What type of angles are 3 and 6



A. Alternate interior angles

B. Alternate exterior angles

C. Supplementary angles

D. Vertical angles

Therefore, the area of the quarter circle of radius 8 cm is 16π square centimeters (or approximately 50.2655 square centimeters if we use a decimal approximation for π).

A circle is a two-dimensional shape that is defined as the set of all points that are a fixed distance (called the radius) from a central point (called the center) in a plane. It is one of the most basic geometric shapes and is often used in a variety of mathematical and scientific contexts. One important thing to note about circles is that they are symmetrical: any line passing through the center of a circle divides the circle into two halves that are mirror images of each other. Circles are commonly used in a variety of contexts, including geometry, trigonometry, physics, engineering, and many other fields. They are also used in everyday life, such as in the design of wheels and other circular objects, the calculation of the areas of circular fields or gardens, and the measurement of circular objects like plates and bowls.

Here,

The formula for the area of a quarter circle is given by:

A = (1/4)πr²

where A is the area of the quarter circle, r is the radius of the circle, and π is the mathematical constant pi (approximately 3.14159).

In this case, the radius of the quarter circle is 8 cm, so we can substitute this value into the formula and simplify as follows:

A = (1/4)π(8 cm)²

A = (1/4)π(64 cm²)

A = 16π cm²

To know more about circle,

https://brainly.com/question/27802544

#SPJ1

Answer: 176 free throws

Step-by-step explanation: 4/5 = 80% 80% of 220 = 176

Since the zeroes are 1/3 which has multiplicity 2, -4 and i, then

The factors of the polynomial are

Multiply the 3 factors

Multiply The first 2 brackets

Add the like terms in the 1st bracket

Multiply the 2 brackets

Add the like terms

Since the leading coefficient is 63, multiply all terms by 7

option c is correct that if the two events are mutually exclusive than they cannot be independent.

As, we know that "mutually exclusive events are those events that do not occur at the same time".

Mutually exclusive events do not share any sample points with each other, so they cannot occur at same time. Thus, if event A and event B are mutually exclusive, they are actually inextricably dependent on each other because A's existence reduces event B's probability to zero and vice-versa.

Therefore, two events with nonzero probabilities cannot be independent and mutually exclusive because if two events are mutually​ exclusive, then when one of them​ occurs, the probability of the other must be zero.

Hence, option c is correct that if the two events are mutually exclusive than they cannot be independent.

Find out more information about mutually exclusive events here:

https://brainly.com/question/17136647

#SPJ4

Given data:

The first equation is 2x+3y=-12.

The second equation is x+y=9.

The second equation can be written as,

y=9-x

Substitute the above value in second equation.

2x+3(9-x)=-12

2x+27-3x=-12

-x=-39

x=39

The value of y is,

39+y=9

y=-30.

Thus, the value of x is 39, and the value of y is -30.

Answer: You multiply the probability of each "event" -- the selection of the desired number, by the probabilities of the other events.

Step-by-step explanation:

The probability of getting 1 as the first number is 1/5 (possibilities are 1,2,3,4,5)

The probability of getting 2 as the second number is 1/4 (possibilities are 2,3,4,5. 1 is gone)

The probability of getting 3 as the third number is 1/3 (possibilities are 3,4,5. 1 and 2 are gone)

So you multiply 1/5 × 1/4 × 1/3

Answer:

\(x=1, x=3, x=7\)

Step-by-step explanation:

Start multiplying and adding all together. You get\(x^3-11x^2+31x-21 =0\).

At this point we're stuck factoring since there exist a formula for the roots, but it's nowhere easy to remember. We start writing down The List (rational root theorem: it's the divisor of the constant term divided by the divisor of the lead coefficent, with a plus or minus, in our case it's \(\pm1, \pm3, \pm7, \pm 21\)) and let's try checking one by one.

