Using the Zero property solve -16tsquared + 28t + 8 = 0

How many square tiles of side 10cm each will be needed to tile a floor which is 300cm long and 150cm wide?

S_A_V [24]

Step 1

Find the area of one tile

we know that

the area of a square is

$A=b^{2}$

where b is the length side of the square

In this problem

$b=10\ cm$

Substitute

$A=10^{2}=100\ cm^{2}$

Step 2

Find the area of the floor

The area of a rectangle is equal to

$A=LW$

where

L is the length of the rectangle

h is the width of the rectangle

In this problem

$L=300\ cm$

$W=150\ cm$

Substitute

$A=300*150=45,000\ cm^{2}$

Step 3

Find the number of tiles needed

by proportion

$\frac{1}{100} \frac{tile}{\ cm^{2}} =\frac{x}{45,000} \frac{tile}{\ cm^{2}} \\ \\x=45,000/100 \\ \\x=450 \ tiles$

therefore

the answer is

$450 \ tiles$

5 0

3 years ago

A charm bracelet costs $65, plus $25 for each charm. The equation −25x+y=65 represents the cost y of the bracelet, where x is th

STatiana [176]

The answer is $90x because 65+25 = 90

5 0

2 years ago

In this task, you will perform multiplication on rational and irrational numbers and determine whether the sets are closed under

velikii [3]

Answer:

The set of rational numbers is closed under multiplication.

The set of irrational numbers is not closed under multiplication.

Although are only few instances where the set of irrational numbers may show closure, but it must be noted that closure property would not extend to the entire set of irrational numbers.

The Product of two rational numbers will be rational.

Step-by-step explanation:

The set of rational numbers contains the set of numbers that can be written as a fraction or ratio between two integers - integer values in the nominator and denominator (denominator ≠ 0).

The set of integers - denoted by Z - can be termed as rational numbers as integer, for instance, 3 can be written as the ration 3/1.

Therefore, when we multiply two rationals, it basically means we are just multiplying two such fractions which will yield another fraction of the same form as integers are closed under multiplication.

Part A) Determining multiplication on rational numbers

Let a/b and c/d be rational numbers where a, b, c and d are integers and (b, d ≠ 0).

For example, a = 2, b = 3, c = 4, and d = 5 a, b, c and d are integers

Lets multiple 2/3 × 4/5 to check what the multiplication of two rational number can bring.

So,

2/3 × 4/5 = (2)(4) / (3)(5) = 8/15

As 8 and 15 are the integers, and can be written in a ratio 8/15 in the nominator and denominator which make it a rational number. Hence, the set of rational numbers is closed under multiplication.

Determining multiplication on irrational numbers

The set of irrational numbers contains the set of numbers that can not be written as a fraction or ratio between two integers.

The product of two irrational numbers will be sometimes irrational.

There will be certain cases sometimes where the product of two irrational numbers will yield irrational number. But, it must be noted that few irrational numbers may multiply to yield a rational number.

For example,

√5 × √2 = √10 which is termed as irrational

√8 × √2 = √16 = 4 which is termed as rational

So, there are only few instances that may show closure, but it must be noted that closure property would not extend to the entire set of irrational numbers.

So, we can safely say that the set of irrational numbers is not closed under multiplication.

Part B) Is the Product of two rational numbers irrational or rational?

Let a/b and c/d be rational numbers where a, b, c and d are integers and (b, d ≠ 0).

Lets multiple a/b × c/d to check if the product of two rational numbers can be rational or irrational.

So,

a/b × c/d = ac / bd where b, d ≠ 0

As ac and bd are also integers, so the sets are closed under multiplication.

So, ac/bd is a ratio having integers in the nominator and denominator which make it a rational number. Hence, the Product of two rational numbers will be rational.

Proving closure property

Let x and y are rational numbers such that

x = a/b and y = c/d where b, d ≠ 0 and a, b, c and d are integers

x × y = a/b × c/d

xy = ac / bd

As ac and bd are also integers, so the sets are closed under multiplication.

So, ac/bd is a ratio having integers in the nominator and denominator which make it a rational number. Hence, the product of two rational numbers will be rational.

For example,

x = a/b = 6/7

y = c/d = 8/9

xy = a/b × c/d

xy = ac / bd = (6)(8) / (9)(7)

xy = 48/63

As 48 and 63 are the integers, and can be written in a ratio 48/63 in the nominator and denominator which make it a rational number. Hence, the set of rational numbers is closed under multiplication.

Keywords: closure property, rational number, irrational number

Learn more about closure property and rational number from brainly.com/question/7667707

#learnwithBrainly

4 0

3 years ago

Can you answer a and b

Scilla [17]

Ask me your other questions.i hope it was helpful

7 0

3 years ago

What is the equation of a line in general form that does not have a y-intercept and goes through the point (3,6) ?

Dennis_Churaev [7]

Answer:

$x = 3$

Step-by-step explanation:

Step 1: Determine the equation

So we know that our equation does not have a y-intercept which means that it doesn't intersect ANYWHERE on the y-axis. Therefore, this means that our equation will be a straight vertical line that doesn't move side to side and just goes straight up and down. We also know that our point is (3, 6) which means that our x-value will be 3 and this is where the equation will be located.

There are several ways to display our answer where x = 3 is the most common way which basically means give me all of the y-values for the same x value of 3. Another way of saying it is x - 3 = 0 which either way when adding 3 to both sides gives you x = 3 which is what I usually go with.

Answer: $x = 3$

4 0

2 years ago

Read 2 more answers