Find m∠Y if m∠Y is six more than three times its supplement.
2 answers:
Answer:
<h2>136.5°</h2>Step-by-step explanation:
" is six more then three times its supplement".
Three times refers to multiply by 3, and six more implies and addition.
Supplement indicates that the sum of those angles is 180°.
So, the problem can be expressed as
Solving for angle Y, we have
And the supplement is
Therefore, the angle is 136.5°.
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1) Resultant fraction:
2) Total soil: pounds
3) Result of the product:
Step-by-step explanation:
1)
In this problem, we want to find the product between the two fractions
and
In order to find this product, we have to multiply the numerators of each fraction and the denominators of each fraction. We get:
Now we simplify, dividing both numerator and denominator by 2:
And the fraction cannot be further simplified.
2)
Here we have:
n = 5 (number of pots that Andy has)
(amount of soil (in pounds) that each pot can contain)
In order to find the amount of soil that Andy needs to fill all the pots, we have to multiply the number of pots (n) by the amount of soil that each pot can contain (s).
If we do so, we find:
Which can be rewritten as a mixed fraction as:
3)
Here we want to find the result of the following product:
In order to do so, we first have to rewrite each fraction as an improper fraction.
For the 1st fraction:
For the 2nd fraction:
Now we can finally find the product of the two fractions:
Where in the last step, we divide both the numerator and the denominator by 6.
Learn more about fractions:
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We need to determine whether is a terminating decimal or a repeating decimal.
Let's solve this question using the long division method
First, let's identify the divisor and dividend. The number to be divided is 11 hence this is the dividend, and it needs to be divided by 128 which is the divisor
Next, since the divisor (128) is greater than the dividend (11) it can not divide 11. Hence, we will introduce a decimal point in quotient, and append a 0 next to 11 and divide 110 by 128. Again, 128 is greater than 110 so we will introduce a 0 in the quotient, and append another 0 next to 110, and will divide 1100 by 128. We will see what multiple of 128 is less than or equal to 1100. That multiple is 8. So we write 8 in the quotient and multiply 128 with 8 and subtract the product (128*8 = 1024) from 1100. The remainder that we get is 76.
Next, we append a 0 to the remainder and divide 760 by 128. Now, we see what multiple of 128 is less than or equal to 760. That multiple is 5. So we write 5 next to the quotient and multiply 128 with 5 and subtract the product (640) from 760. Now, the remainder is 120.
Next, we append a 0 to the remainder and divide 1200 by 128. Now, we see what multiple of 128 is less than or equal to 1200. That multiple is 9. So we write 9 next to the quotient and multiply 128 with 9 and subtract the product (1152) from 1200. Now, the remainder is 48.
Next, we append a 0 to the remainder and divide 480 by 128. Now, we see what multiple of 128 is less than or equal to 480. That multiple is 3. So we write 3 next to the quotient and multiply 128 with 3 and subtract the product (384) from 480. Now, the remainder is 96.
Next, we append a 0 to the remainder and divide 960 by 128. Now, we see what multiple of 128 is less than or equal to 960. That multiple is 7. So we write 7 next to the quotient and multiply 128 with 7 and subtract the product (896) from 960. Now, the remainder is 64.
Next, we append a 0 to the remainder and divide 640 by 128. Now, we see what multiple of 128 is less than or equal to 640. That multiple is 5. So we write 5 next to the quotient and multiply 128 with 5 and subtract the product (640) from 640. Now, the remainder is 0.
Hence, we have solved the entire problem
Last, we look at the quotient i.e. 0.0859375, which is the solution to the problem. We see that the quotient has a definite number of digits in it, and terminates at 5. Hence, this is a terminating decimal.
A repeating decimal is one in which a particular pattern after the decimal point keeps re-occuring, which is not the case here. Hence, is a terminating decimal.
Please refer to the attached image for visualization
