Answers
At centroid medians bisect each other in the ratio 2:1
[tex]\\ \sf\longmapsto OC=2(OD)[/tex]
[tex]\\ \sf\longmapsto 2(3x-2)=5x[/tex]
[tex]\\ \sf\longmapsto 6x-4=5x[/tex]
[tex]\\ \sf\longmapsto 6x-5x=4[/tex]
[tex]\\ \sf\longmapsto x=4[/tex]
The value of x is 4, when we are given O is the centroid of the triangle ABC, OD = 3x - 2, and OC = 5x.
What is the centroid of a triangle?The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians connect. The junction of all three medians is another definition for it. The median is a line that connects the middle of a side to the triangle's opposite vertex. The median is divided by the centroid of the triangle in a ratio of 2:1.
How to solve the question?In the question, we are given that O is the centroid of triangle ABC, and are asked to find the value of x, for which OD = 3x - 2, and OC = 5x.
We know that the median is divided by the centroid of the triangle in a ratio of 2:1.
Thus, the median CD is divided by the ratio of 2:1 as,
2/1 = OC/OD,
or, 2/1 = (5x)/(3x - 2),
or, 2(3x - 2) = 1(5x) {Cross-multiplying},
or, 6x - 4 = 5x,
or, 6x - 5x = 4,
or, x = 4.
Thus, the value of x is 4, when we are given O is the centroid of the triangle ABC, OD = 3x - 2, and OC = 5x.
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Related Questions
(20 points) please help
Answers
Answer: The antonym of multiply is divide.
Answer:
Divide
Step-by-step explanation:
Antonym simply means the opposite of the given word.
So the opposite of multiplication is division thus division is the answer.
HOPE THIS HELPED
plsss asap right nooooow
Answers
Answer:
[tex]\sf 2(3\sqrt{8}+4\sqrt{20}+2\sqrt{24})[/tex]
[tex]\sf 2(3\sqrt{8})+2(4\sqrt{20}+2\sqrt{24})[/tex]
[tex]\sf 12 \sqrt{2}+16 \sqrt{5}+8 \sqrt{6}[/tex]
[tex]\sf 6 \cdot 8^{\frac{1}{2}}+8 \cdot 20^{\frac{1}{2}}+4 \cdot 24^{\frac{1}{2}}[/tex]
[tex]\sf 12 \cdot 2^{\frac{1}{2}}+16 \cdot 5^{\frac{1}{2}}+8 \cdot 6^{\frac{1}{2}}[/tex]
Step-by-step explanation:
Perimeter of a rectangle
Perimeter = 2(width + length)
Given information:
[tex]\textsf{width} = 3\sqrt{8}[/tex]
[tex]\textsf{length} = 4\sqrt{20}+2\sqrt{24}[/tex]
Equivalent Expression 1
Substitute the given information into the formula:
[tex]\sf Perimeter = 2(3\sqrt{8}+4\sqrt{20}+2\sqrt{24})[/tex]
Equivalent Expression 2
Using the distributive property law, this can also be written as:
[tex]\sf Perimeter = 2(3\sqrt{8})+2(4\sqrt{20}+2\sqrt{24})[/tex]
Equivalent Expression 3
Distribute the parentheses and simplify the radicals:
[tex]\begin{aligned}\sf Perimeter & = \sf 2(3\sqrt{8}+4\sqrt{20}+2\sqrt{24})\\& = \sf 6\sqrt{8}+8\sqrt{20}+4\sqrt{24}\\& = \sf 6\sqrt{4 \cdot 2}+8\sqrt{4 \cdot 5}+4\sqrt{4 \cdot 6}\\& = \sf 6\sqrt{4}\sqrt{2}+8\sqrt{4}\sqrt{5}+4\sqrt{4}\sqrt{6}\\& = \sf 6 \cdot 2 \sqrt{2}+8 \cdot 2 \sqrt{5}+4 \cdot 2 \sqrt{6}\\& = \sf 12 \sqrt{2}+16 \sqrt{5}+8 \sqrt{6}\end{aligned}[/tex]
Equivalent Expression 4
Distribute the parentheses and rewrite the square roots as [tex]\sf \sqrt{a}=a^{\frac{1}{2}}[/tex] :
[tex]\begin{aligned}\sf Perimeter & = \sf 2(3\sqrt{8}+4\sqrt{20}+2\sqrt{24})\\& = \sf 6\sqrt{8}+8\sqrt{20}+4\sqrt{24}\\ & = \sf 6 \cdot 8^{\frac{1}{2}}+8 \cdot 20^{\frac{1}{2}}+4 \cdot 24^{\frac{1}{2}}\end{aligned}[/tex]
Equivalent Expression 5
Rewrite the square roots as [tex]\sf \sqrt{a}=a^{\frac{1}{2}}[/tex] :
[tex]\sf Perimeter=12 \cdot 2^{\frac{1}{2}}+16 \cdot 5^{\frac{1}{2}}+8 \cdot 6^{\frac{1}{2}}[/tex]
Which of the following relations represents a function?
