If P is the orthocenter of △ABC, AB = 13, BF = 9,and FC = 5.6, find each measure & the perimeter of triangle ABC.
Answer:
[tex]Perimeter = 38.6[/tex]
Step-by-step explanation:
Given
[tex]A\ B = 13[/tex]
[tex]B\ F = 9[/tex]
[tex]F\ C = 5.6[/tex]
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.
[tex]Perimeter = A B + B\ C + A\ C[/tex]
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:
[tex]B\ C^2 = B\ F^2 + F\ C^2[/tex]
Substitute values for BF and FC;
[tex]B\ C^2 = 9^2 + 5.6^2[/tex]
[tex]B\ C^2 = 81 + 31.36[/tex]
[tex]B\ C^2 = 112.36[/tex]
[tex]B\ C^2= \sqrt{112.36[/tex]
[tex]B\ C = 10.6[/tex]
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:
[tex]A\ B^2 = B\ F^2 + A\ F^2[/tex]
Substitute values for B F and A B;
[tex]13^2 = 9^2 + A\ F^2[/tex]
[tex]169= 81 + A\ F^2[/tex]
[tex]A\ F^2 = 169 - 81[/tex]
[tex]A\ F^2 = 88[/tex]
[tex]A\ F = \sqrt{88[/tex]
[tex]A\ F = 9.4[/tex]
Since F lies on line A C:
[tex]A\ C = A\ F + F\ C[/tex]
[tex]A\ C = 9.4 + 5.6[/tex]
[tex]A\ C = 15.0[/tex]
Recall that:
[tex]Perimeter = A\ B + B\ C + A\ C[/tex]
[tex]Perimeter = 13 + 10.6 + 15.0[/tex]
[tex]Perimeter = 38.6[/tex]
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:
[tex]BC = \sqrt{BF^2 + FC^2}[/tex]
Substitute[tex]BC = \sqrt{9^2 + 5.6^2}\\\\\mathbf{BC = 10.6}[/tex]
△BFA is a right triangle, apply Pythagorean theorem to find FA:
[tex]FA = \sqrt{AB^2 - BF^2}[/tex]
Substitute[tex]FA = \sqrt{13^2 - 9^2}\\\\\mathbf{FA = 9.4}[/tex]
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:
https://brainly.com/question/2515607
A license plate is to consist of digits followed by uppercase letters. Determine the number of different license plates possible if the first and second digits must beâ odd, and repetition is not permitted.A. 71, 610, 739, 200,000 B. 795, 674, 880,000 C. 7, 894, 720 D. 8, 840, 832,000
Answer:
D. 8, 840, 832,000
Step-by-step explanation:
The computation of the number of license plates possible is shown below:
Here the first position could be taken by any of the five odd numbers
The second position could be taken by any of the 4 odd numbers
The third position could be taken by the eight left numbers
The fourth position could be taken by another seven numbers
Als the first digit could be any of the 26 upper case letters and so on
So,
= 5 × 4 × 8 × 7 × 26 × 25 × 24 × 23 × 22
= 8,840,832,000
Therefore option D is correct
Which list shows the absolute values in order from least to greatest? Question 5 options: |−2.36|, |−5.98|, 6.1 0.2, |−0.3|, |0.1| |7.6|, 5.3, 1.3
Answer:
i dont know maybe you should search google. best of Luck
Step-by-step explanation:
PLEASE I NEED HELP ASAP
Answer:
mrs heershap
Step-by-step explanation:
Jay works at a sandwich shop. He needs to make 7 turkey sandwiches. Each sandwich will have 1/3 of a pound of turkey. How many pounds of turkey will Jay need to make the sandwiches? Remember what of means! And remember to press submit after you answer the question
Answer:
Jay will need 2 and 1/3 pounds of turkey.
Step-by-step explanation:
Since Jay uses 1/3 per sandwich and is making 7, multiply 7 by 1/3.
That gets you 7/3s
Convert it into a mixed number.
