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notsponge [240]
2 years ago
7

In a 30°-60°-90° triangle, what is the length of the longer leg when the length of the hypotenuse is 18 inches?

Mathematics
1 answer:
max2010maxim [7]2 years ago
8 0

Answer:

9sqrt(3) in.

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is:

short leg : long leg : hypotenuse

      1        :   sqrt(3)  :          2

If the short leg measures 1, then the hypotenuse measures 2.

The length of the hypotenuse is twice the length of the short leg.

The length of the long leg is sqrt(3) times the length of the short leg.

If the hypotenuse measures 18 in., then the short leg measures 9 in.

Then the long leg measures 9sqrt(3) in.

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Micaela is 2 years older than Sam. In 4 years, the sum of their ages will be 40. How old is Micaela now?
Ann [662]

Answer:

The error is: The solution shows the Sam's age and the problem asked for Micaela's age.

Solution fixed: m=17

Micaela is 17 years old now.

Step-by-step explanation:

The error is: The solution shows the Sam's age and the problem asked for Micaela's age.

To fix the error, you can set up these equations based on the information given:

m=s+2  

(m+4)+(s+4)=40  

Solve for "s" from the first equation:

s=m-2

Substitute this equation into the second equation:

(m+4)+((m-2)+4)=40  

Now you need to solve for "m":

m+4+(m-2+4)=40\\m+4+m+2=40\\m+m=40-4-2\\2m=34\\m=\frac{34}{2}\\\\m=17

Micaela is 17 years old now.

4 0
3 years ago
Read 2 more answers
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zysi [14]

Answer:

7 times

Step-by-step explanation:

Prob of landing on 4: 1/5

1/5 * 35 = 7

7 0
2 years ago
Will markk the brainliest
ivolga24 [154]

Answer:

  1. the range of f^-1(x) is {10, 20, 30}.

  2. the graph of f^-1(x) will include the point (0, 3)

  3. n = 8

Step-by-step explanation:

1. The domain of a function is the range of its inverse, and vice versa. The range of f^-1(x) is {10, 20, 30}.

__

2. See above. The domain and range are swapped between a function and its inverse. That means function point (3, 0) will correspond to inverse function point (0, 3).

__

3. The n-th term of an arithmetic sequence is given by ...

  an = a1 +d(n -1)

You are given a1 = 2, a12 = 211, so ...

  211 = 2 + d(12 -1)

  209/11 = d = 19 . . . . . solve the above equation for the common difference

Now, we can use the same equation to find n for an = 135.

  135 = 2 + 19(n -1)

  133/19 = n -1 . . . . . . . subtract 2, divide by 19

  7 +1 = n = 8 . . . . . . . . add 1

135 is the 8th term of the sequence.

3 0
3 years ago
Choose all of the equations that graph as an increasing function.
Allushta [10]

Answer:

A. y = -(-x) +7 = x + 7

D. y = 0.05x + 10



3 0
3 years ago
Substitution method- y=-x+4 and y=3x
kumpel [21]
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knowing this, y=3
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