{ (-2, 1), (0, 5), (1, -3), (-2, 0)}
{ (-3, 1), (1, 4), (-2, 1), (0, 3)}
{(-1, 3) (-2, 3) (-1, 5) (-2, 5)}
{ (4, 2), (4, 3), (4, 5), (4, 7)}
Answers
Answer:
Option A because functions only point to 1 output.
Combine like terms and write the simplified
Answers
Answer:
4x-3 16t-4
Step-by-step explanation:
Answer:
1. 8x-4x=4x
5-2=3
so the answer will be
4x+3
2.9t-7t+12-8=2t+4.
3.i have no idea
4. 18x^2+12x^2+16x-11x-17+19=30x^2+5x-36.
The sum of ∠1,∠2 and ∠3 is _____________ sum of ∠3,∠4 and ∠5
Greater than
Lesser than
Equal to
Twice the
Answers
Answer:
twice the
Step-by-step explanation:
hope it helps you
Compare with >, < 12.6 and 12.3
Answers
Answer:
12.6>12.3
Step-by-step explanation:
What is the midpoint of the segment that joins the points (-12, 12) and (-6, -1)?
Answers
Answer:
[tex]\boxed {\boxed {\sf ( -9, \frac{11}{2}) }}[/tex]
Step-by-step explanation:
We are asked to find the midpoint of a segment. We essentially calculate the average of the x-coordinates and the y-coordinates using the following formula.
[tex]( \frac {x_1+x_2}{2}, \frac{ y_1 + y_2}{2})[/tex]
In this formula, (x₁ , y₁) and (x₂ , y₂) are the endpoints of the segment. For this problem, the 2 endpoints are (-12, 12) and (-6, -1). If we match the variable and the corresponding value, we see that:
x₁= -12 y₁= 12 x₂ = -6 y₂ = -1Substitute the values into the formula.
[tex]( \frac{-12 + -6}{2}, \frac{12 + -1} {2} )[/tex]
Solve the numerators.
-12 + -6 = -12 -6 = -18 12 + -1 = 12-1 = 11[tex]( \frac{-18}{2}, \frac{11}{2})[/tex]
Divide.
[tex]( -9, \frac{11}{2} )[/tex]
The midpoint of the segment is [tex]\bold {( -9, \frac{11}{2} )}[/tex].
38. Evaluate f (3x +4y)dx + (2x --3y)dy where C, a circle of radius two with center at the origin of the xy
C plane, is traversed in the positive sense.
please i need real time help
Answers
It looks like the integral is
[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy[/tex]
where C is the circle of radius 2 centered at the origin.
You can compute the line integral directly by parameterizing C. Let x = 2 cos(t ) and y = 2 sin(t ), with 0 ≤ t ≤ 2π. Then
[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \int_0^{2\pi} \left((3x(t)+4y(t))\dfrac{\mathrm dx}{\mathrm dt} + (2x(t)-3y(t))\frac{\mathrm dy}{\mathrm dt}\right)\,\mathrm dt \\\\ = \int_0^{2\pi} \big((6\cos(t)+8\sin(t))(-2\sin(t)) + (4\cos(t)-6\sin(t))(2\cos(t))\big)\,\mathrm dt \\\\ = \int_0^{2\pi} (12\cos^2(t)-12\sin^2(t)-24\cos(t)\sin(t)-4)\,\mathrm dt \\\\ = 4 \int_0^{2\pi} (3\cos(2t)-3\sin(2t)-1)\,\mathrm dt = \boxed{-8\pi}[/tex]
Another way to do this is by applying Green's theorem. The integrand doesn't have any singularities on C nor in the region bounded by C, so
[tex]\displaystyle \int_C (3x+4y)\,\mathrm dx + (2x-3y)\,\mathrm dy = \iint_D\frac{\partial(2x-3y)}{\partial x}-\frac{\partial(3x+4y)}{\partial y}\,\mathrm dx\,\mathrm dy = -2\iint_D\mathrm dx\,\mathrm dy[/tex]
where D is the interior of C, i.e. the disk with radius 2 centered at the origin. But this integral is simply -2 times the area of the disk, so we get the same result: [tex]-2\times \pi\times2^2 = -8\pi[/tex].
