Compare the relationships of these numbers.

0.045 is ______________ 0.054

 

Use substitution method to determine the value of the given expression. Use 3 in place of X in the given expression.

\(3x^2-2\frac{1}{3}x\)

First convert the mixed fraction into improper fraction as

\(2 \frac{1}{3}=\frac{\left(3\ast2\right)+1}{3}=\frac{6+1}{3}=\frac{7}{3}\)

Now the expression becomes

\(3x^2-\frac{7}{3}x\)

In place of X insert 3

\(3\left(3\right)^2-\frac{7}{3}\left(3\right)=3\left(9\right)-7=27-7=20\)

When X=3, the equation reduces to 20.

Use 1 pint =16 ounces to convert between pints and ounces

\(56\ ounces\ast\frac{1 pint}{16 ounces}=\frac{7}{2} ounces=3.5 ounces\)

First step is to find the least common divisor of the denominators 19, 25, 5 and 15, which is 1425

Next, multiply each fraction with 1425 as follows

\(\frac{4}{19}\)* 1425=300

\(\frac{4}{25}\)* 1425=228

\(\frac{3}{5}\)* 1425=855

\(\frac{3}{15}\)* 1425=285

From the calculations above, 855 is the largest number among the four computed numbers. Then, it follows that\(\frac{3}{5}\) is the largest number.

A ratio of the form a:b = c:d converted to a proportion equation becomes\( \frac{a}{b}=\frac{c}{d}\)where \(a\ and\ d\neq0\)

Thus, 9:X=5:300 becomes

\(\frac{9}{X}=\frac{5}{300}\)

Cross-multiply to find the value of X

\(9\ast300=5X\)

\(2700=5X\)

Rearranging the above equation

\(5X=2700\)

Divide each side by 5

\(\frac{5X}{5}=\frac{2700}{5}\)

\(X=540\)

The value of X is 540.