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Ludmilka [50]
3 years ago
7

An 8-inch dinner knife is sitting on a circular plate so that its ends are on the edge of the plate. If the minor arc that is in

tercepted by the knife measures 120 degrees, find the length of the diameter of the plate. Round your final answer to two decimal places.
Mathematics
1 answer:
ankoles [38]3 years ago
7 0

The diameter of the plate is 9.24 inches

Step-by-step explanation:

Let us consider the radius to be 'r'

Angle = 120°

Chord length = 8 inches

Chord length = 2rsin(θ/2)

8 = 2r sin(120/2)

8 = 2r sin60°

8/2 = r (√3/2)

4/(√3/2) = r

r = 8/√3

r = 8/1.73

r = 4.62 inches

Diameter of the plate = 2(4.62)

= 9.24 inches

The diameter of the plate is 9.24 inches

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Given: ABC is similar to XYC. If BY = 6, YC = 10, AX = 18, then XC = 10.8 5 30 48
Sidana [21]

Answer:

The correct option is 3. The length of XC is 30.

Step-by-step explanation:

It is given that triangle ABC and triangle XYC are similar.

According to the properties of similar triangles, then corresponding sides of similar triangles are congruent.

In triangle ABC and triangle XYC,

\frac{AB}{XY}=\frac{BC}{YC}=\frac{AC}{XC}

Let the length of XC be x.

From the below figure it is notices that

AC=AX+XC=18+x

BC=BY+YC=6+10=16

\frac{16}{10}=\frac{18+x}{x}

16x=180+10x

6x=180

x=30

Therefore correct option is 3. The length of XC is 30.

3 0
3 years ago
Read 2 more answers
rename each mixed number as an equivalent mixed number with the same denominator. 4 6/9= 7 5/3= 3 7/8= 5 19/14=
denis-greek [22]
4 6/9= 38/9   
7 5/3= 26/3
3 7/8= 31/8
5 19/14 =89/14

5 0
3 years ago
Jane has three boxes she needs to ship. Box X weighs 33 kg more than Box Y and Box Z weighs 12 kg more than Box Y. She
andreyandreev [35.5K]

Answer:

3w+45=557

Step-by-step explanation:

Let the weight of box Y be w kg.

Box X weighs 33 kg more than Box Y, then the weight of box X is

w+33 kg.

Box Z weighs 12 kg more than Box Y, then the weight of box Z is

w+12 kg.

The total weight of all boxes is

w+(w+33)+(w+12)=w+w+33+w+12=3w+45 kg

Jane measured the total weight of all the boxes and it was found to be 557 kg, therefore,

3w+45=557

or

3w=512

3 0
3 years ago
Help help due in 5minutes
Hoochie [10]

Answer:

Step-by-step explanation:

if you multiply any number in the first sequence by 3, you get that number in sequence 2 in the same position as the first number.

6x3=18

7x3=21

8x3=24

9x3=27

10x3=30

4 0
3 years ago
Complete the missing value in the solution to the equation.
Setler [38]
It’s 178-9 that’s the answer
6 0
2 years ago
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