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Svetach [21]
3 years ago
9

8. Is the following statement true or false? Justify your conclusion. If a and b are nonnegative real numbers and a + b =0, then

a = 0. Either give a counterexample to show that it is false or outline a proof by completing a know-show table.
Mathematics
1 answer:
atroni [7]3 years ago
7 0

Answer:

If a + b = 0 then a = 0 and b =0

a  | b | a + b (answer)

0 | 0 | 0

0 | 1  | 1

0 | 2 | 2

1  | 0 | 1

2 | 0 | 2

1  | 1  | 2

2 | 1  | 3

 

Step-by-step explanation:

Considering the following conditions for the real numbers:

a\geq 0\\b\geq 0

Following the rules of these in-equations, it is possible to deduce:

a + b \geq 0

Then, if the proposed statement is:

a + b = 0

The conditions above shall comply the requirements established, but first, analyzing the statement:

If a \geq 0 and b \geq 0 then a + b \geq a, a + b \geq b and a + b \geq 0.

If a = 0 and b a non negative real number, then a + b \geq b, but because to a = 0, then a + b = b. Due to the commutative property of sums, the same behavior will be presented if b = 0 and a a non negative real number.

According to that, if  a + b = 0, then a = 0 and b = 0.

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3. Given AB with coordinates A(-4,5) and B(12,13). Find the horizontal distance and the vertical
SCORPION-xisa [38]

The required distance would be 17.88 units coordinates A(-4,5) and B(12,13) and the horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.

<h3>What is the distance between two points?</h3>

The distance between two points is defined as the length of the line segment between two places representing their distance.

Given AB with coordinates A(-4,5) and B(12,13).

The formula of the distance between two points is A(x₁, y₁) and B(x₂, y₂) is given by: d (A, B) = √ (x₂ – x₁)² + (y₂ – y₁) ².

x₁ = -4, y₁ = 5

x₂ = 12, y₂ = 13

distance = √ (12 – (-4))² + (13 – 5)²

distance = √ (12 + 4)² + (8)²

distance = √ (16)² + (8)²

distance = √ (256 + 64)

distance = √320

distance = 17.88 units

The horizontal distance is 16 units and the vertical distance is 8 units from A to B which are determined by the graphing method.

Learn more about the distance between two points here:

brainly.com/question/15958176

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6 0
1 year ago
Whats the answer to 7c+12c-2=
Aloiza [94]

Answer:

19c-2

Step-by-step explanation:

photomath

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3 years ago
Y^10+7y^5-8<br> Factor completely
saul85 [17]
(y^5-1)(y^5+8)............
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2 years ago
How does $100 gift card affect the measure of center of the data?<br> Attachment
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4 0
3 years ago
The function g(x)=x^2+3. The f(x)=g(x+2)
vekshin1

Answer:

f(x)=x^2+6x+12

Step-by-step explanation:

Given:

The function 'g(x)' is given as:

g(x)=x^2+3

Now, the function 'f(x)' is given as:

f(x)=g(x+2)

So, the function 'f(x)' is a transformation of 'g(x)'.

In order to find f(x), we replace 'x' by (x + 2) in the 'g(x)' function equation. This gives,

g(x+2)=(x+2)^2+3

Using the identity (a+b)^2=a^2+b^2+2ab, we get:

g(x+2)=x^2+3^2+6x+3\\\\g(x+2)=x^2+9+6x+3\\\\g(x+2)=x^2+6x+12

Hence the function f(x) is given as:

f(x)=x^2+6x+12

4 0
3 years ago
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