Find an equation of the circle that satisfies the given conditions. (Use the variables x and y.)
Center (−3, 2); passes through (−6, −6)

Yes, It intersect at positive x-coordinates.

The equation of line in point-slope form which passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, Slope (m) = (y₂ - y₁) / (x₂ - x₁)

Given that;

The function f (x) is defined in graph.

Now, The function g (x) is defined as,

⇒ y - 5 = (10 - 5) / (2 - 1) (x - 1)

⇒ y - 5 = 5 (x - 1)

⇒ y - 5 = 5x - 5

⇒ y = 5x

Clearly, By the graph of functions f (x) and g (x), both intersect at positive x - coordinate.

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Using the formula of simple interest, the time it will take to accumulate to $3200 at a rate of 4.5% is 71.35 years

Simple interest is a method of calculating the interest charge on a loan or deposit. It is based on the principle of earning interest only on the initial amount (principal) that was borrowed or deposited.

The formula for simple interest is:

I = P * r * t

where:

I is the interest amount

P is the principal amount

r is the interest rate (expressed as a decimal)

t is the time period (in years)

Substituting the values into the formula;

A = P(1 + rt)

3200 = 760(1 + 0.045(t))

3200 = 760 + 34.2t

34.2t = 3200 - 760

34.2t = 2440

t = 2440 / 34.2

t = 72.35 years

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Answer: Let's follow the same steps as in the previous example:

Identify the constants and the variables.

The known constant here is 4. Shailyn read 4 fewer books than Oswaldo. Let's call the number of books Oswaldo read "o".

Identify the operations.

The phrase "four fewer" tells us we need to subtract.

Rewrite the phrase as an expression.

"Four fewer books than Oswaldo" is o - 4.

So, the expression that shows how many books Shailyn read last year is o - 4.

Step-by-step explanation:

Answer:we can’t help if it is barely readable

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here's a step by step explanation of how to calculate the number of cakes baked if the bakery baked 96 loaves of bread:

First, determine the number of sets of 12 loaves of bread that were baked:

96 loaves of bread ÷ 12 loaves per set = 8 sets of 12 loaves

Next, determine the number of cakes baked for each set of 12 loaves of bread:

For every set of 12 loaves, 5 cakes are baked.

Finally, multiply the number of sets by the number of cakes baked per set to find the total number of cakes baked:

8 sets × 5 cakes per set = 40 cakes

So, if the bakery baked 96 loaves of bread, they would have baked 40 cakes.

Answer:

40

Step-by-step explanation:

12 times 8 equals 96 and 5 times 8 equals 40, there for 40 cakes will be backed

The amount of money that Amelia is expected to raise is given as follows:

£78.13.

The outcomes of a person winning, and their probabilities, as given as follows:

Hence the probabilities of winning and losing are given as follows:

Then the distribution of earnings for each person is given as follows:

Hence, considering 250 people, the expected amount raised is given as follows:

E(X) = 250/16 x (2.5 x 6 - 1 x 10)

E(X) = £78.13.

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Answer:

To find the value of b_n in an arithmetic sequence given by the recursive definition b_1 = 8 and b_n = b_{n-1} - 3, we can use the formula for the nth term in an arithmetic sequence:

b_n = b_1 + (n-1)d

where d is the common difference. In this case, d = -3.

So, we can plug in the values for b_1 and d to find b_n:

b_n = 8 + (n-1)(-3)

b_n = 8 - 3(n-1)

Now, to find the value of b_n for a specific n, we just need to substitute the value of n into the equation for b_n. For example, if we want to find b_14, we would substitute n = 14:

b_14 = 8 - 3(14-1)

b_14 = 8 - 3(13)

b_14 = 8 - 39

b_14 = -31

So, the value of b_14 is -31, and the answer is (1) 14.

The area of the equilateral triangle with side length 10 cm is 25 cm².

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

To find the area of an equilateral triangle, we need to find the height first. The height of an equilateral triangle is equal to the length of the perpendicular line from the center of the triangle to one of its sides.

To find the height, we can divide the equilateral triangle into two 30-60-90 triangles. The height is equal to half of the hypotenuse of one of these triangles, which can be calculated as:

10 cm / 2 = 5 cm

Now that we have the height, we can find the area of the equilateral triangle as follows:

Area = ½ * base * height

Area = ½ * 10 cm * 5 cm

Area = 25 cm²

Hence, The area of the equilateral triangle with side length 10 cm is 25 cm².

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The measure of angle 1 is given as follows:

m < 1 = 42º.

To obtain the measure of angle 1 in the kite, we must consider that the consecutive angles are complementary, that is, the sum of their measures is of 90º.

Relative to angle 1, we have that:

m < 4 + m < 1 = 90º.

For the bottom left triangle, the internal angle measures are given as follows:

Considering that the sum of the measures of the internal angles of a triangle is of 180º, the measure of angle 4 is obtained as follows:

m < 4 + 42 + 90 = 180

m < 4 = 58º.

