Answer:
at least 1.9 feet
if x is how much she intends to knit, inequality is x ≥ 1.9
<span>Square root of 90 to the nearest tenth 9.5</span>
Answer:
so required angles are 50.7°and 129.3°
Step-by-step explanation:
Let the angle be x
another angle = x + 78.6°
so,
x + x + 78.6° = 180° {being sum of supplementary angle}
so, 2x + 78.6° = 180°
or, 2x = 180° - 78.6°
or, x = 101.4/2
so, x = 50.7°
so another angle = x + 78.6°
= 50.7° + 78.6°
= 129.3°
Answer:
Constructive Proof
Step-by-step explanation:
Let x be a positive integer
x must be equal to sum of all positive integers exceeding it
i.e.
x = x + (x - 1) + ( x - 2) + ......... + 2 + 1
Equivalently,
x = ∑i (where i = 1 to x)
The property finite sum;
∑i (i = 1 to x) = x(x + 1)/2
So,
x = x(x + 1)/2 ------- Multiply both sides by 2
2 * x = 2 * x(x + 1)/2
2x = x(x + 1)
2x = x² + x ------- subtract 2x from both sides
2x - 2x = x² + x - 2x
0 = x² + x - 2x ----- Rearrange
x² + x - 2x = 0
x² - x = 0 ------ Factorise
x(x - 1) = 0
So,
x = 0 or x - 1 = 0
x = 0 or x = 1 + 0
x = 0 or x = 1
But x ≠ 0
So, x = 1
The statement is only true for x = 1
This makes sense because 1 is the only positive integer not exceeding 1
1 = 1
It is a Constructive Proof
A proof is constructive when we find an element for which the statement is true.
Answer: Time spent on Question C=3 9/10
Step-by-step explanation:
Total Time to do the entire quiz= 20 minutes
Time spent on Question A=10 7 /10 minutes
Time spent on Question B=5 2/ 5 minutes
Time spent on Question C=Total Time to do the entire quiz-(Time spent on Question A+Time spent on Question B)
20mins- (10 7 /10 +5 2/ 5)
20mins - ( 15 7+4 /10)
20mins - ( 15 11/10=16 1/10))
20mins -16 1/10
19 10/10 -16 1/10
Therefore Time spent on Question C= 3 9/10
