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3 years ago

Solve for y. 2/3+y−1/9=7/9 Enter your answer in the box

1 answer:

3 0

Adding 1/9 to both sides, we get 2/3+y=8/9. Next, 2/3 can be multiplied by 3/3 to get 6/9 due to that 3*3=9 and using the identity property. We then subtract 6/9 from both sides to get y=2/9

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Which of the following is the perimeter of a triangle with side lengths of 7 inches, 8 inches, and 13 inches?

Juli2301 [7.4K]

Answer: p=28 inches

Step-by-step explanation:

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3 years ago

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How do you verify this trigonometric identity? cos^2 θcot^2 θ = cot^2 θ - cos^2 θ

sattari [20]

<h3>Explanation:</h3>

Replace cos^2(θ) with 1-sin^2(θ), and cot(θ) with cos(θ)/sin(θ).

cos^2(θ)cot^2(θ) = cot^2(θ) - cos^2(θ)

(1 -sin^2(θ))cot^2(θ) = . . . . . replace cos^2 with 1-sin^2

cot^2(θ) -sin^2(θ)·cos^2(θ)/sin^2(θ) = . . . . . replace cot with cos/sin

cot^2(θ) -cos^2(θ) = cot^2(θ) -cos^2(θ) . . . as desired

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3 years ago

A company manufactures two different sizes of boat lifts. The smaller lift requires 1 hour in the welding department and 2 hours

qaws [65]

Answer:

The solution that optimizes the profit is producing 0 small lifts and 50 large lifts.

Below are all the steps explained in detail.

The graph is attached.

Explanation:

1. Name the variables:

x: number of smaller lifts
y: number of larger lifts

2. Build a table to determine the number of hours each lift requires from each department:

Number of hours

small lift large lift total per department

Welding department 1x 3y x + 3y

Packaging department 2x 1y 2x + y

3. Constraints

150 hours available in welding: x + 3y ≤ 150
120 hours available in packaging: 2x + y ≤ 120
The variables cannot be negative: x ≥ 0, and y ≥ 0

Then you must:

draw the lines and regions defined by each constraint
determine the region of solution that satisfies all the constraints
determine the vertices of the solution region
test the profit function for each of the vertices. The vertex that gives the greatest profit is the solution (the number of each tupe that should be produced to maximize profits)

4. Graph

See the graph attached.

Here is how you draw it.

x + 3y ≤ 150
draw the line x + 3y = 150 (a solid line because it is included in the solution set)
shade the region below and to the left of the line

2x + y ≤ 120
draw the line 2x + y ≤ 120 (a solid line because it is included in the solution set)
shade the region below and to the left of the line

x ≥ 0 and y ≥ 0: means that only the first quadrant is considered

the solution region is the intersection of the regions described above.

take the points that are vertices inside the solutoin region.

5. Test the profit function for each vertex

The profit function is P(x,y) = 25x + 90y

The vertices shown in the graph are:

(0,0)
(0,50)
(42,36)
(60,0)

The profits with the vertices are:

P(0,0) = 0
P(0,50) = 25(0) + 90(50) = 4,500
P(42,36) = 25(42) + 90(36) = 4,290
P(60,0) = 25(60) + 90(0) = 1,500

Thus, the solution that optimizes the profit is producing 0 smaller lifts and 90 larger lifts.

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3 years ago

1. Find the common difference of the sequence: 31, 26, 21, 16, ...

hichkok12 [17]

Answer:

it is subtract 5

Step-by-step explanation:

8 0

3 years ago

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In how many ways can ann, bob, chuck, don and ed be seated in a row such that ann and bob are not seated next to each other?

balandron [24]

The 5 people can seat in a row in 5! ways
But we need to exclude the ways that ann and bob are seated next to each other which is = 4! * 2!

So, the number of ways can ann, bob, chuck, don and ed be seated in a row such that ann and bob are not seated next to each other = 5! - 4! * 2! = 72

=====================================================

Another solution:

If ann seated in one of the ends, the number of ways = 3*2

If ann didn't seat in one of the ends , the number of ways = 2*3

So, the total number of ways that can ann, bob be seated = 3*2 + 2*3 = 12

The remaining persons can seat with a number of ways = 3! = 6
So, the total ways that the five persons can seat = 12*6 = 72

7 0

3 years ago