Find the measure of each angle in the triangles shown.

The intervals in which the function is decreasing are:

{(-∞, -3), (1, 4)}

A function is decreasing if, when reading the graph from left to right, the graph goes downwards.

Here we can see that the graph is decreasing in the intervals:

(-∞, -3)  (leftmost part)

And in the interval:

(1, 4)

In all the other intervals the function is increasing.

Then the answer is:

Intervals: {(-∞, -3), (1, 4)}

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Answer:

x = √(-x) + 6 are x = 9 and x = -12

Step-by-step explanation:

To find the solution for "x" in the equation x = √(-x) + 6, we can follow these steps:

Start with the original equation: x = √(-x) + 6.

Square both sides of the equation to eliminate the square root on the right-hand side: (x)^2 = (√(-x) + 6)^2.

Simplify the right-hand side by applying the distributive property: (x)^2 = (√(-x))^2 + 2(√(-x))(6) + (6)^2.

Simplify further by noting that (√(-x))^2 = -x: (x)^2 = -x + 72 + 36.

Combine like terms: (x)^2 = -x + 108.

Move all terms to one side of the equation: (x)^2 + x - 108 = 0.

This is now a quadratic equation. We can solve for "x" by factoring, using the quadratic formula, or by graphing. Factoring or using the quadratic formula would be appropriate methods in this case.

Factoring the quadratic equation, we get: (x - 9)(x + 12) = 0.

Setting each factor equal to zero and solving for "x", we get two possible solutions: x - 9 = 0 or x + 12 = 0.

Solving for "x" in each case, we get: x = 9 or x = -12.

So, the solutions to the equation x = √(-x) + 6 are x = 9 and x = -12.

[tex]x_{1} =2\\ \\x_{2} =-3[/tex].

[tex]x=\sqrt{-x+6}[/tex]

[tex](x)^{2} =(\sqrt{-x+6})^{2} \\ \\x^{2} =-x+6[/tex]

Standard form: [tex]ax^{2} +bx+c=0[/tex]

[tex]x^{2} +x-6=0[/tex]

a= 1 (because x² doesn't show an explicit coefficient)

b= 1 (because x doesn't show an explicit coefficient)

c= -6

Quadratic formula: [tex]\frac{-b+-\sqrt{b^{2} -4ac} }{2a}[/tex]

[tex]x_{1} =\frac{-(1)+\sqrt{(1)^{2} -4(1)(-6)} }{2(1)} =2\\ \\x_{2} =\frac{-(1)-\sqrt{(1)^{2} -4(1)(-6)} }{2(1)}=-3[/tex]

[tex]x_{1} =2\\ \\x_{2} =-3[/tex].

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Option three log3 + log(x+4) is the equivalent to the logarithm expression  log3(x+4).

It is given that logarithm expression is log3(x+4).

It is required to simplify the above equation.

It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

aᵇ = c

logₐc = b

We have logarithm expression:

log3(x+4)

We know the log property that we can split a logarithm into two logarithms if it contains the product of two numbers ie.

log xy = logx + logy

By using this property we get:

log3(x+4)

= log3 + log(x+4)

Because 3 and (x+4) are two different numbers, not (x+4).

Thus, option three log3 + log(x+4) is the equivalent to the logarithm expression log3(x+4).

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a) addition;

+ | 9 | 7 | 2

6 | 15 | 3 | 6

3 | 6 | 15 | 6

12 | 5 | 6 | 17

b) multiplication;

x | 4 | 9 | 5

6 | 2 | 42 | 35

3 | 8 | 24 | 20

9 | 72 | 5 | 35

To find the missing values, look at each row and column individually and apply the appropriate addition rule.

In the first row, 9+7=16, so the missing value in the first row is 2.

In the second row, 6+15=21, so the missing value is 3. To find the other missing value, we can look at the first column. 3+9=12, so the missing value is 6.

In the third row, 3+6=9, so the missing value is 6. To find the other missing value, look at the second column. 6+15=21, so the missing value is 6.

