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3 years ago

Betty is making 6 skirts. Each skirt uses 2/3 of a yard. How many yards does she need?

Mathematics

1 answer:

AysviL [449]3 years ago

8 0

Answer:

She needs 4 yards.

Step-by-step explanation:

To multiply fractions, you just multiply the whole number by the numerator of the fraction.

<em>The numerator is the top number of a fraction.</em>

<em>The denominator is the bottom number of a fraction.</em>

You can think of the whole number 6 as the fraction 6/1.

Multiply 6/1 by 2/3

6x2=12

1x3=3

So, 6/1x2/3=<u>12/3</u>

<u></u>

Now you need to simplify the fraction

Because the numerator is a muliple (number that can be devided by) of 3, devide the numerator by the denominator.

12÷3=4

<h2>So betty needs 4 yards of fabric to make 6 skirts.</h2>

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3 years ago

Remember that you can multiply by the reciprocal of the divisor when you divide by a fraction. find each quotient. simplify if p

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3 years ago

The profit P (in thousands of dollars) for an educational publisher can be modeled by P 52b31 5b21b where b is the number of wor

Anna007 [38]

Answer:

The lesser number of workbooks are 1,000

Step-by-step explanation:

The correct question is

The profit P (in thousands of dollars) for an educational publisher can be modeled by P=-b³+5b²+b where b is the number of workbooks printed (in thousands). Currently, the publisher prints 5000 workbooks and makes a profit of $5000. What lesser number of workbooks could the publisher print and still yield the same profit?

we have

$P=-b^3+5b^2+b$

For $P=\$5,000$

substitute in the equation and solve for b

Remember that the profit and the number of workbooks is in thousands

P=5

$5=-b^3+5b^2+b$

Using a graphing tool

Solve the cubic function

The solutions are

x=-1

x=1

x=5

therefore

The lesser number of workbooks are 1,000

<u><em>Verify</em></u>

For b=1

$P=-(1)^3+5(1)^2+1$

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3 years ago

The partial fraction decomposition of 9 x 11 6 x 2 23 x 21 can be written in the form of f ( x ) 2 x 3 g ( x ) 3 x 7 , where

svlad2 [7]

Answer:

$f(x) = -1$

$g(x) =6$

$\frac{-1}{2x + 3} + \frac{6}{3x + 7}$

Step-by-step explanation:

The question is unreadable, however the real polynomial is:

The polynomial fraction is:

$P = \frac{9x + 11}{6x^2 + 23x + 21}$

And the decomposition is:

$\frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}$

The solution is as follows:

$P = \frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}$

Substitute the expression for P

$\frac{9x + 11}{6x^2 + 23x + 21} = \frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}$

Expand the numerator of the polynomial

$\frac{9x + 11}{(2x + 3)(3x + 7)} = \frac{f(x)}{2x + 3} + \frac{g(x)}{3x + 7}$

Take LCM

$\frac{9x + 11}{(2x + 3)(3x + 7)} = \frac{f(x)*(3x + 7) + g(x)*(2x + 3)}{(2x + 3)(x + 7)}$

Cancel out both denominators

$9x + 11} = f(x)*(3x + 7) + g(x)*(2x + 3)$

Represent f(x) as A and g(x) as B

$9x + 11} = A*(3x + 7) + B*(2x + 3)$

Open bracket

$9x + 11} = 3Ax + 7A + 2Bx + 3B$

$9x + 11} = 3Ax + 2Bx+ 7A + 3B$

$9x + 11} = (3A + 2B)x+ 7A + 3B$

By comparison:

$3A + 2B = 9$ ---- (1)

$7A + 3B =11$ ---- (2)

Make B the subject in (1)

$B = \frac{9 - 3A}{2}$

Substitute $B = \frac{9 - 3A}{2}$ in (2)

$7A + 3(\frac{9 - 3A}{2}) = 11$

Multiply through by 2

$2*7A +2* 3(\frac{9 - 3A}{2}) = 11*2$

$14A + 3(9 - 3A) = 22$

$14A + 27 - 9A = 22$

Collect Like Terms

$14A - 9A = 22-27$

$5A = -5$

$A = \frac{-5}{5}$

$A = -1$

Recall that:

$B = \frac{9 - 3A}{2}$

$B = \frac{9 - 3 * -1}{2}$

$B = \frac{9 + 3}{2}$

$B = \frac{12}{2}$

$B = 6$

A = -1 and B = 6

$3A + 2B = 9$ ---- (1)

$7A + 3B =11$ ---- (2)

So:

$f(x) = A$

$f(x) = -1$

$g(x) =B$

$g(x) =6$

And the decomposition is:

$\frac{-1}{2x + 3} + \frac{6}{3x + 7}$

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2 years ago

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lidiya [134]

Answer:

Step-by-step explanation:

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3 years ago