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Sedaia [141]
4 years ago
9

What is the answer? I need help please

Mathematics
1 answer:
Rudiy274 years ago
8 0

Answer:

150 pillows

Step-by-step explanation:

As given,

The amount of Lace Trim in stock is 135 yd

For making a single pillow \frac{9}{10} yd lace trim is needed

Hence, the number of pillows that can be made by 135 yd lace trim is

(135÷\frac{9}{10})

=>150 pillows

Again,

The amount of Corduroy Fabric in stock is 168 yd

For making a single pillow \frac{7}{18} yd corduroy fabric is needed

Hence, the number of pillows that can be made by 168 yd corduroy fabric is

(168÷\frac{7}{8})

=>192 pillows

Again,

The amount of Cotton Filling in stock is 104 lb

For making a single pillow \frac{2}{3} lb cotton filling is needed

Hence, the number of pillows that can be made by 104 lb cotton filling is

(104÷\frac{2}{3})

=>156 pillows

Now,

Since, we have to use all three materials for manufacturing a pillow, we can make highest 150 pillows by the amount of materials in stock. We can't make more than 150 pillows because lace trim will run out after using in in 150 pillows.

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Determine the inverse of the function f(x) = log3(4x + 5) − 6.
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Answer:

f inverse of x is equal to 3 to the power of the quantity x plus 6 end quantity minus 5 all over 4

Step-by-step explanation:

The function f(x)=\log_3 (4x+5)-6 can be thought of as a series of steps, one operation at a time:

Start with x

Multiply by 4

Add 5

Take the \log_3

Subtract 6

That gives you a function value f(x).

To get the inverse function, read that list from the bottom up (in reverse order, using inverse operations at each step).

Start with x  (a bit confusing, because this  x  represents the function value you get at the end of the above list).

Add 6   (add is the inverse operation of subtract)

Raise 3 to the ...    3^{\text{result of previous step}

Subtract 5

Divide by 4

f^{-1}(x) = \frac{3^{x+6}-5}{4}

Let's test this out.  Find f(1).

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Now put -4 into the inverse function.

f^{-1}(-4)=\frac{3^{-4+6}-5}{4}=\frac{3^2-5}{4}=\frac{9-5}{4}=\frac{4}{4} =1

The final result is the number we started with when we put 1 into <em>f</em>(<em>x</em>).

Finding an inverse is reversing the action of the function  <em>f</em>  by doing inverse operations in "backwards" order.

A lot of authors have you do this by switching  x  and  y  in the formula for a function, then solving for  <em>x</em>.

y = \log_3(4x+5)-6\text{  switch x and y}\\\\x = \log_3(4y+5)-6\\\\x+6 = \log_3(4y+5)\\\\3^{x+6}=4y+5\\\\3^{x+6}-5=4y\\\\\frac{3^{x+6}-5}{4}=y

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2 years ago
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