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snow_tiger [21]
3 years ago
5

The rectangular prism shown has a length of 10 cm, a width of 10 cm, and a height of 6 cm. Find the length of the inner diagonal

AD of the prism. Note that AD is the hypotenuse of right triangle ACD. (Round your answer to the nearest hundredth.)

Mathematics
1 answer:
melamori03 [73]3 years ago
8 0
<h3>Answer:</h3>

15.36 cm

<h3>Explanation:</h3>

The Pythagorean theorem tells you ...

... AC² = AB² + BC² . . . . . relation for face diagonal

... AD² = AC² + CD² . . . . . relation for space diagonal

Subsituting the expression for AC² given by the first equation, the second equaiton becomes ...

... AD² = AB² + BC² + CD²

... AD² = (100 cm²) + (100 cm²) + (36 cm²) = 236 cm²

Taking the square root, we have ...

... AD = √236 cm = 2√59 cm

... AD ≈ 15.36 cm

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Lilit [14]

Answer:

90

Step-by-step explanation:

First, we should find the area of the trapezoid, and then subtract the area of the removed triangle in order to find the shaded area.

Area of the trapezoid

1) Area of the rectangle in the middle.

Base Length: 10

Height Length: 10

Area: 10 x 10 = 100

2. Area of the triangles on the side

Base Length: (14 - 10)/2 = 2

Height Length: 10

Area: 2 x 10 x 1/2 = 10

There are two triangles: 10 x 2 = 20

Area of the trapazoid: 100 + 20 = 120

Area of the triangle that's been removed

Base Length: 10

Height Length: 10 - 4 = 6

Area: 10 x 6 x 1/2 = 30

Shaded area

Area of the trapezoid - Area of the triangle

120 - 30 = 90

Area of the shaded region is 90.

4 0
2 years ago
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. A car repair center services 920 cars in 2012. Th
OverLord2011 [107]

Answer:

N = 920(1+0.03)^4t

Step-by-step explanation:

According to the given statement a car repair center services 920 cars in 2012. The number of cars serviced increases quarterly at a rate of 12% per year after 2012.

Rate is 12 % annually

rate in quarterly = 12/4= 3%

We will apply the compound interest equation:

N=P( 1+r/n)^nt

N= ending number of cars serviced.

P=  the number of cars serviced in 2012,

r = interest rate

n = the number of compoundings per year

t= total number of years.

Number of compoundings for t years = n*t = 4t

Initial number of cars serviced=920

The quarterly rate of growth = n=4

r = 3%

The growth rate = 1.03

Compound period multiplied by number of years = 920(1.03)^4t

Thus N = 920(1+0.03)^4t

N = number of cars serviced after t years...

5 0
3 years ago
How many ways are there to choose three donuts from 4 varieties if there must be an odd number of glazed donuts? the number of g
Salsk061 [2.6K]

1 glazed and 2 others     or     3 glazed and 0 others

           1 x 3 x 3               +                 1 x 1 x 1

                9                     +                       1

                                       10

Answer: 10

3 0
3 years ago
Find the solution to the system of linear equations y = 5x + 4 and y = −3x + 12 using the intersection method. Check your answer
Umnica [9.8K]

Answer:

The solution to the system of linear equations is (1,9).

Step-by-step explanation:

The given system of linear equations

y=5x+4            ... (1)

y=-3x+12           .... (2)

Subtract equation (2) from equation (1) to eliminate y.

y-y=(5x+4)-(-3x+12)

0=5x+4+3x-12

On combining like terms, we get

0=(5x+3x)+(4-12)

0=8x-8

Add 8 on both sides.

0+8=8x-8+8

8=8x

Divide both sides by 8.

1=x

The value of x is 1.

Substitute x=1 in equation (1).

y=5(1)+4

y=5+4

y=9

The value of y is 9.

Therefore the solution to the system of linear equations is (1,9).

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3 years ago
Asher has about a probability of winning then Ethan has which could be the outcome that Ashlee needs to win the game select thre
mash [69]

Answer:

There are 36 total possible outcomes.

Rolling a sum of 11 or higher, there are 3 possible rolls, to make a 3/36 = 1/12 probability.

Rolling a sum of 4 there are also 3 possibilities, so the chance would be the same.

Rolling a sum of 9, there are 4 possibilities, which is a better chance.

Rolling a sum less than 5, there is 6 possibilities, which is a better chance.

Rolling greater than 5 but less than 7 means rolling a sum of 6, there are 5 chances, which is a better chance.

Rolling greater than 9 but less than 11, means rolling a 10, there are 3 possibilities, which is the same.

Rolling greater than 2 and less than 4 means rolling a 3, there are 2 possibilities, which is less.

The answers would be:

Rolling a sum of 9,

Rolling a sum less than 5

Rolling greater than 5 but less than 7

5 0
3 years ago
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