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lapo4ka [179]
3 years ago
8

Will mark brainliest! Questions are in the picture!

Mathematics
1 answer:
alexdok [17]3 years ago
8 0

Answer:

52.9 inches .

Step-by-step explanation:

Given that the triangular indentation has an area of 100 in.² and the base and height of this traingle are represented by expressions 3x and x+3 respectively . We need to find out the <u>perimeter </u>to the nearest tenth.

As we know that the area of triangle is ,

\rm\longrightarrow Area_{\triangle}=\dfrac{1}{2}(base)(height)

Substituting the respective values,

\rm\longrightarrow 100\ =\dfrac{1}{2}(x+3)(3x)\\\\\rm\longrightarrow 2(100) = 3x(x+3)\\\\\rm\longrightarrow200 = 3x^2+9x\\\\\rm\longrightarrow 3x^2+9x-200=0

On using the <u>Quadratic</u><u> formula</u> , we have;

\rm\longrightarrow x =\dfrac{-9\pm\sqrt{9^2-4(3)(-200)}}{2(3)} \\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{81+1200}}{6}\\\\\rm\longrightarrow x =\dfrac{-9\pm \sqrt{1281}}{6}

On simplifying above , we will get ,

\rm\longrightarrow x = 6.802,-9.802

Since sides can't be negative, therefore,

\rm\longrightarrow\underline{\underline{ x =6.802}}

Therefore ,

  • \rm\longrightarrow Base = 3x =3(6.802)in = 20.406\ in\\
  • \rm\longrightarrow Height = x +3=6.802+3=9.802\ in

Next let's find out the <u>hypotenuse </u>using Pythagoras theorem, as ;

\rm\longrightarrow h=\sqrt{ b^2+p^2}\\

\rm\longrightarrow h =\sqrt{ (20.406)^2+(9.802)^2}\\

\rm\longrightarrow h =\sqrt{416.40+96.07}\\

\rm\longrightarrow h = 22.63\ in

Now we may find perimeter as ,

\rm\longrightarrow P = p + b + h \\

\rm\longrightarrow P = (22.63 + 9.802 + 20.406)in.

\\\rm\longrightarrow P = 52.89 \ in.\\

\rm\longrightarrow \underline{\underline{ Perimeter = 52.9\ in .}}

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3 years ago
Find AB.<br> Round to the nearest tenth.<br> 61°
anzhelika [568]

Answer:

AB ≈ 14.3

Step-by-step explanation:

We're given <em>two sides </em>(BC and CA) and an <em>angle </em>(C)<em> between them</em>; the <em>law of cosines </em>is a good tool for calculating the third side of the triangle here. To remind you, the law of cosines tells us the relationship between the sides of a triangle with side lengths a, b, and c:

c^2=a^2+b^2-2ab\cos{C}

Where C is the angle between sides a and b. c is typically the side we're trying to find, so on our triangle, we have

c=AB\\a=BC=16\\b=CA=5\\C=m\angle C=61^{\circ}

Substituting these values into the law of cosines:

c^2=16^2+5^2-2(16)(5)\cos{61^{\circ}}\\c^2=256+25-160\cos{61^{\circ}}\\c^2=281-160\cos{61^{\circ}}\\c=\sqrt{281-160\cos{61^{\circ}}}\\c\approx 14.3

6 0
3 years ago
Read 2 more answers
Two glass containers are shown. Both are right rectangular prisms. Container 1 is filled with water and Container 2 is empty.
dmitriy555 [2]

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Answer:

  18 in

Step-by-step explanation:

The volume of each container is the product of its dimensions:

  V = LWH

We can let h represent the unknown height of Container 2. The volumes are equal when ...

  32·18·12 = 24·16·h

  (32·12·18)/(16·24) = h =18 . . . . . divide by the coefficient of h, simplify

The missing height of Container 2 is 18 inches.

6 0
3 years ago
Simplify.<br> Х+4/3x^2+7x - 20
pickupchik [31]

Answer:4/3x²+8x−20

Step-by-step explanation:Combine Like Terms:

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4

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x2+7x+−20

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4

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x2)+(x+7x)+(−20)

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8 0
3 years ago
The mean age of 9 women in an office is 27 years old. The mean age of 7 men in an office is 25 years old. What is the mean age (
marta [7]

Answer:

26 years

Step-by-step explanation:

Given:

The mean age of 9 women = 27 years old

The mean age of 7 men = 25 years old

Question asked:

What is the mean age (nearest year) of all the people in the office?

solution:

By using, mean = sum of observations divided by number of entities

The mean age of 9 women = 27 years old

\frac{sum of ages}{number of women} = 27

Sum  of ages of women = 27 \times9 = 243\\ years

The mean age of 7 men = 25 years old

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Total sum of ages of men and women in the office = 243 + 175

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Total number of people in the office = 9 women + 7 men = 16

The mean age of all the people in the office = Total sum of ages of men and women in the office divided by Total number of people in the office

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Therefore,  the mean age (nearest year) of all the people in the office = 26 years

6 0
3 years ago
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