In the last row, 12+5=17, so the missing value is 6. To find the other missing value, look at the third column. 6+6=12, so the missing value is 5.

For the appropriate multiplication rule:

In the first row, 5 is a factor, and the only possible value of x that can give 5 when multiplied by 5 is 1. Therefore, x=1, and fill in the rest of the row using multiplication: 1x4=4 and 1x9=9.

In the second row, 6 is a factor, and the only possible value of 42 that can be divided by 6 is 7. Therefore, 6x7=42. To find the missing value in the third column, divide 35 by 7, which gives 5.

In the third row, 4 is a factor, and the only possible value of 24 that can be divided by 4 is 6. Therefore, 4x6=24 for the third row. To find the missing value in the fourth column, divide 20 by 5, which gives 4.

In the last row, 9 is a factor, and the only possible value of 72 that can be divided by 9 is 8. Therefore, 9x8=72, for the last row. To find the missing value in the third column, we can divide 35 by 7, which gives 5.

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The coordinates of vertex D are (2, -2).

Given that ABCD is a parallelogram.

Coordinates of A = (1, 3) and B = (5, 1) and C = (-2, 0).

Let the fourth coordinates of the point D be (x, y).

So, the slope of AB and CD will be equal since ABCD is parallelogram and opposite sides of parallelogram are parallel and slopes of parallel are equal.

Slope of CD = (y - 0)/(x - (-2)) = y/(x + 2)

Slope of AB = (1 -3)/(5 - 1) = -2/4 = -1/2

So, y/(x + 2) = -1/2

2y = -x - 2

x + 2y = -2 ........... (i)

again slopes of AC and BD are equal for the same reason.

Slope of AC = (3 - 0)/(1 - (-2)) = 3/3 = 1

Slope of BD = (y - 1)/(x - 5)

So, (y - 1)/(x - 5) = 1

y - 1 = x - 5

x - y = 4 ...........(ii)

equation (i) - equation (ii) we get,

(x + 2y) - (x - y) = -2 -4

3y = -6

y = -2

Putting y = -2 in equation (ii) we get,

x - (-2) = 4

x = 4 - 2 = 2

So the coordinates of fourth point are (2, -2).

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The question is in another language. The English translation of the question will be -

"Solve and explain the following problem step by step:

From a parallelogram ABCD we know A(1,3), B(5,1), C(-2,0). Find the coordinates of vertex D."

Answer:

There are various sources of accounting information, which are as follows:

1. Financial transactions: The primary source of accounting information is financial transactions such as sales, purchases, payments, receipts, and other financial activities of the business.

2. Accounting records: Accounting records such as journals, ledgers, trial balance, and financial statements are also the sources of accounting information.

3. Bank statements: Bank statements are a primary source of accounting information, as they provide information on bank balances, cash inflows, and outflows.

4. Invoices and bills: Invoices, bills, and receipts provide information on purchases and sales made by the business.

5. Management reports: Internal management reports, such as budgets, variance analysis, and performance reports, provide valuable information on the financial performance of the business.

6. Tax returns: Tax returns provide information on the business's tax obligations and payments.

7. Shareholder reports: Shareholder reports provide information on the financial performance of a company to its shareholders.

Overall, these sources of accounting information provide valuable information on the financial performance of a business, and they play a crucial role in decision-making, performance evaluation, and financial planning.

Answer:

50

Step-by-step explanation:

Substitute the value of the variable into the expression and simplify.

The standard error of the estimate has been given in  the table that was presented in the question as  3.4835.

Standard error is a term that is used in statistics to measure the accuracy with which a sample would be the representation of a given a population.

In other words, we can say that it shows  the variability or dispersion of a sample statistic, this could be the  the sample mean or sample proportion, that is gotten through the true population value.

The standard error is stated already in the question as Standard Error 3.483483

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With the numbers gotten from the abacus counting, you can compare with the complete question to see if the student is correct or not.

From the given image, we can see that we are supposed to check if the answers given by the student is correct.

