If P is the orthocenter of △ABC, AB = 13, BF = 9,and FC = 5.6, find each measure & the perimeter of triangle ABC.
Answers
Answer:
\(Perimeter = 38.6\)
Step-by-step explanation:
Given
\(A\ B = 13\)
\(B\ F = 9\)
\(F\ C = 5.6\)
Required
Calculate the perimeter of A B C
To calculate the perimeter of A B C, we sum up the sides of the triangle
i.e.
\(Perimeter = A B + B\ C + A\ C\)
AB is given in the question already.
So, we need to calculate B F and F C
To solve for BF, we consider triangle B F C
Using Pythagoras Theorem, we have:
\(B\ C^2 = B\ F^2 + F\ C^2\)
Substitute values for BF and FC;
\(B\ C^2 = 9^2 + 5.6^2\)
\(B\ C^2 = 81 + 31.36\)
\(B\ C^2 = 112.36\)
\(B\ C^2= \sqrt{112.36\)
\(B\ C = 10.6\)
Next, we calculate A C.
To calculate A C, we need to calculate A F, considering triangle B F A
Using Pythagoras Theorem, we have:
\(A\ B^2 = B\ F^2 + A\ F^2\)
Substitute values for B F and A B;
\(13^2 = 9^2 + A\ F^2\)
\(169= 81 + A\ F^2\)
\(A\ F^2 = 169 - 81\)
\(A\ F^2 = 88\)
\(A\ F = \sqrt{88\)
\(A\ F = 9.4\)
Since F lies on line A C:
\(A\ C = A\ F + F\ C\)
\(A\ C = 9.4 + 5.6\)
\(A\ C = 15.0\)
Recall that:
\(Perimeter = A\ B + B\ C + A\ C\)
\(Perimeter = 13 + 10.6 + 15.0\)
\(Perimeter = 38.6\)
Hence, the perimeter is 38.6
Given that P is the orthocenter of triangle ABC, applying the properties of an orthocenter of a triangle and the Pythagorean Theorem, each measure and the perimeter of △ABC are:
AB = 13BC = 10.6AC = 15Perimeter = 38.6Recall:
An altitude is the line that connects the vertex of a triangle to the opposite side of which it is perpendicular to that side.Orthocenter is the point where all three altitudes intersect each other.Given that P is the orthocenter of triangle ABC, where,
AB = 13BF = 9FC = 5.6Perimeter of △ABC = AB + BC + AC
First, we need to find BC and AC.
△BFC is a right triangle, apply Pythagorean theorem to find BC:
\(BC = \sqrt{BF^2 + FC^2}\)
Substitute\(BC = \sqrt{9^2 + 5.6^2}\\\\\mathbf{BC = 10.6}\)
△BFA is a right triangle, apply Pythagorean theorem to find FA:
\(FA = \sqrt{AB^2 - BF^2}\)
Substitute\(FA = \sqrt{13^2 - 9^2}\\\\\mathbf{FA = 9.4}\)
AC = FA + FC
SubstituteAC = 9.4 + 5.6
AC = 15
Perimeter of △ABC = AB + BC + AC
SubstitutePerimeter of △ABC = 13 + 10.6 + 15
Perimeter of △ABC = 38.6 units
Therefore, given that P is the orthocenter of triangle ABC, applying the properties of an orthocenter of a triangle and the Pythagorean Theorem, each measure and the perimeter of △ABC are:
AB = 13BC = 10.6AC = 15Perimeter = 38.6Learn more here:
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Related Questions
PLEASEE HELP NOW!!!!!
Answers
Answer:
B
Step-by-step explanation:
when u, v are nonzero vectors, then span{u, v} contains the line through u and the origin, as well as the line through v and the origin.
Answers
The span of the two vectors is the set of all linear combinations of the two vectors. This means that any point on the line through u and the origin, as well as any point on the line through v and the origin, can be written as a linear combination of u and v.
1. Start by taking two non-zero vectors u and v.
2. The span of the two vectors is the set of all linear combinations of the two vectors, which means that any point on the line through u and the origin, as well as any point on the line through v and the origin, can be written as a linear combination of u and v.
3. Therefore, span{u, v} contains the line through u and the origin, as well as the line through v and the origin.
The span of two non-zero vectors u and v contains the line through u and the origin, as well as the line through v and the origin. Any point on these two lines can be written as a linear combination of u and v.
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what is the area of the figure?
