Answer:
4,5,6,7
Step-by-step explanation:
-1 < x ≤7 , x > 3 means that 3 < x ≤ 7
Answer:
(x, y) = (5, 1)
Step-by-step explanation:
To <em>eliminate</em> x, you can double the second equation and subtract the first.
... 2(x +4y) -(2x -3y) = 2(9) -(7)
...11y = 11 . . . . . simplify
... y = 1 . . . . . . divide by 11
Using the second equation to find x, we have ...
... x + 4·1 = 9
... x = 5 . . . . . subtract 4
_____
<u>Check</u>
2·5 -3·1 = 10 -3 = 7 . . . . agrees with the first equation
(Since we used the second equation to find x, we know it will check.)
Answer:
x = 100°
Step-by-step explanation:
As the given shape is a regular polygon, the triangles created by extending the sides are <u>isosceles triangles</u>.
To calculate the base angles of the isosceles triangle, find the interior angle of the regular polygon:
Therefore:
As angles on a straight line sum to 180°, the <u>base angle</u> of the isosceles triangle is:
= 180° - interior angle
= 180° - 140°
= 40°
Interior angles of a triangle sum to 180°.
⇒ 2 base angles + x = 180°
⇒ 2 × 40° + x = 180°
⇒ 80° + x = 180°
⇒ x = 180° - 80°
⇒ x = 100°
Answer:
0.749
Step-by-step explanation:
We start by calculating the z-score
Mathematically:
z-score = (x-mean)/SD
z-score = (75-77)/3 = -2/3 = -0.67
The probability we want to calculate is;
P( X > -0.67)
we can use the standard normal distribution table for this
Using this table, the probability has a value 0.74857 which is 0.749 to the nearest thousandth
