$\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(2,1)\qquad C(4,7)\qquad \qquad \stackrel{\textit{ratio from A to C}}{3:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{3}{2}\implies \cfrac{A}{C} = \cfrac{3}{2}\implies 2A=3C\implies 2(2,1)=3(4,7)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill$

$\bf B=\left(\cfrac{(2\cdot 2)+(3\cdot 4)}{3+2}\quad ,\quad \cfrac{(2\cdot 1)+(3\cdot 7)}{3+2}\right)\implies B=\left( \cfrac{4+12}{5}~,~\cfrac{2+21}{5} \right) \\\\\\ B=\left(\cfrac{16}{5}~~,~~\cfrac{23}{5} \right)\implies B=\left( 3\frac{1}{5}~~,~~4\frac{3}{5} \right)$

8 0

3 years ago

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A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the

dangina [55]

The system of equations that could be used to determine the number of small cars rented and the number of large cars rented is;

x + y = 10

x + y = 105x + 7y = 66

<h3>Simultaneous equation</h3>

Small car = 5 people
Large car = 7 people
Total cars = 10
Total number of people = 66

Let

Number of small cars rented = x

Number of large cars rented = y

x + y = 10

x + y = 105x + 7y = 66

Learn more about simultaneous equation:

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3 0

2 years ago

Bob withdrew money from an ATM, put the receipt in an envelope, and filled in the information in his check register.

lora16 [44]

Answer:It is important to record each transaction so Bob knows how much money is in his account. That prevents being overdrawn. Recording debits and deposits helps with budgeting. It is good to keep receipts in case of any bank errors.

Step-by-step explanation:

5 0

3 years ago

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WILL GIVE BRAINLIEST A set of numbers is shown:

ad-work [718]

10 and 15 dear^^ 5(15) + 3(15) =28

4 0

2 years ago