MATHEMATICS HIGH SCHOOL

A bottle of water contains 450ml. How many litres of water are there in 8 of these bottles

Answers

Answer 1

Answer:

Answer:

3.6 litres

Step-by-step explanation:

1 bottle = 450ml

8 bottles = 450 × 8

= 3600ml

1000ml = 1 litre

3600ml = 3.6 litres (3600÷1000)

Answer 2

Answer:

Answer:

3.6 litres

Step-by-step explanation:

1 bottle = 450ml

8 bottles = 450 × 8

= 3600ml

1000ml = 1 litre

3600ml = 3.6 litres (3600÷1000)

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20 pointsA vat contains 18 gallons of liquid when a drain pipe opens and the liquid begins to leave the vat at a rate of 4 gallons per hour.

Use the Line Tool to graph the amount of liquid remaining in the vat at any hour, x.

Answers

Step-by-step explanation:

Let x be the number of hours.

We have been given that a vat contains 18 gallons of liquid when a drain pipe opens and the liquid begins to leave the vat at a rate of 4 gallons per hour.

To graph the amount of liquid first of all we will find the equation of line for our given situation.

Since we know that equation of a line in slope-intercept form is: $y=mx+b$ , where, m = slope and b = y-intercept or initial value.

As liquid is leaving the vat at a rate of 4 gallons per hour, this means that amount of liquid in vat in decreasing 4 gallons per hour. As slope is also known as rate of change, so slope of our given line will be -4. A negative slope means that with each increase in x our y will decrease by 4.

As initially there were 18 gallons of liquid in vat, so our y-intercept will be 18.

Upon substituting our given values in slope-intercept form of equation we will get,

$y=-4x+18$

Let us find x-intercept by substituting y=0 in our equation.

$0=-4x+18$

$4x=18$

$(4x)/(4)=(18)/(4)$

$x=4.5$

Now we will draw a line connecting our y-intercept and x-intercept from (0,18) to (4.5,0).

Please find the attachment for the graph of the given line.

Which equation shows an example of the associative property of addition?a.(–4 + i) + 4i = –4 + (i + 4i)
b.(–4 + i) + 4i = 4i + (–4i + i)
c.4i × (–4i + i) = (4i – 4i) + (4i × i)
d.(–4i + i) + 0 = (–4i + i)

Answers

The associative property states that we can regroup the terms of an expression and obtain the same result.

We have then:

$a + (b + c) = (a + b) + c$

The expression that complies with this property is given by:

$(-4 + i) + 4i = -4 + (i + 4i)$

Answer:

An equation that shows an example of the associative property of addition is:

a. (- 4 + i) + 4i = -4 + (i + 4i)

The correct option is $\boxed{\bf option (a)}$ i.e., $\boxed{\left({-4+i}\right)+4i=-4+\left({i+4i}\right)}$ .

Further explanation:

Concept used:

The associative property of the addition states that the addition of numbers cannot affect by the grouping of the number.

$\boxed{A+\left({B+C}\right)=\left({A+B}\right)+C}$

Here, in the above equation the value of $A+\left({B+C}\right)$ is always equal to the value of $\left({A+B}\right)+C$ whether the grouping of number is changes or not.

Calculation:

Now check the option to get the answer.

First check option (a)

$\left({-4+i}\right)+4i=-4+\left({i+4i}\right)$

In the above equation the grouping of the number is changed.

Now check the values of left hand side and right hand side.

$\begin{aligned}\left({-4+i}\right)+4i&=-4+\left({i+4i}\right)\n-4+5i&=-4+5i\end{gathered}$

The value of LHS is same as RHS.

Therefore, option (a) is correct.

Now check option (b)

$(-4+i)+4i=4i+(-4i+i)$

The term $i$ should be associated with $4i$ but it is associated with $-4i$ .

Therefore the option (b) is incorrect.

Now check option (c)

$4i* (-4i+i)=(4i-4i)+(4i* i)$

The above expression does not follow any property.

Therefore the option (c) is incorrect.

Now check option (d)

$(-4i+i)+0=-4i+i$

The above expression follows additive property not associative property.

Therefore the option (d) is incorrect.

Thus, the correct option is $\boxed{\bf option (a)}$ i.e., $\boxed{\left({-4+i}\right)+4i=-4+\left({i+4i}\right)}$ .

Learn more:

1. A problem on simplification: brainly.com/question/573729

2. A problem on domain and range: brainly.com/question/3412497

Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Simplification

Keywords: Associative property, equation, property, addition, associative property of Addition, additive property, grouping terms, left hand side, right hand side, LHS, RHS.

What is the function doing in the interval -37 poin
Decreasing
Increasing