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mr Goodwill [35]
3 years ago
10

Determine whether a triangle with sides .20 inches 48 inches and 52 inches long is a right triangle. Justify your answer.

Mathematics
1 answer:
MariettaO [177]3 years ago
8 0
To find out whether or not a triangle is a right triangle, you have to figure out whether or not it satisfies the Pythagorean Theorem.

The Pythagorean Theorem says that the sum of the squares of the side lengths, represented by variables a and b, must equal the square of the hypotenuse, represented by c. 

a² + b² = c²

20² + 48² = 52²

400 + 2304 = 2704

2704 = 2704

When we plug in the side lengths and simplify the Theorem, it results in a true statement, so we can conclude that yes, the triangle is a right triangle.
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Solve the following quadratic by factoring.
Lina20 [59]

Answer:

4, -1

Step-by-step explanation:

We can reverse the FOIL (First, outside, inside, last) method to break down the equation. The question is asking to solve by factoring so you want to find the right combination of numbers this equation can be broken down into:

x^2 - 3x - 4 = 0

Because we want x squared, x needs to be multiplied by itself, so we can put x in the first slot for each.

(x + or - ?) ( x + or - ?) = 0

Then we need to find numbers that could be added to get -3 and multiplied to get -4. The only set of numbers that works for this is -4 and 1. Note that the sign you put in front of each number has an impact on your answers. With this we get:

(x - 4) (x + 1) = 0

To test that this is equal to the original equation, simply multiply it out using FOIL.

x * x = x^2

x * 1 = x

x * -4 = -4x

-4 * 1 = -4

Putting each component into an equation:

x^2 + x - 4x - 4 = 0

Simplifying:

x^2 - 3x - 4 = 0

Once we are sure it is still the same equation, we find the solutions. We know 0 multiplied by anything equals 0, so to get 0 as the answer, one of the sets in the parentheses must equal 0. (It doesn't matter what the other one is as long is one equals 0)

Therefore, we have 2 solutions, 4, and -1 because if x is 4, 4-4 is 0 which solves the equation, and if x is -1, then -1 + 1 is 0 which also solves the equation.

You can also check your answers by plugging them back into the original equation.

5 0
3 years ago
Becky collected this data about the number of boys and girls playing different instruments which answer option best represents t
alekssr [168]
Data? I need the data! Not trying to provoke, but in order to answer this I need data...
4 0
3 years ago
What 2 numbers multiply to be 108 but subtract to be 6
mel-nik [20]
No 2 numbers do this.

Possible numbers that can multiply to 108:

<span>1 x 108 = 108
2 x 54 = 108
3 x 36 = 108
4 x 27 = 108
6 x 18 = 108
9 x 12 = 108
12 x 9 = 108
18 x 6 = 108
27 x 4 = 108
36 x 3 = 108
54 x 2 = 108
108 x 1 = 108 

Possible numbers on that list that when subtracted equate to 6:

None</span>
3 0
2 years ago
Which of the following is the multiplicative inverse of 12x/5? a)5/12x b)12x/5 c)- 5/12x d)- 12x/5
fgiga [73]
The product of a number and its multiplicative inverse is 1.
12x/5 * 5/12x = 1

Therefore, the multiplicative inverse of 12x/5 is 5/12x
7 0
3 years ago
katy had 162 pieces of candy. everyday she gave 6 pieces to her little brother. which function can be used to find how many cand
GrogVix [38]

Answer:

6x = 162 or 162 = 6x

Step-by-step explanation:

x = days, since how many days is unknown, we substitute it as x

3 0
2 years ago
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