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lianna [129]
4 years ago
14

What is the length of CD? In this diagram, ABC ~ EDC.

Mathematics
1 answer:
Alex777 [14]4 years ago
5 0

Hey there!

Answer:

CD = 3.

Step-by-step explanation:

Since the triangles are similar, we can set up a ratio to determine the other side-lengths:

\frac{12-x}{18} =\frac{x}{6}

Cross multiply:

6(12-x) = 18x

Distribute the '6':

72-6x = 18x

Combine like terms and simplify:

72 = 24x

x = 3

Therefore, the length of CD is 3.

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A town park has two biking trails. Marsh Trail is 5 3/10 miles long. Woodland trail is 2 4/5 Miles long. How much longer is Mari
torisob [31]

Answer:

21/2

Step-by-step explanation:

The answer can be determined by substracting the lengrh of the woodland trail from the Marsh trail

5\frac{3}{10} - 2\frac{4}{5}

3\frac{3 - 8}{10}

2\frac{5}{10}

converting the fraction to its simplest form gives 21/2

5 0
3 years ago
A spring has natural length 20 cm. Compare the work W1 done in stretching the spring from 20 cm to 30 cm with the work W2 done i
sashaice [31]

Answer:

W1 = W2 = 50k Joules (assuming W1 and W2 have the same force constant, k)

W1 - W2 = 0

Step-by-step explanation:

Work done in stretching a spring is given by 1/2ke^2

Where, k is force constant and e is extension

e1 = 30cm - 20cm = 10cm

W1 = 1/2k(e1)^2 = 1/2×k×10^2 = 50k Joules

e2 = 40cm - 30cm = 10cm

W2 = 1/2k(e2)^2 = 1/2×k×10^2 = 50k Joules

W1 = W2 = 50k Joules provided W1 and W2 have equal force constant

Therefore, W1 - W2 = 0

7 0
3 years ago
13. WILL MARK BRAINLIEST!! HELP!​
Umnica [9.8K]

Answer:

\large\boxed{\dfrac{x+2}{x^2-6x-16}\div\dfrac{1}{9x}=\dfrac{9x}{x-8}}

Step-by-step explanation:

\dfrac{x+2}{x^2-6x-16}\div\dfrac{1}{9x}=\dfrac{x+2}{x^2+2x-8x-16}\cdot\dfrac{9x}{1}\\\\=\dfrac{(x+2)(9x)}{x(x+2)-8(x+2)}=\dfrac{(x+2)(9x)}{(x+2)(x-8)}\\\\\text{cancel}\ (x+2)\\\\=\dfrac{9x}{x-8}

8 0
3 years ago
There are 80 people waiting to tour the science museum. The tour guide takes 4 groups of 16 people each. The remaining people wi
Anna11 [10]

Answer:

16 people

Step-by-step explanation:

Given that :

Number of people to tour = 80

Number per group = 16

Number of groups = 4

Total number of people who make up the entire groups :

Number per group * number of groups

16 * 4 = 64

The number of people in the last tour group :

80 - 64

= 16 people

7 0
3 years ago
2. What is the probability of spinning an A on the first spinner and an odd number
pychu [463]

Answer: <em>1/10</em>

Step-by-step explanation: These two events are independent, meaning the outcome of the first event doesn't affect the outcome of the second.

To find the probability of independent events, first, find the

probability of each event, then multiplies the probabilities.

The probability of spinning an A on the first spinner is 1/5

since there is 1 favorable outcome and 5 total outcomes.

The probability of spinning an odd number on the second spinner

is 3/6 which simplifies to 1/2 since there are 3 favorable outcomes,

spinning a 1, 3, or another 3 since these are odd numbers.

So now we have 1/5 × 1/2 and when multiplying fractions,

we multiply across the numerators and denominators to get 1/10.

So the probability of spinning an A, then an odd number is 1/10.

5 0
3 years ago
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