The center of a circle is at (7, –3) and it has a radius of 9. What is the equation of the circle?(x – 7)2 + (y + 3)2 = 3

(x + 7)2 + (y – 3)2 = 3

(x + 7)2 + (y – 3)2 = 81

(x – 7)2 + (y + 3)2 = 81

Answers

Answer 1

Answer: Given:
center (7,-3)
radius = 9

Equation of the circle:
(x-h)² + (y-k)² = r²
(x-7)² + (y-(-3)² = 9²
(x-7)² + (y+3)² = 81 Last option.

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bro i had 10,000 points on brainly, and some weird a.i. deleted all my answers to all the questions i answered so now i only have 732 points?!

A triangle has two sides of length 18 and 17. What is the smallest possible whole-number length for the third side?

Answers

a, b, c - sides of a triangle

a + b > c

a + c > b

b + c > a

--------------------------

We have a = 18 and b = 17. Substitute:

18 + 17 > c

35 > c → c < 35

--------------------------

18 + c > 17 subtract 18 from both sides

c > -1

--------------------------

17 + c > 18 subtract 17 from both sides

c > 1

--------------------------

c < 35 and c > -1 and c > 1.

Therefore 1 < c < 35

Answer: The smallest possible whole number length of third side is 2.

Final answer:

The smallest possible whole-number length for the third side of a triangle with the other two sides being 18 and 17 is 2, based on the rule that each side of a triangle must be less than the sum and more than the absolute difference of the other two sides.

Explanation:

In the realm of geometry, there is a rule for a triangle that states the length of any side of a triangle must be less than the sum of the lengths of the other two sides, but greater than the absolute difference of those two sides. Given a triangle with two sides of lengths 18 and 17, we apply this rule.

To find the smallest possible whole number length for the third side, we calculate the absolute difference of the existing two sides: |18 - 17| = 1.

But, since we are looking for a whole number, the smallest possible length for the third side cannot be 1, it must be more than 1. Therefore, the smallest possible whole-number length for the third side is 2.

Learn more about Triangle Side Length here:

brainly.com/question/32440372

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A hallway is 9 yards how long is the inches in the hallway

Answers

1 yard=36 inches
9 times 1=9
multiply both sides by 9
9 times 1 yard=9 times 36 inches
9 yard=324 inches

Hello! To find out how many inched the hallway is, you first need to know how many inches are in a yard. You need to find the operation that will be needed for this problem, and I'm assuming you don't know, what you want to do is ask yourself,"What am I trying to find? Wold this best be accomplished with subtraction or division, or multiplication or addition? Am I looking for what the difference between two, or how many items are needed for even groups? Do I want to find out how long something will be when added to something else, or multiplied?

I hoped this helped! If you have any further questions pertaining to this problem, feel free to shoot me a message or another question! Good luck :)

Chromium-51 has a half-life of 28 days. If Georgia leaves a bottle of 10,000-milligram capsules in her medicine cabinet for a year, what will be the strength in milligrams of each capsule? Round to the nearest milligram

Answers

For finding the strength of the capsules after one year, we will use half-life formula. The formula is:

A = A₀ $((1)/(2))^(t)/(h)$

where, A= Final amount

A₀ = Initial amount

t= time elapsed

h= half-life

Here, in this problem A₀ = 10000 milligram, t= 1 year or 365 days

and h= 28 days

So, A = 10000 $((1)/(2) )^(365)/(28)$

⇒ A = 10000 $((1)/(2))^1^3^.^0^4$

⇒ A = 1.187

So, the strength of the capsules after one year will be 1.187 milligrams.

If h(2) = 3 and h'(2) = -7, find d/dx(h(x)/x) x = 2.

Answers

Answer: -17/4

Work Shown

$\frac{d}{d\text{x}}\left(\frac{h(\text{x})}{\text{x}}\right) = \frac{\frac{d}{d\text{x}}(h(\text{x}))*\text{x}-h(\text{x})*\frac{d}{d\text{x}}(\text{x})}{\text{x}^2} \ \text{ .... quotient rule}\n\n\frac{d}{d\text{x}}\left(\frac{h(\text{x})}{\text{x}}\right) = \frac{h'(\text{x})*\text{x} - h(\text{x})}{\text{x}^2}\n\n$

Evaluate that at x = 2.

$\frac{h'(\text{x})*\text{x} - h(\text{x})}{\text{x}^2}\n\n=(h'(2)*2 - h(2))/(2^2)\n\n=(-7*2 - 3)/(2^2)\n\n=-(17)/(4)\n\n$

Therefore,

$\frac{d}{d\text{x}}\left(\frac{h(\text{x})}{\text{x}}\right)=-(17)/(4) \ \text{ when h(2) = 3, h'(2) = -7, and x = 2}\n\n$

Given that g(4)=9 and g(-11)=k, find the value of k that would result in a slope of 5 between the two points.

Answers

Answer:

$k=-66$

Step-by-step explanation:

So we are given two values:

$g(4)=9 \text{ and } g(-11)=k$

They can be interpreted as: (4,9) and (-11,k).

So, we want to find the value of k such that the slope of the line between the two points would be 5.

Recall the slope formula. It is:

$m=(y_2-y_1)/(x_2-x_1)$

Let (4,9) be x₁ and y₁ and let (-11,k) be x₂ and y₂. Substitute 5 for m. Therefore:

$5=(k-9)/(-11-4)$

Simplify the denominator:

$5=(k-9)/(-15)$

Multiply both sides by -15. The right side cancels:

$-15(5)=(-15)(k-9)/(-15)\n -75=k-9$

Now, add 9 to both sides. The right side cancels.

$(-75)+9=(k-9)+9\nk=-66$

Therefore, k is -66.

What is the value of x?

Answers

straight line = 180, so 180-100=80, a triangle = 180, x equals to 180-(70+80) =30, the answer is a

This is actually a relatively simple problem, but because the other angle is missing, it seems complex.

The angle adjacent to the 100 degree outside the triangle is 80 degrees. We know this because it is a supplementary angle, or an angle that, when added along with another angle’s measurement, makes 180 degrees. The line is straight, so the other angle must be 80 degrees to add up with the 100 to make 180 degrees.

Now that we know the other unknown angle, we can use the fact that the sum of angles within a triangle make 180 degrees. The two angles inside the triangle that we know make 150 degrees (80 plus 50), so the final angle ‘x’ must be 30 degrees (180-150=30).

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