A sailboat travels at an average speed of 8 km/h. How many kilometers are traveled in 20 h at that speed?

Paul makes 6 stacks of cans on a shelf in his kitchen. He puts 2 cans in each stack. Which equation and answer show the total nu

saw5 [17]

If there are 6 stacks with 2 cans in each stack, then you would times 6 x 2 = 12

3 0

3 years ago

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

he quadrilateral PQRS in the diagram is a parallelogram. Let P'Q'R'S' be the image of PQRS after applying a dilation centered at

yKpoI14uk [10]

Answer:

P”Q=3PQ

Step-by-step explanation:

6 0

3 years ago

You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $2.89 a p

ASHA 777 [7]

Answer:

1. Going to the close store is cheaper.

Step-by-step explanation:

The difference in the prices of chicken is 3.19 -2.89 = 0.30 per pound, so for 5 pounds of chicken, the far store offers a price that totals 5×$0.30 = $1.50 less.

The difference in travel distances is 8.4 -2.4 = 6 miles, so the total round-trip distance difference is 12 miles. The cost of gas is ...

($3.81 /gal)/(23 mi/gal) = $0.1656 /mi

so the cost of gas for the 12-mile longer trip would be

12×$0.1656 ≈ $1.99

Traveling to the far store, you would spend $1.99 more on gas to save $1.50 on the price of chicken. Going to the close store is cheaper.

3 0

3 years ago

You invested money in two funds. Last year, the first fund paid a dividend of 9% and the second a dividend of 3%, and you receiv

Elden [556K]

If the amount of money you invested in the first fund is x and the second fund y, then 9% (or 0.09 by moving the decimal 2 spots)*x+0.03*y=1047 since the first fund paid 9% and the second 3%. In addition, for this year, we get
0.1*x+0.01*y=811.
We also have 0.09*x+0.03*y=1047, so we can multiply the top equation by -3 and add it to the second to get -0.21x=-1386. Dividing both sides by -0.21, we get x=6600. In addition, since 0.1*x+0.01*y=811, we can plug 6600 in for x to get 660+0.01*y=811 and by subtracting 660 from both sides we get 0.01*y=151. Multiplying both sides by 100 (since 0.01*100=1), we get y=15100

6 0

3 years ago