Let us consider a circle of radius 2 cm. If an arc of this circle subtends an angle of 20 radian to the centre, then what is the length of the arc and area of the sector such formed?​

Answer:

Step-by-step explanation:

C

Answer:

C.) Rich lost 20 pounds

Step-by-step explanation:

I hope you have a good rest of your day!

Factor by grouping: 16x³ +28x² - 28x - 49 = 0 is  (4x² - 7) (4x - 7) = 0

Large polynomials can be divided into groups based on a common factor. As a result, we may factor each distinct group and then merge like words. We refer to this as factoring by grouping.

We have the equation,

16x³ +28x² - 28x - 49 = 0

In order to solve the equation by using factor by grouping:

We find common terms in between,

So, we arrange the terms,

16x³ +28x² - 28x - 49 = 0

4x² (4x - 7) -7 (4x - 7) = 0

Here, we have common term (4x-7).

Factor out the common binomial.

(4x² - 7) (4x - 7) = 0

Therefore, (4x² - 7) (4x - 7) = 0 is the factor.

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The predicted fuel efficiency for a speed of 30 mph will be 26.50 mpg when the least-squares regression line is given.

If the data demonstrates a stronger link between two variables, the line that best matches this linear relationship is known as a least-squares regression line, and it minimizes the vertical distance between the data points and the regression line. A regression line is a straight line that illustrates how a response variable y varies when an explanatory variable x changes. The line is a mathematical model that predicts the value of y given a value of x. A regression line predicts the value of y for a given value of x. A regression line is discovered through regression analysis. When the explanatory variable changes, the regression line shows how much and in which direction the response variable changes.

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Answer:

5,400

Step-by-step explanation:

do the exponent which is 10x10=100 then add it to 5,300

Answer:

Step-by-step explanation:Given the variable n

we have to write the expression of variable n adding with 5 then multiply the product by 4 then subtract 7 from the result

add variable n with 5 is (n+5)

multiply the result by 4 is (n+5)

subtract 7 from the result is ((n+5))-7

So the expression is ((n+5))-7

Answer:

Step-by-step explanation:

Triangle MLK

Answer:

6x-18 is the simplest that it can go. brainliest plsss

The quotient is n^2+5n-5 and the remainder is 9. The solution has been obtained by using the synthetic division.

What is synthetic division?

Synthetic division is typically used to identify the zeroes of polynomials and is described as "a simplified method of dividing a polynomial with another polynomial equation of degree 1."

We are given the expression as (n^3+3n^2-15n+19)

The expression is to be divided by (n-2)

So, by using the synthetic division, we get

2 |  1     3     -15      19    

     -     2      10     -10        

     1     5      -5       9    

Quotient =  n^2+5n-5

Remainder = 9

Hence, the quotient is n^2+5n-5 and the remainder is 9.

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\(ax^2+bx+c=a(x-x_1)(x-x_2)=>\\\text{Ans:} (x-3)(x+2)\)

Based on the definition of supplementary angles and properties for algebraic handling, we conclude that the measure of angle 6 is equal to 108°.

According to the Euclidean geometry, a line crossed by a non-parallel line generates four pairs of supplementary angles. Two angles are supplementary if and only if the angles are adjacent to each other and the sum of their measures is equal to 180°.

Then, we know that the mathematical model is m ∠ 6 + m ∠ 7 = 180° = 72° + m ∠ 7 = 180°. Thus, m ∠ 7 = 108°. Based on the definition of supplementary angles and properties for algebraic handling, we conclude that the measure of angle 6 in the system generated by two non-parallel lines is equal to 108°.

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Answer:

blank #1 is $588.00

blank #2 is approximately 870 bananas

Answer:

The range of this set of numbers is 9

Step-by-step explanation:

The range is the greatest number subtracted by the lowest number

in this problem that is 21-12

Answer:

9

Step-by-step explanation:

range = highest number in a set minus the lowest number in a set, in your case:

21 - 12 = 9

The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.

The ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.

12⅝ = 101/8 = 12.645

12.62 = 12.62

√146 = 12.0830

12.39 = 12.39

12¾ = 51/4 = 12.75

Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.

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The area of the actual plot of land, in acres is given by 320000 acres.

Here given the figure is a Trapezium.

We know that the area of the Trapezium with parallel sides of length ' a ' and ' b ' and height between them is ' d ' is given by = (1/2)*(1 + b)*d

We know that, 1 cm = 2 miles.

So, 10 cm = 20 miles

15 cm = 15*2 = 30 miles

Here in given trapezium the length of parallel sides are 10 cm and 15 cm. that is 20 miles and 30 miles respectively.

Height between them is = 10 cm = 20 miles.

So the area of the land is = (1/2)*(20 + 30)*20 = 50*10 = 500 square miles.

we know that 1 square miles = 640 acres

So the area in acres = 500*640 = 320000 acres.

