Find angles in isosceles triangles

a) The coordinates of point A are given as follows: (-4,1).

b) The point B is plotted in red on the image given for this problem.

c) The coordinates of point C are given as follows: (-4,-2).

The general format of an ordered pair is given as follows:

(x,y).

In which the coordinates are given as follows:

Then the coordinates of point C are given as follows:

Hence the ordered pair is given as follows:

(-4, -2).

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The Effective Annual Rate (EAR) for the given nominal annual interest rates with different compounding periods are 12.55% for quarterly, 7.23% for monthly, 17.47% for daily and 12.75% for continuous compounding.

a. The Effective Annual Rate (EAR) for 12% compounded quarterly is 12.55%. To calculate this, we use the formula EAR = (1 + r/n)^n - 1, where r is the nominal annual interest rate and n is the number of times interest is compounded in a year. Plugging in the values, we get EAR = (1 + 0.12/4)^4 - 1 = 0.1255 or 12.55%.

b. The Effective Annual Rate (EAR) for 7% compounded monthly is 7.23%. To calculate this, we use the same formula as before. Plugging in the values, we get EAR = (1 + 0.07/12)^12 - 1 = 0.0723 or 7.23%.

c. The Effective Annual Rate (EAR) for 16% compounded daily is 17.47%. To calculate this, we use the same formula as before. Plugging in the values, we get EAR = (1 + 0.16/365)^365 - 1 = 0.1747 or 17.47%.

d. The Effective Annual Rate (EAR) for 12% with continuous compounding is 12.75%. To calculate this, we use the formula EAR = e^r - 1, where e is the mathematical constant approximately equal to 2.71828 and r is the nominal annual interest rate. Plugging in the values, we get EAR = e^(0.12) - 1 = 0.1275 or 12.75%.

In summary, we can say that the Effective Annual Rate (EAR) for the given nominal annual interest rates with different compounding periods are 12.55% for quarterly, 7.23% for monthly, 17.47% for daily and 12.75% for continuous compounding. The EAR takes into account the effect of compounding on the nominal interest rate, providing a more accurate representation of the true cost of borrowing or the true return on an investment.

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Answer:

543

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

40 - 5 = 35 years till the son will be 40, his fathers age

40+35 = 75, the dad's age 35 years in the future when the son is 40

C

The mistake the arrangers made is in the second inequality. They considered the number of caps to be bought should be at least 5 times greater than the number of blouses, not the other way around. The correct inequality should be C

The correct answer is D) The first inequality should be s + h ≤ 1800.

The organizers made an error in the first inequality. The given inequality 10s + 8h ≤ 1800 represents the total cost of buying shirts (10s) and hats (8h) should be less than or equal to $1800. However, this does not take into account the fact that the organizers want to buy at least 5 times as many shirts as hats, as indicated by the second inequality h ≥ 5s.

The correct way to represent this constraint is by using the equation s + h ≤ 1800, which ensures that the total number of shirts and hats purchased does not exceed $1800 in cost. This is because the organizers want to make sure that the total cost of shirts and hats combined does not exceed the budget of $1800.

By solving algebraically......

1)

2)

3)

4)

5)

6)

7)

8)

Hope this answers your question!

Answer:

I don't know what the options are, but my equation is (1/4) * n = 9

Step-by-step explanation:

n yards

Each strip = 1/4 yard

9 bracelets made

9 = (1/4) * n

The total capacity of pool in gallons is 1625.

Let us assume the water in the pool be x liters. Forming the equation according as per the statement in question -

x + 300 = 80% of total volume - Equation 1

Forming the equation according to second statement -

30% × x = 300

30/100 × x = 300 - Equation 2

Finding the initial volume of water using equation 2-

x = 300×100/30

Cancelling zero and performing division and multiplication to find the initial volume of water

x = 1000 gallons

Now finding the total volume or capacity of pool by keeping the value of x in first equation -

1000 + 300 = 80/100 × total volume

Total volume = 1300×100/80

Performing multiplication and division to find the total capacity of pool

Total capacity of pool = 1625 gallons

Hence, the total capacity of pool in gallons is 1625.

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Answer:

0.0652173

Step-by-step explanation:

Given that :

6 chocolate chip cookies

6 peanut butter cookies

6 sugar cookies

6 oatmeal cookies

Total number of cookies purchased = (6+6+6+6) = 24

Probability, P= required outcome /total possible outcomes

This is a selection without replacement probability problem :

P(peanut butter cookies) = 6/24 = 1/4

Then ;

P(chocolate chip cookie) = 6/23

Hence,

P(peanut butter cookies then chocolate chip cookie) = 1/4 * 6/23 = 0.0652173

Answer:

The 3rd picture is the right one

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer from edmentum/plato

Answer:

height = 8.5 feet

Step-by-step explanation:

Area of a triangle formula:

a=1/2bh

substitute what's given

93.5 = (1/2)22h

93.5=11h

divide both sides by 11 to isolate h

h=8.5 ft

An argument is a value or reference passed to a method or function when it is called. It is provided by the code that calls the method and is used as input for the method's operation.

