Answers
Answer:
centroid (2, 2.666666666...)
circumcenter (2, 1.75)
orthocenter (2, 2.5)
Step-by-step explanation:
the coordinates of the centroid of a triangle are
((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)
so, we have
(-4 + 2 + 8)/3 = 6/3 = 2 = x
(0 + 8 + 0)/3 = 8/3 = y = 2.666666666...
the circumcenter is the crossing point of the lines going perpendicular through the midpoint of each side.
the orthocenter is the crossing point of the lines going perpendicular on each side through the opposing vertices (the heights of the triangle).
so, we need to calculate additionally the slopes of 2 sides and their midpoints before we can get these 2 centers. the third side would only confirm the result but not provide additional information.
A = (-4, 0), B = (2, 8), C = (8, 0)
midpoint D of AC = ((-4 + 8)/2, (0+0)/2) = (2, 0)
the slope of AC is
(y2 - y1)/(x2 - x1) = (0 - 0)/(8 - -4) = 0/12 = 0 (a flat line)
the slope of the perpendicular line is -1/slope of original line. which is -1/0 = -infinity.
but don't worry, that means it is a constant line x = ...
and since it has to go through the midpoint D, the perpendicular line is x = 2
midpoint E of BC = ((2+8)/2, (8+0)/2) = (5, 4)
the slope of BC is
(0-8)/(8-2) = -8/6 = -4/3
so, the slope of the perpendicular line is 3/4.
that line is then y = 3/4 x + b
it has to go through the midpoint E
4 = 3/4 × 5 + b = 15/4 + b
16 = 15 + 4b
4b = 1
b = 1/4
so, the full perpendicular line is
y = 3/4 x + 1/4
crossing both perpendicular lines is simply using the first in the second equation :
y = 3/4 × 2 + 1/4 = 6/4 + 1/4 = 7/4 = 1.75
for the orthocenter we can use the same slopes, but the lines go now through the opposing vertices instead through the side midpoints.
so, line 1 is going through B, which makes it also x = 2.
line 2 is going through A, so
0 = 3/4 × -4 + b
0 = -1 + b
b = 1
line 2 is then
y = 3/4 x + 1
crossing these 2 lines gives us
y = 3/4 × 2 + 1 = 6/4 + 4/4 = 10/4 = 5/2 = 2.5
Related Questions
Given f() = -4x + 3, find f(-3)
Answers
Answer:
The answer is 15
Step-by-step explanation:
f(x) = -4x + 3, f(-3)
f(-3) = -4x + 3
f(-3) = -4(-3) + 3
f(-3) = 12 + 3
f(-3) = 15
Thus, The answer is 15
Answer:
f(-3)=-4(-3)+3
=12+3=15
Step-by-step explanation:replace x with -3
how do I get the average of two numbers when one has more than the other
Answers
Answer:
[tex]\large\ The \ average \ of \ two \ numbers\ =\frac{\text{the sum of the two numbers} }{2}[/tex]
Step-by-step explanation:
[tex]\large\ The \ average \ of \ two \ numbers\ =\frac{\text{the sum of the two numbers} }{2}[/tex]
Let x and y be two numbers then the average of x and y is :
[tex]\large \frac{x+y}{2}[/tex]
Example :
The average of 4 and 16 is :
[tex]\frac{4+16}{2} = \frac{20}{2} = 10[/tex]
solve the following
Answers
Step-by-step explanation:
1.
so 90 km on 17 liters.
that is a 90/17 ratio (or proportion).
that means it runs 90/17 km on 1 liter.
and therefore (90/17)×20 on 20 liters.
90×20/17 = 105.8823529... km
2.
the ratio is 66/22 based on the RPMs.
66/22 = 3/1 = 3
so, the larger gear has then 3×6 = 18 teeth.
3.
the ratio is 150/75 based on the RPMs.
the circumference of a circle is
2×pi×r
so, it is a linear relationship with the radius r (and therefore the diameter d).
so, the diameter of the larger pulley is 2×10 = 20 in
4.
the ratio here is 18/6.
