a) Write a similarity statement.
b)lf BC = 2 and DC = 10. AD =

According to algebraic identities ,

[tex] \cos( \frac{ \theta}{2} ) = \sqrt{ \frac{1 + \cos(\theta) }{2} } \\ [/tex]

Therefore ,

[tex]\boxed{ { \cos}^{2} (\frac{\theta}{2} ) = \frac{1 + \cos(\theta) }{2} } \\ [/tex]

hope helpful! :)

Answer:

Using the half-angle formula for cosine, we can express cos(θ/2) in terms of the values of cos θ and sin θ:

cos(θ/2) = ±√[(1 + cos θ)/2]

The sign of the square root depends on the quadrant in which θ/2 lies.

Since we are given cos^2 θ/2, we need to eliminate the square root in the expression for cos(θ/2). To do this, we can use the fact that:

sin^2 θ/2 = 1 - cos^2 θ/2

Substituting the expression for cos^2 θ/2 from the previous identity, we get:

sin^2 θ/2 = 1 - cos^2 θ/2 = 1 - cos^2 (θ/2)

Solving for cos(θ/2) in terms of sin(θ/2), we get:

cos(θ/2) = ±√[1 - sin^2 θ/2]

Substituting the expression for sin^2 θ/2 from above, we get:

cos(θ/2) = ±√[cos^2 θ/2]

The sign of the square root depends on the quadrant in which θ/2 lies. Therefore, the completed identity for cos^2 θ/2 is:

cos(θ/2) = ±cos θ/2

Step-by-step explanation:

By answering the above question, we may state that As a result, around expressions 10:35 AM, Ariana and Leon began their clothing shopping.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.  

We must take the time they spent at the mall overall from the moment they departed in order to determine when Ariana and Leon began looking for clothing.

To make adding up the times easier, let's first convert all the times to minutes:

Clothing shopping takes an hour, or 60 minutes.

Restaurant: 55 minutes

In a video arcade, two hours are equal to 120 minutes plus 10 minutes.

Total time spent at the mall is 245 minutes (60 + 55 + 130).

If they left the mall at 1:40, then we need to take 245 minutes away from that time.

1:00 PM minus 245 minutes equals 10:35 AM.

As a result, around 10:35 AM, Ariana and Leon began their clothing shopping.

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If matric learners do not obtain the marks they need to enter their chosen study programmes, there are several strategies they can implement to still achieve their academic and career goals:

1. Consider alternative study programmes: Matric learners who did not obtain the marks they need for their first choice of study programme should consider other programmes that may be similar or related to their original choice. They can also look at bridging courses, diploma programmes or short courses that will enable them to develop the skills and knowledge they need for their chosen career.

2. Upgrade matric results: Some learners may choose to re-write some of their matric subjects to improve their results. This can be done through night school, part-time courses or through online platforms. This will require dedication, hard work and perseverance, but it can be an effective way to meet the entry requirements for their desired study programmes.

3. Attend a tertiary institution with lower entry requirements: Matric learners who do not meet the requirements for their desired study programme at their first choice institution can consider attending another institution with lower entry requirements. This will enable them to obtain a qualification in their chosen field, which they can use to pursue further studies or career advancement.

4. Take a gap year: Taking a gap year to gain work experience or travel can provide learners with valuable skills and experiences that can enhance their application for their chosen study programme in the future. This time can also be used to upgrade their matric results or to explore other interests and career options.

In conclusion, while not obtaining the marks required to enter a chosen study programme can be disappointing, it is important for matric learners to remain positive and proactive. By considering alternative study programmes, upgrading matric results, attending institutions with lower entry requirements, or taking a gap year, learners can still achieve their academic and career goals.

Answer:

Step-by-step explanation:

Given functions:

    [tex]r(x)=x^2+5x+14[/tex]

    [tex]c(x)=x^2-4x+5[/tex]

where:

Profit is calculated by subtracting expenses from revenue.

Therefore, the composite function for profit is:

Since x represents the number of months the store has been open:
(r - c)(5) is the amount of profit generated by the George's store 5 months after it has been open.

To calculate the total amount of profit in the first 5 months, substitute x = 5 into the composite function:

[tex]\begin{aligned}\implies (r-c)(5)&=r(5)-c(5)\\&=(5^2+5(5)+14)-(5^2-4(5)+5)\\&=(25+25+14)-(25-20+5)\\&=(50+14)-(5+5)\\&=64-10\\&=54\end{aligned}[/tex]

Since the revenue and expenses functions are measured in hundred of dollars, so too is the profit function. Therefore, the amount of profit generated in 5 months is $5,400.

