We have that
1)<span>Circle W has center (−3, 0) and radius 8
the equation of a circle W is
(x+3)</span>²+(y)²=8²
2)<span>Circle V is a translation of circle W, 2 units down.
the center of circle V--------> (-3,0-2)---------> (-3,-2)
3)</span><span>Circle V is a dilation of circle W with a scale factor of 2.
then the radius circle V is 8*2------> 16 units
</span>the equation of a circle V is
(x+3)²+(y+2)²=16²
therefore
case <span>A. Circle V and circle W are similar.---------> is correct
</span>because I can transform circle V to circle W using only translations, rotations and scaling (In the case of circles, no rotations are necessary).
case <span>B. Circle V and circle W have the same center.-------> is not correct
case </span><span>C. The radius of circle V is 16.-----------> is correct
case </span><span>D. The center of circle V is (−5, 0).----------> is not correct
the answer is
</span> case A. Circle V and circle W are similar.---------> is correct
case C. The radius of circle V is 16.-----------> is correct
√(15+x) = 2x+3
take sqr for both side
15x+10=(2x+3)^2
15x+10=4x^2+9+2*2x*3
15x+10=4x^2+9+12x
4x^2-3x--1=0
solve it u will x=1,-1/4
You already have the GCF=2
16-10 = 2(4-5) when factored
Hope that helps
<h3>
Answer: D) 3/150</h3>
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Explanation:
With the use of a calculator, we see that,
- 11/19 = 0.57894736842106...., the decimals eventually repeat; but unfortunately my calculator ran out of room to show the repeating portion
- 4/7 = 0.5714285714285714..., the block "571428" repeats forever
- 1/3 = 0.333333.... the 3s go on forever
- 3/150 = 0.02
So 3/150 converts to the terminating decimal 0.02
The word "terminate" means "stop". In the other decimal values, the decimal digits go on forever repeating the patterns mentioned.
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A non-calculator approach will have us simplify 3/150 into 1/50 after dividing both parts by the GCF 3. Then notice how 50 has the prime factorization of 2*5*5. The fact that the denominator 50 can be factored in terms of only 2's and 5's is enough evidence to conclude that the fraction converts to a terminating decimal.
If the denominator factors into some other primes, other than 2s and 5s, then we don't have a terminating decimal. So that's why 11/19, 4/7 and 1/3 convert to non-terminating decimals.
Answer:
The value of x is -3.
Step-by-step explanation:
To find x, we have to put everything in base 6 and continue to simplify. Since we know that 216 is 6^3, we can replace that.
6^x = 1/216
6^x = 1/(6^3)
Now, when there is a power in the denominator, we know we can move it to the numerator by making it negative. We can do that to get the bases to match.
6^x = 1/(6^3)
6^x = 6^-3
Now that they are both put in simple base 6 systems, we can just eliminate the bases and assume that the powers are equal. This lets us know that x = -3.
