Which graph represents the solution of x2 + y2 < 25 and y2 <6x?

Answers

Answer 1

Answer:

The center of the circle is found at h,k

These values represent the important values for graphing and analyzing a circle.

Center: 0,0

And also,

Algebra Graph x^2+y^2=25 x2 + y2 = 25 x 2 + y 2 = 25 This is the form of a circle.

And also,

Simple and best practice solution for X2+y2=25 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework. If it's not what You are looking for type in the equation solver your own equation and let us solve it.

And also,

Match the values in this circle to those of the standard form. The variable r r represents the radius of the circle, h h represents the x-offset from the origin, and k k represents the y-offset from origin. The center of the circle is found at (h,k) ( h, k).

And also,

Ox (0) 6°x= 1) 6x ** + y = 25 SOLUTION (a) Since f(x) = 25 - x2 0, we can interpret this integral as the area under the curve y = 25 - x2 from 0 to 5 . But since y2 = 25 - x2 , we get x2 + y2 = 25, which shows that the graph of fis a quarter-circle with radius 5 in the top figuer

And also,

(3x2y2)3 Final result : 32x2y2 Reformatting the input : Changes made to your input should not affect the solution: (1): "y2" was replaced by "y^2".

And thats all!

Answer 2

Solution graph is image 2.

We first graph \(x^2+y^2=25\). This is a circle with center = (0,0) and radius = \(\sqrt{25} =5\).

For \(x^2+y^2<25\), we'll shade inside the circle.

\(y^2=6x\) is a parabola.

we make a table for it.

x   -1   0   1

y   -6  0   6

For \(y^2<6x\) we'll shade inside the parabola.

So the graph will be image 1.

So the solution region is image 2.

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Which Graph Represents The Solution Of X2 + Y2 &lt; 25 And Y2 &lt;6x?
Which Graph Represents The Solution Of X2 + Y2 &lt; 25 And Y2 &lt;6x?

Related Questions

Pleassseeee hhheeelllppp

Pleassseeee hhheeelllppp

Answers

Answer:

a). Figure A and C

b). Figure D and F

Step-by-step explanation:

a). From the given figures, sides of figure (A) and figure (C) appear to be congruent.

   Therefore, pair of triangles A and C will be congruent by SSS property of congruence.

b). If two figures are similar, their corresponding sides will be proportional.

   Since sides of the rectangles given in figures (D) and (F) are proportional, both will be similar.

The price of a jacket is discounted 20%. The original price of the jacket was $60. What is the discounted price of
the jacket?

Answers

Answer:

48

Step-by-step explanation:

20% of 60 is 12. You subtract 12 from 60, to get the discounted price.

706.5 - 549.5 divided by 6 | SIMPLIFIEDDD giving 5O POINTS mark BRAINLIEST

Answers

Answer: 2.166 repeating

More info

Subtract 706.5 - 549.5

That equals 157.

Divide 157 by 6

You get 2.1666666667, or 2.166 repeating

it would be 614.916666 with the 6 going on forever because you know PEMDAS

Help pls :) (15 pts)

Help pls :) (15 pts)

Answers

Answer:

the y is -2 and there's is no slope i think

Step-by-step explanation:

help me please i dont know what to do

help me please i dont know what to do

Answers

Answer:

x = 14.4

Step-by-step explanation:

First of all, the triangle has three sides, so let's use hero's formula to find the area.

A = √[p(p - a)(p - b)(p - c)]

Where;

a, b and c are the 3 given sides of the triangle and;

p = (a + b + c)/2

p = (18 + 30 + 24)/2

p = 72/2

p = 36

Thus;

A = √(36(36 - 18)(36 - 30)(36 - 24))

A = √46656

A = 216 Sq.units

Now, we also know from general formula of a triangle that;

A = ½bh

Where;

b is base and h is height

In the given image;

b = 30

h = x

Thus;

½ × 30 × x = 216

Rearranging, we have;

x = 216 × 2/30

x = 14.4

Both numbers have three significant figures. How many significant figures should be recorded for the answer to the division problem below?

\(43.6 \div 21.2\)
= [?] significant figures​

Answers

Answer:

8 significant figures should be provided.

Step-by-step explanation:

I believe I am correct, but check your answer anyways.

