A 45° sector in a circle has an area of 13.75π cm².

What is the area of the circle?

Use 3.14 for pi.

Enter your answer as a decimal in the box.

Answer:

B. 2 points

Step-by-step explanation:

1 point is a dot in space, 2 can make a line

Answer:

c!

Step-by-step explanation:

Answer:

{-5, 3}

Step-by-step explanation:

7 is a factor common to all three terms of this polynomial function.  Thus, after the first attempt to factor it, we have 7(x^2 + 2x - 15).  The quadratic factors into (x + 5)(x - 3).  Setting these = to zero individually, we get

x + 5 = 0, or x = -5, and

x - 3 + 0, or x = 3

Thus, the zeros of the given f(x) =7x2 + 14x − 105 are {-5, 3}.

Answer:

k=4

Step-by-step explanation:

Given

A line x=7

The line has only y-intercept which means that it is a vertical line.

As the two points are

A(10,2) and B(k,2)

The y-intercepts of both the points are same i.e. y=2 which means that the line fomed by joining A and B is a horizontal line.  

As x=7 is a vertical line and bisects the horizontal line, the mid-point of line AB will be the point where first line (x=7) bisects the second which is (7,2).

The x-coordinate of mid-point is 7 because the vertical line has 7 as x-intercept and y-intercept is two because the horizontal line has y-intercept 2.

So,

Mid-point=((10+k)/2  ,2)=(7,2)

Comparing the x-coordinate

(10+k)/2=7

10+k=7*2  

10+k=14

k=14-10

k=4

Answer:

Option [tex]42.1\ in^{2}[/tex]

Step-by-step explanation:

we know that

The area of the region that is inside the square and outside the circle is equal to the area of the square minus the area of the circle

see the attached figure to better understand the problem

Step 1

Find the area of the square

Remember that

The area of the square is

[tex]A=b^{2}[/tex]

where

b is the length side of the square

we have

[tex]b=14\ in[/tex]

substitute

[tex]A=14^{2}=196\ in^{2}[/tex]

Step 2

Find the area of the circle

Remember that

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]r=14/2=7\ in[/tex]

substitute

[tex]A=\pi(7^{2})=153.9\ in^{2}[/tex]

Step 3

Find the area of the region

[tex]196\ in^{2}-153.9\ in^{2}=42.1\ in^{2}[/tex]

1) y = kx . . . . . for some constant k

.. Here y is directly proportional to x , where k is the constant of proportionality

2) y = k/x . . . . for some constant k

.. Here y is inversely proportional to x , again k is the constant of proportionality.

3) y = 2x +52

..

Here y is linearly related to the x , it is neither directly proportional nor inversely proportional.

What is the measure of BC

Solution:

As per Inscribed Angle Theorem: If an angle is inscribed in a circle, then the measure of the intercepted arc is twice the value of the measure of the inscribed angle.

So, as we can see in the diagram the angle inscribed in the circle is 65°.

So, the measure of intercepted arc BC is twice ∠BDC

Or, BC=2*65°

BC=130° Answer

GDP calculations should include 'final goods and services' and 'new products' to reflect a nation's current economic activity accurately while preventing double counting.

The question pertains to what should be included when calculating the Gross Domestic Product (GDP). The options given were a. final goods and services, b. intermediate goods and services, c. last year's products, and d. new products. According to the principles of economics, GDP is the market value of all final goods and services produced within a country in a given period of time.

It is crucial to understand that GDP calculations include only new products that are produced within the current year to reflect the nation's current economic activity. This method helps statisticians avoid the mistake of double counting, which would inflate GDP figures inaccurately. Consequently, the correct selections are a. final goods and services and d. new products.

Final answer:

To find the largest interior angle y in a triangle with exterior angles in the ratio 2:3:4, we use the fact that the sum of a triangle's exterior angles is 360° to find the value of each exterior angle, then deduce y as the supplement of the largest exterior angle, resulting in y being 20°.

Explanation:

To find the value of the largest interior angle y in a triangle where the exterior angles are in the ratio 2:3:4, we start by understanding that the sum of the exterior angles of any triangle is 360°.

This means that the exterior angles in this triangle are 2x, 3x, and 4x degrees, respectively, where x is a common multiple.

Given that the sum of these angles must be 360°, we can write the equation 2x + 3x + 4x = 360°, simplifying to 9x = 360° and solving for x gives us x = 40°.

The largest exterior angle is 4x, which equals 160°. Since the exterior angle is supplementary to the interior angle it shares a vertex with, the largest interior angle y is therefore 180° - 160° = 20°.

