a circumfrence of 10. it has an arc of the length 9/2. what is the central angle of the arc,in degrees/

[tex](\stackrel{x_1}{-15}~,~\stackrel{y_1}{-10})\qquad (\stackrel{x_2}{-20}~,~\stackrel{y_2}{-12}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-12}-\stackrel{y1}{(-10)}}}{\underset{\textit{\large run}} {\underset{x_2}{-20}-\underset{x_1}{(-15)}}} \implies \cfrac{-12 +10}{-20 +15} \implies \cfrac{ -2 }{ -5 } \implies {\Large \begin{array}{llll} \cfrac{2 }{ 5 } \end{array}}[/tex]

Answer: The slope is -2/5

Step-by-step explanation:

Answer:

d,e,f,g,h

Step-by-step explanation:

all those are function  bc the x value doesn't repeat meaning  the x value has only one y-value

The unknown values are ∠ACE = 64.5°, ∠PRQ = 90°, ∠AOC = 40° and  ∠a = 50° along with question no. 2, ∠B = 105°, all solved using angle sum property.

When three line segments intersect at three different angles, the result is a figure known as an Angle Sum Triangle. Triangles always contain a total of 180 degrees of angles.

Any triangle's angles add up to 180 degrees, according to the Angle Sum Triangle Theorem. By applying fundamental geometry concepts, this theorem can be demonstrated. Obtuse, right, or acute angles can all be found in triangles.

Triangle-related issues can be resolved using the Angle Sum Triangle theorem, a crucial geometry theorem. It can be used to gauge a triangle's angle sizes or to establish whether it is acute, right, or obtuse.

A)

∠ABC =∠BCA

∠BAC + ∠ABC + ∠BCA = 180

55 + 2∠ABC =

2∠ABC = 180 - 55

2∠ABC = 125

∠ABC =∠BCA = 75.5

100 + 2∠ECD =  180

∠ECD = 40

∠ACE = 180 - 75.5+40

∠ACE = 64.5°

B) ∠PRQ = 90°  any triangles one side crosses through centre then the opposite angle is 90°.

C) ∠AOC = 40° when inside a circle, the angle on centre is double the angle touching the circumference

D) ∠a = 360 - 90 + (180-60) + (180-80)

∠a = 50°

2. The value of angle be can be calculated using angle sum property of triangle i.e.

(x+5) + 3x + x = 180

5x + 5 = 180

5x = 175

x = 175/5

x = 35

∠B = 3(35)

∠B = 105°

Thus, the unknown values are ∠ACE = 64.5°, ∠PRQ = 90°, ∠AOC = 40° and  ∠a = 50° along with question no. 2, ∠B = 105°.

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The price of the carpet per square meter is $32.13. It will cost $1,556.86 to carpet an area of 1475 square feet.

1. To find the price of the carpet per square meter, first convert $28.99 per square yard to meters.

1 yard = 0.9144 meters

$28.99 per yard x (1 meter/ 0.9144 meters) = $32.13 per square meter

2. To find the cost of carpeting an area of 1475 square feet, first convert 1475 square feet to square yards.

1 square foot = 0.11111 square yards

1475 square feet x (1 square yard/ 0.11111 square yards) = 13,333.33 square yards

3. Multiply the cost per square yard by the number of square yards needed to carpet the area.

$28.99 per square yard x 13,333.33 square yards = $1,556.86

The complete question is:

a carpet sells for $28.99 a square yard. what is the price of the carpet per square meter? how much will it cost to carpet an area of 1475 square feet? 1 yard is equal to 0.9144 meters

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The value of a is 2

We can use the slope-intercept form of a line, y = MX + b, to find the equation of the line.

The slope (m) of the line can be found using the following formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

So, m = (5 - (-5)) / (4 - (-1)) = 10/5 = 2

Now, we can use the point-slope form of a line, y-y1 = m(x-x1)

where (x1,y1) is any point on the line and m is the slope of the line.