Answers
Answer:
area = 62ft
Step-by-step explanation
so you section the polygon into a big rectangle and 2 small rectangles
the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft
the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft
now add the areas you got, 50+12 which is 62ft
hope this helps:)
Hagen rolls a six-sided number cube. the sides are numbered 1 through 6. all sides are equally likely to be rolled.
Answers
Answer:
Step-by-step explanation:
what is it ?
Answer:1/6
Step-by-step explanation: for a clear picture, zoom in on it
answers? Not sure!!!
Answers
Answer:
\(-\frac{8}{45}\)
Step-by-step explanation:
Multiply the numerator by the reciprocal of the denominator.
4/5( −2/9)
Sets Sets M and Fare defined as follows: M = {a,b,c,d} F = {c, d, e, f} Find the intersection of M and F.
Answers
The intersection of sets M and F contains the elements "c" and "d".
To find the intersection of sets M and F, we need to identify the elements that are common to both sets.
M = {a, b, c, d}
F = {c, d, e, f}
The intersection of M
and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.
Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".
Therefore, the intersection of M and F can be expressed as:
M ∩ F = {c, d}
So, the intersection of sets M and F contains the elements "c" and "d".
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What transformation that will change the orientation of a figure but not the orientation of the vertices?
Answers
Answer:
Step-by-step explanation:
A transformation that changes the orientation of a figure but not the orientation of the vertices is called a "reflection."
A reflection is a transformation that flips a figure over a line, called the "line of reflection." The line of reflection can be a line on a coordinate plane, or it can be a line in the space of the figure. The transformed figure, or the image, is a mirror image of the original figure, with respect to the line of reflection. The line of reflection is the perpendicular bisector of the line connecting any two non-adjacent vertices of the figure, then the figure's orientation remains unchanged but it's flipped over that line.
For example, if you reflect a square over its diagonal line, the square will be flipped but its vertices will still be in the same order, so the orientation won't change.
Your laptop died and you need a new one for work NOW! The one you need will cost $500. You do not have the cash in your checking account, so you decide to borrow the money from your savings account. You have $9,000 in your savings account gaining 3% interest per year. If you don't replace the $500 in the savings account, how long will it take before the balance again reaches $9,000?
Answers
Answer:
2 years
Step-by-step explanation:
If you have $9000 in the saving account, and you take $500, you are left with:
$9000 - $500 = $8500
in one year you will have 3% more of the 8500 which is:
8500/100*3 = $255
so in one year the number on your savings account is:
8500 + 255 = $8755
and by the next year you will have 3% more of the 8755 which is:
8755/100*3 = $262.65
so in two years the number on your savings account is:
8755 + 262.65 = $9017.65
which is a little bit more than the $9000.
so it will take 2 years until the calance again reaches $9000
Please mark braniliest if this reaches 2 answers because I want to get to Expert ;w;
I need help with this math
Answers
Answer:
500 and 4.3
Step-by-step explanation:
A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.
5000 × 0.1 = 500
4300 × 0.001 = 4.3
Thus, the answers [in order] are 500 and 4.3
Hope this helps and feel free to ask any questions.
f(x)=(x-1)(x-2)(x-3)(x-4)(x-3)(x-2)(x-2)/[(x-2)(x-4)(x-2)]
Answers
Answer:
Step-by-step explanation:
(x-2)(x-2)(x-4)
solve each rational equation. list excluded values
x+4/x+5=6/x^2+10+25
Answers
x+4/x+5=6/x^2+10x+25
We will begin by first finding the LCD (Least Common Denominator) which is:
(x+5)(x+5)= (x+5)^2
Multiplying both sides of the equation by the LCD, we get:
(x+4)(x+5)(x+5) = 6(x+5)^2
Expanding both sides of the equation and simplifying further, we get:
x^3 + 14x^2 + 61x + 80 =0
Now, we can use the rational root theorem to identify the possible rational roots of the polynomial equation. The possible rational roots are:
±1, ±2, ±4, ±5, ±8, ±10, ±20, ±40, ±80
Testing these rational roots, we get that x = -4 is a root of the polynomial. Using synthetic division, we can then factor the polynomial as:
(x+4)(x^2 + 10x + 20) = 0
This gives us the solutions:
x = -4, x = -5 + 3sqrt(2)i and x = -5 - 3sqrt(2)i
Therefore, the excluded values are x = -5 and x = -5 ± sqrt(2)i.
At a grocery store, you want to buy 2/12 Ib of cheese. What decimal should the digital scale show?