3 goes into 7 twice, with one third left over.
So, Jay needs 2 1/3.
hope this helped!
Answer:
approximately 2.3 pounds of turkey. Trust the BlueDragon
Step-by-step explanation:
7 times 1/3= 2.33333
Tom bought a new mirror for his house. One side of the mirror is 38 inches and the other side is 30 inches. What is the length of the diagonal of the mirror? a. 68 inches b. 23 inches c. 34 inches d. 48 inches
Answer:
d. 48 inches
Step-by-step explanation:
We assume the mirror is a rectangle
We solve for the length of a diagonal using Pythagoras Theorem
a² + b² = c²
c = √a² + b²
Where c = diagonal
a = 30 inches
b = 38 inches
c = √30² + 38²
c = √2344
c = 48.414873748 inches
Approximately = 48 inches
picture attached please help!
EASY QUESTION WILL GIVE BRAINLIEST!!!
Tyler has a baseball bat that weighs 28 ounces.
Find this weight in kilograms and in grams. (Note: 1 kilogram 35 ounces).
Make a table
riddle #2
I am a five digit even number.
all of my digits are factor of 24.
4/5 of my digits are even.
The digit in my thousands place equals the perimeter of a 2×2 array.
The digits in my ten thousand places is twice the value of the digits in the hundreds place, but half the value of the digits in the thousands places.
The digit in my tens places equal the number of lines of symmetry in an isosceles triangle.
Answer:
28416
Step-by-step explanation:
No digits can be repeated
"All my digits are factors of 24" This means that the possible digits are: 1, 2, 3, 4, 6, 8
"The digits in my thousands place equals the perimeter of a 2x2 array" That would be 8
"The digits in my ten thousand places is twice the value of the digits in the hundreds place, but half the value of the digits in the thousands place" That would be 4, which also means that the ten thousands place is 2
"The digits in my tens place equal the number of lines of symmetry in an isoceles triangle" There is only 1 lines of symmetry
This means that we have 2841(?)
Because this number is even and no digits can be repeated, the only possible digits from those available is 6
Therefore the number is 28416
John invest $5,000 in one account and $8,000 in an account paying 4% more in interest. He earned $1,230 in interest after one year. At what rates did he invest
Given:
John invest $5,000 in one account and $8,000 in an account paying 4% more in interest.
Total interest in one year = $1230
To find:
The rates of the investments.
Solution:
Let x% be the rate of interest on investment $5000.
Then, (x+4)% is the rate of interest on investment $8000.
Total interest is $1230. So,
[tex]5000\times \dfrac{x}{100}+8000\times \dfrac{x+4}{100}=1230[/tex]
[tex]50x+80(x+4)=1230[/tex]
[tex]50x+80x+320=1230[/tex]
[tex]130x=1230-320[/tex]
[tex]130x=910[/tex]
Divide both sides by 130.
[tex]x=\dfrac{910}{130}[/tex]
[tex]x=7[/tex]
Now,
[tex]x\%=7\%[/tex]
[tex](x+4)\%=(7+4)\%=11\%[/tex]
Therefore, $5,000 is invested at 7% and $8,000 is invested at 11%.
will mark brainlist
One number is 9 more than twice the other number. Their sum is 54. Find the numbers.
Please help me with this problem
(0.3d−1.5)/3 1/3 =0.84: 7/15
How is 2+ (2) similar to adding 2+2 how is different explain your answer
Answer:
2+2 is 4-1=3 quick maths
Step-by-step explanation:
Answer:
2+(2) is the same to adding 2+2 because the "(" " )" just mean the you have to add the 2 + 2 just like----- 2+2
Find three positive numbers whose sum is 100 and whose product is a maximum.
