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3 years ago

You attend a working dinner with four other colleagues. Since alcohol

Mathematics

1 answer:

murzikaleks [220]3 years ago

4 0

Using proportions, it is found that the amount owed for each bill are given as follows:

$31.33 for food $9.90 for alcohol.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount.

In this problem, each of the bills are split equally among the five people, hence the fraction is 1/5.

Thus:

1/5 x 156.65 = $31.33

1/5 x 49.50 = $9.90.

Hence the amount owed for each bill are given as follows:

$31.33 for food $9.90 for alcohol.

More can be learned about proportions at brainly.com/question/24372153

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How many solutions does this linear system have? y = y equals StartFraction 2 over 3 EndFraction x plus 2. X 2 6x – 4y = –10 one

nordsb [41]

The system of equations provides a unique solution(one solution) at (-0.6, 1.6).

<h2>Given to us,</h2>

$y=\dfrac{2}{3}x+2$
$6x-4y=-10$

<h3>Equation 2</h3>

As we already have the value of y from equation 1, substitute its value in equation 2,

$6x-4y=-10$

$6x-4(\dfrac{2}{3}x+2)=-10$

$6x-\dfrac{8}{3}x-8=-10$

$\dfrac{6x}{1}-\dfrac{8}{3}x=-10+8$

$\dfrac{6x\times 3}{1\times 3}-\dfrac{8}{3}x=-2$

$\dfrac{18x-8x}{3}=-2$

$10x=-6\\$

$x=\dfrac{-6}{10} \\\\x=-0.6$

<h3>Equation 1,</h3>

$y=\dfrac{2}{3}x+2$

substitute the value of x in equation 1,

$y=\dfrac{2}{3}(\dfrac{-6}{10})+2\\\\y = \dfrac{-2}{5}+2\\\\y= \dfrac{-2+10}{5}\\\\y = \dfrac{8}{5}\\\\y=1.6$

As we can see the system of equations provides a unique solution(one solution) at (-0.6, 1.6).

Learn more about the system of equations:

brainly.com/question/12895249

3 0

3 years ago

Use a graphing calculator to solve the equation -3 cost= 1 in the interval from . Round to the nearest hundredth.

RSB [31]

In place of t, or theta, I'm going to utilize x instead. So the equation is -3*cos(x) = 1. Get everything to one side and we have -3*cos(x)-1 = 0

Let f(x) = -3*cos(x)-1. The goal is to find the root of f(x) in the interval [0, 2pi]

I'm using the program GeoGebra to get the task done of finding the roots. In this case, there are 2 roots and they are marked by the points A and B in the attachment shown

A = (1.91, 0)
B = (4.37, 0)

So the two solutions for theta are
theta = 1.91 radians
theta = 4.37 radians