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puteri [66]
3 years ago
5

What is the standard equation with center (4, -5) and radius 11

Mathematics
1 answer:
Marina86 [1]3 years ago
3 0

Answer: (x-4)² +(y+5)²=121

Step-by-step explanation:

Happy to help :)

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I NEED HELP!! please show all work
PtichkaEL [24]

Take the logarithm of both sides. The base of the logarithm doesn't matter.

4^{5x} = 3^{x-2}

\implies \log 4^{5x} = \log 3^{x-2}

Drop the exponents:

\implies 5x \log 4 = (x-2) \log 3

Expand the right side:

\implies 5x \log 4 = x \log 3 - 2 \log 3

Move the terms containing <em>x</em> to the left side and factor out <em>x</em> :

\implies 5x \log 4 - x \log 3 = - 2 \log 3

\implies x (5 \log 4 - \log 3) = - 2 \log 3

Solve for <em>x</em> by dividing boths ides by 5 log(4) - log(3) :

\implies \boxed{x = -\dfrac{ 2 \log 3 }{ 5 \log 4 - \log 3 }}

You can stop there, or continue simplifying the solution by using properties of logarithms:

\implies x = -\dfrac{ \log 3^2 }{ \log 4^5 - \log 3 }

\implies x = -\dfrac{ \log 9 }{ \log 1024 - \log 3 }

\implies \boxed{x = -\dfrac{ \log 9 }{ \log \frac{1024}3 }}

You can condense the solution further using the change-of-base identity,

\implies \boxed{x = -\log_{\frac{1024}3}9}

5 0
2 years ago
What is 32.043 in expanded form?
SashulF [63]
30 + 2 + 0.04 + 0.003
7 0
3 years ago
NO LINKS!!!! Find the equation of the circle below​
inysia [295]

Answer:

(x+3)^2+(y-2)^2=9

Step-by-step explanation:

<u>Equation of a circle</u>

(x-a)^2+(y-b)^2=r^2

where:

  • (a, b) is the center
  • r is the radius

From inspection of the diagram, the center of the circle <em>appears</em> to be at point (-3, 2), although this is not very clear.  Therefore, a = -3  and  b = 2.

Substitute these values into the general form of the equation of a circle:

\implies (x-(-3))^2+(y-2)^2=r^2

\implies (x+3)^2+(y-2)^2=r^2

Again, from inspection of the diagram, the <u>maximum vertical point</u> of the circle appears to be at y = 5.  Therefore, to calculate the radius, subtract the y-value of the center point from the y-value of the maximum vertical point:

⇒ radius (r) = 5 - 2 = 3

Substitute the found value of r into the equation:

\implies (x+3)^2+(y-2)^2=3^2

Therefore, the final equation of the given circle is:

\implies (x+3)^2+(y-2)^2=9

7 0
2 years ago
Read 2 more answers
7 1/4 times 2 x 2 + (8 1/2 - 2) divided by 3
11111nata11111 [884]
The answer is 31 1/6, I hope this helps!
6 0
2 years ago
What is 3 root of 27
daser333 [38]
It is 3.

You can check this by seeing 3^3 ie. 3x3x3, which comes out as 27.
You can check the cube root on a calculator.
4 0
3 years ago
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