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2 years ago

an angles measure is 6 degrees more than 3 times the measure of its complwment. find the measure of the angles.

Mathematics

1 answer:

irina1246 [14]2 years ago

3 0

Answer:

The angles are 22.5 and 67.5.

Step-by-step explanation:

A complement is the angle that when added to the given angle gives 90 degrees.

Therefore, the angle x is 3 times larger than its complement.

This means that x is 3/4 of 90 degrees and complement is 1/4 of 90 degrees.

Therefore, the angles are 22.5 and 67.5.

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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 = 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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Nick had 14 jelly beans in a bag. His mother put a handful of jelly beans in the bag. When Nick counts his jelly beans, he disco

horsena [70]

Answer:

14 + j = 28

Step-by-step explanation:

I hope this helps :)

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3 years ago

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How would you graph the solution set of x - 6 < - 3?

melomori [17]

Move all terms not containing x to the right side of the inequality. You should get x<3

This is what your line should look like. The circle will be open because the is not line under the less than sign. And it will be going toward the left because it is less than greater than is graphed to the right.

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3 years ago

Solve this system using the linear combination method. Show your work.

kipiarov [429]

Answer:

Let's solve for x.

4x+2y=5

Step 1: Add -2y to both sides.

4x+2y+−2y=5+−2y

4x=−2y+5

Step 2: Divide both sides by 4.

−2y+5

−1

Let's solve for x.

−4x−5y=7

Step 1: Add 5y to both sides.

−4x−5y+5y=7+5y

−4x=5y+7

Step 2: Divide both sides by -4.

−4x

−4

5y+7

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Step-by-step explanation:

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2 years ago

Please Help asap . picture attach

FinnZ [79.3K]

Answer: B) 0 real roots

---------------------------------------

The general rule is...
if D > 0, then you have two different real roots (see note below)
If D = 0, then you have exactly one real root
If D < 0, then you have no real roots (the two roots are imaginary/complex)
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D = b^2 - 4ac

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6 0

3 years ago