Thus, the value of y is 20°.

Final answer:

To find the total distance to town, the distance walked (1.5 miles) and run (1.75 miles) were calculated, and it was found that the student is 3.25 miles away from home. This is halfway to town, so the total distance to town is 6.5 miles.

Explanation:

To solve the problem, we will calculate the distance traveled by walking and running and then use these to find the total distance to town.

Step 1: Calculate the distance walked

First, we convert the walking time into hours since the speed is given in miles per hour. Half an hour of walking at 3 miles per hour will cover:

Distance walked = Speed × Time = 3 mph × 0.5 hours = 1.5 miles

Step 2: Calculate the distance run

Since 15 minutes is a quarter of an hour, we can calculate the distance run at 7 miles per hour as:

Distance run = Speed × Time = 7 mph × 0.25 hours = 1.75 miles

Step 3: Determine the total half distance

Now, we combine the distances to find the halfway point to town:

Total half distance = Distance walked + Distance run = 1.5 miles + 1.75 miles = 3.25 miles

Step 4: Find the full distance to town

Since this is half the distance, the full distance to town is:

Full distance = Total half distance × 2 = 3.25 miles × 2 = 6.5 miles

Conclusion

Therefore, the total distance from the student's house to town is 6.5 miles.

Final answer:

The total distance from the house to town is found by doubling the sum of the distances walked and run, which were 1.5 miles and 1.75 miles, respectively. The full distance to town is 6.5 miles.

Explanation:

To solve for the distance from your house to town, we will use the information provided about your walking and running times and speeds. Since you walked for half an hour (0.5 hours) at a speed of 3 miles per hour and ran for 15 minutes (0.25 hours) at a speed of 7 miles per hour, and this brought you halfway to town, we can set up the following equation:

Distance walked = Speed walked × Time walked
= 3 mph × 0.5 hours
= 1.5 miles

Distance run = Speed run × Time run
= 7 mph × 0.25 hours
= 1.75 miles

The total distance you traveled to get halfway to town is the sum of the distance walked and the distance run:

Total distance halfway = Distance walked + Distance run
= 1.5 miles + 1.75 miles
= 3.25 miles

Since 3.25 miles is only halfway to town, the full distance to town is twice that amount:

Full distance to town = 2 × Total distance halfway
= 2 × 3.25 miles
= 6.5 miles

Therefore, the total distance from your house to town is 6.5 miles.

Answer:the correct answer is 71142 just multiply 334 and 213

Step-by-step explanation:

Answer:

  $9474.40

Step-by-step explanation:

A spreadsheet can be used to calculate the amortization of the loan. The one attached uses rounding to the penny for all dollar amounts. The result is that the payment amount is rounded down, and the final payment is about 12¢ short. The total repaid on the loan will be slightly more than the product of payment amount ($124.99) and number of payments (72).

The total cost of the boat is the sum of down payment, loan amount, and interest amount. That sum is $9474.40.

Answer:

Length = 6 cm, width = 9 cm

Step-by-step explanation:

I believe the answer is (-2,-1)   after the original point (2,1) goes through the change of -y,x

Answer:

Option B is correct.

The coordinate of A' is (-2 , -1)

Explanation:

The coordinates of ABCD are A = (-1,2) , B(1,1) , C =(1,-1) and D(-2,-2).

Rotation means moving the shape  around a fixed point clockwise or anticlockwise, and by a certain number of degrees.

Rule for 90° counterclockwise rotation about the origin: [tex](x,y) \rightarrow (-y,x)[/tex]

or we can say that switch x and y in the coordinates and make y value opposite.

Then, the coordinate of A' :

[tex]A(-1,2) \rightarrow A'(-2 ,-1) [/tex]

Therefore, the coordinate of A' in the quadrilateral A'B'C'D' is, (-2 ,-1)

Changes made to your input should not affect the solution:

 (1): "p3"   was replaced by   "p^3".  1 more similar replacement(s).

 1.1    p9 divided by p3 = p(9 - 3) = p6

Answer:

[tex](p^9)^{-2}=p^{-18}[/tex]

Step-by-step explanation:

[tex](p^9)^{-2}[/tex]

To simplify the given expression we apply exponential property.

Multiply the outside exponent with inside exponent

[tex](a^m)^n= a^{mn}[/tex]

when we multiply the outside exponent -2 inside 9 , it becomes -18

So the given expression becomes

[tex](p^9)^{-2}=p^{-18}[/tex]