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3 years ago

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Over a 1.35-hour period of time, a family walk 0.75 km, stop to talk to the neighbor, and then walk another 1.15 km before reach

ing their destination. What is the average speed of the family during their walk?

1 answer:

Diano4ka-milaya [45]3 years ago

4 0

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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 problem solving template is a tool which can be used to help solve difficult problems. For this sample work you will use the

slega [8]

Answer:

27

Step-by-step explanation:

8 0

3 years ago

An instructor asked her students how much time (to the nearest hour) they spent studying for the midterm. The data are displayed

BARSIC [14]

Based on the data displayed in the histogram, the percentage of students who study 2 or more hours for the midterm is 88%.

<h3>What percentage study 2 hours or more?</h3>

First, find the number of students studying:

= 3 + 9 + 6 + 3 + 2 + 1 + 1

= 25

The number of students studying 2 or more hours for the exam are:

= 9 + 6 + 3 + 2 + 1 + 1

= 22 students

The percentage studying for two hours or more is:

= 22 / 25

= 88%

Find out more on percentages at brainly.com/question/25567167.

#SPJ1

8 0

1 year ago

If tb=5x and tu=4x-1 and ub=2x-1 what does x equal

Sunny_sXe [5.5K]

If C is a point between AB then we can write AC + CB = AB

Same way we can write tu + ub = tb
tu = 4x - 1 , ub = 2x - 1 and tb = 5x
So we can write it as

$4x - 1+ 2x - 1 = 5x$

$6x - 2 = 5x$

$6x - 5x = 2$

$x = 2$

So x is = 2.

3 0

3 years ago

Triangle MNO is reflected over the x-axis and then translated up 4 and right 3.

stepan [7]

Answer:

Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis.

Step-by-step explanation:

The pre-image consists of points:

(1, 3), (2, 1), (-1, 2)

Translating them down 4 units, we get:

(1, 3-4), (2, 1-4), (-1, 2-4)

(1, -1), (2, -3), (-1, -2)

Translating them right 3, we get:

(1+3, -1), (2+3, -3), (-1+3, -2)

(4, -1), (5, -3), (2, -2)

Reflecting them over the x-axis., we get:

(4, -(-1)), (5, -(-3)), (2, -(-2))

(4, 1), (5, 3), (2,2)

which correspond to the points of the image

5 0

2 years ago

Read 2 more answers