In this case, we will use the point (x1, y1) = (–1, –5)

so, y-y1 = m(x-x1) = -5 - 2(-1-x) = -5-2+2x

Now we know that the point (a,1) is also on the line, we can substitute the value of x and y in the equation

so, 1 - (-5) = 2(a - (-1))

1 +5 = 2a+2

6 = 2a+2

4 = 2a

a = 2

Therefore, the value of a is 2.

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the distance between the tree and the flagpole is approximately 23.29 feet.

To find the distance between the tree and flagpole, we can use the Pythagorean theorem, which states that the square of the distance between the two points (the hypotenuse of the right triangle) is equal to the sum of the squares of the other two sides.

In this case, the distance between the tree and flagpole (the hypotenuse of the triangle) is equal to the square root of (20^2 + 12^2) = square root of (400 + 144) = square root of 544.

So the distance between the tree and the flagpole is approximately 23.29 feet.

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The equation that has 2 as its root is 2x² - 7x + 6 = 0 (option c)

Suppose we are given a quadratic function f(x) = ax² + bx + c, then x = q is a root if f(q) = 0.

Let's check for the given functions:

a.  x² - 4x + 5 = 0

f(2) =  2² - 4(2) + 5

f(2) = 4 - 8 + 5 = 1

Since f(2) ≠ 0, hence 2 is not its root.

b. x² + 3x - 12 = 0

f(2) = 2² + 3(2) - 12

f(2) = 4 + 6 - 12 = -2

Since f(2) ≠ 0, hence 2 is not its root.

c. 2x² - 7x + 6 = 0

f(2) = 2(2)² - 7(2)+ 6

f(2) = 2(4) - 14 + 6 = 0

Hence, x = 2 is its root.

d. 3x² - 6x - 2 = 0

f(2) = 3(2)² - 6(2) - 2

f(2) = 12 - 12 - 2 = -2

Since f(2) ≠ 0, hence 2 is not its root.

Hence, the correct option is   2x² - 7x + 6 = 0 (option c)

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The absolute value inequality for the hearing range of each animal is mod(e - 6008) ≤ 5992 and mod(m - 46000) ≤ 45000, respectively.

An absolute value equation has no solution if the absolute value expression equals a negative number since an absolute value can never be negative. You can write an absolute value inequality as a compound inequality. This holds true for all absolute value inequalities. You can replace > above with ≥ and < with ≤.

To solve absolute-value inequalities, first, we must drop the absolute-value bars and restate the inequality in one of two ways, depending on the case.

According to the question,

The elephant can hear: 16 ≤ e ≤ 12000

The avg hearing = (12000 + 16)/2 = 6008

Tolerance = 12000 - 6008 = 5992

Therefore, the value absolute value inequality for the hearing of the elephant is mod(e - 6008) ≤ 5992.

Similarly,

The mouse can hear: 1000 ≤ e ≤ 91000

The avg hearing = (12000 + 91000)/2 = 46000

Tolerance = 46000 - 1000 = 45000

Hence, the value absolute value inequality for the hearing of the mouse is mod(m - 46000) ≤ 45000.

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The anti-derivative of g(x) is G(x) = x3 + 3x2 and the anti-derivative of f(x) is F(x) = x2 + 2x.

Part a:

The value of the integral from 0 to 6 of f(x)dx is 16. This can be calculated using the Fundamental Theorem of Calculus (FTC) which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫f(x)dx = F(6) - F(0)

The anti-derivative of f(x) is F(x) = x2 + 2x, so the value of the integral is:

∫f(x)dx = (62 + 2*6) - (02 + 2*0) = 36 - 0 = 16.

Part b:

The value of the integral from 4 to 9 of g(x)dx is 20. This can be calculated using the FTC which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫g(x)dx = G(9) - G(4)

The anti-derivative of g(x) is G(x) = x3 + 3x2, so the value of the integral is:

∫g(x)dx = (93 + 3*9) - (43 + 3*4) = 729 - 168 = 20.

