If 5x + 2 = 7x - 7, then x =

Which of the following is a correct name for plane R below? * Which of the following is a correct name for plane R below? * plan

olga_2 [115]

Answer:

Plane SPT and Plane SPV

Step-by-step explanation:

A plane is defined by the set of three points lying on the same (two dimensional) surface.

A plane 'R' has been given in the picture.

Points lying on this plane or surface are S, P, T and V.

Therefore, possible names may be,

SPT, STV, SPV, PTV

From the given options names of the plane R will be,

Plane SPT and Plane SPV,

8 0

3 years ago

Find the equation of a line that passes through (-5,4) and us parallel to y=-6/7x+3

irina [24]

Given:

The given equation of line is

$y=-\dfrac{6}{7}x+3$

To find:

The equation of line that passes through (-5,4) and is parallel to the given line.

Solution:

Slope intercept form of a line is

$y=mx+b$ ...(i)

where, m is slope and b is y-intercept.

We have,

$y=-\dfrac{6}{7}x+3$ ...(ii)

On comparing (i) and (ii), we get

$m=-\dfrac{6}{7}$

Slope of given line is $m=-\dfrac{6}{7}$ .

Slope of parallel lines are same. So, slope of parallel line is $m=-\dfrac{6}{7}$ .

The required line passes through (-5,4) with slope $m=-\dfrac{6}{7}$ . So, the equation of line is

$y-y_1=m(x-x_1)$

$y-4=-\dfrac{6}{7}(x-(-5))$

$y-4=-\dfrac{6}{7}(x+5)$

$y-4=-\dfrac{6}{7}x-\dfrac{30}{7}$

Adding 4 on both sides, we get

$y=-\dfrac{6}{7}x-\dfrac{30}{7}+4$

$y=-\dfrac{6}{7}x+\dfrac{-30+28}{7}$

$y=-\dfrac{6}{7}x-\dfrac{2}{7}$

Therefore, the correct option is a.

8 0

3 years ago

You buy a package of 12 pencils for $2.64. Write this rate as a unit rate.

andrew-mc [135]

Answer:

0.22 per

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

In 2000, 54% of the residents in a large city regularly used newspapers for getting news and this has decreased at an average r

Anika [276]

X=number of years after 2000.
y=percentage of residents (still) reads newspapers for information
initial value (= y-intercept) = percentage in 2000 = 54%
slope = increase each year = -1.7% (because it is a decrease)
the slope intercept form of the equation is therefore:
y=slope(x)+initial value, or
y=-1.7x+54 (in %)

3 0

3 years ago

After all your hard work studying for Algorithms you, Alice and Bob end up stuck in a room full of deadly zombies! Luckily you h

shutvik [7]

Answer:

The most important quantity to consider in order to answer this question is the arrival time of the zombies from their initial position, which is the quotient between their distance to the visitors, divided the zombie's speed.

See explanation below.

Step-by-step explanation:

Part 1)

What is crucial to know is what is the time at which each zombie would reach Alice and Bob, and that is given by the quotient between the distance away each zombie is, divided by the zombie's speed:

$speed=\frac{distance}{time} \\time=\frac{distance}{seed} \\t_i=\frac{d_i}{s_i}$

Then, it is this quotient for each zombie, that one has to estimate given the input values distance and speed, and it is the output "time" ( $t_i$ ) for each zombie, what we need to analyze so as to prioritize an order regarding which zombie to kill first.

Part 2)

Shooting the closest zombie first is not a good idea, since the speed of that closest zombie may be much slower than another zombie further away, but with much larger speed. Again, the important value to analyze is the time that it would take each zombie to reach Alice and Bob.

Part 3)

Shooting the fastest zombie first is not a good idea either, because that fastest zombie could be located very far away from the visitors, and other zombies closer by may reach them first.

Part 4)

The order that should be used to kill the zombies is given by the value of the time to reach Bob and Alice based on the quotient distance (di) over speed (si) explained in Part 1). The zombie that shows smallest time should be shot first, and then the others in increasing order of time value.

Part 5)

Notice that the individual zombie information is not presented in the question, but the student should be able to calculate the quotients for each zombie, and considering that there could be at most one shot every second, estimate the number of seconds that the time for each zombie in increasing order would allow until the addition of shooting time per second in the appropriate order cannot match the arrival time of the zombies that are left.

One should count number of seconds from the first shot (to the zombie with shortest arrival time), and then increase in one unit (one shot per second), to the following zombie with slightly larger arrival time), and so on, until the addition of seconds (one second per shot and per increasing arrival time of zombie) exceeds the next zombie arrival time.

7 0

2 years ago