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The question is incomplete. The complete question will be -

"The figure shown represents a plot of land and is drawn using a scale in which 1 cm equals 2 miles. one square mile is 640 acres. how large is the actual plot of land, in acres?"

The division of the polynomials will be x² + xy + y².

It should be noted that a polynomial simply means an expression that is composed of variables that are combined by using the mathematical operations. Polynomials are the sums of terms of the form k⋅xⁿ, where k is the number and n is a positive integer. An example, 3x+2x-5 is a polynomial

It should be noted that the polynomial given is:

= (x³ + y³)/(x + y)

= [(x - y)(x² + xy + y²) / (x - y)]

= x² + xy + y².

Therefore, the division of the polynomials will be x² + xy + y².

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The sketch answers to question 8, 9 and 10 is given in the image attached.

A link is known to be intersecting if two or more lines are said to have cross one another in a given plane.

Note that the intersecting lines are known to be one that often share a common point, and it is one that can be seen on all the intersecting lines, and it is known to be the point of intersection.

Looking at the image attached, you can see how plane A and line c intersecting at all points on line c and also GM and GH and line CD and plane X as they are not intersecting

Therefore, The sketch answers to question 8, 9 and 10 is given in the image attached.

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See attachment for math work.

The scale factor for two hexagonal prisms is obtained as 5.20 : 1.

What is scale factor?

The scale factor of a shape refers to the amount by which it is increased or shrunk. It is applied when a 2D shape, such as a circle, triangle, square, or rectangle, needs to be made larger.

Since the two figures are similar, their corresponding lengths, widths, and heights are proportional.

Therefore, the scale factor between them is the ratio of any corresponding lengths.

One possible choice is to use the height of the two hexagonal prisms as the corresponding length.

Let h1 be the height of the first hexagonal prism, and h2 be the height of the second hexagonal prism.

Then we have -

scale factor = h2 / h1

To find the heights, we can use the formula for the volume of a hexagonal prism -

V = (3√3 / 2) × (base area) × height

For the first hexagonal prism, we are given that V = 432 yd³.

We can solve for the base area by rearranging the formula -

base area = (2/3√3) × (V / height)

Plugging in the values, we get -

base area = (2/3√3) × (432 / h1)

base area = 96 / h1√3

For the second hexagonal prism, we are given that V = 11664 yd³.

Again, we can solve for the base area -

base area = (2/3√3) × (V / height)

base area = 2592 / h2√3

Since the two hexagonal prisms are similar, their base areas are proportional.

Therefore, we can set up a proportion -

base area of first hexagonal prism / base area of second hexagonal prism = scale factor²

(96 / h1√3) / (2592 / h2√3) = scale factor²

Simplifying the fraction, we get -

scale factor² = (1/27) × (h2 / h1)

But we know that V1 / V2 = (h1 / h2)^2, since the volumes are proportional to the cube of the height.

So we can substitute V1 = 432 and V2 = 11664 -

432 / 11664 = (h1 / h2)²

h1 / h2 = √(432 / 11664) = √(1/27) = 1 / 3√3

Plugging this into the formula for the scale factor, we get -

scale factor = h2 / h1 = 3√3 / 1 = 3√3

Therefore, the scale factor of the figure on the left to the figure on the right is 3√3 : 1, or in decimal form approximately 5.20 : 1.

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Answer:

14

Step-by-step explanation:

12 / 2 = 6

Diego scored 6 points

6 + 8 = 14

Andre scored 14 points

Answer:

There are 84 senior professors who attended the lecture.

Step-by-step explanation:

There were 95 people in the auditorium, and 11 of them were not senior professors. In order to find the number of senior professors, we have to subtract those 11 non-professors from the 95 people in the room, which equals 84 senior professors.

Answer:

4x+20

Step-by-step explanation:

Bottom length is:

x

Second length is:

2x+8

Last length is:

x+12

Perimeter is adding up all of these lengths:

x+2x+8+x+12:

Simplify:

4x+20

Answer:

(-3, 7)

Step-by-step explanation:

ok so first take the square root of both sides, so you get (x-2)=5, since the square root gets rid of the power, and the square root of 25, is 5, and since we did a square root, we also have to do the - + thing, so the equation really is now x-2=(+-)5

subtract 2 from both sides, and you get x=(+-)5+2

Solving for x we get -5+2=-3

and also

5+2=7 since there was a positive, and a negative 5.

therefore x would equal (-3, 7)

hope this helps, please mark as brainliest.

The true statements about the parabola include the following:

B. The equation (x - 4)² + (y - 3)² = (y - 1)² represents this parabola.

C. The point (2, 3) is on the parabola.

D. The point (8, 6) is the same distance from the point (4, 3) as it is from the line y = 1.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the focus (4, 2), we would determine the distance where this point (8, 6) lies on the parabola:

y = a(x - h)² + 2

6 = a(8 - 4)² + 2

6 = a(4)² + 2

6 = 16a + 2

16a = 6 - 2

16a = 4

a = 4/16

a = 1/4.