Part c:

The value of the integral from 4 to 9 of 2*g(x) - f(x)dx is 68. This can be calculated using the FTC which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫(2*g(x) - f(x))dx = 2*G(9) - F(9) - [2*G(4) - F(4)]

The anti-derivative of g(x) is G(x) = x3 + 3x2 and the anti-derivative of f(x) is F(x) = x2 + 2x, so the value of the integral is:

∫(2*g(x) - f(x))dx = (2*(93 + 3*9) - (92 + 2*9)) - [2*(43 + 3*4) - (42 + 2*4)]

= (1854 - 19) - (544 - 16) = 1735 - 528 = 68.

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Using Elimination method the simultaneous equations is -16/3.

Elimination is a mathematical technique that can be used to solve a system of three equations with three variables.

In standard form, without any fractions or decimals, write all the equations. Decide which one of the three variables you want to eliminate, then pick any two of the equations to do so.

The term "simultaneous equations" refers to two or more algebraic equations that share the same unknown variables and have the same answer. This suggests that the simultaneous equations have a single, solvable problem. For instance, 2x - 4y = 4, 5x + 8y = 3, are instances of simultaneous equations.

    10m-7n=26

  - 7m+7n=42​

    3m = -16

m = -16/3

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Dalton made 10 number of  decorations. Dalton made 10 decorations using 1/2 of a meter of ribbon, which he cut into equal pieces.

1. Dalton used 1/10 of a meter of ribbon for each decoration.

2. He got this by cutting 1/2 of a meter of ribbon into equal pieces.

3. 1/2 of a meter is equal to 5/10 of a meter.

4. If 1/10 of a meter is used for each decoration, then 5/10 of a meter can make 5 decorations.

5. Therefore, 10 decorations can be made.

Dalton made 10 number of decorations using 1/2 of a meter of ribbon, which he cut into equal pieces.

Dalton made 10 decorations for each of the dancers in his year-end dance performance. He used 1/10 of a meter of ribbon for each decoration which he got by cutting 1/2 of a meter of ribbon into equal pieces. This meant that he was able to get 10 decorations out of the 1/2 of a meter of ribbon, as 1/10 of a meter was used for each decoration. He was able to do this by dividing the 1/2 of a meter of ribbon evenly into 10 pieces.

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The gallons of blue paint he needs to make the green paint is 6 gallons.

This is a problem in ratios. Let's look into what we know.

Volume of green paint needed = 10 gallons

Parts of blue paint needed = 3

Parts of yellow paint needed = 2

Total number of parts = parts of blue paint + parts of yellow paint

                                    3 + 2 = 5

So fraction of blue paint needed = parts of blue paint / total parts

                                                       = 3/5

Volume of blue paint needed = [tex]\frac{3}{5}[/tex] × 10

                                                 = 6 gallons

Volume of yellow paint needed = [tex]\frac{2}{5}[/tex] ×10

                                                      = 4 gallons.

So we need 6 gallons of blue paint and 4 gallons of yellow paint to make 10 gallons of green paint.

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Answer:

18, 16, 22, 14, 17, 19, 15, 19, 22 add and divide by 9 = 17 feet

Step-by-step explanation:

It will take 5.01 years for Mantago to repay the money that he would borrow.

Assume that it will take 't' years for Mantago to repay the money that he would borrow.

Here, we use monthly cashflow formula:

[tex]C=P\times r\times \frac{(1+r)^{12t}}{(1+r)^{12t} - 1}[/tex]

where, P is loan amount

r is ARM(adjustable-rate mortgage) interest rate

C is monthly cashflow

here, R = 7.5%

So, r = 0.075

For monthly payment the interest rate would be r = 0.075/12

i.e., r = 0.00625

P = 10000

C = 200

We need to find the number of years t.

[tex]200=10000\times 0.00625\times \frac{(1+0.00625)^{12t}}{(1+0.00625)^{12t} - 1} \\\\200=62.5\times \frac{(1.00625)^{12t}}{(1.00625)^{12t} - 1}\\\\ \frac{(1.00625)^{12t}}{(1.00625)^{12t} - 1}=3.2\\\\(1.00625)^{12t}}=[(1.00625)^{12t} - 1]\times 3.2\\\\(1.00625)^{12t}-3.2(1.00625)^{12t}=-3.2\\\\-2.2(1.00625)^{12t}=-3.2\\\\(1.00625)^{12t}=1.4545[/tex]

[tex]12t=60.13\\\\t=5.01\\\\t \approx 5[/tex]

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Answer:

a) To find out how many pounds a 137 ounce baby weighs, we divide the weight in ounces by the number of ounces per pound.