Answer:
The numbers are;
x = 100/3, y = 100/3, z = 100/3
Step-by-step explanation:
Given the data in the question;
so let the numbers be; x , y and z
so
x + y + z = 100
now
G(x,y,z) = x + y + z - 100
F(x,y,z) = xyz
Fx = yz, Gx = 1
Fy = xz, Gy = 1
Fz = xy, Gz = 1
Fx = λ × Gx
yz = λ
Similarly, xz = lambda
And xy = lambda
From above clearly, x = y = z
x + y + z = 100
so
3x = 100
x = 100/3
since, x = y = z therefore, each number is equal to 100/3
x = 100/3, y = 100/3, z = 100/3
We want to find 3 positive numbers such that their sum is 100 and the product is maximum.
The maximum product is P = 37,025.93
Let's say that our 3 numbers are:
A, B, and C.
We must have:
A + B + C = 100
The product of these 3 numbers is:
P = A*B*C
For the restriction, we can write:
A = 100 - B - C
Now we can replace that in the product equation to get:
P = (100 - B - C)*B*C
P = 100*B*C - C*B^2 - B*C^2
Now we want to maximize this, to do it, we need to find the zeros of the derivate of the function. This is a two-variable function, but the dependence on C is exactly the same as the dependence on B, so we can find the zero of deriving with respect to one of these only.
dP/dB = 100*C - 2*C*B - C^2 = 0
C*(100 - 2*B - C) = 0
One solution is C = 0, the other is:
C = 100 - 2*B
And from the first restroctopm:
A + B + C = 100
we can get:
C = 100 - A - B
Then:
100 - A - B = 100 - 2*B
Then we get A = B
And if we derive the equation for C instead of B, we will get similar results that will lead to:
A = B = C.
This is what maximizes the product, then we have:
A + B + C = 3*A = 100
A = 100/3 = 33.33
P = (33.33)^3 = 37,025.93
This is the maximum product.
If you want to learn more, you can read:
https://brainly.com/question/11212148
14. (01.04)
On the graph of the equation 3x + 2y = 18, what is the value of the y-intercept?
-9
-6
6
9
Answer:
6
Step-by-step explanation:
U divide 18 by 3.
Answer:
9
Step-by-step explanation:
In slope-intercept form of linear equation y = mx + b , value of "b" is y-intercept.
Let solve 3x + 2y = 18 for "y"
2y = - 3x + 18
y = [tex]-\frac{3}{2}[/tex] x + 9 ⇒ 9 is y-intercept.
===========
There is another way to solve this kind of problems:
Coordinates of y-intercept are (0, y) .
3(0) + 2y = 18
2y = 18
y = 9
(0, 9)
WILL GIVE BRAINLIEST! PLEASE ANSWER!
Answer:
You have the right answer ( y=4x )
Step-by-step explanation:
Hope this helped, Have a Great Day!!
Paul has $78 in the bank and saves $30 each week. What is the initial value? Be sure to use negative signs if needed.
Answer:
The initial value is $78
Step-by-step explanation:
Given
[tex]Base\ Amount = \$78[/tex]
[tex]Additional = \$30[/tex] (weekly)
Required
Determine the initial value
The initial value is the amount he has in its bank account before making his weekly savings.
From the question, we have that his initial balance is $78.
Hence, the initial value is $78
However, his weekly balance can be expressed as:
[tex]Balance = Base\ Amount + Additional * number\ of weeks[/tex]
Represent number of weeks with x; So, we have:
[tex]Balance = 78 + 30 * x[/tex]
[tex]Balance = 78 + 30 x[/tex]
Which of these figures shows parallel lines? Help please
Answer:
B a parrelel line means there not inerscting
Step-by-step explanation:
Here is five number cards
Answer:
Thank you
Step-by-step explanation:
write the slope-intercept form of the equation of the equation. PLEASE HELP. i will give brainliest.
Answer: Slope intercept form: y = mx + b
A. y = 4/7 x + 27/7
Screenshot attached.
Step-by-step explanation: Slope is m. In this example, it is 4/7. The y-intercept is b. in this example it is 2 in the question and 27/7 in the answer choice.
