I used to hate fractions. But in time, you learn to love them. This is because there's a big difference between fractions and decimals, even though when you divide the actual fraction it comes out to a decimal. Decimals go on and on sometimes, and it would be impossible to write out all those numbers, especially when taking a timed test, for example. Fractions, in this case, would be much more useful (as long as you know how to use them to your advantage). Fractions are basically all those decimal numbers wrapped up into a single, simple division. It makes the outcome of your answer much more accurate than if you estimate every decimal you get throughout a math problem. The more you estimate throughout the problem-solving process, the less accurate your final answer will be. Hence why teachers will usually tell you to estimate when you're putting down the final answer. Fractions are complex at times, so it may be easier to use them in decimal form for certain situations (especially if the decimal form is short and sweet). A world without fractions will result in many, many inaccurate situations involving mathematical knowledge.

3 0

2 years ago

The width of a rectangle is 6 kilometers less than twice its length. if its area is 108 square kilometers, find the dimensions

Art [367]

Hi there!

Answer:
length = 9 kilometres
Width = 12 kilometres

Let's solve this problem step by step!
To find our answer we need to set up and solve an equation.

Let the length of the rectangle be represented by x.
The width of the rectangle can therefore be expressed by 2x - 6.

The area of a rectangle can be found by using the formula:
A = width × length

Plug in the data from the formula
A = x (2x - 6).

Simplify using rainbow technique.
$x(2x - 6) = 2 {x}^{2} - 6x$

Now we've found the simplified expression that expresses the area of the rectangle. Therefore, we can now set up and start solve the equation.

$2 {x}^{2} - 6x = 108$
Subtract 108

$2 {x}^{2} - 6x - 108 = 0$
Divide by 2.

${x}^{2} - 3x - 54$
$(x - 9)(x + 6) = 0$
Rule AB = 0, gives A is 0 or B is 0.

$x - 9 = 0 \\ x = 9 \\ \\ x + 6 = 0 \\ x = - 6$

The length of the rectangle, which was represented by x, must be 9 (since it cannot be a negative number).

Length
$x = 9$
Width
$2x - 6 = 2 \times 9- 6 = 18 - 6 = 12$

Answer:
length = 9 kilometres
Width = 12 kilometres

~ Hope this helps you!

6 0

2 years ago

Substitutions <br> y=x+4<br> y=3x+0

cluponka [151]

Answer:

x = 2

Step-by-step explanation:

since both equal y, you can set them equal to each other

x + 4 = 3x + 0

subtract x on both sides

4 = 2x

divide by 2 on both sides

2 = x

♡♡ hope this helped ♡♡

4 0

2 years ago

Read 2 more answers

Ralph buys a desk that regularly sells for $250 and a desk chair that regularly sells for $145. both items are on sale at 15% of

Lunna [17]

C) (0.85 + x/100)(250+145) does not give the correct answer.

Explanation
A) works; adding the two costs together is 250+145=395. We multiply this by 0.85 because 100%-15%=85%=0.85. We also have x% tax, which is represented by x/100, added to 100% of the value, or 1.00. Altogether this gives us
395(0.85)(1+x/100) = 395(0.85 + (0.85x/100)) = 395(0.85) + 395(0.85x/100)
= 395(0.85) + 395(0.0085x)
B) works; we have 250+145 for the original price; we have 85% = 0.85 of the value; we also have 100% + x%, which is (100+x)/100.
C) does not work; (0.85+x/100)(395) does not take into consideration that you are finding the tax after taking the 85%. This will simplify out to
0.85*395 + (x/100)(395) = 335.75 + 395x/100 = 335.75 + 3.95x, which is too much.
D) works; simplifying the expression from A, we have 395(0.85) + 395(0.0085x) = 335.75 + 3.3575x.

6 0

3 years ago