Graph 3x + 2y = 6. Can someone help with this

Answers

Answer 1

Answer:
Here are two ways to graph it. You can decide which one seems easier to understand or easier to do:

==> Manipulate the equation into the "slope-intercept" form, where 'y' is
all alone on one side and everything else is on the other side:

3x + 2y = 6

Subtract 3x from each side:   2y = -3x + 6

Divide each side by 2 : y = -3/2 x +3

This is the form you want. Just looking at it, it tells you that the slope
of the line on the graph is (-3/2), and it crosses the y-axis at +3 .
That's enough information to draw the line.
===============================================

=> Another way:

Look at the x-axis and the y-axis on the graph paper ... without any graph drawn on it yet. Just look at the 2 axes.

With an 'x'-number and a 'y'-number, you can find any point on it. Right ?

OK. Notice that at every point on the y-axis, x = 0 . And at every point
on the x-axis, y = 0. This can be very very helpful.

Now take your equation: 3x + 2y = 6 .

You know that the graph is going to be a straight line. And it's pretty obvious that if the line isn't horizontal or vertical, then it has to cross both the x-axis and the y-axis somewhere. If you had an easy way to find the two points where it crosses the axes, you could join those 2 points and you'd have your line !

You DO have an easy way to find those points !

If x=0, then the point is on the y-axis. Take your equation, make x=0, and it'll show you where the line crosses the y-axis:

   3(0) + 2y = 6 .

    2y = 6 .

Divide each side by 2 : y = 3 .

There's one point on the line: (0, 3)

Now remember that if y=0 the point is on the x-axis. So take your equation
and make y=0:

      3x + 2(0) = 6

3x = 6

Divide each side by 3 :    x = 2

There's another point on the line, where it crosses the x-axis: (2, 0) .

Shazam ! You have the 2 points where the line crosses the x- and
y- axes. Mark each one with a little dot, put your ruler down along
them, draw a line between them, and extend it as far in each direction
as you want to. That's the graph of your equation.

Answer 2

Answer: Plot these coordinates then draw a line through them and that is the line.

(2,0) x intercept
(0,3) y intercept

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What is the volume of a sphere with a radius of 4 cm? Use 3.14 for pi. Round to the nearest hundredth. 50.24 cm³ 66.99 cm³ 200.96 cm³ 267.95 cm³

Answers

Answer:

Volume: 267.95 cm³

Step-by-step explanation:

Volume of Sphere

: $(4)/(3)\pi r^(3)\n= (4)/(3)\pi 4^(3)\n= (4)/(3)\pi(64)\n= (4)/(3)(3.14)(64)\n= (4)/(3)(200.96)\n= (803.84)/(3) = 267.946$

Rounding to nearest hundreth: 267.95

Answer:

267.95

Step-by-step explanation:

Just use the formula, 4/3πr³

Which type of quadrilateral has two pairs of parallel sides and four congruent sides?A. trapezium
B. kite
C. trapezoid
D. rhombus

Answers

Rhombus or letter D.

What are the coordinates of the midpoint of the line segment with endpoints R(4,−7) and S(−3,5)?

Answers

The answer is (.5,-1)

Let $ A $ and $ B $ be events with $ P(A)=1 / 3 $ and $ P(B)=2 / 3 $. Let $ N $ be the number of events from among $ A $ and $ B $ that occur. (For instance, if $ A $ occurs but $ B $ does not, then $ N=1 $.) Suppose that the occurrence of events in $ A $ and $ B $ are independent. Find, for example, the probability that no events occur.

Answers

Answer:

( 2/9 )

Step-by-step explanation:

Okay, so since the events A and B are independent, the probability that both of them do not occur is the product of their individual probabilities of not occurring.

The probability of event A not occurring, denoted as ( P(A') ), is equal to 1 minus the probability of A occurring. Similarly, the probability of event B not occurring, denoted as ( P(B') ), is equal to 1 minus the probability of B occurring.

So, ( P(A') = 1 - P(A) = 1 - 1/3 = 2/3 ) and ( P(B') = 1 - P(B) = 1 - 2/3 = 1/3 ).

Since A and B are independent, the probability that both A and B do not occur is simply the product of their individual probabilities of not occurring:

[ P(N = 0) = P(A' cap B') = P(A')P(B') = (2/3) times (1/3) = 2/9 ]

So, the probability that no events occur is ( 2/9 ).

Hope this helps! :)

16 is what percent of 64

Answers

16 / 64 is the same as 1/4 because 16 is 1/4 of 64.

1/4 in percent form is 25%

So, 16 is 25% of 64.

To get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 64 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 64, so we can write it down as 100%=64.
4. We know, that x% equals 16 of the output value, so we can write it down as x%=16.
5. Now we have two simple equations:
1) 100%=64
2) x%=16
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=64/16
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for 16 is what percent of 64

100%/x%=64/16
(100/x)*x=(64/16)*x - we multiply both sides of the equation by x
100=4*x - we divide both sides of the equation by (4) to get x
100/4=x
25=x
x=25

now we have:
16 is 25% of 64

An action movie production team needs glass spheres to hold a green liquid that looks like an explosive. If all of the available 3,392.92 cubic inches of the liquid is to be poured into 30 glass spheres, what should the diameter of each sphere be? Assume that each sphere is filled to the top.

Answers

The volume of a sphere:
$V=(4)/(3) \pi r^3$
r - the radius

3392.92 cubic inches are poured into 30 spheres.
$3392.92=30 * (4)/(3) \pi r^3 \n \n3392.92=40\pi r^3 \ \ \ \ \ \ \ \ \ \ \ \ |/ 40 \n \n84.823=\pi r^3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |/ \pi \n \nr^3=(84.823)/(\pi) \n \nr=\sqrt[3]{(84.823)/(\pi)} \n \nr \approx \sqrt[3]{27} \n \nr \approx 3$

The diameter is twice the radius.
The diameter of each sphere should be approximately 6 inches.

Answer:

6 inches

Step-by-step explanation:

correct on Plato/ edmentum courseware

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