, does not fit this range, as it represents a range of time values and not a range of numerical values.
Option C, which states that a tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%, does not fit this range either, as it represents two separate ranges of values.
Option D, which states that the point value of a test item is more than 1.25 points and less than 1.5 points, fits this range as well.
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The coordinates of the midpoints of the four sides of a square are S(-4, 11), Q(2, 5), U(-4, -1), and A(-10, 5).
Determine the perimeter and area of the square.
5
O perimeter is 144 units; area is 48 square units
O perimeter is 48 units; area is 144 square units
O perimeter is 24√/2 units; area is 72 square units
O perimeter is 72 units; area is 24√/2 square units
The perimeter and area of the square are 24√2 units and 12 units² respectively
What is the perimeter and area of the square?
To determine the perimeter and area of the square, we have to find the lengths of the sides.
But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.
SQ = √(x₂ - x₁)² + (y₂ - y₁)²
SQ = √(2 - (-4)² + (5 - 11)²
SQ = 6√2
Let's find for QU
QU = √(-4 - 2)² + (-1 - 5)²
QU = 6√2
Let's find for UA ;
UA = √(-10 - (-4))² - (5 - (-1)²
UA = 6√2
And the distance from AS = 6√2
The perimeter of the square = 4 * (6√2)
Perimeter = 24√2 units
The area of the square is l²
Area of the square = (6√2)²
Area of square = 12 units²
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Prepare the journal entry to record Jevonte Company's issuance of 29,000 shares of its common stock assuming the shares have a
a. $3 par value and sell for $16 cash per share.
b. $3 stated value and sell for $16 cash per share.
View transaction list
Journal entry worksheet
<
2
Record the issuance of 29,000 shares of common stock assuming the shares
have a $3 par value and sell for $16 cash per share.
Note: Enter debits before credits.
Transaction
General Journal
Cash
Common stock, $3 par value
Paid-in capital in excess
Debit
Credit
The journal entry to record the transaction is given:
Account Debit Credit
Cash $464,000
Common Stock, $3 par value $87,000
Paid-in capital in excess of par $377,000
What is a journal entry?A journal entry is used to record a business transaction in the accounting records of a business.
A journal entry is usually recorded in the general ledger. Alternatively, it may be recorded in a subsidiary ledger that is then summarized and rolled forward into the general ledger
Assuming the shares have a $3 par value and sell for $16 cash per share:
Cash reeived from issuance of 29,000 common shares = 29,000 x $16 = $464,000
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Sketch the graph of the following function. Describe how
the graph can be obtained from the graph of the basic
exponential function ex.
f(x) = 2 (4-ex)
Use the graphing tool to graph the equation.
someone help pls, im not sure what to put in the little box for the vertical shift and vertical shrink
The vertical shift and vertical shrink of the exponential function are 2 and 1/2 respectively and the graph of the function is attached below
What is the graph of exponential function?A curve displaying an exponential function is known as an exponential graph. A curve with a horizontal asymptote and a rising or decreasing slope characterizes the graph of an exponential function. i.e., it begins as a horizontal line, grows or drops gradually, and then the growth or decay accelerates.
The vertical shift and vertical shrink of the function f(x) = 1/2(4 - eˣ) are 2 and 1/2
The vertical shift = 2
vertical shrink = 1/2
Kindly find the attached graph below
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A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a diamond
Answer: The odds against selecting a diamond are 3:1 (or 3/4)
Step-by-step explanation: Which means that there are 3 ways to not select a diamond and only 1 way to select a diamond. The odds in favor of selecting a diamond are 1:3 (or 1/4), which means that there is only 1 way to select a diamond and 3 ways to not select a diamond.
A coach left woodlands and travelled towards Muar at an average speed of 50 Km/h.
Half an hour later, a car left Woodlands, travelled along the same route, and reached
Muar at 12.30 p.m. The distance between the two places was 150 km. The coach reached
Muar at 1.00 p.m
a) At what time did the car leave Woodlands?
b) What was the average speed of the car?
