if an arc of 60 degrees has an arc length of 50pi what is the circumference

Answer:

[tex]\displaystyle \boxed{ (x - 6)^2 + (y - 2)^2 = 64 }[/tex]

General Formulas and Concepts:
Precalculus

Circle Equation:
[tex]\displaystyle (x - h)^2 + (y - k)^2 = r^2[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

Center (6, 2)

r = 8

Step 2: Find Equation

∴ we have found the equation for the circle with given properties.

---

Topic: Precalculus

Unit: Conics

The equation of a circle is  [tex]{{x}^{2}}+{{y}^{2}}-12x-4y-24=0[/tex].

A circle is a shape made up of all points in a plane that are at the same distance from a central point.

Equation of the circle [tex]\[{{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}\][/tex] where (h,k) is the coordination of the center and r is the radius

put the values of h, k and r in the equation of the circle

[tex]{{\left( x-6 \right)}^{2}}+{{\left( y-2 \right)}^{2}}={{8}^{2}}[/tex]

[tex]{{x}^{2}}+{{y}^{2}}+36+4-12x-4y=64[/tex]

[tex]{{x}^{2}}+{{y}^{2}}-12x-4y-24=0[/tex]

therefore, the equation of the circle is[tex]{{x}^{2}}+{{y}^{2}}-12x-4y-24=0[/tex].

Learn more about cone here – https://brainly.com/question/11833983

#SPJ2

Answer:

the sum of the first 10 terms is: 79.921875

Step-by-step explanation:

Notice that this is a geometric series, of the sequence that has "40" as the first term, and the following ones are obtained by multiplying by the common ratio "1/2".

So the common ratio [tex]r=\frac{1}{2}[/tex], and the first term [tex]a_1=40[/tex], then, recalling the formula for the partial sum of n terms of a geometric sequence:

[tex]S_n=\frac{a_1\,(1-r^n)}{1-r}[/tex]

we can find the sum of this sequence's first 10 terms (n=10):

[tex]S_n=\frac{a_1\,(1-r^n)}{1-r} \\S_{10}=\frac{40\,(1-(\frac{1}{2}) ^{10})}{1-\frac{1}{2} } \\S_{10}=79.921875[/tex]

Step-by-step explanation:

The answer is 2 : 3 because the value of a is 2 and c is 3

Answer:

1/4

Step-by-step explanation:

If you have four colors on the spinner and you want to land on the green spot and there is 1/4 chances

Answer:

A. (x+4) (2x+3)

Step-by-step explanation:

Answer:1cm?

Step-by-step explanation:

Answer:

8.86 square cm

Step-by-step explanation:

Area of shaded region = Area of rectangle - Area of circle

[tex] = 3 \times 4 - \pi {r}^{2} \\ = 12 - 3.14 \times {1}^{2} \\ = 12 - 3.14 \\ = 8.86 \: {cm}^{2} [/tex]

The number 123 because it is the only number that is not divisible by 9.

In a positional numeral system, a numerical digit is a single sign that can be used singly or in combination to represent numbers.

A digit is a part of a set that, when combined, makes up a numeration system.

For example 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits.

Given the digits,

36, 99, 9, 123

If we divide by 9 then

36/9 ⇒ remainder 0

99-9⇒ remainder 0

9 ⇒ remainder 0

But

123/9 ⇒ remainder 6

Hence "The number 123 because it is the only number that is not divisible by 9".

To learn more about digits,

https://brainly.com/question/10913044

#SPJ2

Answer:

37.5 cm 2

Step-by-step explanation:

The area of the first figure, the rectangle is 30cm2. The base which is 5cm, times the height which is 6cm equals 30cm2. The triangle's area is 7.5cm2 because the height which is 3cm times the base which is 5cm equals 15cm. Because it's a triangle tho, we have to find half of it which  7.5cm2. 30cm2+7.5cm2 equals 37.5cm2.

Answer:

23 and 7

Step-by-step explanation:

Multiply 23 and 7 to get 161. Subtract 7 from 23 and get 16

Answer: 23 and 7

Step-by-step explanation: When you multiply 23 x 7, you will get the answer 161.