Value \(+1\) gives a zero on the LHS, it means the polynomial is divisible by \((x-1)\). By doing the division, or writing it as \((x-1)(ax^2+bx+c) = x^3-11x^2+31x-21\), multiplying on the LHS and then finding the values of a, b, and c (easiest for me, your mileage may vary) we can write our expression, finally, as

\((x-1)(x^2-10x+21) =0\) At this point you can either apply the quadratic formula or decompose again the second factor as

\((x-3)(x-7)\) by finding two numbers whose sum is -10 and product is 21, ie -3 and -7. At this point the expression

\((x-1)(x-3)(x-7)=0\) is true if \(x=1, x=3, x=7\)

Answer:

32 pages per hour

Step-by-step explanation:

Answer:

Step-by-step explanation:

ΔABC ≅ ΔDEF

The length AB = 28 and the length of DE = 7. Since these are corresponding sides, we know that DEF= 1/4 (ΔABC)

So, since ΔABC = 160, we know that ΔDEF will be 1/4 of that, meaning that ΔDEF is 40.

ΔDEF = 40cm²

Answer:

10 cm2

Step-by-step explanation:

The ratio per side is 28/7 = 4

When two similar figures have a ratio of 4:1, the difference between their areas is:

\((4)^{2} :(1)^{2}\)

\(16:1\)

That is, the dimension of the area of the largest figure is 16 times larger than the smallest figure.

So for this case:

the area of the larger figure is

ΔABC = 160 sq.cm

Then the area of the minor figure is:

ΔDEF= 160/16 = 10 sq.cm

Hope this helps

The ratio of Jay’s age to Kiaria’s age to Martha’s age is 1/2

Algebraic expressions are simply defined as expressions made up of mathematical operations such as addition, subtraction, multiplication, division, bracket, parenthesis, etc.

These expressions are also made up of variables, terms, coefficients, constants, as well as factors.

From the information given, we have that;

Let Jays age be x

The expression is written as;

Kiaria age = 7 + x

Marthas age = 2( 7 + x) = 14 + 2x

Total of their ages = 77

Jay + Kiaria + Martha = 77

Substitute the values

x + 7 + x + 14 + 2x = 77

collect like terms

4x = 77 - 21

subtract like terms

4x = 56

Make x the subject

x = 56/ 4

x = 14

Ratio of their ages = 7 + x : 14 + 2x

= 7 + 14 : 14 + 28

= 21 : 42

= 1/ 2

Thus, the ratio of Jay’s age to Kiaria’s age to Martha’s age is 1/2

Learn more about algebraic expressions here:

https://brainly.com/question/4344214

#SPJ1

Answer:

try to see the rules for this question and you will get answer

have a nice day  

Step-by-step explanation:

a) Two equivalent expressions to model the purchase made by Mrs. Singh, who bought 9 folders and 9 notebooks at the cost of each folder $2.50 and each notebook $4.00 respectively, are:

b) The total cost of the purchase by Mrs. Singh is $58.50.

Algebraic expressions involve the combination of variables, numbers, constants, and values using mathematical operands (addition, subtraction, division, and multiplication).

The unit cost of folders = $2.50

The unit cost of notebooks = $4.00

The number of folders bought = 9

The number of notebooks bought = 9

Let the number of folders bought = x

Let the number of notebooks bought = y

Folders: 2.50x

Notebooks: 4.00y

Folders: 2.50x = $22.50 ($2.50 x 9)

Notebooks: 4.00y = $36.00 ($4 x 9)

Total costs = $58.50

Learn more about algebraic expressions at https://brainly.com/question/4344214.

#SPJ1

The length of LN in the triangle below is (LN)²=33²-11². It is obtained by applying the pythogorous theorem in the triangle MLN. Option A is correct,

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.

According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.

In triangle MLN applies the pythogorous theorem;

\(\rm h^2=p^2+b^2 \\\\ MN^2=ML^2+LN^2 \\\\ 33^2=11^2+LN^2 \\\\ LN^2=33^2-11^2\)

Hence option A is correct.