Answer:
a) 10:30 a.m.
b) 75 km/h
Step-by-step explanation:
You want to know the leaving time and speed of a car from Woodlands to Muar if it left half an hour later and arrived half an hour earlier than a coach that traveled the 150 km distance at a speed of 50 km/h and arrived at 1 p.m..
Travel timeThe travel time of the coach is found from the relation ...
time = distance/speed
time = (150 km)/(50 km/h) = (150/50) h = 3 h
Then the coach left Woodlands at ...
1 pm -3 h = 10 am
a) Leaving timeThe car left half an hour later than the coach, so left at 10:30 a.m..
b) SpeedThe car arrived at Muar at 12:30 p.m. so had a travel time of ...
12:30 -10:30 = 2 h
The speed over the 150 km distance is given by ...
speed = distance/time
speed = (150 km)/(2 h) = (150/2) km/h = 75 km/h
The average speed of the car was 75 km/h.
__
Additional comment
The car passed the coach at 11:30 a.m., when both had covered half the distance.
find the extreme values of [tex]f(x,y) =x^{2} +y^2\\[/tex]
The function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.
What is a function?
A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.
The function f(x,y) = x² + y² represents the sum of the squares of the variables x and y. To find the extreme values of this function, we need to take the partial derivatives with respect to x and y and set them equal to zero.
∂f/∂x = 2x = 0
∂f/∂y = 2y = 0
From these equations, we can see that the critical point occurs at (x,y) = (0,0).
To determine whether this is the maximum or minimum, we can use the second partial derivative test. The second partial derivatives are:
∂²f/∂x² = 2
∂²f/∂y² = 2
∂²f/∂x∂y = 0
At (0,0), ∂²f/∂x² > 0 and ∂²f/∂y² > 0, so the critical point is a minimum.
Therefore, the function f(x,y) = x² + y² has a minimum value of 0 at the point (0,0) and has no maximum value.
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Help me pleaseeeee :(
I'm taking linear algebra right now so this one hits home :)
Elementary Row Operations (EROs) are very important and not too difficult, so let's dive into the problem!
You're given the matrix below and asked to perform a single ERO to produce a matrix with a 1 at the position (1,1):
[tex]\begin{bmatrix}3 & 10 & 5\\2 & -1 & 1\end{bmatrix}[/tex]
Think of the two rows as separate entities in the matrix. Ultimately we want to have the index (1,1) currently holding the number 3 to become the number 1. To do this, logically you just need to subtract 2. Now, looking at the rows we have, a simple row operation is quite apparent.
Simply subtract row 2 from row 1, shown below:
[tex]\begin{bmatrix}3-2 & 10-(-1) & 5-1\\2 & -1 & 1\end{bmatrix}[/tex]
Now, simplify and you will have the answer:
[tex]\begin{bmatrix}1 & 11 & 4\\2 & -1 & 1\end{bmatrix}[/tex]
Notice that our matrix now has the required number 1 in row 1 and column 1, therefore, the matrix above is our answer! Let me know if you have any questions!
The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 30 to 10 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is negative one third, which means that the swimmer completes a lap in one third of a minute.
The slope of the line is −3, which means that the swimmer will complete 3 laps every minute.
The slope of the line is 10, which means that the swimmer will finish the race after 10 minutes.
The slope of the line is 30, which means that the swimmer must complete 30 laps in the race.
The given slope of the graph is explaining about the swimmer's lap completion throughout the time of 10 minutes.
In the given graph on the x-axis, we can find the time (in minutes) of 10 minutes.
On the y-axis, the graph represents the number of laps the swimmer is completing.
When we observe closely, the slope is giving very important information. At initial time=0, the no. of laps remaining for swimmer is 30. We can show this data clearly as below:
Number of laps remaining----------Time (in minutes)
30 --- 0
27 --- 1
24 --- 2
21 --- 3
18 --- 4
15 --- 5
12 --- 6
9 --- 7
6 --- 8
3 --- 9
0 --- 10
From the above slope data, we can conclude that for every 1 minute of time elapsing, the swimmer is completing 3 laps.