Answers
Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form
Answers
The expression that represents this inequality must relate both temperatures, then it would look like this: -40°F < x < 140°F.
How to write this situation with an inequality?To express this situation in an inequality we must include the temperature values. Additionally, we must include the greater than (>) or less than (<) symbols to relate the values.
According to the above, the expression would look like this:
-40°F < x < 140°FNote: This question is incomplete because some information is missing. Here is the information:
A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F.
Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form.
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The perimeter and area of a rectangle are 22 cm
and 30 cm² respectively. Find the length and
breadth of the rectangle
Answers
The perimeter and area of a rectangle are (5,6) and (6,5).
The perimeter method for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width. when you are given the size of a square form, you may simply plug within the values of L and W into the formula that allows you to clear up for the fringe.
A perimeter is a closed course that encompasses, surrounds, or outlines either a two-dimensional shape or a one-dimensional period. The perimeter of a circle or an ellipse is known as its circumference. Calculating the perimeter has several practical programs.
The perimeter P of a rectangle is given by means of the method, P=2l+2w, in which l is the period and w is the width of the rectangle. The place A of a rectangle is given with the aid of the components, A=lw, wherein l is the length and w is the width.
The perimeter of the rectangle:
P=2l+2w=22
divide 2 into both sides
l+w=11 -------------> (1)
w=11-l
Area of the rectangle:
l*w=30
l(11-l)=30
11l-l^2-30=0
l^2-11l+30=0
By factor method,
(l-5)(l-6)=0
l=5,6.
Substitute this value in w,
l=5 implies w=6
l=6 implies w=5
There we have two solutions.
The length and breadth of the rectangle is
(5,6) and (6,5).
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.
Five more than the product of a number and 8 equals 9.
Use the variable b for the unknown number.
Answers
The unknown number, represented by the variable b, is 1/2, which satisfies the equation "Five more than the product of a number and 8 equals 9."
To solve the equation "Five more than the product of a number and 8 equals 9" using the variable b for the unknown number, we can express this statement as an equation:
8b + 5 = 9
To solve for b, we need to isolate the variable on one side of the equation. Let's simplify the equation step by step:
Subtract 5 from both sides to get rid of the constant term:
8b + 5 - 5 = 9 - 5
8b = 4
Divide both sides of the equation by 8 to solve for b:
8b/8 = 4/8
b = 1/2
Therefore, the solution to the equation is b = 1/2. This means that when we substitute b = 1/2 into the equation, the equation will hold true:
8(1/2) + 5 = 9
4 + 5 = 9
Both sides of the equation are equal, confirming that b = 1/2 is the solution.
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• describe how to use bundled things to explain regrouping in the subtraction problem 231-67. Make math drawings to aid your explanation.
Answers
The information regarding the addition is explained below.
How to explain the additionAdding 29 + 46:
Student 1: May use the traditional column addition method, lining up the digits in the ones, tens, and hundreds place and carrying over if necessary.
Student 2: May use the breaking apart method, where they break apart the numbers into smaller parts (e.g. 20 + 40) and then add the pieces together.
Student 3: May use a number line, counting up from 29 by the increments of 46 until they reach the sum.
Subtracting 54 - 28:
Student 4: May use the traditional column subtraction method, lining up the digits in the ones, tens, and hundreds place and borrowing if necessary.
Using bundled things to explain regrouping in the addition problem 167 + 59:
First, separate the numbers into bundles of ten.
Next, show how you can regroup the ones as ten ones to make a bundle of ten.
Then add the tens and hundreds place to get the answer 226.
Using bundled things to explain regrouping in the subtraction problem 231 - 67:
First, separate the numbers into bundles of ten.
Next, show how you can regroup the tens as ten tens to make a bundle of a hundred.
Then subtract the hundreds place and the tens place to get the answer 164.
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What an equation that represents the line.
Answers
Answer: The answer is y = 2x + 2
Which of the following are remote interior angles of Z5? Check all that apply.
Answers
Answer:
e
Step-by-step explanation:
Answer:
B and C
Step-by-step explanation:
The answer is Angle 1 and Angle 2.
Customers at a certain pharmacy spend an average of $54.40, with a standard deviation of $13.50.What are the largest and smallest amounts spent by the middle 50% of these customers?
