Numerical expressions, one half the sum of nine and three
2 answers:
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Answer: 7√2
Step-by-step explanation: To simplify a square root where the number inside the radical is not a perfect square like the square root of 98, we start by making a factor tree for the number inside.
98 factors as 2 · 49 and if you know your perfect squares,
you should be able to recognize 49 as 7 · 7.
What we are looking for in our factor tree
are pairs of factors that are the same.
If a factor pairs up, it will come out of the radical.
If a factor does not pair up, then it stays inside the radical.
So here, since our 7's pair up, a 7 will come out of the radical.
Since the 2 does not pair up, it stays inside the radical.
So our answer is 7√2.
The boy scout was walking on trail YZ from point Y to Z.
Then he decided to go to trail YX. He could have gone back to point Y, made a 90-deg turn and start walking along trail YX. He did not do that.
To go from trail YZ to trail YX, when he got to point Z, he made a 47-deg right turn onto segment XZ which is the short curt between trails YZ and YX.
He walked along ZX until he got onto trail YX at point X. Point X is 29 meters from point Y.
The figure shows angle theta as the 47-degree turn he made.
He walked along the shortcut ZX. When he got to point X, he was on trail YX. The point he got onto trail YX is point X and it is 29 m from point Y.
The question is what is the distance of the shortcut, XZ?
You have a right triangle, XYZ, with legs YX and YZ, and with hypotenuse XZ. You are given one of the acute angles as 47 deg. You are looking for the length of the hypotenuse, XZ.
For the given angle theta, XY is the opposite leg.
XZ is the hypotenuse of the triangle.
The trig ratio that relates the opposite leg to the hypotenuse is the sine.
Then he decided to go to trail YX. He could have gone back to point Y, made a 90-deg turn and start walking along trail YX. He did not do that.
To go from trail YZ to trail YX, when he got to point Z, he made a 47-deg right turn onto segment XZ which is the short curt between trails YZ and YX.
He walked along ZX until he got onto trail YX at point X. Point X is 29 meters from point Y.
The figure shows angle theta as the 47-degree turn he made.
He walked along the shortcut ZX. When he got to point X, he was on trail YX. The point he got onto trail YX is point X and it is 29 m from point Y.
The question is what is the distance of the shortcut, XZ?
You have a right triangle, XYZ, with legs YX and YZ, and with hypotenuse XZ. You are given one of the acute angles as 47 deg. You are looking for the length of the hypotenuse, XZ.
For the given angle theta, XY is the opposite leg.
XZ is the hypotenuse of the triangle.
The trig ratio that relates the opposite leg to the hypotenuse is the sine.