Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof to prove that they are.

The given trinomial is [tex]2a^2+5ab+7b^2[/tex]. The trinomial can be factored as (2a+7b)(a+b).

A trinomial is an algebraic expression consisting of three terms. It can be written in the form ax² + bx + c, where a, b, and c are constants and x is a variable. Trinomials are also used to solve equations, such as quadratic equations.

To factor this trinomial, we will first split the trinomial into two groups. The two groups are (2a, 7b) and (a, b).

Now we will multiply the first terms of both the groups.

We will get 2a × a = 2a².

This is the first term of the trinomial. Now we will multiply the second terms of both the groups.

We will get 7b × b = 7b².

This is the last term of the trinomial. Now we will multiply the first term of the first group and the second term of the second group.

We will get 2a × b = 2ab.

This is the middle term of the trinomial.

Hence, the trinomial can be factored as (2a+7b)(a+b).

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If a company starts with 3 employees and plans to triple the number of employees each year, then the number of employees can be represented by the function: f(n) = 3^n

To find the function to represent this situation we have to consider the information. In this formula we have to incluide the following information:

The number of employees at the end of the n year is equal to 3 raised to the power of n.

where,

n = number of years since the start of the company.

So, for example, if we want to know how many employees the company will have at the end of the second year, we can plug in n = 2 into the function:

According to the above, the company will have 9 employees at the end of the second year, and if we want to know how many employees the company will have at the end of the third year, we can plug in n = 3 into the function:

So, the company will have 27 employees at the end of the third year.

In general, the formula tells us that the number of employees at the end of the nth year is equal to 3 raised to the power of n.

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The graph of equation 1/2(x+1)=(y – 5)^2 looks like graph of a horizontal parabola.

Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.

How to graph equation?

one-half(x + 1) = (y – 5)^2, written symbolically, is (1/2)(x - [-1]) = (y – 5)^2

or x + 1 = 2(y – 5)^2.

Because the y term is squared, we know immediately that the graph is a horizontal (not vertical) parabola.  

This equation can be written as

x = 2 - 1

The standard equation of a horizontal parabola with vertex (h, k) is

x = c + h.  Comparing this to the given quadratic:  

we see that k = 5 and h = -1.  This tells us that the vertex of this graph is (-1, 5), and that the graph is stretched horizontally because c = 2 is greater than 1.

To graph this, it's best to make a short table of points, as follows, remembering that y is the independent value and x depends on y through the equation given above.

y    x = 2(y – 5)^2 - 1    (x, y)

0    x = 49                    (49, 0)

2    x = 2(-3)^2 - 1         (17, 2)

1   x = 2(-4)^2 - 1          (31,  1)

vertex (already found) (-1, 5)

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Answer:

45.73 square feet.

Step-by-step explanation:

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference and r is the radius.

We can rearrange this formula to solve for r:

r = C / 2π

Plugging in the given value of C = 24 feet, we get:

r = 24 / (2π)

r ≈ 3.819 feet

Now that we know the radius of the circle, we can use the formula for the area of a circle to find the approximate area of the park:

A = πr^2

Plugging in the value of r, we get:

A ≈ π(3.819)^2

A ≈ 45.73 square feet

Therefore, the approximate area of the circular park is 45.73 square feet.

Answer: A = 45.82 ft²

Step-by-step explanation:

Given:

C= 24 ft

Formulas needed:

C=2[tex]\pi[/tex]r    where r is radius

Circumference is the perimeter of the circle.  Length of outside line

and

Area:

A=[tex]\pi r^{2}[/tex]

Area the measurement of the shape or area that you want to cover.

Solution:

C=2[tex]\pi[/tex]r              >substitute C=24     and solve for r

24=2[tex]\pi[/tex]r            > divide both sides by 2[tex]\pi[/tex]

[tex]\frac{24}{2\pi }[/tex]  = r               >use 3.14 for [tex]\pi[/tex]

[tex]\frac{24}{2*3.14}[/tex]  = r          >plug into calculator

r=3.82

Now that we have r   we can solve for A

A=[tex]\pi r^{2}[/tex]

A=(3.14)(3.82)²     >plug into calc

A = 45.82 ft²

The calculated approximation of log(15/2) is 0.9

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

log(10) = 1.1

log(11) = 1.2

log(6) = 0.9

Also, we have

log(15/2)

Applyingthe quotient logarithmic law, we have

log(15/2) = log(15) - log(2)

15 and 2 cannot be derived directly from 10, 11 and 6

So, we solve independently using a calculator

log(15) = 1.2

log(2) = 0.3

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

log(15/2) = 1.2 - 0.3

Evaluate

log(15/2) = 0.9

Hence, the approximation is 0.9

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Answer: The median amount of sales each day was $7,000.

Step-by-step explanation:

To find the median amount of sales each day, we need to arrange the sales amounts in order from smallest to largest. Doing so, we get:

4,000 5,000 6,000 7,000 8,000 9,000

Since there are an odd number of values, the median is the middle value, which is 7,000. Therefore, the median amount of sales each day was $7,000.

The middle value of this dataset is 7,000, so the median amount of sales each day is $7,000.

The value that divides the mathematical numbers or expressions in half is known as the median. The midway number of data points is known as the median value. Then, organize the data points in ascending order before calculating the median.

Given information:

Gert's Groceries recorded the total amount of sales each day.

To find the median of a set of data, we need to order the data from least to greatest and then find the middle value(s).

4,000 5,000 6,000 7,000 8,000 9,000

The middle value of this dataset is 7,000, so the median amount of sales each day is $7,000.