However, there are no data to compare from, so I would show the total sum of each of the abacus computed.

1. For GG, the total is 19

GB = 22

2. GG= 17

GB = 15

BB= 4

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Answer:

n ≥ 4

Step-by-step explanation:

9n+18-5n ≥ 34

4n +18 ≥ 34

4n ≥ 34-18

4n ≥ 16

n ≥ 16/4

n ≥ 4

You can also verify it by putting value of n in original eq

9(4)+18-5(4) ≥ 34

36+18-20 ≥ 34

34 ≥ 34

Answer:

[tex]\pi \times \frac{3}{4} [/tex]

inches

OR

[tex] \frac{3}{8} \pi \: x {}^{2} [/tex]

The perimeter of the window in inches is 138 inches.

It will cost $110.40 to insulate the perimeter of the window.

To change the measurements to inches, we can use the fact that 1 foot is equal to 12 inches. So:

The height of the window in inches is (3 feet x 12 inches/foot) + 5 inches = 36 inches + 5 inches = 41 inches.

The width of the window in inches is (2 feet x 12 inches/foot) + 4 inches = 24 inches + 4 inches = 28 inches.

(a) The perimeter of the window in inches is the sum of the lengths of all four sides. We can use the formula for the perimeter of a rectangle to find it:

Perimeter = 2(length + width)

Plugging in the values we found:

Perimeter = 2(41 inches + 28 inches) = 138 inches

So the perimeter of the window in inches is 138 inches.

(b) We must divide the cost per inch by the perimeter in order to determine the cost of insulating the perimeter:

The following equation can be used to calculate the cost:

Cost = Perimeter x Cost per Inch

Cost = 138 inches x $0.80/inch = $110.40

So it will cost $110.40 to insulate the perimeter of the window.

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The measurements only result in one triangle.

When we apply the Law of Sines, we get:

sin(B) = (16.7/14)sin(35)

sin(B) = (16.7/14) sin(B) = 0.580sin(35)

sin(B) ≈ 0.580

We obtain either B = 35.8 degrees or B = 144.2 degrees when we take the inverse sine of both sides.

We know that C = 180 - 35 - 35.8 109.2 degrees since the total of the angles in a triangle is 180 degrees.

The length of the third side, c, can be determined using the Law of Cosines as follows: c 10.8

We have c 31.2 for B 144.2 degrees.

A legal triangle with side lengths of 14, 16, and 10 with angles of 35, 35.8, and 109.2 degrees is one where B 35.8 degrees.

As a result, the measurements only result in one triangle.

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The requried solution of the given trigonometric function is sin7π/12 is  (√3 + 1)/(2√2).

We know that 7π/12 = 9π/12 - 2π/12.

So, we can rewrite sin(7π/12) as sin(9π/12 - 2π/12).

Using the trigonmetric identity,
sin(A - B) = sinAcosB - cosAsinB, we can rewrite sin(9π/12 - 2π/12) as sin(9π/12)*cos(2π/12) - cos(9π/12)*sin(2π/12).

We know that,
sin(2π/12) = sin(π/6) = 1/2 and cos(2π/12) = cos(π/6) = √3/2.

Also, sin(9π/12) = sin(3π/4) = 1/√2 and cos(9π/12) = cos(3π/4) = -1/√2.

Substituting these values, we get:

= sin(7π/12) = sin(9π/12 - 2π/12)

= sin(9π/12)cos(2π/12) - cos(9π/12)sin(2π/12)

= (1/√2)(√3/2) - (-1/√2)(1/2)

= (√3/2√2) + (1/2√2)

= (√3 + 1)/(2√2)

Therefore, sin(7π/12) = (√3 + 1)/(2√2).