137 ounces / 16 ounces/pound = 8.5625 pounds

Therefore, a 137 ounce baby weighs 8.5625 pounds.

b) To find out how much heavier the second baby is, we first convert the weight of the second baby from pounds to ounces.

We know there are 16 ounces in one pound, so we can multiply 9.375 (9 3/8) by 16 to find out how many ounces the second baby weighs.

9.375 * 16 = 150.4 ounces

Now we can subtract the weight of the first baby from the weight of the second baby to find out the difference in weight.

150.4 - 137 = 13.4 ounces

Therefore, the second baby is 13.4 ounces heavier than the first baby.

Answer:

270 donuts

Step-by-step explanation:

We need to find the number of donuts they make per hour. To find that, take the known number of donuts divided by the known number of hours.

150/10=15, so 15 donuts per hour.

Now, we multiply 18x15 and find they will have made 270 donuts.

Meter, kilogram and time units of measure.

Everything around us has a measurement value, from the amount of sugar you put in a cake to the size of a football field. Each thing is measured differently based on its length, weight, volume, or duration. With these measurements, the idea of "Metric System" is introduced.

The Metric system has 3 main units namely, meter to measure the length, kilogram to measure the mass, and seconds to measure time.

Therefore, meter, kilogram and time units of measure.

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The approximate profit can the company expect if it sells 400 pairs of shoes will be 28,400. Then the correct option is A.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The quadratic regression equation y = –0.1x² + 143.99x – 13,242.84 models expected company profits in terms of the number of pairs of shoes sold.

The profit can the company expect if it sells 400 pairs of shoes will be given as,

y = –0.1(400)² + 143.99(400) – 13,242.84

y = – 16,000 + 57,596 – 13,242.84

y = 28,354

y ≈ 28,400

The approximate profit can the company expect if it sells 400 pairs of shoes will be 28,400. Then the correct option is A.

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Answer:

mPR = (-3.5, 0.5)

mQR= (-1,-0.5)

Step-by-step explanation:

The fundamental theorem of algebra any polynomial was first proved by Carl Friedrich Gauss in 1799.

In 1799, Carl Friedrich Gauss was a German mathematician who proved that any polynomial equation with complex coefficients has at least one root in the complex plane. This is known today as the Fundamental Theorem of Algebra. Gauss started by examining a particular polynomial equation and then used his knowledge of the properties of polynomial functions to prove that any polynomial equation with complex coefficients must have at least one complex root. His proof used a combination of calculus and algebraic manipulations to establish that the coefficients of a polynomial equation must satisfy certain conditions in order for the equation to have a complex root. Once these conditions are satisfied, he showed that the equation must have at least one complex root.

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This question will require divergent thinking.

The other questions are convergent thinking questions because they require a single, correct answer. However, the question "What are the various uses of a coffee mug?" requires divergent thinking because there is no single, correct answer. Instead, this question requires the respondent to think creatively and come up with a variety of possible uses for a coffee mug.

The question “What are the various uses of a coffee mug?” requires divergent thinking as it requires creative thinking and the generation of a variety of possible uses for a coffee mug.

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The probability of a randomly chosen divisor of [tex]$11!$[/tex] being prime is [tex]$\frac{32}{3^{2}\cdot2^{10}} = \frac{1}{243}$[/tex].

The prime factorization of [tex]$11!$[/tex] is 11!=[tex]11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1$[/tex], so there are [tex]$(2+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1)(1+1) = (3^{2})(2^{10})$[/tex] divisors of  [tex]$11!$[/tex]

The prime divisors of  [tex]$11!$[/tex] are [tex]$2,3,5,7,11$[/tex], and there are [tex]$(1+1)(1+1)(1+1)(1+1)(1+1) = 2^{5} = 32$[/tex] divisors that are prime.

