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klemol [59]
3 years ago
11

Simplify (3x-5)+(5x+1)

Mathematics
2 answers:
Semenov [28]3 years ago
8 0
Group the common terms together

3x + 5x - 5 + 1

then add or subtract them

8x - 4
Soloha48 [4]3 years ago
4 0
Here is a step by step solution to your problem

3x − 5 + 5x + 1

=3x + −5+5x + 1

Combine Like Terms:

=3x + −5 + 5x + 1

=(3x + 5x) + (−5 + 1)

=8x + −4

Answer:
=8x − 4
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How do u find angle mesurements in a triangle
alexgriva [62]
The sum of all the angles must be 180 degrees.
3 0
3 years ago
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer d
andrey2020 [161]

Answer:

The maximum value is 1/27 and the minimum value is 0.

Step-by-step explanation:

Note that the given function is equal to (xyz)^2 then it means that it is positive i.e f(x,y,z)\geq 0.

Consider the function F(x,y,z,\lambda)=x^2y^2z^2-\lambda (x^2+y^2+z^2-1)

We want that the gradient of this function  is equal to zero. That is (the calculations in between are omitted)

\frac{\partial F}{\partial x} = 2x(y^2z^2 - \lambda)=0

\frac{\partial F}{\partial y} = 2y(x^2z^2 - \lambda)=0

\frac{\partial F}{\partial z} = 2z(x^2y^2 - \lambda)=0

\frac{\partial F}{\partial \lambda} = (x^2+y^2+z^2-1)=0

Note that the last equation is our restriction. The restriction guarantees us that at least one of the variables is non-zero. We've got 3 options, either 1, 2 or none of them are zero.

If any of them is zero, we have that the value of the original function is 0. We just need to check that there exists a value for lambda.

Suppose that x is zero. Then, from the second and third equation we have that

-2y\lambda = -2z\lambda. If lambda is not zero, then y =z. But, since -2y\lambda=0 and lambda is not zero, this implies that x=y=z=0 which is not possible. This proofs that if one of the variables is 0, then lambda is zero. So, having one or two variables equal to zero are feasible solutions for the problem.

Suppose that only x is zero, then we have the solution set y^2+z^2=1.

If both x,y are zero, then we have the solution set z^2=1. We can find the different solution sets by choosing the variables that are set to zero.

NOw, suppose that none of the variables are zero.

From the first and second equation we have that

\lambda = y^2z^2 = x^2z^2 which implies x^2=y^2

Also, from the first and third equation we have that

\lambda = y^2z^2 = x^2y^2 which implies x^2=z^2

So, in this case, replacing this in the restriction we have 3z^2=1, which gives as another solution set. On this set, we have x^2=y^2=z^2=\frac{1}{3}. Over this solution set, we have that the value of our function is \frac{1}{3^3}= \frac{1}{27}

4 0
3 years ago
HELP ASAP!!
kiruha [24]

Answer:

Step-by-step explanation:

hello:

here an solution

3 0
2 years ago
What is the area of a semicircle whose perimeter is 72cm
Nuetrik [128]

Answer:

A = 307.9 sq/cm

Step-by-step explanation:

Find the radius of the semi-circle

diameter + half the circumference = 72 cm

2r + pi*r = 72

r(2+pi) = 72

 

r = 72%2F%28%282%2Bpi%29%29

r = 14

:

what will be the area of that semicircle?

A =1%2F2*pi%2A14%5E2

A = 307.9 sq/cm

7 0
3 years ago
PLS HELP
dybincka [34]
12.826+2.93= 15.756

Since you have to round it, your final answer would be 15.8
6 0
3 years ago
Read 2 more answers
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