Find the equation of the line passing through the points (3,7) and (-2,5)

The area of the sector is 297π units squared.

The arc length of a 330° sector is 33π. Therefore, let's find the area of the sector.

Let's find the radius of the circle.

length of arc = ∅/ 360 × 2πr

where

Therefore,

33π = 330 / 360 × 2π × r

cross multiply

660πr = 11880π

divide both sides by 660π

r = 11880π / 660π

r = 18 units

Therefore,

area of the sector = 330 / 360 × π × 18²

area of the sector = 106920 / 360 π

area of the sector = 297π units²

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The value of x will be 16.

Given ,

Parallelogram with two sides:

side 1 = 3x + 20

side 2 = 5x - 12

In parallelogram the opposite side are equal and parallel.

Thus,

side 1 and side 2 will be equal and parallel.

Equating both sides to get the value of x,

3x + 20 = 5x - 12

x = 16

Hence the value of x can be found out by property of parallelogram.

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Answer:

Step-by-step explanation:

It's c

-4 1/6

Plug in the number for a and you get -2 1/3 - 11/6

make the first number into a fraction, so -7/3

-7/3 - 11/6

common denominator, so, -14/6 - 11/6, which equals -25/6

simplify: -4 1/6

Hope that helps!

Answer:

The answer is

[tex] \frac{ - 25}{6} [/tex]

-4⅙

Step-by-step explanation:

[tex]a - \frac{ - 11}{6} [/tex]

[tex]a = - 2 \times \frac{1}{3} [/tex]

[tex] \frac{ - 7}{3} - \frac{ - 11}{6} [/tex]

[tex] = \frac{ - 25}{6} [/tex]

The value of the equation 6 sinθ=5 for θ is 56.4 degrees

From the question, we have the following parameters that can be used in our computation:

6 sinθ=5

Express the equation properly

So, we have the following representation

6 sin(θ) = 5

Divide both sides of the equation by 6

This gives

sin(θ) = 5/6

Evaluate the quotient

sin(θ) = 0.833

Take the arc sin of both sides

θ = sin⁻¹(0.833)

Evaluate

θ = 56.4

Hence, the value of the equation for θ is 56.4 degrees

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Complete question

Approximate θ in the equation, to the nearest 0.1 degrees

6 sin(θ) = 5

The value of the ring in 2030 would be; 2,034

Given that the Purchase price of the Diamond ring= $900

Value of ring increase by 7% each year.

First find a number of the year between 2012 and 2040,

Time period= 2030 - 2012    

∴ Time period of value appreciation is 18 years.

Now, finding the value of a diamond ring increased after 28 years.

The value of ring increased after 18 years= 900 x 0.07 x 18

∴ Increased value of diamond ring after 18years= $1,134

Next, Value of diamond ring after 18 years= 1,134 + 900

Hence, value of a diamond ring in 2030 is $2,034

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Answer:

53 is prime. How are you in collage?

A prime number is a number that is only divisible by 1 and the number itself (examples include 3, 11, 19). The prime numbers between 40 and 60 are 41, 43, 47, 53, and 59.

Answer:

Step-by-step explanation:

x²-5x+29=8x-6

x²-13x+35=0

[tex]x=\frac{13 \pm\sqrt{(-13)^2-4(1)(35)} }{2(1)} \\x=\frac{13 \pm\sqrt{169-140} }{2} \\x=\frac{13 \pm\sqrt{29} }{2}[/tex]

The equation for the distance of the point (x, y), from the center of the circle is; (x - 4)² + (x - 2)² = 5²

The general form of the equation of a circle with center (h, k) is; (x - h)² + (y - k)² = a², where the radius of the circle is; a

The radius of a circle is the distance from the center to a point (x, y) on the circumference, therefore, the equation for the distance of the point (x, y) from the center of the circle, is equivalent to the equation for a circle, where the distance of the point (x, y) from the center is the radius.

The coordinates of the center of the circle, (h, k) = (4, 2)

The radius of the circle, r = a = 5

The equation for the distance (x, y) from the center, which radius of the circle, with center (4, 2), is therefore;

Equation of a circle; (x - h)² + (y - k)² = a²

Equation from the center; (x - 4)² + (y - 2)² = 5²

Where;

5 = The radius, a = The distance from the center of the circle

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Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than Twice the number of years Mrs. Bright has worked.

The number of years Mrs. Bright has worked for the company. We know that Mr. Oswald has been in the company for 24 years, which is three times the number of years Mrs. Bright has worked.

