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3 years ago

the length of a rectangle is 3 more than the width. if the area is 40 square inches, what are the dimensions.

Mathematics

1 answer:

tankabanditka [31]3 years ago

5 0

40 3 .......................

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Given that (x+y+z)(xy+xz+yz)=18 and that x^2(y+z)+y^2(x+z)+z^2(x+y)=6 for real numbers x, y, and z, what is the value of xyz?

worty [1.4K]

Answer:

Step-by-step explanation:

$(x+y+z)(xy+xz+yz)=18$ Equation 1

$x^2(y+z)+y^2(x+z)+z^2(x+y)=6$ Equation 2

What is the value of $xyz$ where each variable represents a real number?

Let's expand equation 1:

$(x+y+z)(xy+xz+yz)=18$

$x(xy)+x(xz)+x(yz)+y(xy)+y(xz)+y(yz)+z(xy)+z(xz)+z(yz)=18$

Simplify each term if can:

$x^2y+x^2z+xyz+y^2x+xyz+y^2z+xyz+z^2x+z^2y=18$

See if we can factor a little to get some of the left hand side of equation 2:

The first two terms have $x^2$ and if I factored $x^2$ from first two terms I would have $x^2(y+z)$ which is the first term of left hand side of equation 2.

So let's see what happens if we gather the terms together that have the same variable squared together.

$x^2y+x^2z+y^2x+y^2z+z^2y+z^2x+xyz+xyz+xyz=18$

Factor the variable squared terms out of each binomial pairing:

$x^2(y+z)+y^2(x+z)+z^2(y+x)+xyz+xyz+xyz=18$

Replace the sum of those first three terms with what it equals which is 6 from the equation 2:

$6+xyz+xyz+xyz=18$

Combine like terms:

$6+3xyz=18$

Subtract 6 on both sides:

$3xyz=12$

Divide both sides by 3:

$xyz=4$

4 0

3 years ago

How do you know that the systems of equations are consistent? How do you know that they are independent?

Shalnov [3]

Answer:

If a system has at least one solution, it is said to be consistent. If a consistent system has exactly one solution, it is independent.

Step-by-step explanation:

3 0

3 years ago

RS = 12, ST = 2x, RT = 34

Harrizon [31]

Answer:

x=11

Step-by-step explanation:

34(RT) minus 12(RS)=22. 22 divided by 2 equals 11.

6 0

3 years ago

What is 5/8 x 1/10 im dumb plz help me ;-;

andrezito [222]

The answer should be: 5/8 x 1/10 = 1/16.

3 0

3 years ago

(07.01 MC)

ratelena [41]

I choose A. 0, because the angles are complementary

5 0

3 years ago

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