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NNADVOKAT [17]
3 years ago
15

Find the length to the nearest centimeter of the diagonal of a square 30 cm. on a side

Mathematics
1 answer:
tiny-mole [99]3 years ago
8 0

Answer:

42 cm.

Step-by-step explanation:

Please find the attachment.

Let x be the length of diagonal of the square.

We have been given that length of each side of a square is 30 cm. We are asked to find the length of the diagonal of square to the nearest centimeter.

We can see from our diagram that triangle AC is the diagonal of our square.

Since all the interior angles of a square are right angles or equal to 90 degrees, so we will use Pythagoras theorem to find the length of diagonal.

AC^2=AD^2+DC^2  

Upon substituting our given values in above formula we will get,

x^2=(30\text{ cm})^2+(30\text{ cm})^2

x^2=900\text{ cm}^2+900\text{ cm}^2

x^2=1800\text{ cm}^2

Let us take square root of both sides of our equation.

x=\sqrt{1800\text{ cm}^2}

x=42.4264\text{ cm}\approx 42\text{ cm}

Therefore, the length of diagonal of our given square is 42 cm.

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2/5 divided by 1/8. Simplest form
serg [7]

Answer:

1/20 or in a decimal 0.05

Step-by-step explanation:

Hope This helps :)

7 0
3 years ago
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The sum of a number and twice its square is 105. Find the number
IRISSAK [1]
N+2^2=105
105-4=101
n=101
hope it helps please mark me as brainliest
 
3 0
3 years ago
A sector of a circle has a central angle of 100 degrees. If the area of the sector is 50pi, what is the radius of the circle
MrMuchimi

The radius of the circle having the area of the sector 50π, and the central angle of the radius as 100° is <u>6√5 units</u>.

An area of a circle with two radii and an arc is referred to as a sector. The minor sector, which is the smaller section of the circle, and the major sector, which is the bigger component of the circle, are the two sectors that make up a circle.

Area of a Sector of a Circle = (θ/360°) πr², where r is the radius of the circle and θ is the sector angle, in degrees, that the arc at the center subtends.

In the question, we are asked to find the radius of the circle in which a sector has a central angle of 100° and the area of the sector is 50π.

From the given information, the area of the sector = 50π, the central angle, θ = 100°, and the radius r is unknown.

Substituting the known values in the formula Area of a Sector of a Circle = (θ/360°) πr², we get:

50π = (100°/360°) πr²,

or, r² = 50*360°/100° = 180,

or, r = √180 = 6√5.

Thus, the radius of the circle having the area of the sector 50π, and the central angle of the radius as 100° is <u>6√5 units</u>.

Learn more about the area of a sector at

brainly.com/question/22972014

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8 0
1 year ago
Need to know this now pls !!! NEED THE PROCESS , TOO!!!<br><br> x squared - 18x = -117
nydimaria [60]

Answer:

x = 9 + 6i or x = 9 - 6i

Step-by-step explanation:

x² - 18x + 117 = 0

Complete the square and solve:

(x - 9)² - 81 + 117 = 0

(x - 9)² + 36 = 0

(x - 9)² = -36

x - 9 = ±sqrt(-36)

x - 9 = ±sqrt(-1).sqrt(36)

i = imaginary number = sqrt(-1)

x - 9 = ±6i

x = 9 ± 6i

There are no real solutions, only imaginary ones

9 + 6i and 9 - 6i

3 0
3 years ago
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Type the correct answer in the box. Round your answer to the nearest integer.
umka21 [38]

Answer:

m∠ADC = 132°

Step-by-step explanation:

From the figure attached,

By applying sine rule in ΔABD,

\frac{\text{sin}(\angle ABD)}{\text{AD}}=\frac{\text{sin}(\angle ADB)}{AB}

\frac{\text{sin}(120)}{35}=\frac{\text{sin}(\angle ADB)}{30}

sin(∠ADB) = \frac{30\text{sin}(120)}{35}

                 = 0.74231

m∠ADB = \text{sin}^{-1}(0.74231)

             = 47.92°

             ≈ 48°

m∠ADC + m∠ADB = 180° [Linear pair of angles]

m∠ADC + 48° = 180°

m∠ADC = 180° - 48°

m∠ADC = 132°

4 0
3 years ago
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