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Sergio [31]
3 years ago
13

Triangles D E F and P Q R are shown. Given that StartFraction D F Over P R EndFraction = StartFraction F E Over R Q EndFraction

= three-halves, what additional information is needed to prove △DEF ~ △PQR using the SSS similarity theorem? DE ≅ PQ ∠D ≅ ∠P StartFraction D E Over E F EndFraction = three-halves StartFraction D E Over P Q EndFraction = three-halves
Mathematics
2 answers:
geniusboy [140]3 years ago
7 0

Answer:

D. DE/PQ= 3/2

Step-by-step explanation:

2020 edg

alukav5142 [94]3 years ago
3 0

Answer:

The correct option is;

DE/PQ = 3/2 which is StartFraction DE Over PQ Endfraction = three-halves

Step-by-step explanation:

The information given bout the triangles are;

DF/PR = FE/RQ = 3/2

Therefore since the given sides of triangle DEF are 3/2 times the sides of triangle PQR, the given sides of triangle DEF have been scaled 3/2 times to get the given sides of triangle PQR

Therefore, to prove that ΔDEF ~ ΔPQR, the ratio of the third side of triangle DEF, that is DE, to the third side of triangle PQR, which is PQ must be three-halves.

You might be interested in
A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing e
Mars2501 [29]

Answer:

1.  The lawyer has 34 investors that contribute with $3,000 and has 26 investors that contribute with $6,000.

2. The jar has 26 nickels and 44 dimes that worth $5.70.

3. The concession stand has sold 1600 sodas and 1400 hotdogs

Step-by-step explanation:

For all the problems we are going to follow the same process that will consist on 1. Define the variables. 2. Formulate the system of two linear equations 3. Solve by the elimination method 4. Give the answer.

  • First problem.

- Variables:

x = number of investors that contribute with $3,000

y = number of investors that contribute with $6,000

- System of equations.

First equation will be the result of adding the number of investors that will give us a total of 60 investors then:

x + y = 60

Second equation is the result of multypling the number of investors by its invest and adding between them to get the $258,000 they have raised:

3,000x + 6,000y = 258,000

The system will be:

x + y = 60

3,000x + 6,000y = 258,000

- Solve by the elimination method.

To cancel x we are going to multiply by -3000 in both sides of the first equation and we will leave the second equation the same but in the first row to make easier the calculations then:

3,000x + 6,000y = 258,000

(x + y ) (-3,000) = 60 (-3,000) <em>   solve the multiplications </em>

3,000x + 6,000y = 258,000

<u>-3,000x - 3,000y = -180,000 </u><em>   solve the operations</em>

0 + 3,000y = 78,000     <em>clear y</em>

y = \frac{78,000}{3,000}    <em>solve the division</em>

y = 26

For calculate x, replace the y value in the first equation and solve it

x + 26 = 60

x = 60 - 26

x = 34

- Answer

The lawyer has 34 investors that contribute with $3,000 and has 26 investors that contribute with $6,000.

  • Second problem

- Variables:

x = number of nickels

y = number of dimes

- System of equations.

First equation will be the result of adding the number of nickels and dimes that will give us a total of 70 coins in the jar then:

x + y = 70

Second equation is the result of multypling the number of coins by its value and adding between them to get the $5.70 that the jar worth:

0.05x + 0.1 y = 5.70

The system will be:

x + y = 70

0.05x + 0.1 y = 5.70

- Solve by the elimination method.

To cancel x we are going to multiply by -0.05 in both sides of the first equation and we will leave the second equation the same but in the first row to make easier the calculations then:

0.05x + 0.1 y = 5.70

(x + y ) (-0.05) = 70 (-0.05) <em>   solve the multiplications </em>

0.05x + 0.1 y = 5.70

<u>-0.05x - 0.05y = -3.50 </u><em>   solve the operations</em>

0 + 0.05y = 2.20     <em>clear y</em>

y = \frac{2.20}{0.05}    <em>solve the division</em>

y = 44

For calculate x, replace the y value in the first equation and solve it

x + 44 = 70

x = 70 - 44

x = 26

- Answer

The jar has 26 nickels and 44 dimes that worth $5.70.

  • Third problem.

- Variables:

x = number of sodas sold by $2

y =  number of hotdogs sold by $3

- System of equations.

First equation will be the result of adding the number of sodas and hotdogs that is of 3000 then:

x + y = 3000

Second equation is the result of multypling the number of sodas and hotdogs by its price and adding between them to get the $7400 of the receipts:

2x + 3y = 7400

The system will be:

x + y = 3000

2x + 3y = 7400

- Solve by the elimination method.

To cancel x we are going to multiply by -2 in both sides of the first equation and we will leave the second equation the same but in the first row to make easier the calculations then:

2x + 3y = 7400

(x + y ) (-2) = 3000 (-2) <em>   solve the multiplications </em>

2x + 3y = 7400

<u>-2x - 2y = -6000 </u><em>   solve the operations</em>

0 + 1y = 1400     <em>clear y</em>

y = \frac{1400}{1}    <em>solve the division</em>

y = 1400

For calculate x, replace the y value in the first equation and solve it

x + 1400 = 3000

x = 3000 - 1400

x = 1600

- Answer

The concession stand has sold 1600 sodas and 1400 hotdogs

6 0
3 years ago
Tricia recorded the number of pets owned by each of her classmates. these data points represent the results of her survey. 0, 3,
SOVA2 [1]

The dot plot of the data recorded by Tricia about number of pets owned by each of her classmates looks like scattered and some points are in one line.

Given number of pets owned by each of her classmates are: 0, 3, 2, 4, 1, 0, 0, 3, 2, 1, 2, 1, 1, 3, 4, 2, 0, 0, 1, 1, 1, 0, 3.

We have to create dot plot of the data given in the question.

Firstly we have to give a code to each value which represents friend of Tricia.

A dot plot is a statistical chart which have points but they are presented in dot form. Each dot shows a value .There are two common, yet different versions of the dot chart.

After giving codes the table will look like:

Friend                       Number of pets

1                                      0

2                                      3

3                                      2

4                                      4

5                                      1

6                                      0

7                                      0

8                                      3

9                                      2

10                                    1

11                                    2

12                                    1

13                                    1

14                                    3

15                                    4

16                                    2

17                                    0

18                                    0

19                                    1

20                                    1

21                                    1

22                                    0

23                                    3

Learn more about dot plot at brainly.com/question/15853311

#SPJ4

8 0
2 years ago
From the sum of -265 and -156 subtract the sum of 356 and -250
earnstyle [38]

Answer:

315

Step-by-step explanation:

The sum of -265 and -156:

-265 + (-156)

= -265-156

= -421

The sum of 356 and -250:

356 + (-250)

= 356-250

= 106

The sum of both:

-421 + 106

= -315

Hope this helped!

6 0
3 years ago
To start a board game, the player who rolls two sixes gets to go first. What is the probability that a player will roll two
Crank

Answer:

1 over 36

Step-by-step explanation:

4 0
3 years ago
Least greatest ordering integers
morpeh [17]

1. 5, 19, 24, 46, 77, then 98


2. -62, -47, -11, 38, then 56


5 0
3 years ago
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