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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please solve thank you
Answer:
(0, 1 )
Step-by-step explanation:
The y- intercept is where the line crosses the y- axis
On the y- axis the x- coordinate of any point is zero
From the table when x = 0 , y = 1
Then y- intercept is (0, 1 )
Help me with math please really need it
Answer:
Not too sure about this one, but I hope this helps.
Step-by-step explanation:
basically I just used the formula y=mx+b
m is the slope
and b is the y intercept
Round off 731 and 164 to the nearest tens.find The difference of the rounded off numbers.round off the difference to the nearest hundred
Answer:
731 and 164 rounded off to the nearest tens is 730 and 160.
the difference is 570
570. rounded off to the nearest hundred is 600
P- 24000 R-10% T-2 years find the sum
Answer:
here
I =p×t×r/100
= 24000×2×10/100
= 4800
again,
sum = p+I
= 24000+4800
= 28800
Translate the sentence into an equation.
The sum of 5 times a number and 6 is equal to 7
What is Matilda's number?
Answer:
11
Step-by-step explanation:
The answer will be 11
as she is thinking of prime number so
111 is not a prime number
aswell as 77 is not a prime number
11 is a prime number and is also a multiple of 11
Answer:
11
Step-by-step explanation:
Going into the final exam, which will count as two tests, has test scores of 77 , 82, 72 , 63 and 92 What score does need on the final in order to have an average score of 80?
Answer:
you either need to score a perfect on one exam and get a 80 on the second or get two 90s on both exams.
Step-by-step explanation:
Plz help me with this
9514 1404 393
Answer:
see attached
Step-by-step explanation:
a) A table and graph are attached.
__
b) The relationship is NOT PROPORTIONAL. The line does not go through the origin (0, 0).
the newspaper reported that on the "big board," where 1.24 billion shares were traded, 1,366 stocks fell and 1,788 rose. On the NASDAQ, where 1.76 billion shares were traded, 1,587 fell and 2,068 rose. Comparing the fractions of stocks that fell to the stocks that rose, which market had the largest fraction?
Using proportions, it is found that the Big Board market had the largest fraction.
------------------------
Big board:
Total of 1366 + 1788 = 3154 stocks.Of those, 1788 rose.The proportion that rose is:
[tex]p_B = \frac{1788}{3154} = 0.5669[/tex]
------------------------
NASDAQ:
Total of 1587 + 2068 = 3655 stocks.Of those, 2068 rose.The proportion that rose is:
[tex]p_N = \frac{2068}{3655} = 0.5658[/tex]
[tex]p_B > p_N[/tex], thus, the Big Board market had the largest fraction.
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Please help
Find the equation to the line below.
1 1
y = [? ]x +
[ ]
Jungwon has $15. Notepads cost $2.50 each. How many notepads can Jungwon buy?
Can someone help me solve these 3 trig identity problems? I am stuck on these last 3... I will give brainliest!
(calculators are allowed)
Answer:
1. 1,246
2. 0,545
3. 0,9539
Step-by-step explanation:
semoga membantu :)
Please help with my question.
Answer:
C
Step-by-step explanation:
-4*(-2)=7(r+9)
8=7r+63
-7r=55
r=-55/7=-7 6/7
The midpoint of AB is (1, 2). The coordinates of A are (-3,6).Find the coordinates of B.
Midpoint has coordinates [tex](x_m,y_m)[/tex] which equal to,
[tex]x_m=\frac{x_1+x_2}{2}[/tex]
[tex]y_m=\frac{y_1+y_2}{2}[/tex]
We know the coordinates of a midpoint as well as the coordinates of [tex]A(x_1,y_1)[/tex] so we should be able to find coordinates of [tex]B(x_2,y_2)[/tex].
First solve both equations for [tex]x_2[/tex] and [tex]y_2[/tex] respectively,
[tex]x_2=2x_m-x_1[/tex]
[tex]y_2=2y_m-y_1[/tex]
Now insert the data,
[tex]x_2=2\cdot1-(-3)=\boxed{5}[/tex]
[tex]y_2=2\cdot2-6=\boxed{-2}[/tex]
The coordinates of B are therefore [tex](5,-2)[/tex].
Hope this helps :)
The midpoint of AB is (1, 2) the coordinates of A are (-3,6) coordinates of B coordinates of point B are (5, -2).
To find the coordinates of point B given that the midpoint of AB is (1, 2) and the coordinates of A are (-3, 6), use the midpoint formula:
Midpoint formula: M(x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)
Given that M is the midpoint (1, 2) and A is (-3, 6), we have:
(1, 2) = ((-3 + x2) / 2, (6 + y2) / 2)
Solve for x2 and y2:
For x-coordinate:
1 = (-3 + x2) / 2
2 = -3 + x2
x2 = 2 + 3
x2 = 5
For y-coordinate:
2 = (6 + y2) / 2
4 = 6 + y2
y2 = 4 - 6
y2 = -2
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A number is multiplied by 9 , and that product is added 3. The sum is equal to the product of 3 and 7 . Find the number.
Answer:
The unknown number is 2.
Step-by-step explanation:
Let x represent the unknown number.
It is multiplied by 9 then added to 3. Hence, it can be represented by the expression:
[tex]9x + 3[/tex]
The sum is equal to the product of 3 and 7, or 21. Therefore:
[tex]9x + 3 = 21[/tex]
Solve for x. Subtract 3 from both sides:
[tex]9x = 18[/tex]
And divide both sides by 2. Hence:
[tex]x = 2[/tex]
In conclusion, the unknown number is 2.
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?
