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sergiy2304 [10]

3 years ago

11

Find the missing length indicated

2 answers:

faltersainse [42]3 years ago

6 0

Answer:

D) 20

Step-by-step explanation:

Len [333]3 years ago

4 0

Answer:

D) 20

Step-by-step explanation:

they are asking for the longest length of the triangle. as you can see, 20 is just over 15, and from the diagram, the missing length is just over 15 so we can apply our knowledge to come to the answer of 20.

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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:

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

The sum of two numbers is 61. If the larger number is seven less than three times the smaller number, find both numbers.

Julli [10]

Answer:

x = 17, y = 44

Step-by-step explanation:

3 0

3 years ago

To the Pythagorean Theorem

Aloiza [94]

Answer:

x = 29

Step-by-step explanation:

$c^{2} = a^{2} + b^{2}$

$c^{2} = 20^{2} + 21^{2}$

$c^{2} = 400 + 441$

$c^{2} = 841$

$\sqrt{c^2} = \sqrt{841}$

$c = 29$

4 0

2 years ago

A cylinder with a radius of 4 yd and a volume of 80yd (find the height)

Afina-wow [57]

Answer:

Height of the cylinder = 1.60yd

Step-by-step explanation:

Volume of a cylinder =

V = πr^2h

V - volume of cylinder

π - 3.142

r - radius of cylinder

h - height of cylinder

We are provided with

V - 80

r - 4

π - 3.142

h - ?

80 = 3.142 * 4^2 * h

80 = 50.272 * h

To find h, divide both sides by 50.272

80/50.272 = 50.272h/ 50.272

1.599 = h

h = 1.60yd

7 0

3 years ago

Read 2 more answers

Which ordered pairs lie on the graph of the exponential function f(x) = 3 (1/4)x

sineoko [7]

The first two pairs.. just substitute the x-coordinate and find y

8 0

3 years ago