Answers
Answer:
Largest is \(x_2 = \$ 63.506\)
Smallest is \(x_1 = \$ 45.29\)
Step-by-step explanation:
From the question we are told that
The mean is \(\mu = \$ 54.40\)
The standard deviation is \(\sigma = \$ 13.50\)
The largest and the smallest amount spent by 50% of the costumer is mathematically represented as
\(P(x_1 < X < x_2) = P(\frac{ x_1 -\mu}{\sigma } < \frac{X - \mu }{ \sigma } < \frac{ x_2 -\mu}{\sigma } ) = 0.50\)
=> \(P(x_1 < X < x_2 ) = P(\frac{x_1 - 54.40}{ 13.50} < X < \frac{x_2 - 54.40}{ 13.50} ) = 0.50\)
Given that this is normally distributed we have that
\(P(X <- \frac{x_1 - 54.40}{ 13.50} ) = 0.25\)
and
\(P(X < \frac{x_2 - 54.40}{ 13.50} ) = 0.25\)
From the normal distribution curve that z-score having a probability of 0.25 is
0.6745
So
\(\frac{x_1 - 54.40}{ 13.50} = -0.6745\)
=> \(x_1 = \$ 45.29\)
and
\(\frac{x_2 - 54.40}{ 13.50} = 0.6745\)
=> \(x_2 = \$ 63.506\)
The total cost after tax to repair Deborah’s computer is represented by 0.08(50h)+50h, where h represents the number of hours it takes to repair Deborah’s computer. What part of the expression represents the amount of tax Deborah has to pay? Explain.
Answers
The part of the expression for the amount of Tax Deborah has to pay is 0.08(50h)
What is tax?A tax is a compulsory financial charge or some other type of levy imposed on a taxpayer (an individual or legal entity) by a governmental organization.
Tax is charged on the total cost of a particular good or service, at a pre-determined rate called the rate of tax.
In the question, we are informed that the total cost after tax to repair Deborah's computer is represented by 0.08 (50h) +50h, where h represents the number of hours it takes to repair Deborah's computer.
We know that the total cost = Tax + Fixed Cost,
where tax = tax rate x fixed cost.
Hence, the total cost function can be written as:
Total cost = Tax Rate(Fixed cost) + Fixed Cost.
Comparing the given expression of the total cost, 0.08(50h) + 50h, with this expression, 0.08(50h) represents the tax part, where 0.08 is the tax rate and 50h is the fixed cost.
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how can you find the area and perimeter?
Answers
After answering the presented questiοn, we can cοnclude that The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape
What is equatiοn?An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.
The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape. Here are sοme cοmmοn fοrmulas:
1. Rectangle:
• Area: A = length x width
• Perimeter: P = 2(length + width)
2. Square:
• Area: A = side x side (οr A = side²)
• Perimeter: P = 4 x side
3. Circle:
• Area: A = π x radius²
• Circumference (perimeter): C = 2π x radius (οr C = π x diameter)
4. Triangle:
• Area: A = (base x height) / 2
• Perimeter: P = side1 + side2 + side3
5. Trapezοid:
• Area: A = ((base1 + base2) x height) / 2
• Perimeter: P = side1 + side2 + side3 + side4
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Fred did 600 J of work in 60 seconds. Calculate his power.
O
A. 600 W
B. 100 N
C. 500 N
OD. 10 W
Answers
Answer:
To calculate Fred's power, we can use the formula:
Power = Work / Time
Given that Fred did 600 J of work in 60 seconds, we can substitute the values into the formula:
Power = 600 J / 60 s
Power = 10 W
Therefore, the correct answer is:
D. 10 W
Step-by-step explanation:
Answer:
Power = Work/Time
Power = 600 J/60 s = 10 W
Therefore, the answer is D. 10 W.
Step-by-step explanation:
pls help, basic algebra problem with guidance
Answers
Answer:
x = 43000/9 or 4777.7 (i'm not 100% sure on this, so i apologize if i'm incorrect)
Step-by-step explanation:
The equation you were given was:
amount of solution • rate of concentration = amount of pure acid
By looking at the question, you can conclude that the amount of solution being used is 18%. You need to turn that into a decimal, therefore it'd be 0.18.
You can also conclude that the amount of pure acid being used is 860 milliliters. So, from this, you're able to fill in 2 parts of the equation:
0.18 • x = 860 mL
Now, all there's left to do is solve for x! To do this ,you'll need to rearrange the multiplication problem into a division problem.