18/6 = 3/1 = 3.
again, this relates to the circumference, which is a linear relationship with the radius or diameter.
the smaller gear has then 72/3 = 24 teeth.
5.
the ratio is 2/3.
so, the larger pulley has 3450×2/3 RPM.
= 2,300 RPM
6.
2.5 kg cost 110.
that is a 2.5/110 ratio :
and that means we get 2.5/110 kg for one unit of money.
and therefore we get 80 × 2.5/110 kg for 80 units of money.
80 × 2.5/110 = 8 × 2.5/11 = 20/11 = 1.818181818... kg
The perimeter of a rectangular painting is 298 centimeters. If the length of the painting is 94 centimeters, what is its width?
Answers
Step-by-step explanation:
Length = 94 cm
breadth = ?
Perimeter = 298 cm
Now..............
Perimeter = 2 ( l + b )
298cm = 2 ( 94 cm + b )
298 / 2 = 94 + b
149 cm = 94 + b
b = 149 - 94 cm
b = 55 cm
Answer:
Value of it's width is 55 cm .Step-by-step explanation:
In the question we have given perimeter of rectangular painting that is 298 cm , length of the painting is 94 cm , and we have asked to find the width of the rectangular painting . So perimeter of rectangle is ,
[tex] \purple{ \boxed{Perimeter \: of \: rectangle = 2 ( l + w ) }}[/tex]
Where ,
l = length of rectanglew = width of rectangleNow , we are substituting value of length and equating it with given perimeter :
[tex] \longrightarrow \: 2(94 + w) = 298[/tex]
Now, our last step is of calculations . So from here we are calculating ,
[tex] \longrightarrow \: 94 + w = \frac{298}{2} [/tex]
[tex] \longrightarrow \: 94 + w= 149[/tex]
[tex] \longrightarrow \: w = 149 - 94[/tex]
[tex] \longrightarrow \: \blue{\boxed{ \bold{w = 55 \:cm}}}[/tex]
Therefore, width of rectangular painting is 55 cm .#Keep LearningEmily threw a ball up in the air from her tree house. It followed the path given by the parabola y equals short dash 2 x squared plus 14 x plus 60, where x is the distance from the tree house (in feet), and y is the height of the ball (in feet). At what distance from the tree house did the ball strike the ground?
Answers
The distance from the tree house that the ball strike the ground is 10feet
Equation of a parabolaGiven the path of the ball expressed by the parabola equation:
y = -2x^2+14x +60
The point where the ball strikes the ground is the point where y = 0. Substitute into the equation to have:
-2x^2+14x +60 = 0
x^2 - 7x - 30 = 0
Factorize the result
x^2 - 10x + 3x - 30 = 0
x(x-10)+3(x-10) = 0
x - 10 =0
x = 10
Hence the distance from the tree house that the ball strike the ground is 10feet
Learn more on function here: https://brainly.com/question/25638609
If alpha and beta are the zeros of the polynomial 2x2+5x+k, find k such that (alpha)2+(beta)2+(alpha)*(beta)=24
Answers
Answer:
k = -35.5
Step-by-step explanation:
When α and β are zeros of the polynomial 2x² +5x +k, it can be written in factored form as ...
2x² +5x +k = 2(x -α)(x -β)
When the factored form is expanded, it becomes ...
= 2x² -2(α+β)x +2αβ
Comparing this to the original, we see that ...
5 = -2(α+β)k = 2αβ__
Then the given expression can be used to find k:
α +β = -5/2 . . . . . solved the first relation for α+β
(α +β)² = (α² +β² +αβ) +αβ = 24 +αβ
(-5/2)² = 24 +αβ . . . . . . . use -5/2 for α+β
αβ = 25/4 -24 = -17.75 . . . . . solve for αβ
Then the value of k is ...
k = 2αβ = 2(-17.75)
k = -35.5
A rectangular lot is 80 yards wide and 125 yards long.
Give the length and width of another rectangular lot that has the same perimeter but a smaller area.
