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Ede4ka [16]
3 years ago
10

PQR has vertices at P(2, 4), Q(3, 8) and R(5, 4). A similarity transformation maps PQR to ABC, whose vertices are A(2, 4), B(5.5

, 18), and C(12.5, 4). What is the scale factor of the dilation in the similarity transformation?
Mathematics
2 answers:
alukav5142 [94]3 years ago
7 0
Use Pythagorean Theorem to calculate length of sides 

PQ = √(1^2 + 4^2) = √(17) 
QR = √(2^2 + 4^2) = √(20) 
RP = √(3^2 + 0^2) = √(9) 

AB = √(3.5^2 + 14^2) = √(208.25) 
BC = √(7^2 + 14^2) = √(245) 
CA = √(10.5^2 + 0^2) = √(110.25) 

A similarity transformation will maintain the relationship of sides: the smallest side of one triangle should correspond to the shortest side of the other triangle (and so on). 

Ratio of lengths (transformed/original) 

shortest with shortest 
CA/RP = √(110.25)/√(9) = 10.5/3 = 3.5 
middle 
AB/PQ = √(208.25)/√(17) = √(208.25/17) = √(12.25) = 3.5 
longest 
<span>BC/QR = √(245)/√(20) = √(12.25) = 3.5</span>
zhuklara [117]3 years ago
4 0

Answer:

3.5 is the correct answer just had question and it was correct

Step-by-step explanation:


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Please help, been stuck on this for ages!
marishachu [46]

Answer:

\boxed {192 cm^{2}}

Step-by-step explanation:

<u>Find the volume of separate cuboids</u> :

<u>Volume (top cuboid)</u> :

⇒ V = 2 x 6 x (10 - 2)

⇒ V = 12 x 8

⇒ V = 96 cm²

<u>Volume (lower cuboid)</u> :

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⇒ V = 48 x 2

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<u>Volume (prism)</u> :

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8 0
2 years ago
Let R1 and R2 are the remainders when the polynomials x^3 + 2x^2 − 5ax − 7 and x^3 + ax^2 − 12x + 6 are divided by x + 1 and x −
Andru [333]

Answer:

2.44

Step-by-step explanation:

Given: x³ + 2x² - 5ax - 7      and  x³ + ax² - 12x + 6

Also, R1 + R2 = 6

in order to find the value of a:

Let p(x) = x³ + 2x² - 5ax - 7 and q(x) = x³ + ax² - 12x + 6

Using remainder theorem i.e if a polynomial p(x) is divisible by polynomial of form x - a then remainder is given by p(a).

Then,

R1 = p( -1 ) = (-1)³ + 2(-1)² - 5a(-1) - 7 = -1 + 2 + 5a - 7 = 5a - 6

R2 = q( 2 ) = 2³ + a(2)² - 12(2) + 6 = 8 + 4a - 24 + 6 = 4a - 10

Now,

R1 + R2 = 6

5a - 6 + 4a - 10 = 6

9a = 22

a=2.44

Therefore, Value of a is 2.44

7 0
3 years ago
Sofia takes 10mg of a medicine whose concentration in blood decreases by a factor of one half every day. Let t be the number of
adelina 88 [10]

Answer:

L = 10(\frac{1}{2} )^{t-4}

Step-by-step explanation:

If t is the number of days since Sofia took the medication of 10 mg, then the amount of medication in her system after t days will be S = 10(\frac{1}{2} )^{t}.

So, the concentration of medicine in blood decreases by a factor of one half every day.

If we count the number of days from today and Lexi takes 10 mg of the same medicine four days later then the amount of medicine left on her body after t days will be L = 10(\frac{1}{2} )^{t-4}. (Answer)

3 0
3 years ago
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irakobra [83]

Answering pretty sure yes

Step-by-step explanation:

7 0
3 years ago
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saul85 [17]

Answer:

y = -9

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

3 0
3 years ago
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