To learn more about right-angle triangles, refer to https://brainly.com/question/3770177.

#SPJ1

Answer:

There are 16 notes of 20 paise's and 12 notes of 5 paise's.

Explanation:

The amount of notes for of 20 paise and 5 paise coins are not given.

So let there be x 20 paise's coins and y 5 paise's coins.

Equation buildup:

20x + 5y = 380 ___eq 1

20y + 5x = 380 - 60

20y + 5x= 320 ___ eq 2

Make x the subject for both:

1st

\(\rightarrow \sf 20x + 5y = 380\)

\(\rightarrow \sf 20x = 380-5y\)

\(\rightarrow \sf x = 19-0.25y\)

2nd

\(\sf \rightarrow 20y + 5x = 320\)

\(\sf \rightarrow 5x = 320-20y\)

\(\sf \rightarrow x= 64-4y\)

Solve them simultaneously:

\(\sf \rightarrow 64-4y =19 - 0.25y\)

\(\sf \rightarrow -4y+0.25y =19 -64\)

\(\sf \rightarrow -3.75y =-45\)

\(\sf \rightarrow y =12\)

Find x:

\(\sf \rightarrow x = 64-4y\)

\(\sf \rightarrow x = 64-4(12)\)

\(\sf \rightarrow x = 16\)

Answer:

150

Step-by-step explanation:

Knowing that a cube has 6 faces which all are equal.

Thus, Multiply the area of one face by the number of faces to get the total surface area of the cube.

Since, it given that one face is 5 cm

Then, we also must know the formula for area of a cube

Which is:

\(Area=6a^2\)

Thus,

\(Area=6a^2\)

\(Area=6(5)^2\)

\(Area=6(25)\)

\(Area=150\)

Kavinsky

The expected value of a player's winnings on each roll is equal to: D. $30.00

In order to determine the expected value of a player's winnings on each roll, we would list all of the outcomes that are associated with rolling a fair six-sided die.

By rolling a fair six-sided die, we would obtain the following outcomes:

Outcomes = 1, 2, 3, 4, 5, and 6.

Generally speaking, there are only two (2) numbers that are multiples of three (3) in a fair six-sided die and these include the following:

Multiples of three (3) = 3 and 6

When a player rolls a three (3), the player's possible winning is giving by:

Player's winning = 3 × 20 = $60

When a player rolls a three (3), the player's possible winning is giving by:

Player's winning = 6 × 20 = $120

Total winnings = $60 + $120

Total winnings = $180

Now, we can determine the expected value of a player's winnings on each roll:

Expected value = 1/6 × 180

Expected value = $30.

Read more on expected value here: https://brainly.com/question/10675141

#SPJ1

Complete Question:

A game involves rolling a fair six-sided die. If the number facing upward on the die is a whole number multiple of three, the player wins an amount equal to the number on the die times $20. If the number is not a multiple of three, the player gets nothing. What is the expected value of a player's winnings on each roll?

A. $3.33

B. $6.66

C. $8.50

D. $30.00

E. $40.00

The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.

In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.

Given:

The following steps can be used in order to determine the measure of angle a:

Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.

Step 2 - Apply the sum of interior angle property on triangle PQR.

\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)

\(\angle\text{Q}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-60\)

\(\angle\text{R}=60^\circ\)

Step 3 - Now, apply the sum of interior angle property on triangle PSR.

\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)

\(\angle\text{S}+2\angle\text{R}=180\)

\(2\angle\text{R}=180-90\)

\(\angle\text{R}=45^\circ\)

Step 4 - Now, the measure of angle a is calculated as:

\(\angle\text{a}=60-45\)

\(\angle\text{a}=15\)

The measure of angle a is 15 degrees.

For more information on interior angles, refer to the link given below:

https://brainly.com/question/28795639

The conclusion that is correct in a two-tailed test at α = .05 is There appears to be no difference in the mean occupancy rates.