The term that best fits the description "Provided by the code calling the method" is "argument".

An argument is a value or reference that is passed to a method or function when it is called. The argument is provided by the code that calls the method and is used as input for the method's operation.

In contrast, a variable is a named storage location that holds a value, a formal parameter is a variable declared in the method's signature that receives an argument, a constant is a fixed value that does not change during program execution, and an expression is a combination of values, variables and operators that can be evaluated to a single value.

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The solutions of the given equations are:

a. x1 = 10, x2 = -15

b. x1 = -11, x2 = 17

c. x1 = -45, x2 = 296

The given system of equations is as follows:

-8x1 - x2 = kq ----(1)

-7x1 + x2 = k2 ----- (2)

We can write the system of equations in matrix form:

[ -8, -1] [ -7, 1] [x1, x2] = [kq, k2]

Let [ -8, -1] [ -7, 1] be matrix A, [x1, x2] be matrix X, and [kq, k2] be matrix B.

Therefore, A X = B ⇒ X = A-1 B, where A-1 is the inverse of A.

To calculate the inverse of matrix A, we use the following formula:

A-1 = (1 / |A|) [d, -b]

[-c, a]

where |A| is the determinant of matrix A, a, b, c, d are the cofactors of the elements of matrix A.

|A| = ad - bc, and the cofactors of matrix A are:

[a11, a12]

[a21, a22]

a = ( -1 )^2 [a22]

b = (-1)^1 [a21]

c = ( -1 )^1 [a12]

d = ( -1 )^2 [a11]

Now we can find the inverse of matrix A:

A-1 = (1 / |-8 + 7|) [1, 1]

[7, -8]

 = (1 / |-1|) [1, 1]

                   [7, -8]

 = (1 / 1) [1, 1]

               [7, -8]

 = [1, 1]

     [7, -8]

By solving A-1 B, we obtain X.

Now, let's substitute the values of kq and k2 to solve the equation:

a. When kq = k2 = 5, we have:

[1, 1] [7, -8] [5, 5] = X

= [10, -15]

Therefore, x1 = 10 and x2 = -15

b. When kq = 7 and k2 = 3, we have:

[1, 1] [7, -8] [7, 3] = X

= [-11, 17]

Therefore, x1 = -11 and x2 = 17

c. When kq = 1 and k2 = -37, we have:

[1, 1] [7, -8] [1, -37] = X

= [-45, 296]

Therefore, x1 = -45 and x2 = 296

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The figure shows the Venn diagram for the given data.

A diagram depicting mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles.

As per the given data:

Let's denote:

COLD BLOODED ANIMALS = C

WARM BLOODED ANIMALS = W

FISHES = F

Given:

All fishes are cold blooded animals.

Some, but not all, cold blooded animals are fishes

The Venn diagram will be as in the figure.

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Answer: \(305\)

Shown work is on the image below.

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

x + y = 420; y = 6x

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

The smallest and largest fish range in size from 1 cm to 18 m. 18 m then equals 18 x 100 or 1800 cm. ∴ The length of large fish exceeds that of little fish by 1800 times.

The number of parrotfish Carlos purchased is represented by the variable y, whereas the number of angelfish Carlos purchased is represented by the variable x.

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Answer:

15

Step-by-step explanation:

Answer: 6/18 or 0.3

Step-by-step explanation:

If t = 1/6, then you’d multiply that by 1/3. Always remember that you multiply the variable by its coefficient.

(1/3 x 1/6) + 5/18.

1/3 x 1/6 = 1/18 or 0.5

1/18 + 5/18 = 6/18 or 0.3

a) The exponential growth equation is y = ( 1.2 )ˣ

b) The exponential decay equation is y = ( 0.71 )ˣ

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the exponential growth equation be represented as A

Now , the value of A is

y = ( 1.2 )ˣ

where the growth rate is r = 20 %

Let the exponential decay equation be represented as B

Now , the value of B is

y = ( 0.71 )ˣ

where the decay rate is r = 29 %

The graph A represents an exponential decay graph and the graph B represents an exponential growth graph

Hence , the exponential equations are solved

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Using the mean and data given, the 95% confidence interval for the data is approximately (44.25, 59.35).

To calculate the 95% confidence interval for the given data, we can use the following formula:

Confidence interval = mean ± (critical value * standard deviation / sqrt(n))

where:

First, let's calculate the mean, standard deviation, and the critical value.

