The top suface of a desk is composed of 2 rectangles and a triangle. some side lengths of the top surface of the desk are shown

Given:

The figure of triangle ABC.

The area of the triangle ABC is D.

[tex]m\angle B=\sin ^{-1}(\dfrac{m}{n})[/tex]

To find:

The value of m and n in the given expression.

Solution:

Let h be the height of the triangle ABC.

Area of a triangle is:

[tex]Area=\dfrac{1}{2}\times base\times h[/tex]

Where, b is the base and h is the height of the triangle.

[tex]Area=\dfrac{1}{2}\times a\times h[/tex]

The area of the triangle ABC is D.

[tex]D=\dfrac{1}{2}\times a\times h[/tex]

[tex]2D=ah[/tex]

[tex]\dfrac{2D}{a}=h[/tex]                  ...(i)

In a right angle triangle,

[tex]\sin \theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\sin B =\dfrac{h}{c}[/tex]

[tex]\sin B =\dfrac{1}{c}\times \dfrac{2D}{a}[/tex]              [Using (i)]

[tex]\sin B =\dfrac{2D}{ac}[/tex]

[tex]m\angle B =\sin ^{-1}\dfrac{2D}{ac}[/tex]            ...(ii)

We have,

[tex]m\angle B=\sin ^{-1}(\dfrac{m}{n})[/tex]          ...(iii)

On comparing (ii) and (iii), we get

[tex]m=2D[/tex]

[tex]n=ac[/tex]

Therefore, the required values are [tex]m=2D, n=ac[/tex].

Answer:

Given: circle

diameter = 10 cm => radius (R) = 5 cm

Find: measure of angle bounding sector = 11 π sq. cm.

Plan: determine what part of the circle’s total area equals the sector’s area.

Total Area of Circle A = π R^2 = π 5^2 = 25 π sq. cm.

Therefore: Sector Area = 11 π cm^2/25 π cm^2 = 11/25

Since the sector is 11/25 th of the circles area, the sector angle will measure 11/25 th of the circle’s circumference. They are proportional.

C = 2 π R = 2 π (5) = 10 π cm

Sector Arc = measure of sector angle = 11/25 (10 π) =

22π/5 radians

Answer: Sector Arc = 22π/5 Radians

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

37+82=x(sum of two interior opposite angles is equal to the exterior angle formed)

119=x

therefore x=119 degree

7) 20y-8=52

20y=60

y=3

11)2x+17=5x-4

21=7x

x=3

12)2x+7=16-4x

6x=9

x=9/6

x=3/2

x=1.5

14)8y+4=24-2y

10y=20

y=2

15)7-3x=2x+2

5=5x

x=1

16)

[tex] \frac{x - 3}{2} = 5 \\ x - 3 = 10 \\ x = 13[/tex]

Answer:

Answer is C.

Step-by-step explanation:

8÷8= 1

1 whole

Answer:

-16 and 24

Step-by-step explanation:

-16 x 24 = -384

-16 + 24 = 8

In △JKL, segment LK is the leg opposite ∠J and segment JL is the leg adjacent to ∠J. Option B is correct.

∠J refers to angle J, which is one of the angles of the triangle △JKL.

In a triangle, the legs are the two sides that form the angle of interest.

In this case, we are interested in ∠J, so the legs are the two sides that form this angle.

The leg opposite ∠J is the side of the triangle that is not part of forming the angle ∠J or it is the side that is directly across from ∠J. In the given triangle △JKL, segment KL is the side opposite ∠J.

The leg adjacent to ∠J is the side of the triangle that is one of the two sides forming the angle ∠J.

In the given triangle △JKL, segment LJ is one of the sides that forms ∠J and is thus the leg adjacent to ∠J.

Hence, In △JKL, segment LK is the leg opposite ∠J and segment JL is the leg adjacent to ∠J. Option B is correct.

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Complete question:

In △JKL, _______ is the leg opposite ∠J and _______ is the leg adjacent to ∠J.

(A) segment LK; segment JK

(B) segment LK; segment JL

(C) segment JL; segment JK

(D) segment JK; segment LK

Answer:

C = 2pi(r)

= 2pi(5)

≈ 31.416

≈ 31.4

Answer:

Hello! answer: 31.4

Step-by-step explanation:

I'm using 3.14 for pi and

To find circumference you just have to do diameter × pi or radius × 2 × pi since we have the radius we can just do radius × 2 × pi so

5 × 2 × 3.14 = 31.4 so our circumfrence is 31.4 Hope that helps!!

