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borishaifa [10]
3 years ago
8

A rectangle's length is three times its width. Let w denote the rectangle's width. What polynomial represents the rectangle's ar

ea?
Mathematics
1 answer:
Nataliya [291]3 years ago
8 0
Width = W
Length = 3 times w = 3W

Area = length x width = 3W * W = 3W^2
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How do i simplify 1/3√45 using product property
TEA [102]

\frac{1}{3\sqrt{45}} = \frac{1}{3\sqrt{3 x 3 x 5}}  = \frac{1}{9\sqrt{5}} x \frac{\sqrt{5}}{\sqrt{5}} = \frac{\sqrt{5}}{9 x 5} = \frac{\sqrt{5}}{45}

6 0
3 years ago
Huixian needs 171 pens 63 pencils and 27 erasers into identical gift packs so that each item could equally distribiuted among th
Anuta_ua [19.1K]

Answer:

there will 7 pencils, 19 pens and 3 erasers in each bag of gift bag and total number of gifts bag will be 9.

Step-by-step explanation:

Given:

Number of pens = 171 pens

Number of pencils = 63

Number of erasers = 27

We need to number of each items in the bags.

Solution:

First we will find the largest number of gift bags that can be packed.

To find the  the largest number of gift bags that can be packed we need to find the greatest common factor of these numbers.

So we will List  the prime factors for each number:

171 = 3 \times 3 \times 19\\\\63 = 3 \times 3 \times 7\\\\27 = 3 \times 3 \times 3

From above we can say that;

The greatest common factor of three numbers = 3\times3=9

Hence There would 9 gifts bag to packed this item.

Now To find the Number of item in each bag we will divide number of items from the number of gifts bag.

framing in equation form we get;

Number of pencils in each = \frac{63}{9}=7\ pencils

Number of pens in each bag = \frac{171}{9}=19\ pens

Number of eraser in each bag = \frac{27}{9}=3\ erasers

Hence there will 7 pencils, 19 pens and 3 erasers in each bag of gift bag and total number of gifts bag will be 9.

6 0
3 years ago
Determine the next step for solving the quadratic equation by completing the square.
nexus9112 [7]

\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2

the idea behind the completion of the square is simply using a perfect square trinomial,  hmmm usually we do that by using our very good friend Mr Zero, 0.

if we look at the 2nd step, we have a group as x² - x, hmmm so we need a third element, which will be squared.

keeping in mind that the middle term of the perfect square trinomial is simply the product of the roots of "a" and "b",  so in this case the middle term is "-x", and the 1st term is x², so we can say that

\stackrel{middle~term}{2(\sqrt{x^2})(\sqrt{b^2})~}~ = ~~\stackrel{middle~term}{-x}\implies 2xb~~ = ~~~~ = ~~-x \\\\\\ b=\cfrac{-x}{2x} \implies b=-\cfrac{1}{2}

so that means that our missing third term for a perfect square trinomial is simply 1/2, now we'll go to our good friend Mr Zero, if we add (1/2)², we have to also subtract (1/2)², because all we're really doing is borrowing from Zero, so we'll be including then +(1/2)² and -(1/2)², keeping in mind that 1/4 - 1/4 = 0, so let's do that.

-3~~ = ~~-2\left[ x^2-x+\left( \cfrac{1}{2} \right)^2 ~~ - ~~\left( \cfrac{1}{2} \right)^2\right]\implies -3=-2\left(x^2-x+\cfrac{1}{4}-\cfrac{1}{4} \right) \\\\\\ -3=-2\left(x^2-x+\cfrac{1}{4} \right)+(-2)-\cfrac{1}{4}\implies -3=-2\left(x^2-x+\cfrac{1}{4} \right)+\cfrac{1}{2} \\\\\\ -3-\cfrac{1}{2}=-2\left(x^2-x+\cfrac{1}{4} \right)\implies -\cfrac{7}{2}=-2\left(x-\cfrac{1}{2} \right)^2\implies \cfrac{7}{4}=\left(x-\cfrac{1}{2} \right)^2

~\dotfill\\\\ \pm\sqrt{\cfrac{7}{4}}=x-\cfrac{1}{2}\implies \cfrac{\pm\sqrt{7}}{2}=x-\cfrac{1}{2}\implies \cfrac{\pm\sqrt{7}}{2}+\cfrac{1}{2}=x \implies \cfrac{\pm\sqrt{7}+1}{2}=x

8 0
2 years ago
(40 points) Manuel and Jerry are trying to find the value of the expressions (5+7)2. Jerry plans to first square 5,then square 7
Vlada [557]
Manual is correct due to 5^2 and 7^2 being 74 in total while 5+7 is 12 being squared gives you 144 which is the correct answer.
6 0
3 years ago
F(x) = -4x2 + 5x<br> Find f (6)
mina [271]
You would plug in 6 where the x is so it would be -4 times 2 plus 5(6)
7 0
3 years ago
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