Find the sum of (3 – 4i) and (6 + 7i)

Answer:

The answer is below

Step-by-step explanation:

Chancellor Manufacturing makes two pumps for use in household reef aquariums. The Standard pump (Model A) requires 4.5 lbs of stainless steel while the Deluxe lightweight pump (Model B) 3.0 lbs of stainless steel. There are 63 lbs of stainless steel available during this production period. The combined production of both pumps must be at least 12 pumps. There are orders for at least 6 of the lightweight Model B. Lastly, management has decided that no more than 15 Model B pumps be produced.

The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210.

Solution:

a) Let x represent model pump A and let y represent model pump B.

Since There are 63 lbs of stainless steel available, hence:

4.5x + 3y ≤ 63

Both pumps must be at least 12 pumps. Therefore:

x + y ≤ 12

There are orders for at least 6 of the lightweight Model B:

y ≥ 6

Also,  no more than 15 Model B pumps be produced:

y ≤ 15

The cost to produce one Standard pump is $150 and to produce one Deluxe pump is $210. The cost equation is:

Minimize Cost = 150x + 210y

b)

Hence the LP formation is:

Minimize Cost = 150x + 210y

4.5x + 3y ≤ 63

x + y ≤ 12

y ≥ 6

y ≤ 15

x ≥ 0.

c) The LP problem was solved using geogebra online graphing tool.

The points that satisfy the problem are:

(0, 6), (0,12), (6, 6)

At (0,6); cost = 150(0) + 210(6) = 1260

At (0,6); cost = 150(0) + 210(12) = 2520

At (6,6); cost = 150(6) + 210(6) = 2160

Hence the minimum cost is at (0, 6)

Answer:

Step-by-step explanation:

Using first equation in the second gives you

x-3(-2x+1)=11

x+6x-3=11

7x-3=11

7x=14

x=2, making y=-2x+1 become

y=-2(2)+1

y=-4+1

y=-3 so the solution is the point

(2,-3)

Answer:

is the answer

Step-by-step explanation:

5 + 8x < 6x + 12

8x - 6x < 12 - 5

2x < 7

x < 3.5

Answer:

area of a square

= side × side

= 12 × 12

=144cm^2

Answer:

the first one or A. hope this helps.

Step-by-step explanation:

Answer:

[tex]y = \sqrt{ \frac{wz}{x} } [/tex]

hence c. Patrick Mahomes is right.

Answer:

a) 24[tex]ft^2[/tex]

b) 52ft

Step-by-step explanation:

a)

This question asks to find the capacity of the container. This is essentially asking what the volume of the container is. This can be done by multiplying the length by the width by the height.

4 * 2 * 3

= 24

b)

This question is asking how much material was used to make the prism. This is essentially asking what the surface area of the prism is. This can be found by finding the area of all the sides of the prism and then adding it up. Since it is a rectangular prism, opposite faces are congruent, hence one only has to find the area of three faces, add it up, then multiply it by two to find the answer.

2 ( 4 * 2 ) + 2 ( 3 * 4 ) + 2 ( 2 * 3 )

= 2(8) + 2(12) + 2(6)

= 16 + 24 + 12

= 52

Answer:

not parallel

Step-by-step explanation:

Actually they're Perpendicular.

Answer: i think its

Step-by-step explanation: carrot

Answer:

62.5%

Step-by-step explanation:

if they won 15 and lost 9 games then they played a total of 24 games (15+9).  Then you just divid the number of wins (15) by the total number of games they played (24).  SO, 15/24=0.652 or 62.5%

1. He collected 5 gallons of water.

2. We find this out by knowing 5 = 5.

Hope it helps! Good luck! :D

Answer:

The given polygon has 4 vertices and, 4 non-parallel and non equal sides. So the given polygon is a quadrilateral.

Step-by-step explanation:

The given vertices of are (–2, 4), (5, 4), (3, –3), and (–2, 0).

i found this on web

Answer:

The answer is A. Clara drew the figure correctly and correctly identified the four-sided figure as a quadrilateral.

Step-by-step explanation:

Answer: 595

Step-by-step explanation:

Answer:

-35 i think

Step-by-step explanation:

hope dis helps

Answer:

Step-by-step explanation:

I think that you want to know how many total pounds of beans do you have.

Well, to find this, simply find the LCM of 6 and 4. That is 12.

So convert the fractions to have a denominator of 12.

10/12, 9/12

Now add:

(10+9)/12 = 19/12 = 1 7/12

Answer:

Your question isn't full ?ansition?

Step-by-step explanation:

Step-by-step explanation:

2x²+4x+5=0

.....

solve it by using the factorisation method or completing the square method

don't mind the hand writing

am I correct btw

Answer:

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The option (B) (11, -2), (8, -1), (5, 0), (2, 1), and (-1, 2) is correct because the points will lie exactly lie on the inverse of a function.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a graph of a function shown in the picture.

Let's assume the points (2, 0) and (0, 5) lie on the line which is shown in the graph.

The linear function from these two points:

[tex]\rm y=\dfrac{\left(0-5\right)}{\left(2\right)}\left(x-2\right)[/tex]

[tex]\rm y=\dfrac{\left5\right}{\left2\right}\left(x-2\right)[/tex]

To find the inverse of a function interchange the value of x and y:

The inverse function:

[tex]\rm x=\dfrac{\left5\right}{\left2\right}\left(y-2\right)[/tex]

After plotting the points:

(11, -2), (8, -1), (5, 0), (2, 1), (-1, 2)

The points will lie exactly lie on the inverse of a function.

Thus, the option (B) (11, -2), (8, -1), (5, 0), (2, 1), and (-1, 2) is correct because the points will lie exactly lie on the inverse of a function.

Learn more about the function here:

brainly.com/question/5245372

#SPJ1

Answer:

5935 base balls

Step-by-step explanation:

Volume of a cylinder : pi * r² * h

r = Radius, h = height = 6ft

Diameter = 4ft ; Radius = diameter / 2 = 4/2 = 2ft

V = π * 2^2 * 6

V = 75.398223 ft³

Diameter of baseball = 2.8 inches

2.8 inches = 2.8 × 2.8 * 2.8 = 21.952 in³ = 0.0127037 ft³

Hence,

75.398223 ft³ / 0.0127037ft³

= 5935.1370

= 5935 base balls

Answer:

Step-by-step explanation:

a₁ = -3 = (-1)¹×3

a₂ = 6 = (-1)²×2×3

a₃ = -28 = (-1)³×2²×7

a₄ = 72 = (-1)⁴×2³×3²

a₅ = -360 = (-1)⁵×2³×3²×5

a₆ = 2160 = (-1)⁶×2⁴×3³×5

That's as far as I got. I can predict that a₇ is a multiple of -32 and a₈ is a multiple of 64, but I don't see the pattern with the other factors.

the answer is,

541.42%

I think this is the answer.