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Answer:

Step-by-step explanation:

Distribution curve:

The distribution curve for this data set would be a normal distribution, as the data is approximately symmetrical and the mean is close to the center of the data. The mean of the data is 518, and 6 standard deviations from the mean would be:

Lower limit: 518 - (6 x standard deviation)

Upper limit: 518 + (6 x standard deviation)

To calculate the standard deviation, we first need to calculate the variance:

Variance = ∑(xi - μ)^2 / N

Where xi represents each value in the data set, μ is the mean, and N is the total number of values.

Using the values given, we can calculate the variance:

Variance = [(342 - 518)^2 + (518 - 518)^2 + (535 - 518)^2 + (605 - 518)^2] / 4

= 24,270

The standard deviation is the square root of the variance:

Standard deviation = √24,270

= 155.8

Therefore, the lower limit of the distribution curve would be 518 - (6 x 155.8) = 218.4, and the upper limit would be 518 + (6 x 155.8) = 817.6.

Answer:

Method 1:

cos(60°) = 4/x

x cos(60°) = 4

x = 4/cos(60°) = 8

Method 2 (more efficient method):

Since this is a 30°-60°-90° right triangle, the length of the hypotenuse is twice the length of the shorter leg, so x = 8.

The surface area of the cylinder is 408.41 cm^2.

The formula for calculating the surface area of the cylinder is 2πrh.

Here, r is the radius of the cylinder and h is the height of the cylinder.

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Answer:

The answer to the questions is

a)1

b)60°

Step-by-step explanation:

tan 45°=1

sin‐¹(√3/2)=60°

The values of the given trigonometric expression are:

(a) tan 45° = 1

(b) [tex]\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ[/tex]

Use the concept of trigonometric identity defined as:

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions.

There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

(a) The given trigonometric ratio is,

tan 45°

Since we know that,

In the trigonometric ratio table for the measure 45°,

The value of tangent is 1.

Hence,

tan 45° = 1

For the given trigonometric exprssion,

[tex]\text{sin}^{-1}(\frac{\sqrt{3}}{2})[/tex]

Since we know that,

Sin 60° = √3/2

Therefore,

[tex]\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = \text{sin}^{-1}(\text{sin }60^\circ)\\\text{sin}^{-1}(\frac{\sqrt{3}}{2}) = 60^\circ[/tex]

Hence,

The value of the given expression is 60°.

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Answer:

y = [tex]\frac{2}{3}[/tex] x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = [tex]\frac{2}{3}[/tex] , then

y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation

to find c substitute (6, 5 ) into the partial equation

5 = [tex]\frac{2}{3}[/tex] (6) + c = 4 + c ( subtract 4 from both sides )

1 = c

y = [tex]\frac{2}{3}[/tex] x + 1 ← equation of line

Answer:

Answer: (C) $546.36.

Step-by-step explanation:

To find the future value of the CD at maturity, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the future value of the CD

P = the principal amount (the initial amount invested), which is $500

r = the annual interest rate, which is 3% expressed as a decimal (0.03)

n = the number of times the interest is compounded in a year, which is once annually

t = the time the money is invested for, which is 3 years

Substituting the given values into the formula, we get:

A = 500(1 + 0.03/1)^(1*3)

A = 500(1.03)^3

A = 546.36

Therefore, the CD will be worth $546.36 at maturity. Answer: (C) $546.36.

The function that represents this situation is Total amount = 100(1 + 0.029)ᵗ + 15

The situation can be represented by a simple interest formula, where the balance increases every year by a fixed percentage of the principal amount. Let's assume that the initial amount is $100 and the interest rate is 2.90% per year, compounded annually. The formula for the balance after t years is:

B(t) = P(1 + r)ᵗ

Where P is the principal amount, r is the annual interest rate as a decimal, and t is the time in years.

In this case, the balance after t years is:

B(t) = 100(1 + 0.029)ᵗ

At the end of t years, when the money is withdrawn, the bank will give a free $15 gift, so the total amount received by the individual will be:

Total amount = B(t) + 15

So, the function that represents this situation is:

Total amount = 100(1 + 0.029)ᵗ + 15

where t is the number of years the money is saved.