Which expression is a prime polynomial? A. x3 − bx2 B. x2 − 4x − 12 C. x4 + 8xy3 D. x2 − b3

Answers

Answer:

D.) x2 - b3

Step-by-step explanation:

How much would $400 be worth after 6 years, if it were invested at 2%interest compounded annually? (Use the formula below and round youranswer to the nearest cent.)

How much would $400 be worth after 6 years, if it were invested at 2%interest compounded annually? (Use

Answers

Solution

The formula to use is

\(A(t)=P(1+\frac{r}{n})^{nt}\)

From the question, we have

\(\begin{gathered} P=\text{ \$}400 \\ \\ t=6\text{ }years \\ \\ r=2\text{ \%} \\ \\ r=0.02 \\ \\ n=1 \end{gathered}\)

Using the parameters, we have

\(\begin{gathered} A(t)=P(1+\frac{r}{n})^{nt} \\ \\ A(t)=400(1+\frac{0.02}{1})^6 \\ \\ A(t)=400(1.02)^6 \\ \\ A(t)=\text{ \$}450.46 \end{gathered}\)

The answer is

How much would $400 be worth after 6 years, if it were invested at 2%interest compounded annually? (Use

in the diagram below, ABCD is a rectangle.

in the diagram below, ABCD is a rectangle.

Answers

9514 1404 393

Answer:

  BC = 10 ft

Step-by-step explanation:

You may recognize the ratio of the given leg and hypotenuse of triangle BCD is 24 : 26 = 12 : 13. You may recall that the Pythagorean triple (5, 12, 13) is commonly seen in math problems. Here, that means side BC is 2×5 = 10 feet.

__

If you don't recall these helps, you can use the Pythagorean theorem to find BC.

  BC² + DC² = DB²

  BC² = DB² -DC² = (26 ft)² -(24 ft)² = 676 ft² -576 ft² = 100 ft²

  BC = √(100 ft²) = 10 ft

How do you expand ln(1/49^k)

Answers

Answer:

There are a few rules that we can use here:

ln(a^x) = x*ln(a)

ln(a) - ln(b) = ln(a/b)

ln(1) = 0

So here we want to expand:

ln(1/49^k)

First we can use the second property to get:

ln(1/49^k) = ln(1) - ln(49^k)

using the third property, we have:

ln(1/49^k) = ln(1) - ln(49^k) = 0 - ln(49^k)

ln(1/49^k) =  - ln(49^k)

Now we can use the first property to get:

ln(1/49^k) =  - k*ln(49)

Now we can use the fact that:

49 = 7*7 = 7^2

then:

- k*ln(49) = -k*ln(7^2) = -2*k*ln(7)

So we have:

ln(1/49^k) = (-2*ln(7))*k

We can expand it anymore because this is a real number  "(-2*ln(7))" times a variable k.

Can someone please help me with this

Can someone please help me with this

Answers

Answer:

(x = 0, y = 0) and (x = 3, y = 0)

Step-by-step explanation:

Let's test out each pair by substituting the values into the inequalities.

Case 1: x = 0, y = 0

0 <= 6

0 < 6

It works!

Case 2: x = -5, y = -15

-15 <= 10 + 6 = 16

-5 + 15 = 10 < 6

It doesn't work.

Case 3: x = 4, y = -2

-2 <= -8 + 6 = -2

4 + 2 = 6 < 6

It doesn't work.

Case 4: x = 3, y = 0

0 <= -6 + 6 = 0

3 < 6

It works!

Case 5: x = 10, y = 0

0 <= -20 + 6 = -14

From here we can already see that it doesn't work

Case 1 and 4 work!

Rectangle ABCD and A’B’C’D’ are similar.

a. What is the scale factor from ABCD to

A’B’C’D’?

b. What is the scale factor from A’B’C’D’ to

ABCD?

Answers

Where Rectangle ABCD and A’B’C’D’ are similar.

a. the scale factor from ABCD to A’B’C’D’ is 1/2

b. What is the scale factor from A’B’C’D’ to  ABCD is 2

What is scale factor?

In mathematics, a scale factor is the ratio of matching measurements of an item to a representation of that thing. The copy will be bigger if the scaling factor is a full number. The duplicate will be smaller if the scaling factor is a fraction.

