The picture of the question N 1) in the attached figure
Part 1) we know that The measure of the external angle is the semi difference of the arcs that it covers so ∠GET=(1/2)*[arc TN-arc TG]---> 0.5*[180-50]----> ∠ GET=65°
the answer part 1) is the option C)65
Part 2)Which of the following is the equation of a circle with a radius of 2.5 and its center at (4, -3)?
we know that the equation of a circle is (x-h)²+(y-k)²=r² where (h,k) is the center and r is the radius (h,k)-----> (4,-3) r=2.5 so (x-h)²+(y-k)²=r²-----> (x-4)²+(y+3)²=2.5²-----> (x-4)²+(y+3)²=6.25
the answer part 2) is the option C) ( x - 4 ) ^ 2 + ( Y + 3) ^ 2 =6.25
The picture of the question N 1) in the attached figure
Part 1) we know that The measure of the external angle is the semi difference of the arcs that it covers so ∠GET=(1/2)*[arc TN-arc TG]---> 0.5*[180-50]----> ∠ GET=65°
the answer part 1) is the option C)65
Part 2)Which of the following is the equation of a circle with a radius of 2.5 and its center at (4, -3)?
we know that the equation of a circle is (x-h)²+(y-k)²=r² where (h,k) is the center and r is the radius (h,k)-----> (4,-3) r=2.5 so (x-h)²+(y-k)²=r²-----> (x-4)²+(y+3)²=2.5²-----> (x-4)²+(y+3)²=6.25
the answer part 2) is the option C) ( x - 4 ) ^ 2 + ( Y + 3) ^ 2 =6.25
Let's solve the given multiplication and division problems step by step using the math laws.
Multiplication Problems:
1. \(27.31 \times 6.3\):
To multiply decimals, we align the numbers by their decimal places and proceed with the multiplication as usual:
\[27.31 \times 6.3 = 171.753\]
2. \(1238.58 \times 63.24 \times 64.14 \times 12.20 \times 73.45 \times 1034.33 \times 0.313 \times 83.11 \times 8.44 \times 0.224\):
We can multiply all the given numbers together, following the order of operations (multiplication before addition or subtraction):
\[1238.58 \times 63.24 \times 64.14 \times 12.20 \times 73.45 \times 1034.33 \times 0.313 \times 83.11 \times 8.44 \times 0.224 = 1.4209434 \times 10^{18}\]
Division Problems:
1. \(10 \div 21.34\):
To divide decimals, we can move the decimal point of the divisor (21.34) to the right until it becomes a whole number, and move the decimal point of the dividend (10) by the same number of places. Then, we perform the division:
\[10 \div 21.34 = 0.4692\]
2. \(3.2 \div 9.4\):
Similarly, we can divide \(3.2\) by \(9.4\) using the same method:
\[3.2 \div 9.4 = 0.34\]
3. \(100 \div 999.92\):
Dividing \(100\) by \(999.92\) using the same method results in:
\[100 \div 999.92 = 0.10001\]
4. \(18.4 \div 98.6\):
Dividing \(18.4\) by \(98.6\) using the same method results in:
\[18.4 \div 98.6 = 0.18666\]
5. \(121.32 \div 932.4\):
Doing the division for \(121.32 \div 932.4\) gives us:
\[121.32 \div 932.4 = 0.130004\]
6. \(16 \div 256.58\):
Lastly, dividing \(16\) by \(256.58\) using the same method gives us:
\[16 \div 256.58 = 0.06238\]
Please note that the decimal approximations have been rounded for simplicity. To ensure more accurate results, it is recommended to carry out calculations with higher precision.
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