Makenzie graphs the line y= 2x + 13. Which statement is true?

Mathematics

1 answer:

slamgirl [31]3 years ago

5 0

Answer:

The point (-4,5) is on the line

Step-by-step explanation:

You can replace the x and y values to determine if it is a true statement

First Statement

5= 2(-4)+13 -> 5= -8+13 -> 5=5 true

Second Statement

-4=2(5)+13 -> -4= 10+13 -> -4 ≠ 23 false

You can automatically eliminate the next two answers because you already found that the first statement is true and because you can find points using an equation.

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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.