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boyakko [2]
3 years ago
13

Factoring Trinomals (a=1)b^2 + 8b + 7

Mathematics
1 answer:
yulyashka [42]3 years ago
4 0
b^2+8b+7=b^2+b+7b+7=b(b+1)+7(b+1)\\\\=\boxed{(b+1)(b+7)}
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The graph shows the feasible region for the system with constraints:
Dimas [21]

Answer:

The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

The minimum value of the objective function C is 125

Step-by-step explanation:

* Lets look to the graph to answer the question

- There are 3 inequalities

# y ≤ 15 represented by horizontal line (purple line) and cut the

  y-axis at point (0 , 15)

# x + y ≤ 25 represented by a line (green line) and intersected the

  x-axis at point (25 , 0) and the y- axis at point (0 , 25)

# x + 2y ≥ 30 represented by a line (blue line) and intersected the

  x-axis at point (30 , 0) and the y-axis at point (0 , 15)

- The three lines intersect each other in three points

# The blue and purple lines intersected in point (0 , 15)

# The green and the purple lines intersected in point (10 , 15)

# The green and the blue lines intersected in point (20 , 5)

- The three lines bounded the feasible region

∴ The vertices feasible region are (0 , 15) , (10 , 15) , (20 , 5)

- To find the minimum value of the objective function C = 4x + 9y,

  substitute the three vertices of the feasible region in C and chose

  the least answer

∵ C = 4x + 9y

- Use point (0 , 15)

∴ C = 4(0) + 9(15) = 0 + 135 = 135

- Use point (10 , 15)

∴ C = 4(10) + 9(15) = 40 + 135 = 175

- Use point (20 , 5)

∴ C = 4(40) + 9(5) = 80 + 45 = 125

- From all answers the least value is 125

∴ The minimum value of the objective function C is 125

6 0
3 years ago
Read 2 more answers
At which points are the tangents drawn to the ellipse x 2 + y 2 = [ a ] x + [ a ] y parallel to
In-s [12.5K]

The given equation of the ellipse is x^2 + y^2 = 2 x + 2 y

At tangent line, the point is horizontal with the x-axis therefore slope = dy / dx = 0

<span>So we have to take the 1st derivative of the equation then equate dy / dx to zero.</span>

x^2 + y^2 = 2 x + 2 y

x^2 – 2 x = 2 y – y^2

(2x – 2) dx = (2 – 2y) dy

(2x – 2) / (2 – 2y) = 0

2x – 2 = 0

x = 1

 

To find for y, we go back to the original equation then substitute the value of x.

x^2 + y^2 = 2 x + 2 y

1^2 + y^2 = 2 * 1 + 2 y

y^2 – 2y + 1 – 2 = 0

y^2 – 2y – 1 = 0

Finding the roots using the quadratic formula:

y = [-(- 2) ± sqrt ( (-2)^2 – 4*1*-1)] / 2*1

y = 1 ± 2.828

y = -1.828 , 3.828

 

<span>Therefore the tangents are parallel to the x-axis at points (1, -1.828) and (1, 3.828).</span>

3 0
3 years ago
Which object has the same y-intercept as a function y=2/3x-3?
Licemer1 [7]

The 4th option.

The values with no x or y attached are the y intercept

6x - 7y = 21

Subtract 6x from both sides

6x - 7y - 6x = 21 - 6x

-7y = 21 - 6x

Divide both sides by - 7

-7y/-7 = 21/-7 - 6x/-7

Y = -3 +6x/7


The why intercept, -3 is the same as the one in the question


7 0
4 years ago
Six times a number is greater than 20 more than that number. What are the possible values of that number? n less-than 4 n greate
MrRissso [65]

Answer:  answer is b

Step-by-step explanation: because ik

7 0
3 years ago
Read 2 more answers
Which does not belong to the group?<br>a) candle<br>b) flashlight<br>c) mirror<br>d) sun​
Illusion [34]
The mirror does not belong.
6 0
3 years ago
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