Answers
Answer:
70 yards wide and 135 yards long
Step-by-step explanation:
The perimeter of a rectangle will be the same if the sum of length and width is the same. The area will be smaller if the difference between lenth and width is greater.
__
The sum of length and width will be the same if the length is increased by the same amount that the width is decreased. Changing each by 10 yards is one possibility.
A lot 70 yards wide and 135 yards long will have the same perimeter and a smaller area.
_____
Check
Given perimeter: 2(80 +125) = 410 yds.
Modified perimeter: 2(70 +135) = 410 yds. (same)
Given area = 80(125) = 10000 yd².
Modified area: 70(135) = 9450 yd². (smaller)
__
Additional comment
The area is greatest when the difference between the length and width is zero. That is, the rectangle will be a square.
how is 12 x √3/2 = 6√3 ?
Answers
[tex]12x\sqrt{\cfrac{3}{2}}~~ = ~~6\sqrt{3}\implies (6)(2)x\cdot \cfrac{\sqrt{3}}{\sqrt{2}}~~ = ~~6\sqrt{3}\implies \cfrac{(2x)(6\sqrt{3})}{\sqrt{2}}=6\sqrt{3} \\\\\\ \cfrac{2x}{\sqrt{2}}=\cfrac{6\sqrt{3}}{6\sqrt{3}}\implies \cfrac{2x}{\sqrt{2}}=1\implies 2x=\sqrt{2}\implies x=\cfrac{\sqrt{2}}{2}[/tex]
Write a polynomial with zeros 0,-3, and 2 with multiplicities 2,1, and 2, respectively. What is its degree?
Answers
Polynomial is an expression that consists of indeterminates(variable) and coefficients. The degree of the polynomial will be 5.
What are polynomials?
Polynomial is an expression that consists of indeterminates(variable) and coefficients, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
The polynomial with zeros 0,-3, and 2 with multiplicities 2,1, and 2, respectively, can be written as,
[tex](x-0)^2(x+3)^1(x-2)^2\\\\= x^2(x+3)(x^2+4-4x)\\\\=(x^3+3x^2)(x^2+4-4x)\\\\=x^5 +4x^3-4x^4+3x^4+12x^2-12x^3\\\\=x^5 -x^4-8x^3+12x^2\\[/tex]
Hence, the degree of the polynomial will be 5.
Learn more about Polynomial:
https://brainly.com/question/17822016
#SPJ1
In a new video game, Franky had -16 1/2 points. He was able to earn 3/4 of the points he lost back. How many points did he have?
Answers
Answer:
slightly confused on the wording if he got back 3/4 from 16.5 then he earned back 12.375 points
if -16.5 is the 1/4 he didnt get back then he had 66 points
Step-by-step explanation:
find the measure of x,y and z in the figure
Answers
Answer:
y=45°
x=75°
z=60°
Step-by-step explanation:
hard to explain, but I'll try my best. on a single line, it equals 180 when both angles are added up. and the opposite side of an angle is always the same.
Select the correct answer.
A regular octagon has side lengths of 8 centimeters. What is the approximate area
he octagon?
OA. 618 cm2
OB. 512 cm2
OC 309 cm2
OD
473 cm2
Reset
Next
Answers
Answer:
C. 309 cm2
Step-by-step explanation:
A=2(1+sqr2)a^2
A=2(1+sqr2)8^2
≈309.01934
Answer: 309 cm2
Step-by-step explanation:
plato
During which time period was the ANNUAL rate of increase of the speed the GREATEST?
A) from year 1 to year 2
B) from year 1 to year 3
C) from year 1 to year 4
D) from year 1 to year 5
Answers
Answer:
A) year 1 to year 2
Step-by-step explanation:
The increases in speed are found by subtracting the speed from the year before.
1 to 2: 46 -38 = 8
2 to 3: 52 -46 = 6
3 to 4: 57 -52 = 5
4 to 5: 61 -57 = 4
The greatest increase was from year 1 to year 2.
9×(x+7)+5=86.can you help me to solve this question.
