Answer:
75
Step-by-step explanation:
The sum of internal angles in a triangle is equal to 180
58 + 47 + x = 180
105 + x = 180 subtract 105 from both sides
x = 75
Twice. Dividing by ten will move the decimal point one place to the left. Rather than dividing by ten twice, you can divide by 100 once.
Answer:
528
Step-by-step explanation:
(80:100)*660 =
(80*660):100 =
52800:100 = 528
Now we have: 80 percent of 660 = 528
The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
<h3>What is the equation of the ellipse associated with the coordinates of the foci?</h3>
By <em>analytical</em> geometry we know that foci are along the <em>major</em> axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the <em>standard</em> form of the equation of the ellipse is of the following form:
(x - h)² / a² + (y - k)² / b² = 1, where a > b (1)
Where:
- a - Length of the major semiaxis.
- b - Length of the minor semiaxis.
Now, we proceed to find the vertex and the lengths of the semiaxes:
a = 10 units.
b = 8 units.
Vertex
V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)
V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)
V(x, y) = (1.5, 1) + (- 4.5, 1)
V(x, y) = (- 3, 2)
The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
To learn more on ellipses: brainly.com/question/14281133
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Answer:
d. 15
Step-by-step explanation:
Putting the values in the shift 2 function
X1 + X2 ≥ 15
where x1= 13, and x2=2
13+12≥ 15
15≥ 15
At least 15 workers must be assigned to the shift 2.
The LP model questions require that the constraints are satisfied.
The constraint for the shift 2 is that the number of workers must be equal or greater than 15
This can be solved using other constraint functions e.g
Putting X4= 0 in
X1 + X4 ≥ 12
gives
X1 ≥ 12
Now Putting the value X1 ≥ 12 in shift 2 constraint
X1 + X2 ≥ 15
12+ 2≥ 15
14 ≥ 15
this does not satisfy the condition so this is wrong.
Now from
X2 + X3 ≥ 16
Putting X3= 14
X2 + 14 ≥ 16
gives
X2 ≥ 2
Putting these in the shift 2
X1 + X2 ≥ 15
13+2 ≥ 15
15 ≥ 15
Which gives the same result as above.
