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3 years ago

Which of the following statements describes one part of completing the square for x^2 + 4x = 32?

1 answer:

4 0

$x^{2}+4x=32 \\ \\ x^{2}+4x+4=36 \\ \\ (x+2)^{2}=36 \\ \\ |x+2|=6 \\ \\ x+2=6 \ \vee \ x+2=-6 \\ \\ x=4 \ \vee \ x=-8$

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The sum of X^2y and (2xy^2 + x^2y) is 6x^2+2xy^2 but what is it? a monomial or a binomial?

o-na [289]

'Tis a Binomial. if it were a monomial, there would be no operator between 6x^2 and 2xy^2

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3 years ago

A store sells mugs. Each mug costs the same amount. During a sale, the store reduces the price of each mug by $1.75. Wen spends

Ostrovityanka [42]

Answer:

$7.39

Step-by-step explanation:

Let the initial price be x

Then the reduced price is

x - 1.75

If 5 mugs cost $28.20, we have equation:

(x - 1.75)*5 = 28.20
x - 1.75 = 28.20/5
x - 1.75 = 5.64
x = 1.75 + 5.64
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Initial price for 1 mug was $7.39

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2 years ago

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15. The equation of a circle is x +

Ne4ueva [31]

Answer:

Step-by-step explanation:

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3 years ago

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 = 100m.

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 herons formula,

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

where

• s is the simi perimeter = 180m

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

Putting the values,

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

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

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

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

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

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

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

Thus, area of $\triangle$ ABD = 4800 m²

As both the triangles have same sides

So,

Area of $\triangle$ BCD = 4800 m²

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

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

★ Figure in attachment.

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

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1 year ago

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Which data set is represented by the modified box plot?

IgorLugansk [536]

Answer:A

Step-by-step explanation: A has everthing correct the median is between the numbers 92 98 making it 95 these are the numbers is order 79,86,88,88,92,98,100,106,115,136

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3 years ago

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