The equation for line s can be written as y = x + 3. Line t, which is parallel to line s,

WHen you have a graph, how do you find the vertex?

Whitepunk [10]

Answer:

first you have to find the shape then you find the vertex

Step-by-step explanation:

Have a blessed day! stay safe

6 0

3 years ago

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At a price of $p the demand x per month (in multiples of 100) for a new piece of software is given by x 2 + 2xp + 4p 2 = 5200. B

WINSTONCH [101]

Answer:

The rate of decrease in demand for the software when the software costs $10 is -100

Step-by-step explanation:

Given the function of price $p the demand x per month as,

$x^{2}+2xp+4p^{2}=5200$

Also given that, the price is increasing at the rate of 70 dollar per month.

$\therefore \dfrac{dp}{dt}=70$ .

To find rate of decrease in demand, differentiate the given function with respect to t as follows,

$\dfrac{d}{dt}\left(x^2+2xp+4p^2\right)=\dfrac{d}{dt}\left(5200\right)$

Applying sum rule and constant rule of derivative,

$\dfrac{d}{dt}\left(x^2\right)+\dfrac{d}{dt}\left(2xp\right)+\dfrac{d}{dt}\left(4p^2\right)=0$

Applying constant multiple rule of derivative,

$\dfrac{d}{dt}\left(x^2\right)+2\dfrac{d}{dt}\left(xp\right)+4\dfrac{d}{dt}\left(p^2\right)=0$

Applying power rule and product rule of derivative,

$2x^{2-1}\dfrac{dx}{dt}+2\left(x\dfrac{dp}{dt}+p\dfrac{dx}{dt}\right)+4\left(2p^{2-1}\right)\dfrac{dp}{dt}=0$

Simplifying,

$2x\dfrac{dx}{dt}+2\left(x\dfrac{dp}{dt}+p\dfrac{dx}{dt}\right)+8p\dfrac{dp}{dt}=0$

Now to find the value of x, substitute the value of p=$10 in given equation.

$x^{2}+2x\left(10\right)+4\left(10\right)^{2}=5200$

$x^{2}+20x+400=5200$

Subtracting 5200 from both sides,

$x^{2}+20x+400-5200=0$

$x^{2}+20x-4800=0$

To find the value of x, split the middle terms such that product of two number is 4800 and whose difference is 20.

Therefore the numbers are 80 and -60.

$x^{2}+80x-60x-4800=0$

Now factor out x from $x^{2}+80x$ and 60 from $60x-4800$

$x\left(x+80\right)-60\left(x+80\right)=0$

Factor out common term x+80,

$\left(x+80\right)\left(x-60\right)=0$

By using zero factor principle,

$\left(x+80\right)=0$ and $\left(x-60\right)=0$

$x=-80$ and $x=60$

Since demand x can never be negative, so x = 60.

Now,

$2x\dfrac{dx}{dt}+2\left(x\dfrac{dp}{dt}+p\dfrac{dx}{dt}\right)+8p\dfrac{dp}{dt}=0$

Substituting the value.

$2\left(60\right)\dfrac{dx}{dt}+2\left(60\left(70\right)+10\dfrac{dx}{dt}\right)+8\left(10\right)\left(70\right)=0$

Simplifying,

$120\dfrac{dx}{dt}+2\left(4200+10\dfrac{dx}{dt}\right)+5600=0$

$120\dfrac{dx}{dt}+8400+20\dfrac{dx}{dt}+5600=0$

Combining common term,

$140\dfrac{dx}{dt}+14000=0$

Subtracting 14000 from both sides,

$140\dfrac{dx}{dt}=-14000$

Dividing 140 from both sides,

$\dfrac{dx}{dt}=-\dfrac{14000}{140}$

$\dfrac{dx}{dt}=-100$

Negative sign indicates that rate is decreasing.

Therefore, the rate of decrease in demand of software is -100

6 0

3 years ago

Is the sequence geometric? Is so identify the common ratio 1/4, 3/15, 9/64, 27/256, 81/1024....

Likurg_2 [28]

Hello.

Yes, it is geometric and the ratio is 3/4. You can tell because you can divide each one by the one before and you get 3/4. (3/16)/(1/4)=3/4, (9/64)/(3/16)=3/4, and so on.

Have a nice day

7 0

3 years ago

Please please please help!! i need this asap and i have no where else to go!

nadezda [96]

1   1   1       2
2 -3   1 -11 -2R1 + R2 → R2
-1 2 -1 8 R1 + R3 → R3

1 1 1 2
0 -5 -1   -15    R2 ⇔ R3
0 3 0    10

1 1 1 2
0 3 0     10    -R3
0   -5   -1 -15

1 1 1 2
0 3 0     10    1/3 R2
0    5    1    15

1 1 1 2    -R2 + R1
0 1 0     10/3    -5R2 + R3
0    5    1    15

1 0 1 -4/3
0 1 0     10/3    -R3 + R1
0    0    1     -5/3

1 0 0    1/3
0 1 0     10/3
0    0    1     -5/3

Therefore, x = 1/3, y = 10/3, z = -5/3

7 0

3 years ago

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I think of a number, double it and add 14. The result is 36. What is the number?

never [62]

Answer:

11

Step-by-step explanation:

11*2=22, 22+14=36, quick maths

4 0

4 years ago

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