So, Mrs. Bright has worked for 24 / 3 = 8 years in the company.

Now, let's find the number of years Mr. Oswald needs to work for the company to make it twice the number of years Mrs. Bright has worked.

Twice the number of years Mrs. Bright has worked is 2 * 8 = 16 years.

Since Mr. Oswald is already employed for 24 years, we need to find the additional years he needs to work to reach 16 more years.

16 more years - 24 years = -8 years.

The result of -8 years indicates that Mr. Oswald has already worked for more than twice the number of years Mrs. Bright has worked. Therefore, it is not possible for Mr. Oswald to work for more years in order to make it twice the number of years Mrs. Bright has worked.

Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than twice the number of years Mrs. Bright has worked.

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Answer:

2.5

Step-by-step explanation:

half of 10 is 10/2 = 5

so 50% of 5 is 2.5

the amount of cubic feet(Volume) the tent can hold is 165 ft³.

Volume is the space occupied by an object.

To caculate the amount of cubic feet(Volume), the tent can hold, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the right option is (A) 165 ft³.

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Let's just compare the angles to start - - - these are two parallel lines cut by another line (transversal), so there are a lot of equal angles.

Angles 1 and 5 are the same

Angles 2 and the 65 degree angles are the same.

Angles 4 and 8 are the same.

And 3 and 7 are the same.

There are even more similar angles:

1 and 3 are the same. 2 and 4 are the same.

5 and 7 are the same, and 8 and the 65 degree angle are the same.

So without any math, Angles 2, 4 and 8 are all 65 degrees.

So Angle 65 + Angle 5 = 180. Therefore Angle 5 = 115.

Therefore angle 7 is 115. (You could also say that 65+ Angle 7 = 180.)

Since angle 7 is 115, so is angle 3 and angle 1.

So in conclusion

Angle 1: 115

Angle 2: 65

Angle 3: 115

Angle 4: 65

Angle 5: 115

Angle 7: 115

Angle 8: 65

Answer: 2ˣ =  y

Step-by-step explanation:

In order to find the inverse of any function, switch the x and the y, then solve for y.

y = log₂x               >swap/switch variables  and solve for y

x = log₂y              >rewrite in exponential form

2ˣ =  y

The vertices of the image triangle △JKL under the dilation centered at the origin with a scale factor of 5 are:

J′ = (−15, −10)

K′ = (5, 20)

L′ = (20, 10)

To find the vertices of the image of triangle △JKL under the dilation centered at the origin with a scale factor of 5, we need to multiply the coordinates of each vertex by the scale factor.

Let's apply the dilation to each vertex:

J(−3, −2) → J′ [tex]= (5 \times -3, 5 \times -2)[/tex] = (−15, −10)

K(1, 4) → K′ [tex]= (5 \times 1, 5 \times 4)[/tex] = (5, 20)

L(4, 2) → L′ [tex]= (5 \times 4, 5 \times 2)[/tex] = (20, 10)

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Step-by-step explanation:

the surface area is the sum of all areas of the individual outside faces/sides.

so, what do we see here, what outside sides do we have here ?

of course, we have to assume that this is a regular object (left and right sides are the same).

2 right-angled triangles (left and right).

1 rectangle in the back.

1 rectangle at the bottom.

1 times rectangle in the front.

the area of a right-angled triangle is

leg1 × leg2 / 2

in our case that is

6 × 2.5 /2 = 3 × 2.5 = 7.5 mm²

we have 2 of these triangles :

2×7.5 = 15 mm²

the area of the rectangle in the back is

8 × 6 = 48 mm²

the area of the rectangle at the bottom is

8 × 2.5 = 20 mm²

the area of the rectangle in the front is

8 × 6.5 = 52 mm²

the surface of the object is the sum of all that :

15 + 48 + 20 + 52 = 135 mm²

Answer:

Danielle Stevenson receives $2,600 from selling the $160,000 house.

Step-by-step explanation:

To find the amount Danielle Stevenson receives from selling the house, we'll follow these steps:

Calculate the commission earned by Danielle Stevenson: Commission = 6.5% * $160,000.

Commission = 0.065 * $160,000 = $10,400.

Determine the broker's share: Broker Share = 0.5 * Commission.

Broker Share = 0.5 * $10,400 = $5,200.

Calculate the remaining amount after the broker's share: Remaining Amount = Commission - Broker Share.

Remaining Amount = $10,400 - $5,200 = $5,200.