When the scale factor is less than one, you are going from big to small. You are dilating negatively.

When you are going from small to big, you scale factor is reversed. In this case, we had 1/2 in a, in b it became 2/1 which = 2.

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Full Question:

Rectangle ABCD and A’B’C’D’ are similar.

a. What is the scale factor from ABCD to A’B’C’D’?

b. What is the scale factor from A’B’C’D’ to ABCD?

See attached image.

Rectangle ABCD and ABCD are similar.a. What is the scale factor from ABCD toABCD?b. What is the scale

What are the 2  formulas to find the area of a circle

Answers

Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

What is the area of a circle?

The area of a circle is given by the formula A = πr², where r is the radius of the circle.

According to the given information:

The area of a circle can be found using either of the following formulas:

\(\pi r^2\), where π (pi) is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle.

\(A = (d/2)^2π,\) where d is the diameter of the circle. This formula can also be written as \($A = r^2\pi$\), where r is the radius of the circle and A is the area.

Both formulas are equivalent and can be used interchangeably, depending on the given information about the circle.

Therefore, according to the given information, The formulas to find the area of a circle are\(\pi r^2 and (d/2)^2\pi or r^2\pi\).

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Question 1(Multiple Choice Worth 2 points) (Pythagorean Theorem LC) Determine which set of side measurements could be used to form a triangle. 13, 19, 7 25, 12, 13 18, 2, 24 3, 1, 5

Answers

Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

To determine which set of side measurements could form a triangle, we need to check if the sum of the lengths of the two shorter sides is greater than the length of the longest side. This is known as the Triangle Inequality Theorem.

Let's check each set of side measurements:

13, 19, 7:

The sum of the two shorter sides is 7 + 13 = 20, which is greater than the longest side (19). Therefore, this set of side measurements could form a triangle.

25, 12, 13:

The sum of the two shorter sides is 12 + 13 = 25, which is equal to the longest side (25). Therefore, this set of side measurements could form a triangle.

18, 2, 24:

The sum of the two shorter sides is 2 + 18 = 20, which is greater than the longest side (24). Therefore, this set of side measurements could form a triangle.

3, 1, 5:

The sum of the two shorter sides is 1 + 3 = 4, which is less than the longest side (5). Therefore, this set of side measurements could not form a triangle.

Based on the Triangle Inequality Theorem, the sets of side measurements that could form a triangle are:

13, 19, 7

25, 12, 13

18, 2, 24

The set of side measurements 3, 1, 5 could not form a triangle.

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A study examines the relationship between educational preparation and scores on a cultural competency exam. Subjects included are nurses with an associate's degree, nurses with a baccalaureate degree, nurses with a master's degree, and nurses with a doctoral degree. In this example, cultural competency is measured at what level?

a. Dependent variable
b. Independent variable
c. Outcome
d. Significant variable

Answers

Answer:

b. Independent variable

Step-by-step explanation:

Understanding the definition of variables is necessary to grasp the notion of independent and dependent variables. The attributes or sorts of features of specific occurrences or things are specified as variables.

Independent variables are variables that are modified or altered by researchers and the consequences of these modifications are evaluated and compared. 

The term dependent variable relates to a sort of variable that assesses how the independent variable(s) impact the test results.

From the given information:

Education level is the predictor since we understand that nurses' education levels are closely correlated with their cultural competence scores. By applying the concept of the logistic regression model and using education level as an independent variable(predictor), we can simply predict their cultural competency. Thus, cultural competency is measured by using the independent variable.

What formula below can be used to forecast inventory?
(Inventory days / Cost of sales) x 365
(Inventory days / 365) x Cost of sales
(Inventory days / 365) / Revenue
(Inventory days / Revenue) x 365

Answers

Formula can be used -

Forecast Inventory = (Inventory days/Cost of sales) x 365.

Forecast Inventory- Inventory forecasting is a method used to predict inventory levels for a future time period. It also helps keep track of sales and demand so you can better manage your purchase orders.

DIO = (Average Inventory/ COGS)x Number of days in period.                

Where,

DIO= Days Inventory Outstanding.

Average Inventory = (Beginning Inventory + Ending Inventory)/2.