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50 Points! Multiple choice algebra question. Which function represents exponential growth? Photo attached. Thank you!
The exponential growth model is represented by the function y = 10 · 3ˣ. (Correct choice: D)
What function is an exponential growth function?
In this problem we must determine what function does represent an exponential growth model. With this purpose, we must define and understand the following functions:
Exponential growth model
y = a · rˣ, for r > 1.
Exponential decay model
y = a · rˣ, for 0 < r < 1.
Polynomic model
y = ∑ cₙ · xⁿ
The function y = 10 · 3ˣ represents an exponential growth model.
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Which equation represents a line that passes through the point (−12, 6) and is perpendicular to the graph of the equation y = 34
x + 7?
A. y = 43
x + 18
B. y = 34
x + 15
C. y = −43
x − 10
D. y = −34
x − 3
Answer:
C
Step-by-step explanation:
If it is perpendicular to the line y = ¾x+7 then the gradient if the line must be the negative reciprocal of 3/4. The gradient must be - 4/3. So A, B and D are rejected. Left is C
Let's replace now.
For C,
Let's take y=-4/3x-10 into consideration at the point (-12,6)
Y should be equal to 6 when we replace x by -12
Let's try
Y = -4/3(-12) - 10 = 16 - 10 = 6
Yup. C is your answer.
A model rocket is launched with an initial upward velocity of 60 m/s the rocket's height h meters after t seconds h=60t-5t^2 find values for which rockets height is 30 meters
The model rocket will have a height of 30 meters at a time of 0.523 seconds and 11.477 seconds, respectively.
How to determine the time associated with the height of a rocket on air
In this problem we have the case of a model rocket being launched, the height of the rocket in time is described by the following quadratic equation:
h(t) = 60 · t - 5 · t²
Where:
h - Height, in meters.t - Time, in seconds.We need to determine the time associated to a given height of 30 meters above the ground. If we know that h(t) = 30, then the times are, respectively:
30 = 60 · t - 5 · t²
6 = 12 · t - t²
t² - 12 · t + 6 = 0
(t - 11.477) · (t - 0.523) = 0
t = 11.477 s. or t = 0.523 s.
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26 less than twice a number is 4. Find each number
Answer:
15
Step-by-step explanation:
Let's call the number we try to find "[tex]x[/tex]"
In the problem, we know that "26 is less than twice a number" is the same as "4". So we can write this as an equation:
[tex]2x - 26 = 4[/tex]
Now we can solve for x by isolating it on one side of the equation.
First, we isolate "2x" by flipping "-26" to the other side, which will now be "26".
[tex]2x = 4 + 26[/tex]
Then we add
[tex]2x = 30[/tex]
finally, we isolate the x by dividing each side with 2
2x ÷ 2 = 30 ÷ 2
x = 15
(a) In the figure below, two secants are drawn to a circle from exterior point H.
Suppose that HZ=16.8, HX-14, and HY=42. Find HW.
H
w
M
HW = 0
(b) In the figure below, two chords intersect inside the circle at point V.
Suppose that VJ-18, VM-36, and VK=27. Find MN.
MN = 0
Applying the intersecting secants and chords theorem, the indicated measures in the circle is: HW = 35 units; MN = 49.5 units.
How to Apply the Intersecting Secants and Chords Theorem?To find the measures indicated, we will apply the intersecting secants and chords theorem to form an equation, then solve.
a. HZ * HW = HX * HY [based on the intersecting secants theorem]
Plug in the values:
16.8 * HW = 14 * 42
HW = 588/16.8
HW = 35 units
b. VK * VJ = VM * VN [based on the intersecting chords theorem]
Plug in the values:
27 * 18 = 36 * VN
VN = 486/36
VN = 13.5 units
MN = VM + VN = 36 + 13.5
MN = 49.5 units
Learn more about the intersecting chords theorem on:
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