Answers
Answer: x=2
Step-by-step explanation:
9(x+7)+5=86
Step 1: Simplify both sides of the equation.
9(x+7)+5=86
(9)(x)+(9)(7)+5 (Distribute)
9x+63+5=86
(9x)+(63+5)=86 (Combine Like Terms)
9x+68=86
Step 2: Subtract 68 from both sides.
9x+68−68=86−68
9x=18
Step 3: Divide both sides by 9.
[tex]\frac{9x}{9} =\frac{18}{9}[/tex]
x=2
Find the unknown sizes of angles the given figure .
Answers
Answer:
a=96
b=42
c=138
Step-by-step explanation:
as lines BA and BC are equal, angles BAC and BCA are also equal, so b = 42. Now a can be found by 180 - 42 - 42 as sum of angles in a triangle is 180. The line AC is a straight line, so b + c = 180 , so c = 180 - 42 = 138
Acme Movers charges $45 plus $40 per hour to move household goods across town. Hank's Movers charges $55 per hour. For what lengths of time does it cost less to hire Hank's Movers?
Answers
The time when Hank's Movers will cost less is the point when the total charges is both Movers are Equal, the time is at 3 hours
Word ProblemGiven Data
Acme Movers charges $45Plus $40 per hour Hank's Movers charges $55 per hourLet x be the time takenFor Acme, the expression for the total charges is
Total = 45+40x ----------1
For Hank, the expression for the total charges is
Total = 55x ----------------2
Equating both expressions we have
45+40x = 55x
collect like terms
45 = 55x-40x
45 = 15x
divide both sides by 15
x = 45/15
x = 3 hours
Learn more about algebra here:
https://brainly.com/question/22399890
Write the algebraic expression that represents the phrase “the quotient of a number and 4?”
Answers
Answer:
x/4
Step-by-step explanation:
solve the right triangle (all sides and angles) please help!!!
Answers
please help me Find m
Answers
Answer:
60 degree is the value of m
CAN SOMEONE PLSSSSS ANSWER BOTH OF THESE QUESTIONS
I WILL MARK BRAINLIEST
Answers
Answer: B and C
Step-by-step explanation:
404 + 50 + 50 = 504
you are buying 144 magazines total
504/144 = cost of one magazine
cost of one = 3.50
you are paying $60 a year for 12 years
60 x 12 = 720
720/144 = 5
5 - 3.50 = 1.50
2.
120x + 180x = 1080
300x = 1080
x = 1080/300
x = 3.6
3.6 x 60 = 216
Help my sister please she needs help I don’t know because I forgot
Answers
Answer:
15 shrimps
Step-by-step explanation:
We already know that a small shrimp taco has 5 shrimps.
⇒ [tex]\text{1st equation: small shrimp taco = 5 shrimps}[/tex]
We also know that a large taco has 3 times more shrimps than a small taco.
⇒ [tex]\text{2nd equation: shrimps in a large taco = 3(Shrimps in a small taco)}[/tex]
Finding the number of shrimps in a large taco:
Now, simply substitute the number of shrimps in a small shrimp taco in the second equation to find the number of shrimps in a large taco.
⇒ [tex]\text{Shrimps in a large taco = 3(5) shrimps}[/tex]⇒ [tex]\boxed{\bold{\text{Shrimps in a large taco = 15 shrimps}}}[/tex]Answer:
15 shrimp
Step-by-step explanation:
5 shrimp * 3 = 15shrimp
Susie has a rectangular dining room that has an area of 84. What is the area of the largest circular rug Susie can fit in her dining room?
Answers
Answer:
25[tex]\pi[/tex]
Step-by-step explanation:
[tex]\pi[/tex]r^2 is the formula for a circle (in this case, a circular rug)
and we would set it equal to 84 (since we are trying to get the biggest size possible).
We would isolate r so that r^2 = 84/[tex]\pi[/tex], and r would be around 5.17219.
If we were going by rounding 5 would be the largest radius possible and the radius would be 25[tex]\pi[/tex] or about 78.5398 units.
