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noname [10]
3 years ago
11

I need to know if 93 is a multiple of 9×

Mathematics
1 answer:
iris [78.8K]3 years ago
5 0
93 is not a multiple of 9. Multiple of 9 would be 90 or 99. These are multiples of 9 in a range from 0 up to 100:

9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99
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Write and equation of the translated or rotated graph in general form (picture below)
WINSTONCH [101]

Answer:

The answer is hyperbola; (x')² - (y')² - 16 = 0 ⇒ answer (a)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

 xy = -8

∵ A = 0 , B = 1 , C = 0

∴ B² - 4 AC = (1)² - 4(0)(0) = 1 > 0

∴ B² - 4AC > 0

∴ The graph is hyperbola

* The equation xy = -8

∵ We have term xy that means we rotated the graph about

  the origin by angle Ф

∵ Ф = π/4

∴ We rotated the x-axis and the y-axis by angle π/4

* That means the point (x' , y') it was point (x , y)

- Where x' = xcosФ - ysinФ and y' = xsinФ + ycosФ

∴ x' = xcos(π/4) - ysin(π/4) , y' = xsin(π/4) + ycos(π/4)

∴ x' = x/√2 - y/√2 = (x - y)/√2

∴ y' = x/√2 + y/√2 = (x + y)/√2

* Lets substitute x' and y' in the 1st answer

∵ (x')² - (y')² - 16 = 0

∴ (\frac{x-y}{\sqrt{2}})^{2}-(\frac{x+y}{\sqrt{2}})^{2}=

 ( \frac{x^{2}-2xy+y^{2}}{2})-(\frac{x^{2}+2xy+y^{2}}{2})-16=0

* Lets open the bracket

∴ \frac{x^{2}-2xy+y^{2}-x^{2}-2xy-y^{2}}{2}-16=0

* Lets add the like terms

∴ \frac{-4xy}{2}-16=0

* Simplify the fraction

∴ -2xy - 16 = 0

* Divide the equation by -2

∴ xy + 8 = 0

∴ xy = -8 ⇒ our equation

∴ Answer (a) is our answer

∴ The answer is hyperbola; (x')² - (y')² - 16 = 0

* Look at the graph:

- The black is the equation (x')² - (y')² - 16 = 0

- The purple is the equation xy = -8

- The red line is x'

- The blue line is y'

6 0
3 years ago
Read 2 more answers
PLEASE HELP ME!!!! WORTH 10 POINTS!!!
Sidana [21]
<span>slope
m = (1  - 1)/(0 + 2) = 0

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7 0
3 years ago
For a polynomial p(x), the value of p(3) is −2. Which of the following must be true about p(x)?
mr Goodwill [35]

Answer:

D

Step-by-step explanation:

The factor theorem states if (x - h) is a factor of a polynomial p(x) then

p(h) = 0

However, p(h) ≠ 0 then the value obtained is the remainder.

Thus

p(3) = - 2

When p(x) is divided by (x - 3) then the remainder is - 2

8 0
3 years ago
Find the sine of ZI. J 21 D I Write your answer in simplified, rationalized form. Do not round.​
Kitty [74]
What is ZI? Can you specify? thanks
7 0
3 years ago
Nick billups is paid a salary of $ 900 a month, a 2 % commission on all sales, and 1.8 % more on monthly sales over $ 17,500. In
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June :
900 + 0.02(48,500) + 0.018(48500 - 17500) = 
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3 years ago
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