Then the measure of angle 1 is obtained as follows:

m < 1 = 90 - 58

m < 1 = 42º.

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Answer: The present value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:

PV = PMT * [ (1 - (1 + r)^-n) / r ] * (1 + r)

where:

PMT = $300 (the monthly payment)

r = 0.06/12 (the monthly interest rate)

n = 10*12 (the number of periods over 10 years, with 12 months in a year)

Plugging in the values into the formula, we get:

PV = $300 * [ (1 - (1 + 0.06/12)^-n) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - (1 + 0.06/12)^-(10*12)) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - 1.06^-120) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (1 - 0.379362539) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * [ (0.620637561) / (0.06/12) ] * (1 + 0.06/12)

PV = $300 * 10.34300138

PV = $31,029.

So the present value of the annuity due is $31,029. This means that if you were to invest $31,029 today, you would receive a monthly payment of $300 for 10 years at 6% interest compounded monthly.

Step-by-step explanation:

On solving the provided question, we can say that first angle is 37.9° . second angle will be 52.1°.

An angle is a fοrm in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a pοint in the middle known as the angle's vertex. In the plane where the rays are placed, twο rays can produce an angle.

An angle is alsο produced when two planes intersect. They're knοwn as dihedral angles. In plane geοmetry, an angle is the form that two rays or lines with a commοn termination might take. The Latin word "angulus," which means "hοrn," is where the English word "angle" comes from. The two rays, also knοwn as the sides of the angle, have a common termination knοwn as the vertex.

x = first angle

Complementary angle is 14.2 degrees more than the cοmplementary angle.

First angle  = x

Second angle = x + 14.2°

Complementary angle

x+x+14.2=90

2x+14.290

2x 90 14.2

2x = 75.8 x = 37.9

First angle is 37.9°.

Second angle will be:

x+14.2°

⇒37.9°+ 14.2°

⇒52.1°

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Answer:

8.25 gallan=33 quart

Step-by-step explanation:

Answer:

D

Step-by-step explanation: I did it

Answer:

50:7

Step-by-step explanation:

You just put ":" in between the numbers requested.

Answer:

9.5

Step-by-step explanation:

Law of sine:

[tex]\frac{SideXY}{sinZ^{o}} = \frac{SideZY}{sinX^{o}} = \frac{SideXZ}{sinY^{o}}[/tex]

Sum of interior angles = 180°:
∴∠Z° = 180° - 63° - 41°

 ∠Z° = 76°

∴[tex]\frac{14}{sin76^{o}}[/tex]= [tex]\frac{x}{sin41^{o}}[/tex]

Cross- multiplication is applied:

(x)(sin76°) = (14)(sin41°)

x has to be isolated and made the subject of the equation:

x = [tex]\frac{[(14)(sin41^{o})]}{sin76^{o}}[/tex]

x = 9.466

x = 9.5 (Rounded to the nearest tenth)

Answer:

16 years old

Step-by-step explanation:

Let's call Mikhail's age "x". Gabrielle's age is 3 times that, so her age is 3x. The sum of their ages is 64, so:

x + 3x = 64

4x = 64

x = 16

So, Mikhail's age is 16 years old.

Answer:

y = 2

Step-by-step explanation:

If x = -2, what is y = ?

When x = -2 the line crosses the y axis at 2, so y = 2

Using the rules for matrix multiplication we will see that a₁₂ = 144

That would by the second element on the first row of the product matrix.

Remember how the product works, we will get:

a₁₂ = 24*2 + 32*3

a₁₂ = 48 + 96

a₁₂ = 144

The correct option is the last one.

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The correlation coefficient r of the data given is 0.938  

The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables.

Given that a set of data showing the values of variables x and y, we are asked to find the correlation coefficient r of the data given,

We know that,

The correlation coefficient r is a number between and calculated to represent the linear dependence of two variables or sets of data.

Using an Excel tool :- (CORREL function) = CORREL(B3:B10,C3:C10)

We get, r = 0.938

Hence, the correlation coefficient r of the data given is 0.938  

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The number of positive integers that satisfy the conditions is 4

The positive integers are the natural numbers or also called counting numbers. These integers are also sometimes denoted by Z+. The positive integers lie on the right side of 0 on a number line. Z+ → 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,

To satisfy positive integers that will have sum of four with a 1, a 2 or a 3

The integers are

13

31

112

211

therefore there are only 4 positive integers that have sum of 4 with a 1 , a 2 and a3

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Company should provide insurance policies to employees because the employees are assets to them.

An insurance policy is a contract between the insurance company and the person getting the insurance.

Employees are assets of a company.

Companies should look after by insuring this asset like any other asset.

Although it is not the only factor for an employee to stick to a company, it is also one of the contributing factor for the employees to stick to a company longer.