Determine the salesperson's share: Salesperson Share = 0.5 * Remaining Amount.

Salesperson Share = 0.5 * $5,200 = $2,600.

Finally, calculate the amount Danielle Stevenson receives, which is the remaining portion after the broker and salesperson's shares: Amount Danielle Receives = Remaining Amount - Salesperson Share.

Amount Danielle Receives = $5,200 - $2,600 = $2,600.

Therefore, Danielle Stevenson receives $2,600 from selling the $160,000 house.

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A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. A plane intersects the pyramid parallel to its base. The cross section is a rectangle  A plane intersects the pyramid perpendicular to its base and through the top vertex. The cross section is a triangle

A plane intersecting a rectangular prism can create different cross-sectional shapes depending on the orientation of the plane. Let's explore the two scenarios you mentioned:

Plane parallel to the base: When a plane intersects the rectangular prism parallel to its base, the resulting cross section is also a rectangle. The shape of the cross section will have the same dimensions as the base of the rectangular prism.

Plane perpendicular to the base and through the top vertex: In this case, the cross section will be a triangle. The shape of the cross section will be determined by the intersection of the plane with the three sides of the rectangular prism. The base of the triangle will be formed by the side of the rectangular prism, while the other two sides will be formed by the edges connecting the top vertex of the pyramid to the corresponding vertices of the base.

It's important to note that a rectangular prism is different from a pyramid. A rectangular prism has six rectangular faces, while a pyramid has a polygonal base (in this case, a rectangle) and triangular faces converging to a single point called the apex or top vertex.

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Answer:

weight = gxg = 12kg to g = 0.12 and then using formula we get 0.12x0.12 = 1.44 is the weight

Step-by-step explanation:

Answer:

Therefore, the weight of the object is approximately 117.72 Newtons.

Step-by-step explanation:

The weight of an object is given by the formula:

weight = mass x acceleration due to gravity

The acceleration due to gravity on Earth is approximately 9.81 m/s².

So, the weight of an object with a mass of 12 kg is:

weight = 12 kg x 9.81 m/s² = 117.72 N

Therefore, the weight of the object is approximately 117.72 Newtons.

Answer:

Step-by-step explanation:

Rachel already has 7 teaspoons of milk.

so 7 x 5 = 35

So Racheal will need 35 teaspoons of surger.

Using the centimeter ruler:

For the quotients:

2.a. To find 1 ÷ 1/10, divide 1 by the fraction 1/10. Dividing by a fraction is the same as multiplying by its reciprocal, rewrite the problem as 1 × 10/1, which simplifies to 10. Therefore, 1 ÷ 1/10 = 10.

To find 4 ÷ 1/10, divide 4 by the fraction 1/10. Again, rewrite the problem as 4 × 10/1, which simplifies to 40. Therefore, 4 ÷ 1/10 = 40.

b. To find each quotient, we used the fact that dividing by a fraction is the same as multiplying by its reciprocal.

c. Following the same pattern, find 18 ÷ 1/10 by dividing 18 by 1/10. This is the same as multiplying 18 by the reciprocal of 1/10, which is 10/1. Therefore, 18 ÷ 1/10 = 180.

d. To find 4 ÷ 2/10, divide 4 by 2/10. Rewrite the problem as 4 × 10/2, which simplifies to 20. Therefore, 4 ÷ 2/10 = 20.

To find 4 ÷ 8/10, divide 4 by 8/10. Rewrite the problem as 4 × 10/8, which simplifies to 5. Therefore, 4 ÷ 8/10 = 5.

3. a. To divide 5 by 1/10, Rewrite the problem as 5 × 10/1, which simplifies to 50. Therefore, 5 ÷ 1/10 = 50.

b. To divide 5 by 3/10, Rewrite the problem as 5 × 10/3, which simplifies to 16 2/3. Therefore, 5 ÷ 3/10 = 16²/₃.

c. To divide 5 by 9/10, Rewrite the problem as 5 × 10/9, which simplifies to 5 5/9. Therefore, 5 ÷ 9/10 = 5⁵/₉.

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Answer:

$255

Step-by-step explanation:

25% in decimal form is 0.25

300 x 0.25 = 75

25% off means 300 - 75 = 255

answer is $255

The volume of the rectangular pyramid is 144.48 cubic feet.

A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.

The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.

