Answer: The correct answer is: " 3 " .
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Step-by-step explanation:
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The problem given is:
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Evaluate: log 2 base 8 .
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Rewrite as: " 
" ;
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Take note of the following definition of a logarithm:
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" 
" ; ↔ " 
" ;
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in which: 
refers to the "base" ;
refers to the "argument" ;
refers to the "exponent" ;
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As such:
" "
⇔ " 
" ; Solve for "x" ;
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Note:
2⁰ = 1 ;
2¹ = 2 ;
2² = 2 * 2 = 4 ;
2³ = 2 * 2 * 2 = 8 .
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→ " " ;
→ " 
" ; since: " 
" ;
→ as such: " x = 3 " ;
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Thus:
"log 2 base 8 " ;
= 
.
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Hope this helps!
Best wishes to you!
Answer:
19/18
Step-by-step explanation:
The GCF of 9, 3, and 18 is 18.
Each denominator must be multiplied to 18, and as a result what you multiply in the denominator MUST be multiplied in the numerator.
9 * 2 = 18
1 * 2 = 2
2/18
3 * 6 = 18
6 * 2 = 12
12/18
5/18
Add all three fractions together:
12/18 + 5/18 + 2/18 = 19/18
Hey! I'm here <3
Let's go through this.
The standard form formula is ax+by=c. A can't be a fraction <em>or</em> a negative. In order to clear the denominator and the negative, can can multiply both sides by -4. That gets us:
-4y = 3x -12
Then, we can add 4y to both sides, and then add 12 to the other side.
12 = 3x+4y, or 3x+4y = 12. Therefore, the first answer is correct.
For the second one, we do the same thing. We can multiply both sides by -5 to clear the denominator and the negative. That'll get us:
-5y = 2x-15.
We can then add the 5y to the right side and add the 15 to the left.
15 = 2x+5y, or 2x+5y = 15. Therefore, the first answer is correct again.
Next one: parallel lines always have the same slope. So, we know that the slope is going to be 5. We can then use the points given to find b.
14 = 5(2) + b
14 = 10 +b
4 = b.
Therefore, our equation will be y = 5x +4. The last option is the correct
answer.
Now for number 20. For perpendicular slopes, the slope is always going to be the opposite of the reciprocal of the given slope. We see here here that, that isn't the case, therefore it's neither, because it's definitely not the same slope, so not parallel.
Ready for the last one?
<em /><em />If it's perpendicular, we know it's the opposite of the reciprocal, or -2/5. That narrows our answer down to A and C. It seems like the difference between the two is the x+5 or the x+5. Let's clear that up. We see that the x-value is -7. If the formula states to subtract the x, and the x is already negative, that creates a plus, so the answer is c.
I hope my long-paragraph-thing helped you!
