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2 years ago

Good evening every one sorry to brother u but can someone answer this

Mathematics

1 answer:

TEA [102]2 years ago

7 0

Answer:

-5

Step-by-step explanation:

3 - 9 + 1 = -6 + 1 = -5

Hope this helped! I would appreciate a Brainliest!

(BTW, if you can, can you please answer my question? It's due today!)

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How would you factor x²+10x-2=0

attashe74 [19]

This would be easiest to do by completing the square.

x^2+10x-2=0

x^2+10x=2

x^2+10x+25=27

(x+5)^2=27

x+5=±√27

x=-5±√27

(x+5+√27)(x+5-√27)

5 0

3 years ago

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an apple pie was cut into 4 equal slices one slice was quickly eaten what fraction of the pie was left

pantera1 [17]

It is 3/4 of the pie is left because one slice is 1/4 of the pie and taking 1/4 from 4/4 is 3/4

8 0

3 years ago

Find the length of dm in the given fig.

lesya692 [45]

Answer:

$DM=12$

Step-by-step explanation:

(Let the point where the altitude from $D$ intersects $AB$ be called as point $E$ .) First, let's find the area of parallelogram $ABCD$ . The area of a parallelogram is simply $b*h=bh$ , where $b$ is the parallelogram's base and $h$ is the parallelogram's height. If we let $AB$ and $DE$ be the base and height respectively, since we are already given their lengths, we know that the area of parallelogram $ABCD$ will be $AB*DE=15*8=120$ .

Now, how does this information matter, you might ask? Well, we can take either $AB$ <em>or </em> $CB$ to be the base and either $DE$ or $DM$ to be the height. In this case, let's take the latter two options, as we are looking to find the length of $DM$ .

Therefore, we know that the area of parallelogram $ABCD$ can also be found by calculating $CB*DM$ . Since we know the values of the area and $CB$ , we can write the following equation to solve for $DM$ :

$Area = CB*DM$

$120=10*DM$ (Substitute $Area=120$ and $CB=10$ into the equation)

$\frac{120}{10}=\frac{10*DM}{10}$ (Divide both sides of the equation by $10$ to get rid of $DM$ 's coefficient)

$12=DM$ (Simplify)

$DM=12$ (Symmetric Property of Equality)

Hope this helps!

4 0

3 years ago

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

A theater has 20 rows of chairs. The first row has 16 chairs, the second has 18, the third has 20, and so on. In total, the thea

Brilliant_brown [7]

<span>This is an arithmetic progression, i.e. 16,18,20,22,24,26,28.......... where 16 is the number of people seats in 1st row, 18 seats in second row, 20 seats in third row and so on. The Total number of seats in 20 rows = n/2{2a+(n-1)d}. Here, d = 2 , n =20, a = 16. Thus, Sum = 10 {32+ 19*2} = 10 {70} = 700 seats in total. </span>

5 0

3 years ago

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