Answer:

Step-by-step explanation:

hello :

1-x² = (1-x)(1+x) by identity : a²-b²=(a-b)(a+b)

Answer:

x = ± 3

Step-by-step explanation:

Given

5x² - 45 = 0 ( divide through by 5 )

x² - 9 = 0 ( add 9 to both sides )

x² = 9 ( take the square root of both sides )

x = ± [tex]\sqrt{9}[/tex] = ± 3

Thus the roots are x = - 3, x = 3

Final answer:

To solve the quadratic equation 5x^2 - 45 = 0, we rearrange it to x^2 - 9 = 0 and find that the roots are x = 3 and x = -3.

Explanation:

To solve the quadratic equation 5x2 − 45 = 0, we first need to rearrange it to the standard form ax2 + bx + c = 0. In this case, the equation is already in the standard form with a=5, b=0, and c=-45. The next step is to isolate the x2 term by dividing the entire equation by 5, which gives us x2 − 9 = 0. This simplifies to (x - 3)(x + 3) = 0 due to the difference of squares. Thus, the two roots are x = 3 and x = -3.

Answer:

2 Nd one

Step-by-step explanation:

Got it right

Answer:

B.    (x – 2)² + (y + 8)² = 121

Step-by-step explanation:

if i can get brainliest that would be great

Answer: The answer is B. Because she can't go over 146. $10 is a one time fee and she pays $9 per classes.

Answer:

a

Step-by-step explanation:

you must subtract ten from each side to get 136 is less than or equal to 9c then divide by nine to get c=15.111111

Answer:2 weeks

Step-by-step explanation: if you subtract 1800 by 150 for the two weeks you will get 1500 and if you add 1100 by 200 every week you will get a hundred and fifty

Answer:

Two adults and five children

Step-by-step explanation:

(3.75×5)+(5.25×2) = 29.25

  18.75  +   10.5     = 29.25

(:

Answer:$3750

Step-by-step explanation:

Answer:

3650

Step-by-step explanation:

apex

Answer: The answer is D: y=2/5x

Step-by-step explanation:

Let y represent the number of laps George runs, and x the number of minutes it takes him to run those laps. We know that it it takes George 25 minutes to run 10 laps; therefore, the number of laps George runs per minute is 10/25 which is equal to 2/5.

(Make sure you keep your promise(s) lol.)

The area of the given isosceles triangle with 13 cm and 10 cm base will be 60 square cm.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.

An isosceles triangle is a triangle in which two sides are the same.

The given isosceles triangle has been drawn below,

The area of a triangle is given as (1/2) × base × height.

Height = √(13²  - 5²) = 12

Area = (1/2) × 10 × 12 = 60 square cm.

Hence "The area of the given isosceles triangle with 13 cm and 10 cm base will be 60 square cm".

For more about triangles,

https://brainly.com/question/2773823

#SPJ2

To find the area of an isosceles triangle with given side lengths, use the Pythagorean theorem to find the height. Then, apply the formula for the area of a triangle using the base and the calculated height. The area of the given isosceles triangle is 60 square centimeters.

To find the area of an isosceles triangle with a base of 10 cm and two equal sides of 13 cm, we first need to determine the height of the triangle. We can use the Pythagorean theorem to find the height (h).

Since the base splits the isosceles triangle into two right triangles, each having a base of 5 cm (half of 10 cm) and a hypotenuse of 13 cm:

Using the Pythagorean theorem:

→ Hypotenuse (hyp) = 13 cm

→ Base/2 (base) = 5 cm

→ Height (h) = ?

→ hyp² = base² + h²

→ 13² = 5² + h²

→ 169 = 25 + h²

→ h² = 169 - 25

→ h² = 144

→ h = √144

→ h = 12 cm

Now that we know the height, we can use the formula for the area of a triangle:

→ Area = 1/2 × base × height

→ Area = 1/2 × 10 cm × 12 cm

→ Area = 5 × 12

→ Area = 60 square centimeters

Answer: if i can be brainliest that would be great

Bacteria growth occurs exponentially; bacteria divides into 2 every t minutes (similar to the penny doubling every day story). If one gets filled, and the contents divides once, there will be enough for 2 bottles; when these two are ready to divide, there will be enough for 4. This growth process begins very slowly - 1, 2, 4, 8, 16, 32; but it soon speeds up greatly, 64, 128, 256, 512, 1024, 2048.

Answer:

The bacteria took more time to double from 1 cell to a bottle full of cells. Once the bottle was full, each cell in the full bottle doubled, causing an additional bottle to be filled in 5 minutes. Then the 2 full bottles doubled in the next 5 minutes, causing all 3 bottles to be full.

