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Sergeu [11.5K]
2 years ago
9

Theorem: A line parallel to one side of a triangle divides the other two

Mathematics
1 answer:
Nonamiya [84]2 years ago
7 0

Answer: Segment BD = 15

Step-by-step explanation: Ok. So, we know that segment DE is parallel to segment BC and segment EF is parallel to segment AB. The triangle proportionality theorem states that if a line is parallel to one side of a triangle and also intersects the other two sides, the line divides the sides proportionally. To put it more simply; because segment EF is parallel to segment AB, triangles ADE and EFC are proportional and similar. From there we must find the scale factor by which these two triangles are proportional.

We can do this by dividing the corresponding segments by; each other.

24 ÷ 20 = 1.2

Scale Factor = 1.2

Then we divide segment AD (18) by the scale factor (1.2).

18 ÷ 1.2 = 15

Since segment EF is parallel to segment AB, segment EF corresponds and is congruent to segment DB.

So,

Segment BD = 15

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What is the slope of the line that contains points (3,-9) and (-2,16)
Elena L [17]
The slope would be -5

Hope this helps

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6 0
3 years ago
WILL GIVE BRAINLIEST!
Zielflug [23.3K]

Answer:

Collisions

Follow Newton’s Third Law which tells us that

the force exerted by body A on body B in a

collision is equal and opposite to the force

exerted on body B by body A.

During a collision, external forces are ignored.

The time frame of the collision is very short.

The forces are impulsive forces (high force, short

duration).

Collision Types

Elastic: P is conserved, K is conserved

Inelastic: P is conserved, K is NOT conserved

Perfectly Inelastic means the bodies stick together

Problem: Collisions (1993)

10. Which of the following is true when an object of

mass m moving on a horizontal frictionless surface

hits and sticks to an object of mass M > m, which is

initially at rest on the surface?

(A) The collision is elastic.

(B) All of the initial kinetic energy of the less-massive

object is lost.

(C) The momentum of the objects that are stuck together

has a smaller magnitude than the initial momentum of

the less-massive object.

(D) The speed of the objects that are stuck together

will be less than the initial speed of the less-massive

object.

(E) The direction of motion of the objects that are stuck

together depends on whether the hit is a head-on

collision.

Explain your reasoning:

Ans. Again, by conservation of momentum, if the

mass increases, the velocity must decrease. pin = pout

Problem: Collisions (1993)

11. Two objects having the same mass travel

toward each other on a flat surface, each with a

speed of 10 meter per second relative to the

surface. The objects collide head-on and are

reported to rebound after the collision, each

with a speed of 20 meters per second relative

to the surface. Which of the following

assessments of this report is most accurate?

(A) Momentum was not conserved, therefore the report is false.

(B) If potential energy was released to the objects

during the collision, the report could be true.

(C) If the objects had different masses, the report could be true.

(D) If the surface was inclined, the report could be true.

(E) If there was no friction between the objects and the

surface, the report could be true.

Explain your reasoning:

Ans. Momentum is conserved provided that an

external force not be applied. If the objects have

potential energy stored, this could provide the force.

PLEASE MARK AS BRAINLIEST!!!!!!

7 0
3 years ago
F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa
DerKrebs [107]

a. Parameterize C by

\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath

with 0\le t\le1.

b/c. The line integral of \vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath over C is

\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt

=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt

=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt

=\displaystyle10\int_0^1\mathrm dt=\boxed{10}

d. Notice that we can write the line integral as

\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)

By Green's theorem, the line integral is equivalent to

\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy

where D is the triangle bounded by C, and this integral is simply twice the area of D. D is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

4 0
3 years ago
CAN SOMEONE PLZ ANSWER THIS ITS DUE AT 11:59 APRIL 11 2021 AND ILL MARK U BRAINLIST
Luden [163]

Answer:

answer is c

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Carrie started work at 8 a.m. and left at 1:30 p.m. How many hours of work should she record on her time card for the day?
vagabundo [1.1K]
Start:  8 a. m.
Finish:  1 : 30 p.m. = 13 hours 30 minutes
13 h 30 min - 8 h = 5 h 30 min
She should record 5 hours and 30 minutes on her time card for the day.
5 0
4 years ago
Read 2 more answers
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