COGS = Cost of Goods Sold.

Period Length = the number of days in the period such as    an accounting period (that is being examined- the period may be any    time frame - a week, a quarter or annually).

Days Inventory Outstanding = (Average Inventory/COGS) x Period Length.

Ex: - Find Days Inventory Outstanding?

Cost of Goods Sold = $35,000

No. of day in period = 365 (this number is often 365 for the number of days in one year).

Average inventory = $3,000

DIO = ($3,000 / $35,000) x 365 = 31.29 days.

Therefore the formula that can be used to forecast inventory is: (Inventory days / Cost of sales) x 365.

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a survey of 800 households revealed that 400 had only a TV, 100 had only a computer, and 100 had neither a tv nor a computer. how many households have both a tv and a computer?

Answers

The number of households which have both TV and computers are 200.

What  is defined as the Boolean algebra (logical expressions)?Boolean algebra is a branch of algebra in math and mathematical logic where the value of the variables are indeed the truth values both true and false, typically represented 1 and 0, respectively.Synonyms, such as 'Yes' for 'True' as well as 'No' for 'False,' are sometimes used to represent the statement.

Let A be the number of house hold having only TV = 400

Let B be the number of house hold having only computers = 100

Let C be the number of house hold having neither TV nor computer = 100

Let D be the number of house hold having both TV and computer.

Then, the number number of house holds are 800.

A + B + C + D = 800

Put the values;

400 + 100 + 100 + D = 800

D = 800 - 600

D = 200

Therefore, the number of households having both TV and computer are 200.

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Find x. Give reasons to justify your solution. b Lines AB and CD are straight lines.

Find x. Give reasons to justify your solution. b Lines AB and CD are straight lines.

Answers

Answer:

x is 28

Step-by-step explanation:

When two lines intersected in a point, then they formed two pairs of vertically opposite angles. The vertically opposite angles are equal in measures

Let us solve our question

∵ AB and CD are straight lines intersected at O

∴ ∠AOC and ∠DOB are vertically opposite angles

∴ ∠AOD and ∠COB are vertically opposite angles

→ The vertically opposite angles are equal in measures

∴ m∠AOC = m∠DOB

∴ m∠COB = m∠AOD

→ ∠ COB is formed from ∠COE, ∠EOF, and ∠FOB

m∠COB = m∠COE + m∠EOF + m∠FOB

∵ m∠COE = 3x, m∠EOF = x, m∠FOB = x + 12

∴ m∠COB = 3x + x + x + 12

→ Add the like terms

m∠COB = 5x + 12

∵ m∠AOD = 152°

∵  m∠COB = m∠AOD

5x + 12 = 152

→ Subtract 12 from both sides

∴ 5x + 12 - 12 = 152 - 12

∴ 5x = 140

→ Divide both sides by 5

∴ \(\frac{5x}{5}=\frac{140}{5}\)

x = 28

→ To justify the solution substitute x by 28 in m∠COB the answer must

   be 152°

∵ m∠COB = 5x + 12

x = 28

∴ m∠COB = 5(28) + 12

∴ m∠COB = 140 + 12

m∠COB = 152°

∴ The value of x is correct

Determine the domain of the function. f as a function of x is equal to the square root of x plus three divided by x plus eight times x minus two.

All real numbers except -8, -3, and 2
x ≥ 0
All real numbers
x ≥ -3, x ≠ 2

Answers

Answer:

\(\huge \boxed{{x\geq -3, \ x \neq 2}}\)

Step-by-step explanation:

The function is given,

\(\displaystyle f(x)=\frac{\sqrt{x+3 }}{(x+8)(x-2)}\)

The domain of a function are all possible values of x.

There are restrictions for the value of x.

The denominator of the function cannot equal 0, if 0 is the divisor then the fraction would be undefined.

\(x+8\neq 0\)

Subtract 8 from both parts.

\(x\neq -8\)

\(x-2\neq 0\)

Add 2 on both parts.

\(x\neq 2\)

The square root of x + 3 cannot be a negative number, because the square root of a negative number is undefined. x + 3 has to equal to 0 or be greater than 0.

\(x+3\geq 0\)

Subtract 3 from both parts.

