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stiks02 [169]
3 years ago
6

Given the two vertices and the centroids of a triangle, how many possible locations are there for the third vertex?

Mathematics
1 answer:
hoa [83]3 years ago
7 0

Answer:

  1

Step-by-step explanation:

The centroid is the average of the coordinates of the three vertices. If you know two vertices (A and B) and the centroid (Q), then the third vertex (C) is ...

  C = 3Q -A -B

It has only one possible location.

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4x-3y=2<br> 3x=5y=16<br> solve using substitution method
vodomira [7]

\left\{\begin{array}{ccc}4x-3y=2&|\text{add 3y to both sides}\\3x+5y=16\end{array}\right\\\left\{\begin{array}{ccc}4x=3y+2&|\text{divide both sides by 4}\\3x+5y=16\end{array}\right\\\left\{\begin{array}{ccc}x=0.75y+0.5&(*)\\3x+5y=16\end{array}\right\\\\\text{substitute}\ (*)\ \text{to the second equation}\\\\3(0.75y+0.5)+5y=16\qquad\text{use distributive property}\\\\(3)(0.75x)+(3)(0.5)+5y=16\\\\2.25y+1.5+5y=16\qquad\text{subtract 1.5 from both sides}\\\\7.25y=14.5\qquad\text{divide both sides by 7.25}

\boxed{y=2}\\\\\text{substitute the value of y to}\ (*):\\\\x=0.75(2)+0.5\\\\x=1.5+0.5\\\\\boxed{x=2}\\\\Answer:\ x=2\ and\ y=2\to(2,\ 2)

7 0
3 years ago
What is the product of 3x+4 and 6x^{2} −5x+7?
LUCKY_DIMON [66]

(3x + 4)(6 {x}^{2}  - 5x + 7) \\  = 18 {x}^{3}  - 15 {x}^{2}  + 21x + 24 {x}^{2}  - 20x + 28 \\  = 18 {x}^{3}  + 9 {x}^{2}  + x + 28

I hope I helped you^_^

8 0
3 years ago
A.1.5
telo118 [61]

Answer:

x=50 y=10

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Please help me with this question
Bezzdna [24]

Answer:

1.03

Step-by-step explanation:

To find the volume of a prism, find the area of the base and multiply it by the height.

The base is an octagon. The area is found A = 2(1+\sqrt{2})a^2. Substitute a = 0.5.

A = 2(1+\sqrt{2})(0.5^2)\\A = 4.828...(0.25)\\A = 1.21

The volume is 1.21*2.5 = 3.025.

However, there are three holes drilled out half way which each have volume 0.06.

The volume is found as V = πr²h. Substitute r = 0.125 which is half the diameter of 0.25. Since they go half way, the height is h = 1.25.

V = π(0.125)²(1.25) = 0.06.

Since there are 3, they equal 3*0.06 = 0.18.

Subtract this from the volume.

1.21 - 0.18 = 1.03

4 0
3 years ago
A rope pulling a sled is sloped at 15° upward at the point of contact. The tension in the rope is 50.0 N. What is the horizontal
gizmo_the_mogwai [7]

Answer:

The horizontal component of the force is 48 N.

Step-by-step explanation:

The angle that the rope makes with with the horizontal is 15°, that means, the horizontal component of the force F_H is

cos(15^o)=\frac{F_H}{50N}

\boxed{ F_H=50N*cos(15^o)=48N}

4 0
3 years ago
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