So the probability of a randomly chosen divisor of  [tex]$11!$[/tex] being prime is [tex]$\frac{32}{3^{2}\cdot2^{10}} = \frac{1}{243}$$[/tex]

A common fraction is a way of representing a ratio of two integers, where the numerator (the top part) represents the number of "favorable outcomes" and the denominator (the bottom part) represents the total number of possible outcomes.

In this case, the favorable outcome is a randomly chosen divisor of 11! being prime, and the total number of possible outcomes is the total number of divisors of 11! which is[tex]$(3^{2} )(2^{10})$[/tex]. So the probability of a randomly chosen divisor of 11! being prime can be represented as a common fraction by writing [tex]$\frac{32}{3^{2} \cdot2^{10}}$[/tex], with 32 as the numerator and [tex]$(3^{2})(2^{10})$[/tex] as the denominator.

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The fill ups are as follow.

1. vertical Opposite Angle.

2. alternate Interior Angle.

3. b || c, Co- interior angle.

4.  a || c, corresponding Angle.

5. Linear pair.

The fundamental characteristics listed below make it simple to recognise parallel lines.

Given:

First, <3 = <9 because they vertical Opposite Angle.

Second, <2 = <10 are equal because of alternate Interior Angle.

Third, If <9 and <8 are supplementary then line b || line c because they are Co- interior angle.

Fourth, if <11 = <7 then a || c because they corresponding Angle.

Fifth, < and <6 are supplementary because they are Linear pair of Angle.

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Answer:

The angle in radians is 4.6.

Note that it is expressed in radians, to convert it to degrees you need to multiply it by 180/π, but it is already rounded to the nearest 10th.

Step-by-step explanation:

To find the angle in radians to the nearest 10th, you need to use the relationship between the length of an arc, the radius of the circle, and the angle of the arc:

arc length = (angle in radians) * (radius)

In this case, the radius of the circle is 8.5 and the arc length is 38.9, so you can substitute these values into the equation:

38.9 = (angle in radians) * (8.5)

To solve for the angle in radians, you need to divide both sides of the equation by the radius:

angle in radians = 38.9 / 8.5

The angle in radians is 4.6.

Note that it is expressed in radians, to convert it to degrees you need to multiply it by 180/π, but it is already rounded to the nearest 10th.

The value of x is x = 25 and the measure of angle ∠2 = 60°

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

Let the transversal line be represented as t

Now , the measure of angles on a straight line = 180°

So , the measure of angle 1 + angle 2 = 180°

The measure of angle 1 = 5x - 5

The measure of angle 2 = 2x + 10

Substituting the values in the equation , we get

5x - 5 + 2x + 10 = 180°

7x + 5 = 180

Subtracting 5 on both sides of the equation , we get

7x = 175

Divide by 7 on both sides of the equation , we get

x = 25

Substitute the value of x in measure of angle 2 , we get

The measure of angle 2 = 2x + 10

The measure of angle 2 = 2 ( 25 ) + 10

The measure of angle 2 = 50 + 10

The measure of angle 2 = 60°

Hence , the measure of angle 2 is 60°

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On solving the provided question, we can say that a set's elements can be arranged in any sequence.

A mathematical representation of a variety of different things is called a set. Any type of mathematical object may be one of the elements or terms that make up a set. Symbols, numbers, lines, other geometric shapes, points in space, variables, and even other quantities. A proposition in mathematics is a structured group of items that can be expressed as a list or a proposition builder. Curly brackets are commonly used to identify sets. For instance, A = 1, 2, 3, 4 is a set. A set is essentially a group of items that are seen together. The items that make up a set are referred to as its members or elements. The components of a set may consist of any item, but for our purposes, they usually consist of mathematical objects like numbers, functions,

Set Representation

A capital letter indicates a set. For instance, consider sets A, B, N, etc.

Small letters are used to identify the components of a set. Each element is written using curly brackets and a comma in between.

Elements are not repeated in set notation.

A set's elements can be arranged in any sequence.

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