It is a very good benefit for the employee since the premium is paid by the employer for the employee.

Hence companies should provide insurance policies to employees.

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The volume of this cylinder is 1.5 times that of the cone. The cylinder volume is 452.4 in³ while the cone volume is 301.6 in³

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.

Radius of cone/cylinder = diameter/2 = 8 in/2 = 4 in.

Volume of cylinder = π * radius² * height = π * (4)² * 9 = 452.4 in³

Volume of cone = (1/3) * π * radius² * height = (1/3) * π * (4)² * 18 = 301.6 in³

The volume of this cylinder is 1.5 times that of the cone

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Answer:

cost of couch: $846

cost of coffee table: $282

Step-by-step explanation:

Answer:

To convert from kilometers per hour to miles per hour, we use the conversion factor of 1 mile per hour = 1.609 kilometers per hour.

So, 50 km/h = 50 x 1.609 mph = 80.45 mph

Rounding to one decimal place, the answer is 80.5 mph.

The typical speed limit in Europe is,

⇒ 833.3 miles per hour.

We have to given that,

A typical speed limit in Europe is, 50 km/h (kilometers per hour).

We can change the speed limit from kilometers per hour in miles per hour.

⇒ 50 kilometers per hour

⇒ 50 × 1000 / 60 miles per hour.

⇒ 50000 / 60  miles per hour.

⇒ 833.3 miles per hour.

Therefore, The typical speed limit in Europe is,

⇒ 833.3 miles per hour.

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The exact perimeter of the segment is 54.13 inches, and the exact area of the segment is 301.44 square inches.

What is perimeter and area enclosed in circle?

A circle is also defined by two properties: area and perimeter. The formulas for both the measures of the circle are given by; Area of a circle = πr². The perimeter of a circle = 2πr.

Let's call the center of the circle O and the endpoint of the arc A. Let's also call the endpoint of the chord that defines the segment B. Then we have an isosceles triangle OAB, where OA = OB = 24 inches.

1) The perimeter of the segment is equal to the length of the arc plus the length of the chord. To find the length of the arc, we can use the formula:

Arc length = (Ф / 360) * 2πr,

where Ф is the measure of the angle in degrees, r is the radius (which is 24 inches in this case), and π is pi.

In this case, the measure of the angle is 60°, so the length of the arc is:

Arc length = (60 / 360) * 2π * 24 inches

Arc length  = (1/6) * 2π * 24 inches

Arc length  = 4π inches

To find the length of the chord, we can use the formula:

Chord length = 2r * sin(Ф/2), where r is the radius and Ф is the measure of the angle in radians.

First, we need to convert the angle measure from degrees to radians:

60° = 60 * (π / 180) radians = π / 3 radians

Now, we can find the length of the chord:

Chord length = 2 * 24 * sin(π / 6)

Chord length = 24 * 2 * sin(π / 6)

Chord length = 24 * √3 inches

Finally, we can add the length of the arc and the chord to find the perimeter:

Perimeter = 4π + 24 * √3

Perimeter = 4π+41.57

Perimeter = 54.13 inches

2) To find the area of the segment, we can use the formula:

Area = (Ф/ 360) * πr², where Ф is the measure of the angle in degrees and r is the radius.

In this case, the measure of the angle is 60°, so the area of the segment is:

Area = (60 / 360) * π * 24² square inches

Area = (1/6) * π * 576 square inches

Area = 96π square inches

Area = 301.44 square inches

So, The exact perimeter of the segment is 54.13 inches, and the exact area of the segment is301.44 square inches.

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The length of CD can be found to be 7. 21 units .

The length of CD can be found by using the distance formula which is :

= √ [ ( x ₂ - x ₁ ) ² + ( y ₂ - y ₁ ) ² ]

Given the points, ( 3, - 2 ) and ( 7, - 8 ).

The length of CD is :

= √ [ ( 7 - 3 ) ² + ( - 8 - (- 2 ) ) ² ]

= 7. 21

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Answer:

There are approximately 38 cows in the herd.

Step-by-step explanation:

In this problem, we are asked to find the number of cows in a herd, given that 16% of the cows have already given birth to calves and 32 have not yet done so.

Assuming there are no other types of cows in the herd, we can determine that the 32 cows that have not had calves make up 84% of the herd, since they are what is left over when 16% is subtracted from 100% (the whole herd).

[tex]100\%-16\% = 84\%[/tex]

We can now create a equation that shows that 84% of the herd is 32 cows, representing the total number of cows in the herd as x.

[tex]32 \text{ cows} = 84\% \cdot x[/tex]

Finally, to solve for the number of cows in the herd, we can multiply both sides by 100/84.

[tex]\dfrac{100}{84}(32 \text{ cows}) = (84\% \cdot x)\dfrac{100}{84}[/tex]

[tex]x \approx 38 \text{ cows}[/tex]

So, there are approximately 38 cows in the herd.