Mean (μ) = (56 + 24 + 26 + 45 + 64 + 79 + 38 + 40 + 69 + 74 + 34 + 54 + 21 + 74 + 62 + 76 + 59 + 59 + 47 + 66 + 66 + 52 + 53 + 59 + 38 + 30 + 48 + 44 + 23 + 46) / 30 = 51.8

Standard Deviation (σ) = √[(∑(x - μ)²) / (n - 1)]

= √[(∑(56 - 51.8)² + (24 - 51.8)² + ... + (23 - 51.8)² + (46 - 51.8)²) / (30 - 1)]

≈ 17.04

To determine the critical value, we need to consider the sample size and confidence level. Since the sample size is 30 and we want a 95% confidence level, we can use a t-distribution with 29 degrees of freedom. Looking up the critical value in a t-table or using a calculator, we find the value to be approximately 2.045.

Now, let's calculate the confidence interval:

Confidence interval = 51.8 ± (2.045 * 17.04 / √30)

≈ 51.8 ± 7.55

Therefore, the 95% confidence interval for the data is approximately (44.25, 59.35).

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Answer:

Plane 'S'

Step-by-step explanation:

Since a plane is a two dimensional surface on which infinitely many points may lie.

In the picture attached, two planes (two dimensional) have been given.

Plane S

Plane T

Plane 'S' contains three points A, B and C and plane 'T' contains points D and E.

Therefore, the plane which contains points A, B and C is Plane 'S'.

The plane that contains points A, B and C is the plane S.

A plane is simply a 2-dimensional surface or figure.

The above definition of a plane means that, there are only two planes in the given figure.

These planes are:

Hence, the plane which contains points A, B and C is plane S.

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Answer:

P (3, - 2 )

Step-by-step explanation:

Solve the equations simultaneously for point of intersection P

5x + 3y = 9 → (1)

7x - 2y = 25 → (2)

Multiplying (1) by 2 and (2) by 3 and adding will eliminate the y- term

10x + 6y = 18 → (3)

21x - 6y = 75 → (4)

add (3) and (4) term by term to eliminate y

31x + 0 = 93

31x = 93 ( divide both sides by 31 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for x

Substituting into (1)

5(3) + 3y = 9

15 + 3y = 9 ( subtract 15 from both sides )

3y = - 6 ( divide both sides by 3 )

y = - 2

Then P = (3, - 2 )

If f(x) and f¹(x) are inverse functions of each other then value of ƒ˜¹ (8) = 3/2.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have,

f(x) = 2x + 5

Let us consider f(x) as y

So, y= 2x + 5

Now replace x to y and y to x

x= 2y+ 5

Solving for y we get

2y = x - 5

y = (x - 5)/2

\(f^{-1\)(x) = (x - 5)/2

Now, \(f^{-1\)(8) = (8 - 5)/2

\(f^{-1\)(x) = 3/2

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Only matrices of the same size can be added or subtracted.

A matrix is a rectangular array of numbers and is composed of rows and columns. In order to add or subtract matrices, the matrices must have the same number of rows and columns. If the matrices do not have the same size, they cannot be added or subtracted.

For example, if one matrix is a 2x3 matrix, the other matrix must also be a 2x3 matrix. Similarly, if one matrix is a 3x2 matrix, the other matrix must also be a 3x2 matrix. The numbers in each matrix may vary, but the size of the matrices must be the same for the operation to be valid.

When adding or subtracting matrices, the numbers in the same position (row and column) are added or subtracted. For example, if one matrix is [[1,2,3], [4,5,6], [7,8,9]] and the other matrix is [[2,4,6], [8,10,12], [14,16,18]], the resulting matrix would be [[3,6,9], [12,15,18], [21,24,27]].

Adding and subtracting matrices is a useful tool in mathematics and is often used to solve equations and simplify complex problems. It is important to remember that only matrices of the same size can be added or subtracted.

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Answer:

8/12,4/6

Step-by-step explanation:

Answer:

8/12, 4/6 are equal to 2/3

Step-by-step explanation:

The ratio of red marbles to black marbles = 4 : 7

Total no. of marbles = 77

4x + 7x = 77

11x = 77

x = 77/11

x = 7

The no. of red marbles = 4x

= 4 × 7

= 28

The Prime factors of 36 are (2²) * (3²) or 2 * 2 * 3 * 3. Thus, option B is the correct answer.

Prime numbers are numbers that are not divisible by numbers other than 1 or the number itself. Composite numbers are numbers that have more than 2 factors other than 1 and the number itself.

Factors are numbers that when divided by another number leave no remainder. Prime factors are the prime numbers that when multiplied the product we get equal to the original number.

To calculate the prime factor, we use the division method.

In this method, firstly we divide the number by the smallest prime number it is when divided by is completely divisible. In this case, we divide 36 by 2 and get 18 as the quotient.

Again, divide the quotient of the previous division by the smallest prime number it is divisible. So, 18 is again divided by 2 and we get 9.

Repetition of the previous step takes place until we get 1. And 9 ÷ 3 = 3. Then  3 ÷ 3 = 1. Since we get 1, this is the final answer.

Finally, Prime factorization of 36 = 2 × 2 × 3 × 3 or we can write it as (2²) * (3²)

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Answer:

Slope=3 Y-int=4

Step-by-step explanation:

y=mx+b where m is slope and b is y-intercept