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Vinvika [58]
3 years ago
7

Ms. Malone’s homeroom raised $539 for a local charity. Find the opposite of this integer.

Mathematics
1 answer:
Radda [10]3 years ago
4 0

Answer:

It's -539

Step-by-step explanation:

539 is a positive number in this one, so to find the opposite, you'd make the number a negative one, which is -$539

You might be interested in
The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs seven times as
Olin [163]

Answer:

x = ∛(2V/7)

y = ∛(2V/7)

z = 3.5 [∛(2V/7)]

{x,y,z} = { ∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)] }

Step-by-step explanation:

The aquarium is a cuboid open at the top.

Let the dimensions of the base of the aquarium be x and y.

The height of the aquarium is then z.

The volume of the aquarium is then

V = xyz

Area of the base of the aquarium = xy

Area of the other faces = 2xz + 2yz

The problem is to now minimize the value of the cost function.

The cost of the area of the base per area is seven times the cost of any other face per area.

With the right assumption that the cost of the other faces per area is 1 currency units, then, the cost of the base of the aquarium per area would then be 7 currency units.

Cost of the base of the aquarium = 7xy

cost of the other faces = 2xz + 2yz

Total cost function = 7xy + 2xz + 2yz

C(x,y,z) = 7xy + 2xz + 2yz

We're to minimize this function subject to the constraint that

xyz = V

The constraint can be rewritten as

xyz - V = 0

Using Lagrange multiplier, we then write the equation in Lagrange form

Lagrange function = Function - λ(constraint)

where λ = Lagrange factor, which can be a function of x, y and z

L(x,y,z) = 7xy + 2xz + 2yz - λ(xyz - V)

We then take the partial derivatives of the Lagrange function with respect to x, y, z and λ. Because these are turning points and at the turning point, each of the partial derivatives is equal to 0.

(∂L/∂x) = 7y + 2z - λyz = 0

λ = (7y + 2z)/yz = (7/z) + (2/y) (eqn 1)

(∂L/∂y) = 7x + 2z - λxz = 0

λ = (7x + 2z)/xz = (7/z) + (2/x) (eqn 2)

(∂L/∂z) = 2x + 2y - λxy = 0

λ = (2x + 2y)/xy = (2/y) + (2/x) (eqn 3)

(∂L/∂λ) = xyz - V = 0

We can then equate the values of λ from the first 3 partial derivatives and solve for the values of x, y and z

(eqn 1) = (eqn 2)

(7/z) + (2/y) = (7/z) + (2/x)

(2/y) = (2/x)

y = x

Also,

(eqn 1) = (eqn 3)

(7/z) + (2/x) = (2/y) + (2/x)

(7/z) = (2/y)

z = (7y/2)

Hence, at the point where the box has minimal area,

y = x,

z = (7y/2) = (7x/2)

We can then substitute those into the constraint equation for y and z

xyz = V

x(x)(7x/2) = V

(7x³/2) = V

x³ = (2V/7)

x = ∛(2V/7)

y = x = ∛(2V/7)

z = (7x/2) = 3.5 [∛(2V/7)]

The values of x, y and z in terms of the volume that minimizes the cost function are

{x,y,z} = {∛(2V/7), ∛(2V/7), 3.5[∛(2V/7)]}

Hope this Helps!!!

7 0
3 years ago
Y = 2(x – 4)– 6<br> Vertex:<br> y-intercept: _
serious [3.7K]

Answer:

vertex: (4,-6), y= -14

Step-by-step explanation:

vertex can be derived from this formula

(4, -6)

to find y intercept you need to set x=0

y=2(0-4)-6

=-8-6

y= -14

4 0
3 years ago
Can someone Plzzz help me out???
Vitek1552 [10]

Hello from MrBillDoesMath!


Answer:  3


Discussion:

The perimeter of a polygon is the sum of the side lengths.

Perimeter of top polygon is   (x+2) + 2x + (x + 2) + (4x + 1) =  8x + 5

Perimeter of bottom triangle is   4x + 2x + (3x+2 ) =  9x + 2


The perimeters are the same when

8x + 5 = 9x + 2

Subtract 8x from both sides:

5 = (9x - 8x) + 2   or

5 = x + 2

Subtract 2 from each side to get x = 3:

5 -2 = 3 = x


The perimeter of either figure is 29



Regards, MrB

6 0
2 years ago
Last year 80 students signed up for a summer trip to Washington, D.C. This summer 50 students have signed up to go. What is the
Fynjy0 [20]

Given:

Last year 80 students signed up for a summer trip to Washington, D.C.

This summer 50 students have signed up to go.

To find:

The percent decrease in the number of students.

Solution:

We have,

Students in last year = 80

Students in this year = 50

Now,

\text{Decrease}\%=\dfrac{\text{Students in last year - Students in this year }}{\text{Students in last year }}\times 100

\text{Decrease}\%=\dfrac{80-50}{80}\times 100

\text{Decrease}\%=\dfrac{30}{80}\times 100

\text{Decrease}\%=\dfrac{3}{8}\times 100

\text{Decrease}\%=37.5

Therefore, the correct option is B.

7 0
2 years ago
93.2×0.07= ???????<br><br> What is the answer?
kumpel [21]
The answer is 6.524. Hope this helps! :D
3 0
3 years ago
Read 2 more answers
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