\(x\geq -3\)

The domain of the function is \(x\geq -3\), \(x\neq 2\).

The domain of the given function will be x ≥ -3 and x ≠ 2.

What is the domain of a function?

The entire range of independent input variables that can exist is referred to as a function's domain or,

The set of all x-values that can be used to make the function "work" and produce actual y-values is referred to as the domain.

As per the data given in the question,

The given expression of function is,

f(x) = \(\sqrt{\frac{x+3}{(x-8)(x-2)} }\)

The fraction would indeed be undefined if the base of the function were equal to zero, which is not allowed.

x + 8 ≠ 0

x ≠ -8

And, x - 2 ≠ 0

x ≠ 2

Since the square root of a negative number is undefined, x+3 cannot have a negative square root. x+3 must be bigger than zero or identical to zero.

So,

x + 3 ≥ 0

x ≥ -3

So, the domain of the function will be x ≥ -3 and x ≠ 2.

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What is the solution of the system of equations
c+3d = 8 and c = 4d - 6?
1) C=-14, d = -2
2) c= -2, d = 2
3) c = 2, d = 2
4) c= 14, d = -2

Answers

Answer:

It the 3rd one it's correct cuz i worked it out

Can i have a brainliest please!!:)

Step-by-step explanation:

solve your system by substitution.

c+3d=8;c=4d−6

Rewrite equations:

c=4d−6;c+3d=8

Step: Solve c=4d−6for c:

c=4d−6

Step: Substitute4d−6forcinc+3d=8:

c+3d=8

4d−6+3d=8

7d−6=8(Simplify both sides of the equation)

7d−6+6=8+6(Add 6 to both sides)

7d=14

7d

7

=

14

7

(Divide both sides by 7)

d=2

Step: Substitute2fordinc=4d−6:

c=4d−6

c=(4)(2)−6

c=2(Simplify both sides of the equation)

Answer:

c=2 and d=2

 

What is 6^2/3in radical form?

Answers

Answer: ∛36

Solution:

6^(2/3) = ∛6²


∛6² = ∛36 (in radical form)

Answer:

3/6^2

Step-by-step explanation:

First option

Question
Henry has collected data to find that the
typing speeds for the students in a typing
class has a normal distribution. What is the
probability that a randomly selected student
has a typing speed of less than 51 words per
minute if the mean (u) is 47 words per
minute and the standard deviation (o) is 4
words per minute? Use the empirical rule.
• Provide the final answer as a percent.
Provide your answer below:
%

Answers

The probability that a randomly selected student has a typing speed of less than 51 words per minute if the mean (u) is 47 words per minute and the standard deviation (o) is 4 words per minute is; 68%

How to use empirical formula in statistics?

The empirical rule in statistics states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will occur within three standard deviations.

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

x' = 51

μ = 47

σ = 4

Thus;

z = (51 - 47)/4

z = 1

From empirical formula at 1 standard deviation above the means, the probability is 68%.

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solve the equation
what does x equal to
46+x÷6−21=25+6

Answers

Answer:

×=36

Step-by-step explanation:

46+1/6X-21=31

25+1/6X=31

1/6X=31-25

1/6X=6

X=36

In 5 years, Nicole will
be old enough to vote in an election. The minimum age
for voting is at least 18 years. What can you say about
how old she is now? Write and solve an inequality to
show how old Nicole is now. Let a represent Nicole's
age now.

Answers

Answer:

Nicole is 13 years old because x + 5 = 18

Step-by-step explanation:

Rearrange the following steps in the correct order to locate the last occurrence of the smallest element in a finite list of integers, where the integers in the list are not necessarily distinct.

a. return location
b. min ≔a1 and location ≔1
c. min ≔ai and location≔i
d. procedure last smallest(a1,a2,...,an: integers)
e. If min >= ai then

Answers

Answer:

The rearranged steps is as follows:

d. procedure last smallest(a1,a2,...,an: integers)

b. min ≔a1 and location ≔1

e. If min >= ai then

c. min ≔ai and location≔i

a. return location

Step-by-step explanation:

The proper steps to perform the task in the question above is dbeca

Here, the procedure (or function) was defined along with necessary parameters

d. procedure last smallest(a1,a2,...,an: integers)

The smallest number is initialized to the first number on the list and its location is initialized to 1

b. min ≔a1 and location ≔1

The next line is an if conditional statement that checks if the current smallest number is greater than a particular number

e. If min >= ai then

If the above condition is true, the smallest value is assigned to variable min; it's location is also assigned to variable location

c. min ≔ai and location≔i

The last step returns the location of the smallest number

a. return location

What is 7/11 x 1/4 in simplest form

Answers

Answer:

\(\frac{7}{11} * \frac{1}{4}\) = \(\frac{7}{44}\).