Answer:
120 customers on the 2nd day
Step-by-step explanation:
100/1ST DAY
120/2nd day
140/3rd day
160/ 4TH DAY
13. State the restrictions
and then simplify
8x2 +14x-49 /
2x²+x-21
Answer:
Whenever the denom is 0, that's where it's undefined -- or in your case "restrictions"
So factoring 2x^2 + x - 21 gets you (x-3)(2x+7). That means 3 and -7/2 are the restricted values.
To simplify, I'm going to factor it. (Assuming what you wrote is 8x^2 for the numerator)
[(4x-7)(2x+7)] / (x-3)(2x+7)
You can cancel 2x+7 out,
so you get 4x-7/x-3
Find the value of 9 - [4 2 - (3 + 2)]. 8 6 -2
Answer:
-2
Step-by-step explanation:
9 - [4^2 - (3 + 2)]
PEDMAS says parentheses first
Work from the inside out
9 - [4^2 - (5)]
9 - [16-5]
9 - [11]
Subtract
9-11
-2
What is the arc length of arc cd in the circle below. The circle has a radius of 6ft and an angle measure of 30
9514 1404 393
Answer:
π ft ≈ 3.14 ft
Step-by-step explanation:
The angle is 1/12 of the number of degrees in a circle, so the arc length will be 1/12 of the circumference of the circle.
C = 2πr
1/12C = 2/12π(6 ft) = π ft ≈ 3.14 ft
The arc length is about 3.14 feet.
Which of the h values are solutions to the following equation?
h^2=0.36
Choose all answers that apply:
A: h= square root of 0.6
B: h = square root of -0.6
C: h = 0.18
D:h = -0.18
E: None of the above
Answer:
a:h=square root of 0.6
Step-by-step explanation:
thank you for your time today
Answer:
none of the above
Step-by-step explanation:
KHAN
What type of relationship is expressed below?
f(x) = 7x +3
Answer:
Linear Function
Step-by-step explanation:
This is a linear function. A linear function is a function with the degree of 1, where the line increases continuously the whole graph. The growth of the graph is constant, making a straight line. This function is written in slope-intercept form, f(x) = mx+b. Where m is the slope and b is the y-intercept. The function will have 1 solution.
(PLEASE EXPLAIN HOW YOU GOT THE ANSWER) Which inequalities are true? Select the four correct answers.
0 less-than StartRoot 8 EndRoot
StartRoot 8 EndRoot less-than 3
StartRoot 8 EndRoot greater-than StartRoot 7 EndRoot
StartRoot 8 EndRoot less-than 2
StartRoot 8 EndRoot greater-than 8
1 less-than StartRoot 8 EndRoot
9514 1404 393
Answer:
T, T, F, F, T
Step-by-step explanation:
First of all, it is helpful to know ...
√8 ≈ 2.8284
√7 ≈ 2.6458
Now you can check the inequalities:
0 < √8 < 3 . . . . . . true√8 > √7 . . . . . . . . true√8 < 2 . . . . . false√8 > 8 . . . . . false1 < √8 . . . . . . . . . . true0, 1, 2, and √7 are left of √8 on a number line, so are all less than √8.
3 and 8 are right of √8 on a number line, so are greater than √8.
Answer:
T, T, F, F, T.
Step-by-step explanation:
Person above is correct!!
Find the value of x 3(4x+3)
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
One positive number is 5 more than twice another. If their product is 1827, find the numbers.
smaller number =
larger number =
9514 1404 393
Answer:
smaller: 29larger: 63Step-by-step explanation:
If we let x and y represent "one number" and "another", respectively, then the given relations are ...
x = 5 +2y
xy = 1827
Substituting for x gives a quadratic in y:
(5 +2y)(y) = 1827
2y^2 +5y -1827 = 0 . . . . . written in standard form
We can use the quadratic formula to find the positive value of y that satisfies this:
y = (-5 +√(5² -4(2)(-1827)))/(2(2)) = (-5 +√14641)/4 = 116/4 = 29
x = 5 +2(29) = 63 . . . . using the above expression for x
The smaller number is 29; the larger number is 63.
Write down a multiple of 4 between 29 and 37 ?
Answer:
8 or 9
Step-by-step explanation:
4 times 8 equals 32, and 4 times 9 equals 36
i’m genuinely confused, please help
Answer:
2x + 3 + 3x +12 + 90 = 180 (degree )
5x +105=180 (degree )
5x= 180-105 (degree )
5x = 75 (degree )
x = 75/5 (degree )
x = 15 #
therefore, 2x + 3= 2*15 + 3
=30+3
= 33#
3x + 12 = 3*15+12
= 45 +12
= 57#
X^2 -24x-108=0 factorize
Answer:
(x-27)(x+4) = 0
Step-by-step explanation:
I think you have a typo, and meant
x^2 -23x-108
what are two factors of 108 that differ by 23?
x^2 -24x-108 does not factor with rational coefficients.
Think About the Process The length of a rectangle is twice the width. The area of the rectangle is
54 square units. Notice that you can divide the rectangle into two squares with equal area. How
can you estimate the side length of each square? Estimate the length and width of the rectangle.
+
27
B. Estimate
4
C. Estimate 27.
D. Estimate 54
The rectangle is
(Round to the nearest tenth as needed.)
units long and units wide.
0
vo
(10
More
Enter your answer in the edit fields and then click Check Answer.
Answer:
27
Step-by-step explanation:
pls help! I need the answer quickly!
Step-by-step explanation:
The correct answer is 4 (option B)
How would you write 5x5x5x5x5x5 in exponential form
Answer:
5^6
Step-by-step explanation:
This is because the exponent is how many numbers are in the multiplication equation, in this case, five. Because there are six five's being multiplied together, our exponent is six.