Answer:

Step-by-step explanation:

20 degees

Answer:

The graph will shift 3 units down

The side AC is 10 units long.

Measurement of length can be done in a variety of methods, including using handspan, foot span, metres, or other units including millimetres, inches, and metres. There are two types of length measurement units: There are both conventional and nonstandard length measurement units.

The Pythagorean theorem can be used to determine the length of side AC in the triangle ABC given:

AC² = AB² + BC²

AC² = 6² + 8²

AC² = 36 + 64

AC² = 100

AC = 10

As a result, the side AC is 10 units long.

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Answer:whoops it’s b

Answer:

Its A I think

Step-by-step explanation:

Answer: $1560

Step-by-step explanation:

The word "of" in a problem means to multiply.  30% = .30. So, the cost of the printer is .30c.

If we add the cost of the computer, c, to the cost of the printer, .30c, then we get 1.30c. We know that the total is $2028, so our equation is 1.30c = $2028.  

Dividing both sides by 1.30, we get c = $1560.

Answer:

the expression

y -7/x-5 = 1/3 or 2/6

Step-by-step explanation:

Cross multiplying both sides:

3(y-7) = x - 5

3y - 21 = x - 5

3y - x = 21 - 5

3y - x = 16

The simplified equation is 3y-x=16.

Answer:

Step-by-step explanation:

We can expand and simplify the equation as follows:

23(x+3) = 23(x-6)

23x + 69 = 23x - 138

69 = -138

The last equation is clearly false, which means there is no value of x that can satisfy the original equation.

This is an example of a contradiction, where the equation leads to an impossible statement. Therefore, the equation has no solution.

The monthly periodic rate is 1.25%, the finance charge is $6.99 and John's new balance is $566.24.

This monthly periodic rate calculated as

Monthly periodic rate = Annual percentage rate / 12

So, we have

Monthly periodic rate = 15% / 12

Monthly periodic rate = 1.25%

This is the interest charged for the month.

So, we start by calculating the average daily balance using:

Average daily balance = ((Previous month's balance + Current month's purchases and cash advances) - Current month's payments and credits) / Number of days in the month

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

Average daily balance = (428.10 + 281.15) - 150.00) / 31

Average daily balance = $18.04

So, we have

Finance charge = Average daily balance x Monthly periodic rate x Number of days in the month

Finance charge = $18.04 x 1.25% x 31

Finance charge = $6.99

The new balance is calculated as

New balance = Previous month's balance + Current month's purchases and cash advances + Finance charge - Current month's payments and credits

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

New balance = $428.10 + $281.15 + $6.99 - $150.00

New balance = $566.24

Hence, the new balance is $566.24

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Answer:

31/8 or  5 1/8

Step-by-step explanation:

[tex]4-\dfrac{1}{8} = \dfrac{4(8) -1}{8} = \dfrac{32 -1}{8} = \bf \dfrac{31}{8} \\[/tex]

Answer:

Step-by-step explanation:

We know that the life expectancy of the tires is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. Let X be the life expectancy of the tire. Then X ~ N(40,000, 5,000^2).

To find the percentage of tires that will have a life of 34,000 to 46,000 miles, we need to calculate the z-scores for both values using the formula:

z = (X - μ) / σ

where X is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.

For X = 34,000:

z = (34,000 - 40,000) / 5,000 = -1.2

For X = 46,000:

z = (46,000 - 40,000) / 5,000 = 1.2

Now, we need to find the area under the standard normal distribution curve between these two z-scores. We can use a table of standard normal probabilities or a calculator to find this area.

Using a standard normal table or a calculator, we find that the area to the left of z = -1.2 is 0.1151, and the area to the left of z = 1.2 is 0.8849. Therefore, the area between these two z-scores is:

0.8849 - 0.1151 = 0.7698

So, approximately 76.98% of the tires will have a life of 34,000 to 46,000 miles.

The answer to the expression is 24.

Expression is an action or a way of speaking that shows a feeling, opinion, or attitude. It can be done through words, body language, facial expressions, tone of voice, and other forms of communication. Expression is used to communicate ideas, thoughts, emotions, and feelings. It is a fundamental way of connecting with others and conveying meaning.