Answer:
Rounded to one decimal place, the maximum area circular rug that can fit in the dining room is 38.5 square feet.
Please See the attached screenshot for the exact solutions and answer for this question
You deposit $5000 in an account earning 2% interest compounded continuously. How much will you
have in the account in 10 years?
$
Answers
Step-by-step explanation:
Answer:
\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149
Step-by-step explanation:
Standard equation of a circle: \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2
(where (a, b) is the center and r is the radius of the circle)
Substitute the given center (-14, -5) into the equation:
40 POINTS!! Douglas is placing strings of lights around the edge of a circular patio with a diameter of 7.5 meters. The lights are in lengths of 1.45 meters. What is the best approximation for how many strings of lights Douglas needs? Use 3.14 to approximate for π.
5 strings
11 strings
17 strings
122 strings
Answers
Answer:
17
Step-by-step explanation:
...................
x − 6 = -4 what is the solution
Answers
Step-by-step explanation:
[tex]x - 6 = - 4 \\ \\ \implies \: x = - 4 + 6 \\ \\ \implies \: x = 2[/tex]
Answer:
2
Step-by-step explanation:
because if you substitute 2-6 you will get negative 4
PLEASE HELP PLEASE PLEASE HELP
Answers
Answer:
The brightest star in the night sky is Sirius, located 500,000 times further away than the sun. Sirius is also 20 times brighter than the sun, which is why it is so easy to see at night. Our sun is a medium star of average size and brightness.
The cost of sending an overnight package from Kansas City to Miami is $23.50 for a package weighing up to but not
including 1 pound, and $3.80 for each additional pound or portion of a pound. A model for the total cost C in dollars) of
sending the package is C = 23.50 + 3.80Lx), x > 0, where x is the weight (in pounds).
What is the meaning of the coefficient 3.80 in the context of the problem?
O When the package weighs less than one pound, the price of the package is $3.80.
O For every pound that the package weight increases, the price of sending it increases by $3.80.
O For every pound that the package weight increases, the price of sending it increases by $23.50.
When the package weighs less than one pound, the price of the package is $23.50.
Answers
Answer:
For every pound that the package weight increases, the price of sending it increases by $3.80
Step-by-step explanation:
Overnight from KC to Miami = $23.50 for anything less than a pound + $3.80 per additional pound.
This means that for every pound that the package weight increases, the price of sending it increases by $3.80.
sebuah Mobil memerlukan Benson sebanyak 45 liter until menempuh jarak 480 km, jika Mobil tersebut menempuh jarak 320 km, maka banyak bensin Yang diperlukan adalah...
jelaskan ya..
Answers
Answer:
what??? I can't understand you sorry
solve for x ~
[tex]4x - 16 = 64[/tex]
ty ^^
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve for x ~
[tex]\qquad \sf \dashrightarrow \:4x - 16 = 64[/tex]
[tex]\qquad \sf \dashrightarrow \:4(x - 4) = 64[/tex]
[tex]\qquad \sf \dashrightarrow \:(x - 4) = 64 \div 4[/tex]
[tex]\qquad \sf \dashrightarrow \:x - 4 = 16[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 16 + 4[/tex]
[tex]\qquad \sf \dashrightarrow \:x =20[/tex]
[tex] \boxed{ \bf \huge \: Answer \: }[/tex]
[tex] \: \: [/tex]
[tex] \sf \large \: 4x - 16 = 64[/tex]
[tex] \: \: [/tex]
[tex] \sf \large \: 4x = 64 + 16[/tex]
[tex] \: \: [/tex]
[tex] \sf \large \: 4x = 40[/tex]
[tex] \: [/tex]
[tex] \sf \large \: x = \cancel \frac{80}{4} [/tex]
[tex] \: \: [/tex]
[tex] \sf \large x = 20[/tex]
[tex] \: \: [/tex]
Hope It's Helps uh Miss<3"
please help me answer this question.. no links
Answers
Answer:
The answer is 28 Units
It's number 3.
