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3 years ago

Please solve and show work.

Mathematics

1 answer:

loris [4]3 years ago

4 0

Answer:

63.16 in approx.

Step-by-step explanation:

Let the shorter leg be S. Then the longer leg is L = 3S + 3.

The formula for the area of a triangle is A = (1/2)(base)(height). Here, that works out to A = 84 in^2 = (1/2)(S)(3S + 3).

Simplifying, we get 168 in^2 = S(3S + 3), or

3S^2 + 3S - 168 = 0, or

S^2 + S - 56 = 0. This factors as follows: (S - 8)(S + 7) = 0, so the positive root is S = 8. We discard the negative root.

Thus, the shorter leg length is 8 and the longer leg length is 3(8) + 3, or 27.

According to the Pythagorean Theorem, the hypotenuse length is given by

L^2 = 8^2 + 27^2, or

L^2 = 64 + 729 = 793.

L = hypotenuse length = √793, or approx. 28.2 in.

Then the perimeter of the triangle is 8 + 27 + 28.2 in, or approx. 63.16 in

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A number x, rounded to 1 decimal place is 12.3 write down the error interval for x

icang [17]

We know that
A number x, rounded to 1 decimal place is 12.3
so
x>=12.25
and
x < 12.35

the error interval for x is the interval [12.25,12.35)

the answer is
[12.25,12.35)

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3 years ago

If f(x) = |x| + 9 and g(x) = –6, which describes the value of (f + g)(x)?

bazaltina [42]

(f+g)(x) = f(x) + g(x) = (|x| + 9 ) + (-6) =

|x| + 9 - 6 = |x| + 3

Answer is |x| + 3

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4 years ago

For the given set, first calculate the number of subsets for the set, then calculate the

vodomira [7]

Answer:

$\fbox{\begin{minipage}{14em}Number of subsets: 16\\Number of proper subsets: 15\end{minipage}}$

Step-by-step explanation:

Given:

The set A = {5, 13, 17, 20}

Question:

Find the number of subsets of A

Find the number of proper subsets of A

Simple solution by counting:

Subset of A that has 0 element:

{∅} - 1 set

Subset of A that has 1 element:

{5}, {13}, {17}, {20} - 4 sets

Subset of A that has 2 elements:

{5, 13}, {5, 17}, {5, 20}, {13, 17}, {13, 20}, {17, 20} - 6 sets

Subset of A that has 3 elements:

{5, 13, 17}, {5, 13, 20}, {5, 17, 20}, {13, 17, 20} - 4 sets

Subset of A that has 4 elements:

{5, 13, 17, 20} - 1 set

In total, the number of subsets of A: N = 1 + 4 + 6 + 4 + 1 = 16

The number of proper subsets (all of subsets, except subset which is equal to original set A): N = 16 - 1 = 15

Key-point:

The counting method might be used for finding the number of subsets when the original set contains few elements.

The question is that, for a set that contains many elements, how to find out the number of subsets?

The answer is that: there is a fix formula to calculate the total number ( $N$ ) of subsets of a set containing $n$ elements: N = $2^{n}$

With original set A = {5, 13, 17, 20}, there are 4 elements belonged to A.

=> Number of subsets of A: N = $2^{4} = 16$

(same result as using counting method)

Brief proof of formula: N = $2^{n}$

Each element of original set is considered in 2 status: existed or not.

If existed => fill that element in.

If not => leave empty.

For i.e.: empty subset means that all elements are selected as not existed, subset with 1 element means that all elements are selected as not existed, except 1 element, ... and so on.

=> From the point of view of a permutation problem, for each element in original set, there are 2 ways to select: existed or not. There are $n$ elements in total. => There are $2^n}$ ways to select, or in other words, there are $2^{n}$ subsets.

Hope this helps!

8 0

3 years ago

Select True or False.

Lyrx [107]

The expression is False the correct answer would be: −x+12

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3 years ago

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A certain triangle has two 45° angles. What type of triangle is it?

neonofarm [45]

Answer is a right triangle. The angles of a triangle must add to 180 degrees.
You have two 45 degree angles
45 + 45= 90
Now you need 1 more angle to equal 180
180- 90= 90
A right angle is 90 degrees. A right triangle has one right angle and two acute.

3 0

4 years ago