To evaluate the expression, we need to first calculate the values of f(5) and f(-12). For f(5), the function is defined as

f(x) = 2x + 3. Thus, f(5) = 2(5) + 3 = 13. For f(-12), the function is f(x) = -x + 7. Thus, f(-12) = -(-12) + 7 = 19. We can now calculate 3f(5) - f(-12) = 3(13) - 19 = 24.

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Step-by-step explanation:

72 hours total baking during 6 days.

that means 72/6 = 12 hours of baking every day.

3 hours of these 12 hours he used to bake bread.

that leaves 12 - 3 = 9 hours every day for baking cakes.

so, to summarize all this in an arithmetic expression :

x = 72/6 - 3 = 9

The possible values of the density curves is mean μ = 30 mpg and the median = 28 mpg

A mathematical function called a probability distribution explains the likelihood of many alternative values for a variable. Graphs or probability tables are frequently used to represent probability distributions.

The mean of probability distribution is also known as expected value. It is denoted by E ( X ). E(X), or mean μ of a discrete random variable X is calculated by multiplying each value of the random variable by its probability and taking the sum of the values.

Given data ,

Let the probability distribution be represented as P

Now , the value of P from the figure is

The balancing point at which a density curve would be in equilibrium if it were formed of solid material is represented by the curve's mean.

A symmetric density curve has the same median and mean.

So , the mean of the probability density curve is μ = 30 mpg

And , the median of the probability density curve lies between 25 and 30

where median = 28 mpg

Hence , the mean and median of the density curve is solved

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The complete question is attached below.

A density curve showing the fuel efficiency of cars is shown.

Which values are the possible measures of center for this density curve? Check all that apply.

Answer:

A and D

Step-by-step explanation:

e2020

The scale factor is 1.5. And the value of the variables 'x' and 'y' will be 9 and 10, respectively.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

The ratio of the corresponding sides will be constant. Then the scale factor is given as,

SF = 12 / 8

SF = 1.5

The equation is given as,

x / 6 = 12 / 8 = 15 / y

From the first two terms, then we have

x / 6 = 12 / 8

x = 9

From the last two terms, then we have

12 / 8 = 15 / y

y = 10

The scale factor is 1.5. And the value of the variables 'x' and 'y' will be 9 and 10, respectively.

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The statements that are true based on the graph and the context of the problem include the following: B. I and III only.

In Mathematics, the y-intercept is sometimes referred to as an initial value or vertical intercept and the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the information provided about the line on the graph, we have the following:

y-intercept of function = (0, 1,200), which represents the initial cost of the bedroom furniture.

Additionally, the function is positive on its entire domain and the domain is x ≥ 0, which represent the number of years after the bedroom furniture was purchased.

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9 people prefer strawberry.

A pie chart is a circular chart used to represent data as a proportion of a whole. The whole is represented by the complete circle, while the individual parts are represented by slices of the circle, each corresponding to a particular category or value.

Pie charts are often used to display data that is divided into a few distinct categories, where the size of each category can be easily compared. The size of each slice is proportional to the quantity it represents, and the slices are typically labeled with their corresponding categories or values.

Pie charts are a useful tool for quickly and easily visualizing data, and they are commonly used in business, marketing, and other fields. However, it is important to use them appropriately, as they can be misleading if the slices are not sized correctly or if there are too many categories to be displayed effectively.

18% of 50 people prefer strawberry.

To find out how many people prefer strawberry, we can start by finding out what 1% of 50 is:

1% of 50 = 0.01 x 50 = 0.5

Then, we can multiply this value by the percentage of people who prefer strawberry:

0.18 x 50 = 9

Therefore, 9 people prefer strawberry.

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The complete question is:

The inequality for this problem, along with it's solution, is given as follows:

A. x − 4 < 6; x < 10

The segment addition postulate is a geometry axiom that states that when a line segment is divided into a number of smaller segments, the total length is given by the sum of the lengths of each of the smaller segments.

For this problem, we have that BD is a smaller segment of segment BC, hence the inequality is given as follows:

BD < BC.

Replacing with x, the solution is obtained as follows:

x - 4 < 6

x < 6 + 4

x < 10.

Meaning that option a is the correct option.