From the given values:

Thus, the P-value = 0.1791

Interpret results. Since the P-value (0.1791) is greater than the significance level (0.05), we failed to reject the null hypothesis.

From the above test, we do not have sufficient evidence in favor of the claim that there is a difference in the mean occupancy rates.

Thus, option A is correct.

Read more about two-tailed test here:

https://brainly.com/question/4621112

#SPJ1

Answer:

The line with a slope of 1/2 is steeper

Step-by-step explanation:

Here, we want to get which slope is steeper

mathematically, when we want to know the line that has a steeper slope, we compare the value of the slopes

The line with a slope that is of greater value will be steeper

Mathematically, 1/2 is a greater number than 1/3

That simply means 1/3 is less steep and thus, the line with the slope of 1/2 is the steeper line

Organic foods in local stores are typically more expensive than conventional foods. The table compares recent organic and conventional prices per pound for carrots and apples. Using the table, we can determine whether the organic prices vary directly with the conventional prices.

According to the data in the table, it can be noticed that the organic prices do vary directly with the conventional prices because the ratios of organic price per pound to conventional price per pound are constant. Therefore, we can say that the organic prices vary directly with the conventional prices. We can identify k by using the carrot data which is $1.51 per pound and $0.77 per pound.1.51/0.77 = 1.962 k = 1.962Therefore, k = 1.962 does vary directly with the conventional prices. We can also determine if the total cost of organic apples varies directly with the number of pounds of organic apples purchased. If they do, we can identify k. According to the data in the table, we can say that the total cost of organic apples varies directly with the number of pounds of organic apples purchased because the ratios of total cost to the number of pounds are constant.

To know more about conventional visit:

https://brainly.com/question/20973924?referrer=searchResults

#SPJ11

Answer:

7

Step-by-step explanation:

because you take the 6 and the 9 and you see how far apart from each pother that would be 3 so the you add that to the 4 and you get 7.   :)

Answer:

h = 8 inches

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the height )

given A = 24 and b = 6 , then

\(\frac{1}{2}\) × 6 × h = 24 , that is

3h = 24 ( divide both sides by 3 )

h = 8 inches

Answer

$27

Step-by-step explanation:

36/4=9, 9x3=27

Answer:

48

Step-by-step explanation:

Khadija would have to pay $27.8 (7.5 x 4 - 1.7) to buy 4 pounds of apples.

Cost the monitorial associated with the purchase of production of food or service if can include the prices of materials of which is over it and other expenses that are related to the production of the good of service cost is a major fraction when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.

The expression for the cost to buy  x  pounds of apples is: 7.5x - 1.7, where x represents the number of pounds of apples purchased. For example, if Khadija wanted to buy 3 pounds of apples, the cost would be calculated by 7.5x - 1.7, which is equal to 22.6 dollars.

To know more about cost click-
https://brainly.com/question/25109150
#SPJ1

Answer:(x,y)=(1/3 , 4/3)

Step-by-step explanation:

From the given information provided, the percent of apartments in the building that are small is 85%.

If the ratio of small apartments to regular apartments is 17 to 3, this means that for every 17 small apartments, there are 3 regular apartments.

We can think of the total number of apartments in the building as a multiple of the ratio 17:3. Let's call this multiple "x". Then, the total number of small apartments would be 17x, and the total number of regular apartments would be 3x.

The percentage of apartments in the building that are small can be calculated as follows:

percentage of small apartments = (total number of small apartments / total number of apartments) x 100%

= (17x / (17x + 3x)) x 100%

= (17x / 20x) x 100%

= 85%

Learn more about percentage here: brainly.com/question/843074

#SPJ4

The RHS congruency criterion showed ABD ≅ DCA.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

The diameters of a circle with an O-centered center are AOC and BOD.

To Locate:

By RHS, ABD and DCA are congruent.

Solution:

The fact that AOC and BOD are a circle's diameters is a given.