Cannot reduce it. Then it will make the numerator a decimal

Which cannot happen.

\(\frac{7}{44}\) is the answer then

Answer:

7/11 x 1/4 = 0.015

I hoped it helped you.

the formula for converting celsius to fahrenheit is F = 9/5C+32.

a. The lowest temperature in Alaska, -62° C, was recorded on January 23, 1971 at Prospect Creek Camp. Use the formula to convert the recorded temperature to Fahrenheit

b. In February, the average high temperature in Puerto Vallarta, Mexico us 81° F. To the nearest whole number, what is this temperature in degrees Celsius?​

Answers

Answer:

a)-79.6

b)=27

Step-by-step explanation:

a) F=9/5(-62)+32

F=-79.6

b) 81=9/5C+32

81-32=9/5C

49=9/5C

C=27.222

Therefore C=27

Determine whether the system
has no, one, or infinitely many
solutions.
2x + 3y = -17
y = x - 4
A. infinitely many solutions
B. one solution
C. no solutions

Answers

On studing about the nature of system of linear equation the correct option is B.

How to determine the nature of system of linear equations of two variables?

Consider the following two linear equations:

\(a_1x + b_1y + c_1 = 0a_2x + b_2y + c_2 = 0\)

(1) If  \(\frac{a_1}{a_2}\ne \frac{b_1}{b_2}\) them the system of equations have unique solution.

(2) If  \(\frac{a_1}{a_2}= \frac{b_1}{b_2}=\frac{c_1}{c_2}\) them the system of equations have infinitely many solutions.

(3) If  \(\frac{a_1}{a_2}= \frac{b_1}{b_2}\ne \frac{c_1}{c_2}\) them the system of equations have no solution.

Now, consider the given equation.

2x+3y = -17

y = x - 4

Rearrange the above equation as follows:

2x+3y +17 = 0

x - y - 4 = 0

Now, on comparing,

\(a_1=2, a_2=1, b_1=3, b_2=-1, c_1=17, c_2=-4\)

Now, take ratio as follows:

\(\frac{a_1}{a_2}=\frac{2}{1}\\\frac{b_1}{b_2}=\frac{3}{-1}\\\frac{c_1}{c_2}=\frac{17}{-4}\)

It satisfies the first condition hence, there is one solution for the system of equations.

Hence, the correct option is B.

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I want you to find the answer

I want you to find the answer

Answers

The value of length BC is 18.9

What is cosine rule?

Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Therefore,

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

Therefore, the length of BC is 18.9

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In the triangle, the value of the side BC is 18.9cm to 1 decimal place

How to determine BC?

The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The cosine formula states that

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

In conclusion, the value of  the length of BC is 18.9cm

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how are the probability of an event and the probability of its complement related mathematically

Answers

The relation between the probability of its complement is that their sum is 1.

Complement in probability theory is an essential concept that helps us understand the likelihood of an event not occurring. It is a mathematical term that refers to the opposite or negation of an event.

Complement refers to the probability of an event not occurring, given the probability of it occurring. It is often denoted as the complement of an event A and is represented by A’.

The complement of an event A is defined as the set of all outcomes in the sample space that are not in A.

The probability of the complement of A is equal to the probability of all the outcomes in the sample space that are not in A.

The most important properties of the complement of an event is that the probability of an event and its complement always add up to 1. This is known as the law of complementary probability, and is expressed as:

P(A) + P(A’) = 1

This means that if we know the probability of an event occurring, we can easily calculate the probability of its complement by subtracting the probability of the event from 1.

For example, if the probability of event A is 0.7, then the probability of its complement, A’, is 1 – 0.7 = 0.3.

Hence the relation between the probability of its complement is that their sum is 1.

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