860 / 0.18 = x
x = 43000/9 or 4777.7
pls answer need help
Answers
Answer:
7m
Step-by-step explanation:
7m is monomial
Hope it helps you in your learning process
HELP ME PLZ!!!!! ..................................
Answers
Step-by-step explanation:
the the number on the top corner is adding zeros so 6.3 / 10/3 the answer is for that 6.30
2. 904
3. 9040
4. 90400
5. 904000
Joe is holding his kite string 3 feet above the ground, as shown in the
accompanying diagram. The distance between his hand and a point directly under
the kite is 95 feet. If the angle of elevation to the kite is 50°, find the height, h,
of his kite, to the nearest foot.
Answers
Explanation:
Let the distance the kite and a point directly under the kite be ‘d’.
tan = opposite/adjacent
tan(50) = d/95
tan(50) x 95 = d
d ≈ 113.2 ft
h = d + 3 = 113.2 + 3 = 116.2 ft
HELP PLEASE
will mark brainliest
Answers
Explanation: :b
Find the product of 2.7 and 3.59.
Answers
Answer:
9.693 hope this helps!!!
the fraction below represents two factions of the same whole. How much of the 5/6 is in the 1/3?
A.2/5
B.1/2
C.5/9
D.6/9
Answers
Subject: Creative Writing Number of words: 550 Number of sources: 0 Formatting style: APA Short story: Imagine and get in the head of one of your ancestors, and tell their story in a 2-page double-spaced paper. You might imagine the story of one of your ancestor’s adventures or what it was like for them to live through a particular time, or make a particular decision. Remember that although the story should be rooted in reality (i.e., even if it didn’t, it could have happened), the story is fictional, and you can take artistic liberty. You may use any of the following to inspire your story: ● A scar ● A ghost ● An era ● A photograph ● A fear of _______ ● A personality trait or temperament
Answers
Title: Echoes of Legacy
In the depths of history, my ancestor Emma stepped forward with a photograph in her hands. The image revealed a scar on her cheek, a reminder of her resilience.
Title: Echoes of the Past
I had always been fascinated by the old family photograph that hung on the wall. It depicted a man with rugged features, a scar running across his weathered face, and a distant look in his eyes. That man was my ancestor, Samuel McAllister, and it was time for me to step into his world and uncover the mysteries that lay within.
As I closed my eyes, the world around me faded away, and I found myself transported to the 19th century. It was a time of great turmoil, an era defined by the echoes of war and whispers of change. Samuel, a resilient and courageous man, had ventured into the unknown, leaving behind a life of familiarity to seek adventure and fortune in the American West.
Samuel's journey took him through vast landscapes, from bustling cities to untamed frontiers. He encountered characters as diverse as the land itself, from cowboys to Native Americans. Each encounter left an indelible mark on his spirit, shaping him into a man of empathy and understanding.
One evening, as Samuel set up camp beneath a star-studded sky, a ghostly presence appeared before him. It was a specter, translucent and ethereal, silently beckoning him to follow. Filled with curiosity and a sense of foreboding, Samuel pursued the apparition through moonlit forests and winding canyons.
The ghost led him to a hidden cave, its walls adorned with ancient symbols and forgotten tales. In that sacred space, Samuel discovered a hidden treasure—a trove of knowledge passed down through generations. He realized that he had stumbled upon a portal to the past, a bridge connecting him to his ancestors and their wisdom.
Armed with newfound insight, Samuel returned to civilization, but his journey was far from over. He faced personal demons and fears, wrestling with his own identity and the weight of responsibility. Yet, through it all, he carried the spirit of his ancestors within him, drawing strength from their stories and the legacy they left behind.
Samuel's adventures were not without hardship. He witnessed the brutality of war, experienced heartbreak, and confronted his own mortality. But in those moments of adversity, he discovered resilience and compassion, traits that defined his character.
The scar on his face became a symbol of his resilience—a reminder of the battles fought, both physical and emotional. It served as a testament to the scars we all carry, visible or hidden, and the strength that lies within us to overcome adversity.
As I opened my eyes, I realized that I had lived through Samuel's experiences, even if only in my imagination. Through his story, I had unearthed a deeper connection to my roots, understanding the sacrifices and triumphs that shaped my family's legacy.
Samuel's journey continues to resonate within me, a reminder of the importance of embracing our past, exploring our fears, and celebrating the extraordinary within the ordinary. His story lives on, echoing through the corridors of time, inspiring future generations to embark on their own quests of self-discovery and adventure.
Word Count: 546 words
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