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If the number of candies (c) you get from a bag is inversely proportional to the number of people (p) who share the bag, we can represent this relationship mathematically using the formula c = k/Np

where k is a constant of proportionality and N is the total number of candies in the bag.

To understand why this formula represents an inverse relationship, we can rearrange it as:

cp = k/N

In this form, we can see that the product of c and p is constant, while N remains fixed. This means that as the number of people sharing the bag (p) increases, the number of candies per person (c) decreases, and vice versa.

The constant of proportionality (k) depends on the specific bag of candies being considered. For example, if a bag contains 100 candies and is shared among 10 people, then k = 100/10 = 10. Substituting this value of k into the equation above gives:

c = 10/p

which shows that the number of candies per person decreases as the number of people sharing the bag increases.

Therefore, the equation that represents the inverse relationship between the number of candies (c) you get from a bag and the number of people (p) who share the bag is:

c = k/Np, where k is a constant of proportionality and N is the total number of candies in the bag.

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There is a Weak positive association between the amount of goals scored and the number of wins a hockey team has. Most of the data points fall between 4 goals scored and 5  number of wins. Causation cannot be established because their relationship was not in a controlled setting.

When if a relationship between two variables is said to be  negative, it is one that does not just necessarily mean that the association is weak. Although though both variables tend to increase in reaction to one another, a weak positive correlation depicts that the relationship is not very strong.

Therefore, even though  the data tells us that there is a weak positive relationship that exist between the two variables, it is vital to know that that correlation does not equal causation.

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The missing step in the proof include the following: C. QU║AD and UA║DQ because the segments have the same slope.

In Mathematics and Geometry, a parallelogram simply refers to a four-sided geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that is composed of two (2) equal and parallel opposite sides.

In Mathematics and Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂

This ultimately implies that, the slope of the two line segments are equal and the same:

Slope of line segment QU = Slope of line segment AD

-1/3 = -1/3

Slope of line segment UA = Slope of line segment DQ

-5/3 = -5/3

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The options that are valid conclusions about the data include:

More than half of the students are not enrolled in French or Spanish. This conclusion is valid, as 25 out of 120 students are not enrolled in either French or Spanish, and 25 is more than half of 120.

Of the students that are enrolled in French, fewer than half of them are also enrolled in Spanish. This conclusion is valid, as only 30 out of 50 students enrolled in French are also enrolled in Spanish, which is less than half.

Therefore, the valid conclusions are B and E.

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Answer:

We can use proportion to solve this problem.

Let x be the cost of one invitation.

We can set up a proportion:

58/x = 87/1

To solve for x, we can cross-multiply:

58 * 1 = 87 * x

58 = 87x

x = 58/87

x = 0.67

So one invitation costs $0.67.

To find the cost of 70 invitations, we can multiply the cost of one invitation by 70:

70 * $0.67 = $46.90

Therefore, it would cost Madison $46.90 to buy 70 invitations.

The surface area of the regular pyramid is 536.40 square inches

From the question, we have the following parameters that can be used in our computation:

Base length, l = 13 in

Base width , w = 15 in

Height, h = 10 in

The surface area of the regular pyramid is calculated as

Area = lw + 1/2w√[4h² + l²] + 1/2l√[4h² + w²]

Substitute the known values in the above equation, so, we have the following representation

Area = 13 * 15 + 1/2 * 15 *√[4 * 10² + 13²] + 1/2 * 13√[4 * 10² + 15²]

Evaluate

Area = 536.40

Hence, the surface area is 536.40 square inches

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There are three people to choose from to go on the left, and once we have chosen one of them, the other two people can be arranged in 2! ways.

There are 3 * 2! = 6 ways to arrange them if the woman will be on the left in the picture.

There are three people to choose from to go on the left, and once we've decided on one, the other two can be arranged in 2! ways.

Similarly, there are three people to choose from to go in the middle, and once we have chosen one of them, the other two people can be arranged in 2! ways.

Therefore, there are 3 * 2! = 6 ways to arrange them if the woman will be in the middle of the picture.

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