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umka2103 [35]
4 years ago
5

Solve 9^x-10x3^x+9=0

Mathematics
1 answer:
Goshia [24]4 years ago
4 0
Let y = 3^x , then 9^x = (3^2)^x = (3^x)^2 = y^2,  so we can write the equation as

y^2 - 10y + 9 = 0

(y - 9)(y - 1) = 0

giving y = 9 or y = 1

Therefore  3^x = 9    giving x = 2

and 3^x = 1 giving x = 0


so the solution  set is {0, 2}

Note - I have assumed that the 'x' after the 10 means 'multiply'.   Is that correct?
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At a large museum, there are 60 people in each tour group.
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Answer: (2,120) (6,360) (8,480)

Step-by-step explanation: since every group has 60 people 2x60=120 6x60=360 8x60=480

3 0
3 years ago
What is the value of x in the equation 3x-4y=65 when y =4
Dovator [93]
3x - 4(4) = 65

First, simplify 4 × 4 to get 16. / Your problem should look like: 3x - 16 = 65
Second, add 16 to both sides. / Your problem should look like: 3x = 65 + 16
Third, simplify 65 + 16 to 81. / Your problem should look like: 3x = 81
Fourth, divide both sides by 3. / Your problem should look like: x = \frac{81}{3}
Fifth, simplify \frac{81}{3} to 27. / Your problem should look like: x = 27

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3 years ago
Graph the function y=-0.5 sqrt x-3+2
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Df= {x/x-3>=0}
Df= [3, + infinity[
derivative of f(x)
f'(x)= -0.5 x 2 /</span>sqrt (x-3)= - 1/sqrt (x-3) <0, f is a decreasing function for all x in the Df
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3 years ago
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A school requires an entrance exam score that is in the top 3% of the population in order to be accepted.
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A. 485 is %3 of 500, but the deviation sets it slightly lower than that
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The U.S.A. Olympic Synchronized Swimming Team is designing a routine for their upcoming competition. From the center of the pool
Mama L [17]

Answer:

The equation of the circle is;

(x - 2)² + (y - 4)² = 5²  

Step-by-step explanation:

We note that the general equation of a circle is given as follows;

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The radius of the circle

The given parameters are;

The location of the center of the pool to the center of their formation = 2 feet to the right and 4 feet up from the center of the pool

The point through which the circle which they form goes through = A point 3 feet to the left and 4 feet up from the center of their formation

Taking the center of the pool as the origin of the coordinate plane system, we have;

The coordinate of the center of the circle = The coordinate of their motion from the center of the circle

∴ The coordinate of the center of the circle = (2, 4)

∴ (h, k) = (2, 4)

h = 2, k = 4

The coordinate of the point through which the circle passes = (2 - 3, 4 + 4) = (-1, 8)

∴ The length of the radius, 'r', can be found as, r = √((-3)² + 4²) = 5 or r = √((-1 - 2)² + (8 - 4)²) = 5

r = 5

The equation of the circle is therefore presented by substituting the values of 'h', 'k', and 'r', as follows;

(x - 2)² + (y - 4)² = 5².

4 0
3 years ago
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