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anzhelika [568]
3 years ago
7

Simplify (3n - 2m)^2 = Can someone break this down for me? I don't understand why I'm having issues with this.

Mathematics
2 answers:
natta225 [31]3 years ago
8 0

Answer:

Once you simplify the given expression, your answer will be 9n² - 12mn + 4m

Step-by-step explanation:

In this problem, we are given an expression.

(3n - 2m)²

when an expression or equation is raised to the power of 2, then you are going to multiply the base term by itself. For example, if you have 2² or 16², then would you do 2 × 2 and 16 × 16 in order to solve the expressions. We will do the same for this expression.

(3n - 2m)² = (3n - 2m) × (3n - 2m)

We will use the foil method to solve this expression

(3n - 2m)(3n - 2m)

9n² - 6mn - 6mn + 4m

Combine like terms together.

9n² - 12mn + 4m

So, the simplified form of the expression is 9n² - 12mn + 4m

vfiekz [6]3 years ago
3 0

Answer:

9n² - 12mn + 4m²

Step-by-step explanation:

(a+b)² = a² + 2ab + b²

(3n - 2m )² = (3n-2m)(3n-2m) = 3n*3n + 3n*-2m -2m*3n - 2m*-2m

= 9n² - 6nm -6mn + 4m²

= 9n² - 12mn + 4n²

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Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and pro
Neporo4naja [7]

{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}

★ Sanya has a piece of land which is in the shape of a rhombus.

★ She wants her one daughter and one son to work on the land and produce different crops, for which she divides the land in two equal parts.

★ Perimeter of land = 400 m.

★ One of the diagonal = 160 m.

{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}

★ Area each of them [son and daughter] will get.

{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}

Let, ABCD be the rhombus shaped field and each side of the field be x

[ All sides of the rhombus are equal, therefore we will let the each side of the field be x ]

Now,

• Perimeter = 400m

\longrightarrow  \tt AB+BC+CD+AD=400m

\longrightarrow  \tt x + x + x + x=400

\longrightarrow  \tt 4x=400

\longrightarrow  \tt  \: x =  \dfrac{400}{4}

\longrightarrow  \tt x= \red{100m}

\therefore Each side of the field = <u>100m</u><u>.</u>

Now, we have to find the area each [son and daughter] will get.

So, For \triangle ABD,

Here,

• a = 100 [AB]

• b = 100 [AD]

• c = 160 [BD]

\therefore \tt Simi \:  perimeter \:  [S] =  \boxed{ \sf \dfrac{a + b + c}{2} }

\longrightarrow \tt S = \dfrac{100 + 100 + 160}{2}

\longrightarrow \tt S =  \cancel{ \dfrac{360}{2}}

\longrightarrow \tt S = 180m

Using <u>herons formula</u><u>,</u>

\star \tt Area  \: of  \: \triangle = \boxed{\bf{{ \sqrt{s(s - a)(s - b)(s - c) } }}} \star

where

• s is the simi perimeter = 180m

• a, b and c are sides of the triangle which are 100m, 100m and 160m respectively.

<u>Putt</u><u>ing</u><u> the</u><u> values</u><u>,</u>

\longrightarrow \tt  Area_{ ( \triangle \:  ABD)} =  \tt \sqrt{180(180 - 100)(180 - 100)(180 - 160) }

\longrightarrow \tt  Area_{ ( \triangle \:  ABD)} =  \tt \sqrt{180(80)(80)(20) }

\longrightarrow \tt  Area_{ ( \triangle \:  ABD)} =  \tt \sqrt{180 \times 80 \times 80 \times 20 }

\longrightarrow \tt  Area_{ ( \triangle \:  ABD)} =  \tt \sqrt{9 \times 20 \times 20 \times 80 \times 80}

\longrightarrow \tt  Area_{ ( \triangle \:  ABD)} =  \tt \sqrt{ {3}^{2} \times  {20}^{2}  \times  {80}^{2}  }

\longrightarrow \tt  Area_{ ( \triangle \:  ABD)} =  3 \times 20 \times 80

\longrightarrow \tt  Area_{ ( \triangle \:  ABD)} = \red{   4800  \: {m}^{2} }

Thus, area of \triangle ABD = <u>4800 m²</u>

As both the triangles have same sides

So,

Area of \triangle BCD = 4800 m²

<u>Therefore, area each of them [son and daughter] will get = 4800 m²</u>

{\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}

★ Figure in attachment.

{\underline{\rule{290pt}{2pt}}}

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Answer:

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Step-by-step explanation:

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Let x be the number of days.

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Season pass:
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95x > 400 + 30x
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It would take 7 days until the season pass is less expensive than the daily pass.
----------------------
You can check this by plugging in the x.

95x > 400 + 30x
95(7) > 400 + 30(7)
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Naddik [55]

Answer:

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Step-by-step explanation:

Step 1:

3 : 7       Ratio

Step 2:

3x + 7x = 50        Substitute

Step 3:

10x = 50     Add

Step 4:

50 ÷ 10     Divide

Step 5:

x = 5

Answer:

15 girls, and 35 boys     Multiply

Hope This Helps :)

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Aloiza [94]
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