The volume of a rectangular pyramid is given as:

[tex]\sf V = \dfrac{(l)(b)(h) }{3}[/tex]

[tex]\sf V = \dfrac{(8.4)(8.6)(6) }{3}[/tex]

[tex]\sf V = \dfrac{433.44 }{3}[/tex]

[tex]\sf V = 144.48 \ cubic \ feet[/tex].

Hence, the volume of the rectangular pyramid is 144.48 cubic feet.

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Using balanced billing, the monthly payment is $278

Using balanced billing to determine their monthly payment, we simply need to divide their total annual payment by the total number of months in a year. This will result to dividing the entire annual bill by 12 to determine the monthly payment.

Given that the Ross family spent $3,336 for electricity last year, we can calculate their monthly payment as follows:

Monthly payment = Total cost / Number of months

Monthly payment = $3,336 / 12

Monthly payment  = $278

Therefore, the Ross family's monthly payment for balanced billing will be approximately $278.

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The resultant of the force that acts in opposite directions is 7 N.

We have,

We know that the resultant force is the force that has the same effect in magnitude and direction as two or more forces that is acting together. We have to note that the force that is actinmg on an object is a vector quantity. The implication of this is that the magnitude and the direction of the forces that are acting on the body is very important.

By the use of the law of vectors we can be able to write in the case of the question that we have here, we can see that the forces are acting in the opposite directions. The implication of this is that we would have to subtract the forces so as obtain the resultant force.

We have to note that when we have opposite forces, one is said to be positive and the other negative and the resultant force can be found by subtraction. As such the resultant force can be obtained from;

Let the +B force be 12 N

Let the -B force be 5N

12 N - 5 N = 7 N

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The amount of liabilities at December 31, 2019, is $900,000.

To determine the amount of liabilities at December 31, 2019, we can use the accounting equation:

Assets = Liabilities + Stockholders' Equity

Given that the company reported assets of $1,500,000 and liabilities of $700,000 on January 1, 2019, we can set up the equation as follows:

$1,500,000 = $700,000 + Stockholders' Equity

During 2019, assets decreased by $100,000, so the new value of assets at December 31, 2019, would be $1,500,000 - $100,000 = $1,400,000.

Stockholders' equity decreased by $200,000, so the new value of stockholders' equity at December 31, 2019, would be $700,000 - $200,000 = $500,000.

Now we can substitute these values into the accounting equation to solve for liabilities:

$1,400,000 = Liabilities + $500,000

Rearranging the equation, we find:

Liabilities = $1,400,000 - $500,000

Liabilities = $900,000

Therefore, the amount of liabilities at December 31, 2019, is $900,000.

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Answer:

653.3 bacteria

Step-by-step explanation:

A continuously growing population of bacteria is modeled by the function:

[tex]P(t) = P_0 \cdot e^{rt}[/tex]

where:

In this problem, we are given the following values:

We can plug these into the function to solve for [tex]P(2)[/tex].

[tex]P(t) = P_0 \cdot e^{rt}[/tex]

[tex]P(2) = 484 \cdot e^{(0.15 \, \cdot \, 2)}[/tex]

[tex]P(2) = 484 \cdot e^{0.3}[/tex]

Finally, the right side of this equation can be evaluated using a calculator to solve for the population of the bacteria after 2 hours.

[tex]\huge{\text{P(2) = 653.3 bacteria}}[/tex]

Yes, the circular pool will fit into the rectangular section of the yard.

Part A: Given that, the base of the pool has an area of 615.44 square feet.

We know that, the area of a circle is πr².

Here, πr²=615.44

3.14r²=615.44

r²=615.44/3.14

r²=196

r=14 feet

Therefore, the diameter is 14×2=28 feet

Part B: The rectangular section of the yard where he wants to put the pool is 25 feet by 35 feet.

Area of a  rectangular section = Length×Breadth

= 25×35

= 875 square feet

Yes, the circular pool will fit into the rectangular section of the yard.

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"Your question is incomplete, probably the complete question/missing part is:"

Mark wants to put a circular swimming pool in his backyard. The base of the pool has an area of 615.44 square feet, and the rectangular section of the yard where he wants to put the pool is 25 feet by 35 feet. Use this information to answer Parts A and B.

Part A: What is the diameter of the swimming pool?

Part B: Will the pool fit in the rectangular section of the yard?

Answer:

2, answer choice B

Step-by-step explanation:

Slope = rise/run = (y2-y1)/(x2-x1).

You are given points (4,8) and (5,10).

slope = (8-10)/(4-5)

slope = (-2)/(-1)

slope = 2