BD = CA (circle circumferences)

"BAD = CDA" [90° angles in semicircle]

AD = AD (shared by both triangles)

[Using RHS congruence criterion] ABD ≅ DCA

As a result, the RHS congruency criterion showed ABD ≅ DCA.

To learn more about congruency from given link

https://brainly.com/question/385

#SPJ9

Answer:

(x + 3)(5x + 2)

Step-by-step explanation:

\(5 {x}^{2} + 17x + 6 \\ = 5 {x}^{2} + 15x + 2x + 6 \\ = 5x(x + 3) + 2(x + 3) \\ = \huge \red{ \boxed{ (x + 3)(5x + 2) }} \\ \)

The evaluation of P10–Focus 1 indicates that we get by using the equation for the volume of a cuboid and by calculus;

(a) \(L = 4\times x + 4\times 2\cdot x + 4\times \frac{81}{2\cdot x} =12\cdot x + \frac{162}{x^2}\)

(b) \(L_{min}\) = 54 cm

(c) L'' at x = 3, (where \(L_{min}\) = 54 cm) is positive, therefore, x = 3 is a minimum point

P10-Focus2

The area = \(2\times x \times y+\frac{\pi\cdot x^2}{4} =4\), therefore, \(y = \frac{16- \pi \cdot x^2}{8 \cdot x}\)

The minimum point, which is an extremum point is a point where the derivative of the function is 0.

(a) The length of the cuboid = 2·x

The width of the cuboid = x

The volume of the cuboid = 81 cubic centimeters

The thickness of the cuboid is therefore;

Thickness = 81/(2·x × x) = 81/(2·x²)

The sum of the length of the twelve edges, L, is therefore;

\(L=x + x + x + x + x + 2\cdot x + 2 \cdot x + 2 \cdot x + 2\cdot x + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2} + \frac{81}{2 \cdot x^2}\)

Therefore;

\(L=4\times x + 4\times 2\cdot x + 4\times \frac{81}{2 \cdot x^2} =12\cdot x + \frac{162}{x^2}\)

The sum of the lengths of the twelve edges, L, is \(L = 12\cdot x + \frac{162}{x^2}\)

(b) The minimum value of L can be found using calculus by finding the point at which dL/dx = 0 as follows;

\(\frac{dL}{dx} = 12 - \frac{324}{x^3} =0\)

Therefore;

\(12-\frac{324}{x^3}=0\)

\(12 = \frac{324}{x^3}\)

x³ = 324 ÷ 12 = 27

x = ∛(27) = 3

x = 3

The minimum value of L can be obtained when x = 3 as follows;

\(L = 12\cdot x + \frac{162}{x^2}\)

\(L_{min} = 12\times 3 + \frac{162}{3^2} = 54\)

The \(L_{min}\) = 54

The minimum value of L is 54 centimeters

(c) The value of the minimum value of L can be confirmed by further differentiation using the second derivative, L'' as follows;

At the x-value of a minimum point of a function, the value of the further derivative is larger than zero

The further derivative of the specified function is found as follows;

\(L'' = \frac{dL'}{dx} =\frac{972}{x^4}\)

At the critical number, x = 3, from the first derivative, we get;

\(L'' = \frac{972}{3^4} = 12 > 0\)

The value of the further derivative of the function at the point x = 3, is L'' = 12 > 0, therefore the point x = 3 is a relative minimum.

(b) The radius of the quarter circle = x

The area of the figure = 4 m²

The sum of the area of the composite figures are;

\(A = 2 \times x \times y + \frac{\pi \cdot x^2}{4} = 4\)

Therefore;

\(y =\frac{\left(4 - \pi \cdot \frac{x^2}{4}\right)}{2\cdot x} = 16 - \frac{\pi \cdot x^2}{8\cdot x}\)

Rearranging the right hand side expression as a fraction, we get;

\(y = \frac{16-\pi \cdot x^2}{8\cdot x}\)

Learn more about calculus differentiation here:

https://brainly.com/question/20341047

#SPJ1