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3 years ago

Graph the linear inequality. x + 2y = 5

2 answers:

8 0

we can graph the linear function by finding first the x and y intercepts.
x-intercept
x + 0 = 5; x =5P ( 5,0)
y-intercept0 + 2y = 5y = 5/2P(0,5/2)
We connect the two points and extend the line infinitely

choli [55]3 years ago

5 0

So you always want y in front of the equation no matter what so you have x +2y=5 so you take the x and you subtract it to both side making it 2y= 5-x so then you just have to take the 2 to both side so you have to divide it and you will get y= 5/2-x/2 so then to graph it you start with the b which is -x/2 so you go down -1 and over 2 and place your dot adn then go up 5 over 2 and then place you dot and connect them together

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KIM [24]

Answer:

A. a) 24

A. b) 4

B. a) 40320

B. b) 576

Step-by-step explanation:

General formula for Permutations:

$P(n,r) = \frac{n!}{(n - r)!}$

A. Concert seats: 2 couple --- total of 4 persons.

a) without restrictions

Since there are no restrictions, but that the order is important (John, Mary, Paul, Michelle isn't the same as Michelle, Mary, Paul, John), it's a permutation calculation.

Then we calculate the permutations of 4, out of 4, so...

$P(4,4) = \frac{4!}{(4 - 4)!} = 4! = 24$

24 different ways for them to sit.

b) couples together

Now, we can see the problem as having 2 levels of permutations, first the couples, then inside the couples.

There are 2 ways for the first level or order... couples AB or BA, so 2 possibilities.

Inside each couple, man then woman (MW) or woman then man (WM), so 2 possibilities there too on 2nd level.

Overall 2 * 2 = 4 ways to sit by couple.

B) Single file

a) without restrictions

Again, order is important, so another permutation, not a combination. And since we have no restriction, it can be any sequence.

We then have to calculate the number of permutations of 8 out of 8...

$P(8,8) = \frac{8!}{(8 - 8)!} = 8! = 40320$

There are 40,320 ways these 8 kids can pass the door.

b) girls first.

So, the four girls have to enter first.... and these four girls can be in any order.. how many permutations? P(4,4)... so 24 as calculated above.

For the four boys, how many permutations? Yes, again P(4,4)... so 24 again.

Overall, we need to multiply the two... 24 x 24 = 576 ways if the girls enter first, followed by the boys.

8 0

3 years ago

You are selling lemonade for $1.50,a bag of kettle corn for $3,and a hot dog for $2.50 at a fair .write and simplify an expressi

Sergio [31]

<h2>When you sell these three things you would need 3 people (p) to buy them. But together or separate.</h2><h2 /><h2>$1.50 + $3.00+$2.50= $7.00</h2>

6 0

3 years ago

Which expression does the number line represent?

seropon [69]

Answer:

I think the answer is 3÷3/4

Step-by-step explanation:

im not sure, when i worked it out in my head that's the answer that made the most sense

5 0

2 years ago

Write an expression to represent:<br> Nine more than the quotient of two and a number x

Taya2010 [7]

Answer:

9+(2/x)

Step-by-step explanation:

6 0

3 years ago

Which function is the same as y = 3 cosine (2 (x startfraction pi over 2 endfraction)) minus 2? y = 3 sine (2 (x startfraction p

kirza4 [7]

The function which is same as the function y = 3cos(2(x +π/2)) -2 is: Option A: y= 3sin(2(x + π/4)) - 2

<h3>How to convert sine of an angle to some angle of cosine?</h3>

We can use the fact that:

$\sin(\theta) = \cos(\pi/2 - \theta)\\\sin(\theta + \pi/2) = -\cos(\theta)\\\cos(\theta + \pi/2) = \sin(\theta)$

to convert the sine to cosine.

<h3>Which trigonometric functions are positive in which quadrant?</h3>

In first quadrant (0 < θ < π/2), all six trigonometric functions are positive.
In second quadrant(π/2 < θ < π), only sin and cosec are positive.
In the third quadrant (π < θ < 3π/2), only tangent and cotangent are positive.
In fourth (3π/2 < θ < 2π = 0), only cos and sec are positive.

(this all positive negative refers to the fact that if you use given angle as input to these functions, then what sign will these functions will evaluate based on in which quadrant does the given angle lies.)

Here, the given function is:

$y= 3\cos(2(x + \pi/2)) - 2$

The options are:

$y= 3\sin(2(x + \pi/4)) - 2$
$y= -3\sin(2(x + \pi/4)) - 2$
$y= 3\cos(2(x + \pi/4)) - 2$
$y= -3\cos(2(x + \pi/2)) - 2$

Checking all the options one by one:

Option 1: $y= 3\sin(2(x + \pi/4)) - 2$

$y= 3\sin(2(x + \pi/4)) - 2\\y= 3\sin (2x + \pi/2) -2\\y = -3\cos(2x) -2\\y = 3\cos(2x + \pi) -2\\y = 3\cos(2(x+ \pi/2)) -2$

(the last second step was the use of the fact that cos flips its sign after pi radian increment in its input)
Thus, this option is same as the given function.

Option 2: $y= -3\sin(2(x + \pi/4)) - 2$

This option if would be true, then from option 1 and this option, we'd get:
$-3\sin(2(x + \pi/4)) - 2= -3\sin(2(x + \pi/4)) - 2\\2(3\sin(2(x + \pi/4))) = 0\\\sin(2(x + \pi/4) = 0$