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k0ka [10]
3 years ago
12

If f(x) = x and g(x) = X + 2, which statement about the graphs of the functions is true?

Mathematics
1 answer:
Liula [17]3 years ago
7 0

Answer: D

Step-by-step explanation: +2 would be an upwards translation

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Save me the headache
maxonik [38]

(9\sin2x+9\cos2x)^2=81

Taking the square root of both sides gives two possible cases,

9\sin2x+9\cos2x=9\implies\sin2x+\cos2x=1

or

9\sin2x+9\cos2x=-9\implies\sin2x+\cos2x=-1

Recall that

\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta

If \alpha=2x and \beta=\dfrac\pi4, we have

\sin\left(2x+\dfrac\pi4\right)=\dfrac{\sin2x+\cos2x}{\sqrt2}

so in the equations above, we can write

\sin2x+\cos2x=\sqrt2\sin\left(2x+\dfrac\pi4\right)=\pm1

Then in the first case,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=1\implies\sin\left(2x+\dfrac\pi4\right)=\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=\dfrac\pi4+2n\pi\text{ or }\dfrac{3\pi}4+2n\pi

(where n is any integer)

\implies2x=2n\pi\text{ or }\dfrac\pi2+2n\pi

\implies x=n\pi\text{ or }\dfrac\pi4+n\pi

and in the second,

\sqrt2\sin\left(2x+\dfrac\pi4\right)=-1\implies\sin\left(2x+\dfrac\pi4\right)=-\dfrac1{\sqrt2}

\implies2x+\dfrac\pi4=-\dfrac\pi4+2n\pi\text{ or }-\dfrac{3\pi}4+2n\pi

\implies2x=-\dfrac\pi2+2n\pi\text{ or }-\pi+2n\pi

\implies x=-\dfrac\pi4+n\pi\text{ or }-\dfrac\pi2+n\pi

Then the solutions that fall in the interval [0,2\pi) are

x=0,\dfrac\pi4,\dfrac\pi2,\dfrac{3\pi}4,\pi,\dfrac{5\pi}4,\dfrac{3\pi}2,\dfrac{7\pi}4

5 0
3 years ago
Read 2 more answers
Which number is greatest?<br> ооо<br> 6.23 х 1012<br> 6.23x 108<br> Б.23 х 10-<br> o 6.23x 103
lions [1.4K]

Answer:

Option A: 6.23 x 1012

Step-by-step explanation:

Please check provided image.

5 0
3 years ago
Fit a quadratic function to these three points:<br> (-2,8), (0, -4), and (4, 68)<br> Respuesta
zloy xaker [14]

Answer:

f(x) = 4x^2 + 2x - 4.

Step-by-step explanation:

Let the quadratic function be y = f(x) = ax^2 + bx + c.

For the point (-2, 8)  ( x = -2 when y = 8) we have:

a(-2)^2 + (-2)b + c = 8

4a - 2b + c = 8      For (0, -4) we have:

0 + 0 + c = -4   so c = -4.    For (4, 68) we have:

16a + 4b + c = 68  

So we have 2 systems of equations in a and b ( plugging in c = -4):

4a - 2b - 4 = 8

16a + 4b - 4 = 68

4a - 2b = 12

16a + 4b = 72    Multiplying 4a - 2b = 12 by 2 we get:

8a - 4b = 24  

Adding the last 2 equations:

24a = 96

a = 4

Now plugging a = 4 and c = -4 in the first equation:

4(4) - 2b - 4 = 8

-2b = 8 - 16 + 4 = -4

b = 2.

3 0
3 years ago
Solve this
sesenic [268]

A sandwich store charges a delivery fee to bring lunch to an office.

Delivery cost - D

Meatball sandwich cost  - M

One office pays $40.50 for 5 meatball sandwiches.

40.50 = 5M + D

Another office pays $66.50 for 9 meat ball sandwiches

66.50 = 9M + D

A. How much does each meatball sandwich add to the cost of delivery?

D = 40.50 - 5M = 66.50 - 9M

40.50 - 5M = 66.50 - 9M

9M - 5M = 66.50 - 40.50

4M = 26.00

M = 6.50

B. What is the delivery fee

D = 40.50 - 5M = 40.50 - 5(6.50) = 40.50 - 32.50 = 8.00

Check

66.50 = 9M + D = 9(6.50) + 8 = 58.50 + 8.00 = 66.50

3 0
3 years ago
X^2 + 10x + 25 = 0<br><br><br>I feel like I've tried everything and I just don't get it.
loris [4]
If you are factoring it you can factor it into (x+5)^2
8 0
3 years ago
Read 2 more answers
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