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Answer:

Jiri is 48 years old

Step-by-step explanation:

STEP 1

Let Jill's age be equal to: x

Let Pamela's age be equal to :Jiri's age(x) - 15

STEP 2

Total sumof Jiri and Pamela's age= 81

Sum= Pamela's age + Jiri's age

81 = (x-15) + x

81 =x -15 + x

81 = x+x -15

81= 2x -15

Collect like terms

81 + 15= 2x ( recall - changes to + when crossing the =)

96=2x

Divide both sides by 2

96/2 =2x/2

48 = x

Recall Jiri's age is equal to x

Hence Jiri's age is equal to 48

Answer:

Step-by-step explanation:

[tex]6x-10=2x+18[/tex]   (opposite sides of parallelogram are equal)

[tex]4x-10=18[/tex]           (subtracted [tex]2x[/tex] from both sides)

[tex]4x=28[/tex]                   (added 10 to both sides)

[tex]x=7[/tex]                       (divided both sides by 4)

Substitute [tex]x=7[/tex] to find length AB:

[tex]AB=6x-10[/tex]

      [tex]=6[/tex]×[tex]7-10[/tex]

       [tex]=32[/tex]

Olivia will need at least 11 months to reach her savings goal.

What is algebra ?

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It involves the use of letters and symbols to represent values and quantities in mathematical equations and formulas. Algebra is used to solve problems that involve unknown quantities by using rules and operations to manipulate the symbols representing those quantities.

Let's use algebra to solve this problem. Let "m" be the number of months it will take for Olivia to reach her goal of saving at least $7,500.

In one month, Olivia will deposit $650, so after "m" months, she will have deposited:

650m

In addition to this, Olivia already has a balance of $400, so her total savings after "m" months will be:

650m + 400

We want to find how many months "m" it will take for Olivia to save at least $7,500. So we can set up the following inequality:

650m + 400 >= 7,500

Subtracting 400 from both sides:

650m >= 7,100

Dividing both sides by 650:

m >= 10.92

Since we can't have a fraction of a month, we'll round up to the next whole number. Therefore, Olivia will need at least 11 months to save at least $7,500.

Therefore, Olivia will need at least 11 months to reach her savings goal.

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Using the vertical line test we can see that this is not a function.

When we have a graph of a relation, one thing we can do to check if this is a function is do the vertical line test.

If you can draw a vertical line that intercepts the graph more than once, then it is not a function.

Here we can see a circle, multiple lines intercept the graph twice,so this is not a function.

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Correct two-way relative frequency table for the data is option A.

A frequency table is a way to organize and display data in a table format by showing the number of times a certain data point or category appears in a given dataset. It is used in statistics and data analysis to quickly and easily understand the distribution of a set of data.

A frequency table typically consists of two columns: the first column lists the categories or data points, and the second column lists the frequency or count of each category. The categories can be anything from numbers to words, but they should be mutually exclusive and exhaustive, meaning that each data point should fit into one and only one category, and all possible data points should be included in the table.

Frequency tables are commonly used to represent categorical data, such as survey responses, demographic data, and results of experiments. They are also useful for visualizing patterns and trends in the data, such as the most common or rare categories, and can be used to calculate various statistical measures, such as percentages, proportions, and averages.

The correct answer is:

                                    Playing        Listening      Watching         Row Totals

                                    Computer   to Music        Movies/TV

                                    Games      

Drama Club Students 5%            25%          20%          50%

Art Club Students         18.75%     15%          16.25%          50%

Column Totals         23.75%     40%          36.25%          100%

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The complete question is:

The simplest form of the given expression 3√12 × √5  is 6√15.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The given expression is as follows:

3√12 × √5

To solve this problem, we can simplify the expression first:

3√12 × √5 = 3√(12 × 5) = 3√60

To further simplify the expression, we can factor 60 into its prime factors:

60 = 2² × 3 × 5

Here, we can rewrite the expression as:

3√60 = 3√(2² × 3 × 5) = 3 × 2√15

Thus, the values of a and b are a = 6 and b = 15.

Therefore, the simplest form of the given expression is 6√15.

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The correct question is as follows:

The answer to 3 √12 × √5, given in its simplest form, is a√b, where a and b are integers.

Calculate the values of a and b.

Based on the information, we can infer that it is FALSE because it's not possible to construct a triangle with the measures of 4cm, 5cm and 9cm in length on its sides.

To find out if the statement is false or true, we must analyze the information on the lengths of the sides of the triangle and review the construction rules of a triangle to find out if its lengths have any condition.

In accordance with the above, we find that no triangle can be built with these lengths on its sides because, according to the Triangle Inequality Theorem, the sum of two of the sides of the triangle must be greater than the length of the third side. Therefore, if the sum of 4 + 5 results in 9, it is false that we can build a triangle with these measurements.

Note: This question is incomplete. Here is the complete information:

True or false.

Using this information, triangles can be constructed.

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