First clue why A is the answer: the slope must be the same if the lines are parallel
The average of 5 quiz grades is 10. When the lowest grade is dropped and the new average is calculated, it turns out to be 11. What was the score of the dropped grade?
Answer:
The score of the dropped grade is 6
Step-by-step explanation:
To find the average of a set of numbers you need to add all the numbers and divide by how many numbers there are. The problem wants you to solve it in reverse. Let put this into an algebraic equation with a, b, c, d, and e being the variables of the test scores
(a+b+c+d+e)/5=10
Then we can multiply both sides by 5 and get
a+b+c+d+e=50
Lets assume that c is the lowest test score. To calculate the average of that we get
a+b+d+e/4=11
Doing the same thing, we know that a+b+d+e=44
Now compare the two:
a+b+c+d+e=50
a+b+d+e=44
We can now know that c=50-44=6
So, 6 is the score of the dropped quiz. Hope that helped!
write a Pythagorean triplet whose smallest value is 14
Here is one: (14, 48, 50)
What is the area of a square with sides of length 9?
O A. 54 square units
B. 81 square units
O C. 18 square units
O D. 36 square units
SUE
Gina bought 4 bags of grapes that weighed 2.29 pounds each. The grapes were priced at $2.50 per pound. The expression below represents the total cost of the bags of grapes Gina bought, in dollars.
(2.29×2.50)×4
Which expression below is also equivalent to the total cost of the grapes?
( 2.29 + 4 ) × 2.50
4 × ( 2.50 + 2.29 )
( 2.29 × 4 ) + 2.50
2.29×(2.50×4)
Answer:
2.29 × (2.50 × 4) is equivalent.
Step-by-step explanation:
It doesn't matter what order multiplication happens in, it will result in the same answer!
Suppose that the age of all the U.S. first ladies when they married was recorded. The mean age of U.S. first ladies when they married would be a:________A) PopulationB) StatisticC) SampleD) Parameter
Answer:
B) Statistic
Step-by-step explanation:
The mean age of U.S. first ladies when they married would be a Statistic. This is because the mean age would be a specifically targeted value of the population that is being analyzed. In this scenario, the population would be all of the First Ladies, while the Sample would be the data gathered from the population under certain parameters. Statistics can be a variety of different values that revolve around the samples gathered such as average age, average height, max number of blue-eyed First Ladies, etc.
58 students on a bus how many students were fit on a six buses
Answer:
348
Step-by-step explanation:
Grace drew a triangle with sides of equal length. Its measured with sides of 3 cm. What is the perimeter of the triangle?
Answer:
9 cm explained to
Step-by-step explanation:
explained that
Crystal pushes a 20 kg box with a force of 40N. What is the box’s acceleration?
Answer:
2m/s
Step-by-step explanation:
Acceleration = force / mass
Acceleration = 40N / 20 kg
Acceleration = 2 m/s^2
A tree that is 10 feet tall casts a 20 foot shadow. What is the length of the shadow of a nearby 30 foot tall tree
Answer:
It should be 60 feet following the pattern!
It would cast a 60 foot shadow following the pattern but depending on how far the trees are apart the 30 foot tree could also cast a 40 foot shadow:)
Rudy has been paying an annual homeowners insurance premium of $1,106.30 ($0.37 per $100 of value) since
he first purchased his house. For the past six months, Rudy has completed some major improvements to his
house to improve its overall value. If Rudy successfully adds $50,000 to the value of his house, what will his new
annual homeowners insurance premium be?
a. $185.00
b. $315.00
c. $1,291.30
d. $1.351.14
Please select the best answer from the choices provided
Answer:
c. $1,291.30
Step-by-step explanation:
Calculation what will his new annual homeowners insurance premium be
Insurance premium= [$1,106.30+ ($0.37/ $100*$50,000)]
Insurance premium=$1,106.30+$185
Insurance premium=$1,291.30
Therefore what his new annual homeowners insurance premium will be is $1,291.30
Answer:
c
Step-by-step explanation:
edge 2021