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liraira [26]
3 years ago
5

Using properties of parallelograms, RSTU is a parallelogram that has vertices R (-3,1), S (3,4), and T( 6,2(. What are the coord

inates of point U.

Mathematics
1 answer:
ElenaW [278]3 years ago
8 0

Answer:

(0, -1)

Step-by-step explanation:

A parallelogram is a quadrilateral (has four sides) in which opposite sides are parallel to each other. Also for a parallelogram, the opposite sides and angles are equal to each other.

Hence for parallelogram RSTU, RS // TU and RU // ST

Let the coordinate of U be (x , y). Two lines are parallel to each other if their slopes are equal, hence:

Slope of RS = (4 - 1) /[3 - (-3)] = 3/6 = 0.5

Slope of ST = (2 - 4) /[6 - 3] = -2/3

Slope of RU = (y - 1) /[x - (-3)] = (y - 1) / (x + 3)

Slope of TU = (y - 2) /[x - 6]

Slope of RU = Slope of ST

(y - 1) / (x + 3) = -2/3

3y - 3 = -2x -6

2x + 3y = -6 + 3

2x + 3y = -3                  (1)

Slope of RS = Slope of TU

0.5 = (y - 2) /[x - 6]

0.5x - 3 = y  - 2

0.5x - y = 1                  (2)

Solving 1 and 2 simultaneously gives:

x = 0, y = -1

Therefore the coordinates of U = (0, -1)

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Vikki [24]
Part a: 6:3 > 2:1
part b: 9:3> 3:1
4 0
3 years ago
Can jack built 1/5 of a shed in the same time that kyle can build 5/8 of shed,
Helen [10]
<h3>Answer: 3/10 of a shed</h3>

=============================================================

Explanation:

Let's say the shed comes in 40 equal pieces. Each piece takes the same amount of time to assemble. Why am I picking 40? Because 8*5 = 40.

This will allow us to rewrite the fractions with a common denominator.

  • 1/5 = 8/40 .... multiply top and bottom by 8
  • 5/8 = 25/40 .... multiply top and bottom by 5

So Jack can build 8/40 of the shed in the same amount of time Kyle can build 25/40 of the shed.

Instead of writing fractions (which honestly are a pain to deal with), I'm going to write "8 pieces" and "25 pieces" to represent "8/40" and "25/40" respectively. Just keep in mind that there are 40 pieces total.

So again, Jack can assemble 8 pieces in the time it takes Kyle to assemble 25 pieces.

---------------

The ultimate goal is to have Kyle assemble 40 pieces while Jack puts together some unknown number of pieces (some number between 8 and 40). Let's say it's x.

We can then form this proportion

\frac{\text{Jack's initial 8 pieces}}{\text{x pieces}}=\frac{\text{Kyle's initial 25 pieces}}{\text{goal of 40 pieces}}

which simplifies or cleans up to

5/x = 25/40

-----------------

Let's solve for x using cross multiplication

8/x = 25/40

8*40 = x*25

320 = 25x

25x = 320

x = 320/25

x = 12.8

So in the time it takes Kyle to assemble all 40 pieces, Jack can put together 12.8 pieces of the shed. However, we can't have Jack put together some fractional piece, because each "piece" is as small as it gets. We can't get any smaller. It would be like saying a fractional part of an atom or a lego block.

So we'll round 12.8 down to 12.

Jack can assemble 12 pieces in the time it takes Kyle to assemble 40 pieces.

Let's then convert this back to fraction form

12 pieces = 12/40 of a shed = 3/10 of a shed.

8 0
3 years ago
Worth 20 points!! If you answer wrong or something not related to the question I will report you! Thanks :)
KonstantinChe [14]

A

f(x) = 2x + 1

f(3) = 2*3 + 1 = 7

B

g(x) = x^2

g(7) = 7^2

g(7)= 49

C

f(g(x)) = 2(g(x) + 1

f(g(x)) = 2 x^2 + 1

f(g(3) = 2* 3^2 + 1

f(g(3) = 19

D

g(f(x)) = (f(x))^2

g(f(x)) = (2x + 1)^2

g(f(3)) = (2*3 + 1)^2 = (6 + 1)^2 = 49

E

f(g(x)) = 2*g(x) + 1

f(g(x)) = 2*x^2 + 1

f(g(3)) = 2*3^2 + 1

f(g(3)) = 2 * 9 + 1

f(g(3)) = 18 + 1

f(g(3) = 19

F

f(g(x)) = 2(g(x)) + 1

f(g(x)) = 2*x^2 + 1  

4 0
3 years ago
Dont answer this question if you dont know the answer
3241004551 [841]

\huge\boxed{♧ \: \mathfrak{ \underline{Answer} \: ♧}}

here's the solution,

  • \pi = 180

  • \dfrac{\pi}{3}  =  \dfrac{180}{3}

  • \dfrac{\pi}{3}  = 60

=》

f( \theta) = \cos( \theta)   + 2 \cos( \frac{ \theta}{2} )

=》

f(60) =  \cos(60)  + 2 \cos( \frac{60}{2} )

=》

f(60) =  \dfrac{1}{2}  + 2 \cos(30)

=》

f(60) =  \dfrac{1}{2}  +  (2 \times \frac{ \sqrt{3} }{2})

=》

f(60) =  \dfrac{1}{2}  +  \sqrt{3}

=》

f(60) =  \dfrac{1 + 2 \sqrt{3} }{2}

hence, correct option is C.

6 0
3 years ago
Read 2 more answers
Solve the questions
Brilliant_brown [7]

Let's do the trig part first, then the calculus.  First we simplify the integrand.

\cot^3 x \sin ^3 x=\dfrac{\cos^3 x}{\sin^3 x} \sin^3 x= \cos^3 x

The triple angle formula is:

\cos 3x = 4 \cos^3 x - 3 \cos x

or

\cos^3 x = \frac 1 4 (\cos 3x + 3 \cos x)

Now we can integrate:

\displaystyle \int \cot^3 x \sin^3 x \ dx = \int \cos^3 x\ dx= \int \tfrac 1 4 (\cos 3x + 3 \cos x)\ dx

=\frac 1 4 (\frac 1 3 \sin 3x + 3 \sin x) + C

=\frac 1 {12} \sin 3x + \frac 3 4 \sin x + C



5 0
3 years ago
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