Sense -4 and +2 would be 6 digits away from each other, we would then have to figure out, what would 4 times x - 2 would equal "x".
We would do, 4×2 = 8.
8 - 2 = 6.
Sense 6 is the amount of how much -4 and +2 would be from each other, this would then mean that x would then equal 8.
Answer:
<5 ~= <1 - Corresponding Angles Theorem
<1 ~= <7 - Alternate Exterior Angles Theorem
<5 ~= <7 - Vertical Angles Theorem
line I || line m - Transitive Property
Answer: The number is 26.
Step-by-step explanation:
We know that:
The nth term of a sequence is 3n²-1
The nth term of a different sequence is 30–n²
We want to find a number that belongs to both sequences (it is not necessarily for the same value of n) then we can use n in one term (first one), and m in the other (second one), such that n and m must be integer numbers.
we get:
3n²- 1 = 30–m²
Notice that as n increases, the terms of the first sequence also increase.
And as n increases, the terms of the second sequence decrease.
One way to solve this, is to give different values to m (m = 1, m = 2, etc) and see if we can find an integer value for n.
if m = 1, then:
3n²- 1 = 30–1²
3n²- 1 = 29
3n² = 30
n² = 30/3 = 10
n² = 10
There is no integer n such that n² = 10
now let's try with m = 2, then:
3n²- 1 = 30–2² = 30 - 4
3n²- 1 = 26
3n² = 26 + 1 = 27
n² = 27/3 = 9
n² = 9
n = √9 = 3
So here we have m = 2, and n = 3, both integers as we wanted, so we just found the term that belongs to both sequences.
the number is:
3*(3)² - 1 = 26
30 - 2² = 26
The number that belongs to both sequences is 26.
To solve these problems, you must make the denominators of each fraction match, before adding.
2. The answer is 11/10 or 1 and 1/10.
To find this answer, multiply 1/5 by 2/2 to get 2/10. Then add 2/10 to 9/10 get 11/10 or 1 and 1/10 as your answer.
4. The answer is 23/18 or 1 and 5/18.
To find this answer, multiply 7/9 by 2/2 to get 14/18, and multiply 1/2 by 9/9 to get 9/18. Then add 14/18 and 9/18 to get 23/18 or 1 and 5/18 as your answer.
6. The answer is 7/12.
To find this answer, multiply 1/3 by 4/4 to get 4/12 and multiply 1/4 by 3/3 to get 3/12. Then add 4/12 and 3/12 to get 7/12 as your answer.
I hope this helps!
6. The lengths of two tangent lines to a circle are equal, which can be proved using similar triangles. The perimeter is 2*(3+2+5)=10.
14. c=40 degrees, since c and the given 40 angle correspond to the same arc on the circle. b=40, since b and the given angle are alternate interior angles of two parallel lines. d=180-40-40=100 degrees. a=180-d=180-100=80 degrees.
18. a is two times the given angle according to the inscribed angle theorem. a=2*20=40. b=180-a=140. c=90 since the tangent line is perpendicular to the diameter of the circle.
19. b=85, a=95. Connect the two points on the circle near 45 degrees on the diagram. b is the sum of the two angles formed (b is the exterior angle of the small triangle), and the sum is half the central angles they correspond to, which is 360-145-45=170. So b=170/2=85, and a=180-85=95 degrees.
20. Use power of a triangle. 5*(10+5)=6(6+x), x=6.5.