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3 years ago

One sign shows 15 miles in 20 minutes what is the speed in miles per hour.

Mathematics

1 answer:

emmainna [20.7K]3 years ago

7 0

Answer:

45 miles/hour

Step-by-step explanation:

We need the speed in miles per hour so we need to changes minutes to hours

20 minutes * 1 hour /60 minutes = 1/3 hour

Speed = distance/ time

= 15 miles/(1/3 hour)

=15 *3 miles/hour

= 45 miles /hour

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1 year 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:

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

2 years ago

8. Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.

Alchen [17]

x = 9 / tan(30)
x = 9 sqrt(3)

8 0

3 years ago

Read 2 more answers

HELP ME PLEASE<br> Solve for x: -6 – 5x = 29

Lynna [10]

Answer:

x = -7

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (&Roots)

Multiplications

Divisions

Additions

Subtractions

First, add 6 to both sides of the equation:

-5x - 6 = 29

-5x - 6 (+6) = 29 (+6)

-5x = 29 + 6

-5x = 35

Next, divide -5 from both sides of the equation:
(-5x)/-5 = (35)/-5

x = 35/-5

x = -7

-7 is your answer for x.

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2 years ago

Which set of data has the strongest linear association

Bad White [126]

It would be the bottom right because it’s closest to a line

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3 years ago