To prove a rhombus you need to show that the sides are congruent and the diagonals are perpendicular.
Sides:
![d_{RM}=\sqrt{(-4-1)^2+(5-4)^2}](https://tex.z-dn.net/?f=d_%7BRM%7D%3D%5Csqrt%7B%28-4-1%29%5E2%2B%285-4%29%5E2%7D)
![=\sqrt{(-5)^2+(1)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%28-5%29%5E2%2B%281%29%5E2%7D)
![=\sqrt{25+1}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B25%2B1%7D)
![=\sqrt{26}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B26%7D)
![d_{MB}=\sqrt{(1-2)^2+(4+1)^2}](https://tex.z-dn.net/?f=d_%7BMB%7D%3D%5Csqrt%7B%281-2%29%5E2%2B%284%2B1%29%5E2%7D)
![=\sqrt{(-1)^2+(15)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%28-1%29%5E2%2B%2815%29%5E2%7D)
![=\sqrt{1+25}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B1%2B25%7D)
![=\sqrt{26}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B26%7D)
![d_{BS}=\sqrt{(2+3)^2+(-1-0)^2}](https://tex.z-dn.net/?f=d_%7BBS%7D%3D%5Csqrt%7B%282%2B3%29%5E2%2B%28-1-0%29%5E2%7D)
![=\sqrt{(5)^2+(-1)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%285%29%5E2%2B%28-1%29%5E2%7D)
![=\sqrt{25+1}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B25%2B1%7D)
![=\sqrt{26}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B26%7D)
![d_{SR}=\sqrt{(-3+4)^2+(0-5)^2}](https://tex.z-dn.net/?f=d_%7BSR%7D%3D%5Csqrt%7B%28-3%2B4%29%5E2%2B%280-5%29%5E2%7D)
![=\sqrt{(1)^2+(-5)^2}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%281%29%5E2%2B%28-5%29%5E2%7D)
![=\sqrt{1+25}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B1%2B25%7D)
![=\sqrt{26}](https://tex.z-dn.net/?f=%3D%5Csqrt%7B26%7D)
≅
≅
≅ ![\overline{SR}](https://tex.z-dn.net/?f=%5Coverline%7BSR%7D)
Diagonals:
Use the slope formula: ![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![m_{RB}=\dfrac{5+1}{-4-2}](https://tex.z-dn.net/?f=m_%7BRB%7D%3D%5Cdfrac%7B5%2B1%7D%7B-4-2%7D)
![=\dfrac{6}{-6}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B6%7D%7B-6%7D)
= -1
![m_{MS}=\dfrac{4-0}{1+3}](https://tex.z-dn.net/?f=m_%7BMS%7D%3D%5Cdfrac%7B4-0%7D%7B1%2B3%7D)
![=\dfrac{4}{4}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B4%7D%7B4%7D)
= 1
Slopes are opposite reciprocals so they are perpendicular.
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All of the sides are congruent and the diagonals are perpendicular so RMBS is a rhombus.
Expenses of respondents in a survey is a quantitative data and the level of measurement is a ratio scale.
<h3>What is a Qualitative and a Quantitative Data?</h3>
A quantitative data can be described as a type of data that you can measure or counted, and also given a numerical value to, while a qualitative data is a type of data that cannot be expressed using numbers.
Examples of quantitative data include, number of students in a class, weight of students in a class, etc.
Examples of qualitative data include hair color, religion, nationality, etc.
Expenses of respondents can be given numerical values, therefore, expenses of respondents in a survey is a quantitative data and the level of measurement is a ratio scale.
Learn more about quantitative data on:
brainly.com/question/96076
#SPJ1
Answer:
she will have $169.74
Step-by-step explanation: