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3 years ago

What is the total displacement of the object? m

Mathematics

1 answer:

Elan Coil [88]3 years ago

7 0

Answer:What is the total displacement of the object?

562.5 m

Step-by-step explanation:

ed. 2021

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In the diagram below, we have $ST = 2TR$ and $PQ = SR = 20$. Find the length $UV$.

Maslowich

Answer:

Step-by-step explanation:

1. $ST=2TR$ and $SR=20,$ then by segment addition postulate

$ST+TR=SR\\ \\2TR+TR=SR\\ \\3TR=20\\ \\TR=\dfrac{20}{3}\\ \\ST=2\cdot \dfrac{20}{3}=\dfrac{40}{3}$

2. Consider triangles PQU and TSU. These triangles are similar by AA similarity theorem (triangles have congruent vertical angles PUQ and TUS and congruent alternate interior angles PQU and TSU). Similar triangles have proportional corresponding sides, so

$\dfrac{QU}{US}=\dfrac{PQ}{ST}=\dfrac{20}{\frac{40}{3}}=\dfrac{60}{40}=1.5$

$QU=1.5US$

3. Consider triangles QUV and QSR. These triangles are similar by AA similarity theorem. Similar triangles have proportional corresponding sides, so

$\dfrac{QU}{QS}=\dfrac{UV}{SR}\\ \\\dfrac{QU}{QU+US}=\dfrac{1.5US}{1.5US+US}=\dfrac{1.5}{2.5}=0.6$

$\dfrac{UV}{SR}=0.6\Rightarrow UV=0.6SR=0.6\cdot 20=12$

7 0

3 years ago

Read 2 more answers

Consider f(x)=2x-3 and g(x)=/3x-1/find each value. f(3)

grandymaker [24]

Answer:

f(x)= 3, g(x)=8

Step-by-step explanation:

if you plug 3 into the equation 2x-3, you have 6-3, which is 3.

If you plug 3 into the equation 3x-1, you have 9-1, which is 8

4 0

3 years ago

Solve - 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] + 3 ( x - 1 ) (and could you please explain it to me?? I really don't get it.

Mazyrski [523]

Answer:

Step-by-step explanation:

$(x+2)(x-1)= x^2+2x-x-2= x^2 +x -2\\\\( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 =x^2+x-2-x^2+1=x-1\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] =-3(x-1)=-3x+3\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] + 3 ( x - 1 ) =-3x+3+3x-3=6x\\$

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3 years ago

Two sides of a triangle measure

Umnica [9.8K]

Answer:

Step-by-step explanation:

4 + 8 = 12 which is < 13.

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3 years ago

Help for Geometry #6 and 7

Arturiano [62]

Find the area of the rectangle and the 1/2 circle, then subtract the half circle's area from the rectangle's.
Area of the rectangle is 30in.
Area of the 1/2 circle is 19.625.
Subtract
30-19.625
10.375
(Round it to 10.4 in this case)

8 0

4 years ago