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Elina [12.6K]
3 years ago
7

Explain the reasoning please

Mathematics
2 answers:
Svet_ta [14]3 years ago
7 0

Step-by-step explanation:

Something to keep in mind is that anything greater than 0 is positive and anything less than 0 is negative

a is to the right of 0 and 1 making it a positive number

b is to the left of 0 making is a negative number

A. a is greater than 1 and b is a negative number

negative number * positive number = negative number

We already know that a is greater than 1 so ab has to be much less than -1 making ab+1 a negative expression

B. Looking at the number line, you can tell that the distance between 1 and a is a bit less than the distance between 0 and 1

This means that a= 1.x not 2

Because of this, a-2 is negative

C. -b

b is a negative number which means that -b would be positive

D. a+b

Looking at the number line, you can tell that the distance between 0 and a is less than the distance between 0 and b

Therefore, a+b is negative

E. a-b

Since b is already negative, the expression would simplify to two positive numbers being added

This means that a-b can't be negative

F. a-1

The number line shows us that a is greater than 1, therefore, a minus 1 would be positive

I hope this helps in some way or another

zvonat [6]3 years ago
3 0
A minus one would be positive
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Step-by-step explanation:

<u>Given:</u>

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<u>Solution</u>

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Y=4x-18<br><br> Find ordered pairs of intercepts of each line
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Rationalize the denominator and simplify 6/√2-√3
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Answer:

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Explanation:

<span>3<span><span>√5</span>+<span>√6</span></span></span>

We rationalise the denominator by multiplying the expression by the conjugate of the denominator. <span><span>√5</span>−<span>√6</span></span>

<span><span>3⋅<span>(<span>√5</span>−<span>√6</span>)</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span>

<span>=<span><span>3⋅<span>(<span>√5</span>)</span>+3⋅<span>(−<span>√6</span>)</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span></span>

<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span><span>(<span>√5</span>+<span>√6</span>)</span>⋅<span>(<span>√5</span>−<span>√6</span>)</span></span></span></span>

<span>Applying identity
<span><span>(a+b)</span><span>(a−b)</span>=<span>a2</span>−<span>b2</span></span> to the denominator.</span>

<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span><span><span>(<span>√5</span>)</span>2</span>−<span><span>(<span>√6</span>)</span>2</span></span></span></span>

<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span>5−6</span></span></span>

<span>=<span><span>3<span>√5</span>−3<span>√6</span></span><span>−1</span></span></span>

<span>=−3<span>√5</span>+3<span>√6</span></span>

<span>=3<span>√6</span>−3<span>√<span>5
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