PLS HELPPPPPPPPPppppppp
Answers
H,A and S
H,D and S
Y, D and T
All correct
P, H and A not lie on the same line (not collinear)
1. Find the value of x in the figure.
(1 point)
40°
O 40°
O 50°
O 140°
O 180°
Answers
Answer:
the value of x = 40
I hope it's helps you
Answer:
[tex]x = 40 \\ \\ [/tex]
it's vertical angel they are equal each other ( = )
Mrs. Harris treated her 1st period with donuts for averaging the highest on the midterm exam. She bought 25 donuts, By the end of the period, there were 3 donuts remaining. What is the percent decrease?
Answers
Answer:
join me on no comments yet the story is about to the turf and a bagane and pinni geting step by step explanation friendship is not working properly and the story of a y I have a mantra and sister about your self and the story of the story is a bagane unda and the story and the portion of the story of the story of the story is about the event of a y you know if
one leg of a right triangle is 42 inches longer than the other leg, and the hypotenuse is 78 inches. find the lengths of the legs of the triangle
Answers
Answer:
use phythagoras formula of calculating right angles
a^2=b^2+c^2
42^2=b^2+78^2 (substitution + transposement)
b^2=72^2-42^2
b^2=3420 (introduce a square root both sides)
what you do on the left .you also do it on the right
b is the unknown side of the triangle
b=58.48 inched
The lengths of the legs of the right angle triangle is 30 inches and 72 inches.
What is a triangle?A triangle is a closed plane figure formed by joining three noncolinear points.
We know Pythagoras's theorem which states the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
Given one leg of a right-angle triangle is 42 inches longer than the other leg.
Assuming the smallest leg to be x inches.
∴ The other leg is (x + 42) inches also given hypotenuse is 78 inches.
∴ (x + 42)² + x² = 78².
x² + 84x + 1764 + x² = 6084.
2x² + 84x - 4320 = 0.
x² + 42x - 2160 = 0.
As length can not be negative value of x = 30 inches.
∴ The smaller leg is 30 inches and the larger leg is (30 + 42) = 72 inches.
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I need to know the distance between points x and y
Answers
Answer:
Step-by-step explanation:
Distance between two points P(x1,y1) and Q(x2,y2) is given by: d(P, Q) = √ (x2 − x1)2 + (y2 − y1)2 {Distance formula} 2. Distance of a point P(x, y) from the origin is given by d(0,P) = √ x2 + y2.
The product of 2 more than 5 times a number and 4 less than three times a number
Answers
Sorry I'm not sure if I'm right just my thinking...
set the number to be x so that (5x+2)(3x-4)??
Convert 15° to seconds.
(Remember, 1 degree = 60 minutes, 1 minute = 60 seconds)
Answers
Answer:
15 degree = 54,000 seconds
Step-by-step explanation:
15*60*60
which choice is equivalent to the expression below? √40 + 2√10 + √90
Answers
Answer:
2√10 + 2√10 + 3√10 =7√10
Step-by-step explanation:
√40=√10×4 =√10×√4 = 2√10
√90= √10×9 = √10×√9 =3√10
Find the equation of the parabola that has a vertex at (2,0) and a y-intercept of (0,12).
Question 19 options:
A)
y = 3(x + 2)2
B)
y = (x – 2)2
C)
y = (x + 2)2
D)
y = 3(x – 2)2
Answers
Answer:
D
Step-by-step explanation:
standard form would be 3x^2-12x+12
vertex form y=3(x-2)^2
Answer:
y = 3(x + 2)2
Step-by-step explanation:
phương trình vi phân tuyến tính cấp 1: xy' - 2y = 2x^4
Answers
Answer:
.........................
Step-by-step explanation:
............................................................................
Manuela bought 11/12 yard of polka dot fabric and 7/9 yard of flowered fabric which fabric did she buy more of
Answers
Answer:
She bought more polka dot fabric
Step-by-step explanation:
you can cross multiply so 9x11=99 and 12x7=84. Since 99>84, 11/12>7/9
If Y=x-5 and 20y -5y=15 what is the value of X?