Therefore, the required quadratic function in vertex form is given by:

y = a(x - h)² + k

y = 1/4(x - 4)² + 2

When x = 2, we have:

y = 1/4(2 - 4)² + 2

y = 1/4(-2)² + 2

y = 1/4(4) + 2

y = 1 + 2

y = 3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

For a 99 percent confidence interval with a large sample size and a known population standard deviation, the critical value of 2.33 is commonly used.

When constructing a confidence interval, the critical value is determined based on the desired confidence level and the distribution of the sample data. For a 99 percent confidence interval, the critical value to use depends on the specific distribution being considered.

If the sample size is large (typically n ≥ 30) and the population standard deviation is known, the critical value to use for a 99 percent confidence interval is 2.33. This value corresponds to the standard normal distribution (z-distribution) and captures 99 percent of the area under the curve within the confidence interval.

It's important to note that the critical value may vary depending on the confidence level and the assumptions made about the population distribution. However, for a 99 percent confidence interval with a large sample size and a known population standard deviation, the critical value of 2.33 is commonly used.

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The correct option is A. (4, 11) and (0, 7).

The solution of the equations y = x + 7 and y = x² – 3x + 7, the solutions are located at points: (4, 11) and (0, 7).

Estimate the y-intercept, slope, and express the equation in the form of the y-intercept (y = mx + b) to find the graphed equation. The slope is the difference between the y- and x-axis values.

A graph equation is an equation in graph theory where the unknown is a graph. Isomorphic ideas are one of the key issues in graph theory.

The equations are; y = x + 7 and y = x² - 3x + 7

At the solution, the u-values are equal, which gives;

y = y

x + 7 = x² - 3·x + 7

x² - 3·x + 7 - (x + 7) = 0

x² - 4·x = 0

x·(x - 4) = 0

x = 4, or x = 0

When x = 4, y = 4 + 7 = 11

When x = 0,

         y = 0 + 7 = 7

Therefore, the solution for the equations  y = x + 7 and y = x² - 3x + 7 are are located at points: (4, 11) and (0, 7).

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The complete question is-

Based on the graphs of the equations y = x + 7 and y = x² – 3x + 7, the solutions are located at points:

A. (4, 11) and (0, 7)

B. (4, 11) and (–7, 0)

C. (–7, 0) and (1.5, 4.75)

D. (1.5, 4.75) and (0, 7)

Answer:

136

Step-by-step explanation:

Bc i took the flvs test and got it right

The triangle ΔXAC formed by the angle bisectors is an isosceles triangle

The measure of m∠CXA is the option;

136°

Reason:

The given parameters are;

ΔABC = An isosceles triangle

BF, AD, and CE = Angle bisectors, intersect at X

m∠BCA = 44°

m∠XCF = m∠XCD Angles formed by angle bisector CE

We have;

m∠BCA = 44° = m∠XCF + m∠XCD; by angle addition Postulate

∴ 44° = m∠XCF + m∠XCF; by substitution property of equality

44° = 2 × m∠XCF

m∠EAF = m∠XAF + m∠XAE

m∠XAF = m∠XAE;  Angles formed by angle bisector AD

∴ m∠EAF = m∠XAF + m∠XAF

m∠EAF = 2 × m∠XAF

m∠EAF  = 44°; by base angles of isosceles triangle

m∠CXA + m∠XCF + m∠XAF = 180° Angle sum property of a triangle

m∠CXA = 180° - (m∠XCF + m∠XAF )

Which gives;

m∠CXA = 180° - (22° + 22°) = 136°

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By examining the dotplot, you can see the frequency and distribution of the miles run by Roger. For example, there are 4 instances where Roger ran 0.5 miles, 3 instances where he ran 4 miles, and so on.

The dotplot that displays the data correctly is the one titled "Roger's Training" with a number line labeled "Miles Run" that goes from 0.5 to 5 in increments of 0.5. The dotplot should have the following data points:
0.5, 4
1, 1
1.5, 2
2, 2
2.5, 3
3, 2
3.5, 0
4, 3
4.5, 2
5, 1
This dotplot accurately represents the number of miles Roger ran each day over a 20-day period. Each dot represents a data point from the given list of miles run. The number line indicates the range of miles run, starting from 0.5 and ending at 5, with increments of 0.5.
By examining the dotplot, you can see the frequency and distribution of the miles run by Roger. For example, there are 4 instances where Roger ran 0.5 miles, 3 instances where he ran 4 miles, and so on. This visual representation allows you to easily interpret the data and observe any patterns or trends in Roger's training.

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Hello!

\(\boxed{ \bf The~value~of~the~expression~is~2.}\)

__________________________________________________

We can solve this expression using the order of operations.

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

(In some places it might be called BEDMAS).

(9-3)+4(6-7)

Start by solving the brackets (parentheses).

6 + 4(-1)

Next, we must multiply 4 by -1.

6 + (-4)

This can be written as:

6 - 4

= 2

I think you meant to put 2 instead of 20 in the options.