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Juli2301 [7.4K]
3 years ago
9

A carton of staples has 50 packages.The carton contains 25,000 staples in all.Each package has an equal number of staples.How ma

ny staples are in each package? Explain how to use a basic fact to the answer.
Mathematics
1 answer:
erastova [34]3 years ago
8 0

Answer:

Each package contains 500 staples

Step-by-step explanation:

We are told that the carton contains a total of 50 packets each containing an equal amount of staples. If the total number of staples in the packet is 25000,  we have to divide the total number of staples by the total number of packets to find out how many staples each packet has. This calculation is shown below,

\frac{25\,000}{50} =500.

Each packet contains 500 staples. The basic fact we use is the fact that each packet contains the same number of staples.


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Answer:

The solutions to the quadratic equations will be:

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Step-by-step explanation:

Given the expression

x^2-12x\:=\:21

Let us solve the equation by completing the square

x^2-12x\:=\:21

Add (-6)² to both sides

x^2-12x+\left(-6\right)^2=21+\left(-6\right)^2

simplify

x^2-12x+\left(-6\right)^2=57

Apply perfect square formula: (a-b)² = a²-2ab+b²

i.e.

x^2-12x+\left(-6\right)^2=\left(x-6\right)^2

so the expression becomes

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\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}

solve

x-6=\sqrt{57}

add 6 to both sides

x-6+6=\sqrt{57}+6

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x=\sqrt{57}+6

also solving

x-6=-\sqrt{57}

add 6 to both sides

x-6+6=-\sqrt{57}+6

Simplify

x=-\sqrt{57}+6

Therefore, the solutions to the quadratic equation will be:

x=\sqrt{57}+6,\:x=-\sqrt{57}+6

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