Answer:

1,243.88 units² I think

Step-by-step explanation:

22 x 22 = 484

A = (3.14 x 11²)2 = 759.88

759.88 + 484 = 1,243.88 units²

Answer:

4 hours

Step-by-step explanation:

Distance covered = 30 km

Usual Speed of both = 10km/hr

Justin's speed = 1/2 * 10 = 5km/hr

Ari's speed = 3/2 * 10 = 15 km/hr

Time taken = distance / speed

Justin's time = 30 / 5 = 6 hours

Ari's time = 30 / 15 = 2 hours

Time difference = (6 - 2) = 4 hours

Answer:

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {6}^{2} + {7}^{2} = {c}^{2} \\ 36 + 49 = {c}^{2} \\ 85 = {c}^{2} \\ \sqrt{85} = \sqrt{ {c}^{2} } \\ 9.21954 = c \\ c≈9 \\ [/tex]

Answer:

Step-by-step explanation:

Tienes que multiplicar el seis y el cuatro lo que te multiplicarlo por 3,14y después dividirlo por dos

Answer:21

Step-by-step explanation:

Add them all up

The number of students who collect more than one coin is 12.

A Line plot can be defined as a graph that displays data as points or check marks above a number line, showing the frequency of each value.

Given that, Mr. Petersen counted the number of coins collected by the students in his coin club and prepared the line plot.

We need to find how many students collected more than 1 coin,

Here each X represents a student,

The numbers of mark X above 2 and 3 = 4 and 8

Therefore, total students = 12

Hence, the number of students who collect more than one coin is 12.

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Answer:

[tex] \displaystyle x = \frac{21y + 2}{15} [/tex]

[tex] \displaystyle y = \frac{15x - 2}{21} [/tex]

Step-by-step explanation:

remove parentheses:

[tex] \displaystyle x + 7y = 6x - \frac{2}{3} [/tex]

move x to left hand side and y to right hand side and change its sign:

[tex] \displaystyle x - 6x = -7y - \frac{2}{3} [/tex]

simplify Substraction:

[tex] \displaystyle - 5x = \frac{-21y - 2}{3} [/tex]

divide both sides by -5:

[tex] \displaystyle x = \frac{21y + 2}{15} [/tex]

move x to the right hand side and change its sign:

[tex] \displaystyle 7y = 6x - x- \frac{2}{3} [/tex]

simplify Substraction:

[tex] \displaystyle 7y =5x- \frac{2}{3} [/tex]

simplify substraction:

[tex] \displaystyle 7y = \frac{15x - 2}{3} [/tex]

divide both sides by 7:

[tex] \displaystyle y = \frac{15x - 2}{21} [/tex]

and we are done!

Answer:

d

Step-by-step explanation:

Answer:

9) A. 1 to 2

8) B. 32

Step-by-step explanation:

9) 2 + 4 + 6 = 12 total balls

ratio of golf balls to total is 6:12, which = 1:2

8) 0.75 = 24/x

x = 24(.75) = 32

Step-by-step explanation:

-1.4 or - 14/10

-1.3 or -13/10

-1.2 or -12/10

-1.1 or -11/10

-1.0 or -1/1

Divide each term by −3-3 and simplify.

Inequality Form:

x≥3

Answer:

x≥3

Step-by-step explanation:

Divide both sides by -3.

−3x/ −3 ≤ −9/ −3

x≥3

Answer:

Thats not a full question

Step-by-step explanation:

Answer:

-4

-1

2

5

8

Step-by-step explanation:

Answer:

a) 35,  b) 25,  c) 60

Step-by-step explanation:

The number of girls is 10 more than the number of boys, so it's a good thing to choose a variable to represent the number of boys.

Number of boys:  b

Number of girls:  b + 10

Ratio of girls:boys is 7:5, so

[tex]\frac{b+10}{b}=\frac{7}{5}[/tex]

"Cross multiply" to get

[tex]7b=5(b+10)\\7b=5b+50\\2b=50\\b=25[/tex]

There are 25 boys.  There are 10 more girls, so the number of girls is 35, and the total number of students is 60.

That's a packed classroom!

Answer:

x = 103⁰

Step-by-step explanation:

127+40+90+x = 360⁰

257+x = 360⁰

x = 360⁰- 257⁰

x= 103⁰

The distance between x and y on a number line will be,

⇒ |y - x|

Option B is true.

What is Number system?

A system of writing to express the number is called number system.

Given that;

x and y are two number on number line.

Now,

Since, Distance between x and y is always positive.

And, Distance between x and y is calculated as;

⇒ |y - x|

Thus, The distance between x and y on a number line will be,

⇒ |y - x|

Option B is true.

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My first answer to this question was p<3/34 and I was wrong.

The answer really is p<12/25

Hope this helped God bless you! ❤️

Answer:

262144

Step-by-step explanation:

The sequence increases by a multiple of -4

Therefore, you can either do 4⁹ or you can multiply by -4 until you have done that 9 times