Answers
Answer:
X=6
Step-by-step explanation:
20 × 1 or y = 20
5 × 1 or y = 5
20 - 5 = 15
1 or y + 5 = 6
A music store sold 103 CDs and 102 CD players. If each CD costs $12
and each CD player costs $35, what was the store's total earnings?
$15,500
© $36,200
$24,500
0 $47.000
Answers
Answer:
$15,500
Step-by-step explanation:
It would help if you put the actual question in place
10³ CDs = 1000 at $12 each = $12000
+ 10² Players = 100 at $35 each = $ 3500
Total $15500
103(12) + 102(35) = $4806
Find the HCF of the following by long divosiin method 102,68,136
Answers
Answer:
102=2*3*17
68=2*2*17
136=2*2*2*2*17
The common prime factors are 2 and 17
Highest common factor (HCF)=2*17=34
Hope it helps you.For 68: 1, 2, 4, 17, 34, and 68
For 136: 1, 2, 4 , 8, 17, 34, 68, and 136.
So my answer I think is: 68
Find the domain of the function. (Enter your answer using interval notation.) f(x) = 1 /(x2 + 3x − 4)
Answers
Step-by-step explanation:
The domain of a function is the range of x such that the function is defined.
Now we know the function
[tex]f(x) = \frac{1}{ {x}^{2} + 3x - 4 }[/tex]
is only defined when the denominator is not zero, in other words, when
[tex] {x}^{2} +3x - 4 \neq \: 0[/tex]
or
[tex](x + 4)(x - 1) \neq0[/tex]
[tex]x \ne-4 [/tex]
and
[tex]x \neq +1[/tex]
1/(x^2+3x-4)
1/(x+4)(x-1)
{x|x≠1,-4}
Answer:
(negative infinity, -4) U (-4,1) U (1, infinity)
Suppose you write each letter of the alphabet on a different slip of paper and put the slips into a hat. What is the probability of drawing one slip of paper from the hat at random and getting a vowel?
Answers
Answer:
5/26 chance because there is only five vowels in the alphabet
Answer:
Not counting y as a vowel: 5/26 or a 19.23% chance
Step-by-step explanation:
There are a total of 26 letters in the alphabet.
There are 5 vowels (a, e, i, o, u)
Picking a vowel has a 5 in 26 chance of occurring.
how many numbers of four different digits can be formed from the integers 0,2,4,5,6.
Answers
Answer:
420 even numbers
Step-by-step explanation:
Answer
Total 4 digit even numbers = (Total even numbers) - (Total 3 digit even numbers)
Total even numbers: 4⋅6⋅5⋅4=480
Total 3-digit even numbers: 3⋅5⋅4⋅1=60
Total 4-digit even numbers: 480−60=420 ??
Step-by-step explanation:
If m ABC=25 and m CBD= 35 then m ABD=
Answers
Answer:
Angle ABD = 60
Step-by-step explanation:
Angle ABD = angle ABC + angle CBD
We are given that angle ABC = 25 and angle CBD = 35
So angle ABD = 25 + 35 = 60
Answer:
60
Step-by-step explanation:
to find the length of the entire angle, you will have to add both seperated sides to find it.
<ABC = 25
<CBD = 35
25 + 35 = 60
So, <ABD = 60
Hope this helped.
a farmer enough to last his 40 cattle for 35 days'if he bays more cattle how long can the same food last?consider the cattle finish the feed at the same rate
Answers
Answer:
this is unclear
Step-by-step explanation:
yoy miss typed
Find the value of x 3(4x+3)
Answers
3(4x+3)=12x+9
i don't know what do you need,
if roots, let 12x+9=0
the root is x=-3/4
Enter the equation of the following using line in slope-intercept form. slope = 3; y-intercept is -3
Answers
Answer:
y=3x-3
Step-by-step explanation:
slope intercept form is y=mx+b
you are given m as 3 and b as -3
so substitute
y=3x-3
Sam opened a restaurant. On the first day he had 100 customers. On the fourth day he had 160 customers. If the number of customers per day grew linearly, what was the number of customers on the second day?
Answers
Answer:
120 customers on the 2nd day
Step-by-step explanation:
100/1ST DAY
120/2nd day
140/3rd day
160/ 4TH DAY