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3 years ago

How many terms are in the expression 2x + 3y - 4z?

Mathematics

1 answer:

lana66690 [7]3 years ago

7 0

3 terms

The 2x, 3y, and -4z

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Gandalf the Grey started in the Forest of Mirkwood at a point PP with coordinates (2,−1)(2,−1) and arrived in the Iron Hills at

Alex

Answer:

$(\frac{66}{17},-\frac{9}{17})$

Step-by-step explanation:

Gandalf's Starting Point is given as: P(2,-1)

If he walks in the direction of the vector v=4i+1j

x=4, y=1

The slope of the line which he walked therefore is: $m_1=\dfrac{1}{4}$

First, we determine the equation of the line at P with coordinates (2,-1)

$y-y_1=m(x-x_1)\\y-(-1)=\frac{1}{4}(x-2)\\ y+1=\frac{1}{4}x-\frac{1}{2}\\y=\frac{1}{4}x-\frac{1}{2}-1\\y=\frac{1}{4}x-\frac{3}{2}$

If he changes direction at a right angle, the new path walked is perpendicular to the old path.

DEFINITION: Two lines are perpendicular if the product of their gradients $m_1m_2=-1$

Therefore the gradient $m_2$ of the new path walked $=-4$

At point Q with coordinates (3,3), the equation of the line is:

$y-y_1=m(x-x_1)\\y-3=-4(x-3)\\y=-4x+12+3\\y=-4x+15$

The coordinate where Gandalf the Grey makes a turn is the intersection of the two lines.

$If \: y=\frac{1}{4}x-\frac{3}{2} \:and\: y=-4x+15\\Then:\\\frac{1}{4}x-\frac{3}{2} =-4x+15\\\frac{1}{4}x+4x=15+\frac{3}{2}\\4.25x=16.5\\x=\frac{66}{17}\\y=-4x+15=-4(\frac{66}{17})+15=-\frac{9}{17}$

Therefore, the coordinates where he makes a turn is:

$(\frac{66}{17},-\frac{9}{17})$

6 0

4 years ago

HELP AND HURRY This spinner is spun one time. What is the probability of the arrow not landing on a section with an odd number?

ki77a [65]

Answer:

3/7

Step-by-step explanation:

there are 7 sections total. 1,3,5, and 9 are all odd. so, there are still 3 sections left where there there are even numbers (4,6, and 8.) 3+4=7.

3 out of the 7 sections are even. D.

4 0

2 years ago

Read 2 more answers

A square garden has an area of 103 square feet.

ladessa [460]

This value is $\sqrt{103}$ , or 10.1.

6 0

3 years ago

Simplify (x^8/64)^1/2<br> The answer is x^4/8 but can you please show me how to get the answer.

navik [9.2K]

Answer:

Step-by-step explanation:

Whenever you have exponents raised to another exponent, you multiply the exponents!

3 0

4 years ago

There are 2 1/2 pizzas if each gets an eighth of a pizza how many people get a slice

Butoxors [25]

Answer:

20.

Step-by-step explanation:

That would be 2 1/2 divided by 1/8

= 5/2 / 1/8

= 5/2 * 8

= 40/2

= 20.

8 0

4 years ago