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iris [78.8K]
3 years ago
12

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:

12

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

so

\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\\

5 0
3 years ago
Two sides of a triangle measure
Umnica [9.8K]

Answer:

A.

Step-by-step explanation:

4 + 8 = 12 which is < 13.

3 0
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
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