joe buys a new stereo for $875 and pays for it over two years with 6.5% simple interest. what is his monthly payment?

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:

4

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

Including a 6% sales tax, an inn charges $155.82 per night. Find the inn's nightly cost before tax is added.

Feliz [49]

we know the Inn is charging 155.82 and that's 100% plus 6%, namely 106% of an amout of say that is "x", being the 100%.

since we know that 155.82 is 106%, what is "x"?

$\begin{array}{ccll} amount&\%\\ \cline{1-2} 155.82&106\\ x&100 \end{array}\implies \cfrac{155.82}{x}=\cfrac{106}{100}\implies \cfrac{155.82}{x}=\cfrac{53}{50} \\\\\\ 7791=53x\implies \cfrac{7791}{53}=x\implies 147=x$

3 0

2 years ago

The angle 01 is located in Quadrant I, and sin(01)=1/2 what is the value of cos(01)

vovikov84 [41]

Answer:

The value of Cos(01) is 0.866 or √3/2

Step-by-step explanation:

In this question, we are asked to calculate the value of cos (01) given the value of sin(01)

Now, given the value of sin (01), we can calculate the value of cos (01).

To get the value of 01, we simply find the value of the arc sin 01

Mathematically since sin (01) = 1/2

(01) = arc sin (1/2)

(01) = 30 degrees

Now since 01 = 30 degrees

cos 01 = Cos (30) = 0.8666 or simply √3/2

4 0

3 years ago

Can someone answer this for me ill give brainliest asap!!!!

timama [110]

Answer:

this does not have a linear function the y axes does not have a the same amount of constant change

hope this helps :)

Step-by-step explanation:

8 0

3 years ago

Triangles MOP and MNQ are similar. Find x.

OLga [1]

Aight so if you add the angel mn and no you get eight so that must mean the opposite side must also equal eight, in that case 8-4 is 4, so Qp is 4

correct me if im wrong

3 0

4 years ago

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