Step-by-step explanation:

Answer:

y=-5x+35

Step-by-step explanation:

Use the formula y = mx + b

m = slope, so plug in -5 as the slope

To find x-intercept we set y=0

We want the x-intercept to be 7 so we can plug that into the equation too

0=-5(7)+b

Lastly solve for b and you get your answer

The correct option is b.

The equation of the line with a slope of -5 and an x-intercept of 7 is y = -5x + 35.

The equation that represents a line with a slope of -5 and an x-intercept of 7 is y = mx + b, where m is the slope and b is the y-intercept.

Given that the slope is -5 and the x-intercept is 7, we can substitute these values into the equation to get y = -5x + b.

To find the value of b, we can substitute the x-intercept (7) and y-intercept (0) into the equation and solve for b. Plugging these values in, we get 0 = -5(7) + b. Solving for b gives us b = 35.

Therefore, the equation of the line is y = -5x + 35.

brainly.com/question/21511618

#SPJ3

The complete question is given below:

Which equation represents a line that has a slope of -5 and an X- intercept of 7?

a. y = 5x + 35

b. y = -5x + 35

c. y = -5x - 35

d. y = 35x -5

Answer:

b

Step-by-step explanation:

You would have twice as many hot dogs and 24 is two times 12 and if you add them you get 36.

Answer:

100+50²=2600

Step-by-step explanation:

because 50x2=100 and 50² is 2500. Add those and you get 2600.

The number of bacteria Caleb and Jenna each have in their experiments is 2600.

Given that, Caleb started with 50 bacteria for his science experiment, and the number of bacteria doubled in one day.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

The number of bacteria doubled

= 2×25=50

The number of bacteria was equal to 50 to the second power

= 50²

= 2500

So total = 2500+100=2600

Therefore, the number of bacteria Caleb and Jenna each have in their experiments is 2600.

To learn more about an exponents visit:

https://brainly.com/question/15993626.

#SPJ2

Answer:

Step-by-step explanation:

since we can see that the lines are parallel

and we can see that the both are interior angles and when we sum up both angles we get 180

2x - 5  + 45 = 180

2x  + 40 =180

2x = 180 - 40

2x =140

x = 140/2

x = 70

Answer:

x = 35

Step-by-step explanation:

Solve for x:

5 (x + 20) = 7 x + 30

Expand out terms of the left hand side:

5 x + 100 = 7 x + 30

Subtract 7 x from both sides:

(5 x - 7 x) + 100 = (7 x - 7 x) + 30

5 x - 7 x = -2 x:

-2 x + 100 = (7 x - 7 x) + 30

7 x - 7 x = 0:

100 - 2 x = 30

Subtract 100 from both sides:

(100 - 100) - 2 x = 30 - 100

100 - 100 = 0:

-2 x = 30 - 100

30 - 100 = -70:

-2 x = -70

Divide both sides of -2 x = -70 by -2:

(-2 x)/(-2) = (-70)/(-2)

(-2)/(-2) = 1:

x = (-70)/(-2)

The gcd of -70 and -2 is -2, so (-70)/(-2) = (-2×35)/(-2×1) = (-2)/(-2)×35 = 35:

Answer: x = 35

Answer:

x =  35

Step-by-step explanation:

5(x+20)= 7x+30

5x + 100 = 7x + 30

-30                   -30

5x + 70 = 7x

-5x          -5x

70 = 2x

/2      /2

35 = x

The correct expression that represents a 20% discount off the original price d is 0.8d or d – 0.2d. The other options do not correctly represent a percentage discount from the original price.

The expression that represents a 20% discount off the price of an item that originally cost d dollars would be calculated by first determining what 20% of the original price is, and then subtracting that value from the original price. So if the original price is d, then 20% of d is 0.2d. Subtracting that from d would give us the discounted price. Therefore, the correct expression that represents a 20% discount would be d – 0.2d, which simplifies to 0.8d.

d – 0.2 is not a percentage of d, but rather a fixed amount subtracted from d, and 1 – 0.2d is not meaningful in the context of pricing and discounts. So the expressions that represent a 20% discount off the price are:

The correct answers are the expressions: 0.8d and d – 0.2d.

Answer:

2x - 3y = Z

Step-by-step explanation:

5y + 2z = 2 + 12