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andrew11 [14]
3 years ago
6

Find the roots of the equation x^2 + 16 = 0.

Mathematics
1 answer:
aksik [14]3 years ago
5 0

Answer:

+4 and -4

Step-by-step explanation:

x² + 16=0

x=-√16

x=-4 or +4

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An acute triangle has sides measuring 10 cm and 16 cm. The length of the third side is unknown.
saveliy_v [14]

Answer: Choice B

12.5 < x < 18.9

================================================

Explanation:

We have a triangle with these side lengths:

  • a = 10
  • b = 16
  • c = x = unknown

Let's assume that b = 16 is the largest side of this triangle.

By the converse of the pythagorean theorem, we need b^2 < a^2+c^2 to be true in order for an acute triangle to happen.

So,

b^2 < a^2 + c^2\\\\c^2 > b^2 - a^2\\\\c > \sqrt{b^2-a^2}\\\\x > \sqrt{16^2-10^2}\\\\x > \sqrt{156}\\\\x > 12.4899959967968 \ \text{(approximate)}\\\\x > 12.5

Now let's consider the possibility that the missing side x is actually the longest side.

Using the same theorem as before, we would say,

c^2 < a^2 + b^2\\\\c < \sqrt{a^2 + b^2}\\\\x < \sqrt{10^2 + 16^2}\\\\x < \sqrt{356}\\\\x < 18.8679622641132 \ \text{(approximate)}\\\\x < 18.9\\\\

We found that x > 12.5 and x < 18.9

This is the same as saying 12.5 < x and x < 18.9

Put together, they form the approximate answer of 12.5 < x < 18.9

6 0
2 years ago
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b )

The answer is | 20 - 4 - 12 |

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7 0
3 years ago
Which expressions are equivalent to 2(b+3c)?
Rina8888 [55]

Answer:

B. (b+3c)+(b+3c)

C. 2(b)+2(3c)

Step-by-step explanation:

we have

2(b+3c)

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2(b+3c)=2b+2(3c)=2b+6c

Verify each case

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distribute the number 3

3(b+2c)=3b+3(2c)=3b+6c

3b+6c \neq 2b+6c

therefore

Choice A is not equivalent to the given expression

case B) (b+3c)+(b+3c)

Combine like terms

b+3c)+(b+3c)=(b+b)=(3c+3c)=2b+6c

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therefore

Choice B is equivalent to the given expression

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Multiply both terns by 2

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Choice C is equivalent to the given expression

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The difference between point and the vertx is that a vertex can be used to create different geometric shapes and a point is always part of the shape.

Step-by-step explanation:

Though Vertex and Point sound similar, they are different in many crude aspects. Vertex is defined as the meeting point of two sides, lines or any extended parts. The point, in turn, denotes the singular identity of a place.

Hence vertex can be used to draw any geometrical pattern. It can be done by extending or protruding the given body parts which would result in a new geometrical figure.

Points would constitute every part of that geometrical surface that we wish to identify.

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3 years ago
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