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The system of equations when solved by substitution is x = 1 and y = 0

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

4x+4y=4

y=0

Substitute 0 for y in the first equation

So, we have

4x + 4(0) =4

This gives

4x = 4

Divide by 4

x = 1

Hence, the solution is x = 1 and y = 0

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Step-by-step explanation:

(a) Proportion of minority jurors = 2/12 = 1/6 = 0.1667

(b) Using binomial distribution, P(2 or fewer minorities) = P(0 minorities) + P(1 minority) + P(2 minorities)

P(0 minorities) = (0.53)^12 ≈ 0.005

P(1 minority) = 12C1 (0.47)(0.53)^11 ≈ 0.048

P(2 minorities) = 12C2 (0.47)^2(0.53)^10 ≈ 0.18

P(2 or fewer minorities) ≈ 0.005 + 0.048 + 0.18 ≈ 0.2339

(c) OA. The number of minorities on the jury is unusually low, given the composition of the population from which it came.

Answer:

mark me brilliant

Step-by-step explanation:

There are a total of 4+2=6 students in the seventh grade and 9+1=10 students in the eighth grade, so there are a total of 6+10=16 students in the class.

The probability of selecting a boy from the seventh grade is 2/4 = 1/2, and the probability of selecting a boy from the eighth grade is 9/10.

To find the probability of both events happening, we multiply the probabilities:

P(selecting a boy from seventh grade AND selecting a boy from eighth grade) = (1/2) x (9/10) = 9/20.

Therefore, the probability that the students selected for the competition are both boys is 9/20.

Answer:

12

Step-by-step explanation:

a general linear function can be written as

y= mx +b

where "m" is the pendient and "b" it's the point where the funcion has x=0

so u have to solve your ec. for y

[tex]6x + by = k[/tex]

[tex]by = - 6x + k[/tex]

[tex]y = - \frac{6}{b}x + \frac{k}{b} [/tex]

if u see your graph, when x=0 the function's value is 1, so k/b= 1, then k=b

then if we know b , we know k

as I said, m is the pendient, in this case -(6/b) is the pendient

As u may know, the pendient equals tan(alpha)

in this case alpha its the angle between the positive x axis and the function (the big one), we dont have that angle in a triangle to know its tangent, but we have (180-alpha) the littleone, and its tangent is 1/2 (see your graph)

so, for redunction to the first quadrant we have that

[tex] \tan( \alpha ) = - \tan(180 - \alpha ) = - \frac{1}{2} [/tex]

then,

[tex] - \frac{6}{b} = - \frac{1}{2} [/tex]

b=12

k=12

The value of k if the equation of the line drawn is 6x + by = k will be 12.

A general linear function can be written as; y= mx +b, where "m" is the pendient and "b" it's the point where the funcion has x=0

Given that;

6x + by = k

by = k - 6x

y = k/b - 6x/b

When x=0 the function's value is 1, thus, k/b= 1, then k=b

In this case -(6/b) is the pendient

The angle between the positive x axis and the function (the big one), we dont have that angle in a triangle to know its tangent, but we have (180-alpha) the littleone, and its tangent is 1/2.

then,

-6/b = -1/2

b=12

k=12

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In the given equation, 2x-9÷x-4 = 3, the solution to the equation is x = 3.

A quadratic equation is a second-degree polynomial equation in one variable of the form [tex]ax^2[/tex] + bx + c = 0, where x is the variable, and a, b, and c are constants, with a ≠ 0.

To solve for x in the equation 2x - 9 / (x - 4) = 3, we can begin by multiplying both sides by (x - 4) to eliminate the fraction in the equation:

2x - 9 = 3(x - 4)

Expanding the right side, we get:

2x - 9 = 3x - 12

Now we can simplify by subtracting 2x from both sides:

-9 = x - 12

And adding 12 to both sides:

3 = x

Therefore, the solution to the equation is x = 3.

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Your question seems incomplete, the probable complete question is

Solve for x:

2x-9÷x-4 = 3

Answer:

Step-by-step explanation:

Keeping a temperature record can help Lamar and others stay informed about the climate in their area and make informed decisions based on that information.

Lamar has been recording the high temperature in degrees Fahrenheit for his city over several days and has recorded them in a table. It is essential to keep a record of the temperature to track the weather patterns and make predictions about future weather conditions.

By having this data, Lamar can analyze the temperature trends in his city over time. He may notice that certain times of the year tend to be warmer or cooler than others or that some days are unusually hot or cold.

This information can be valuable for planning outdoor activities or making decisions about the best time to travel

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The probability that the mean IQ score of people in the sample is less than 98 is 0.2533, which is rounded to four decimal places.

Probability is a branch of mathematics that deals with the likelihood of a certain event or outcome occurring. Probability is based on the concept of counting and measuring the chances of something happening. It can be used to provide insight into how likely a certain outcome is to occur, and can be used to make decisions about the future. Probability can also be used to analyze data, identify patterns, and make predictions.

The probability that the mean IQ score of people in the sample is less than 98 can be calculated using the z-score. The z-score is calculated by subtracting the mean from the given value, 98, and then dividing the difference by the standard deviation, 15.0. This gives a z-score of -0.67.

Using the z-table, the probability of the mean IQ score of people in the sample being less than 98 can be calculated. The probability is 0.2533. Therefore, the probability that the mean IQ score of people in the sample is less than 98 is 0.2533, which is rounded to four decimal places.

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Answer:

Step-by-step explanation:

X axis come first then the y axis, p needs to start at 3 then go 4 units up and 3 units to the left and then you get (3,4)

Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{17}\\ a=\stackrel{adjacent}{d}\\ o=\stackrel{opposite}{15} \end{cases} \\\\\\ d=\sqrt{ 17^2 - 15^2}\implies d=\sqrt{ 289 - 225 } \implies d=\sqrt{ 64 }\implies d=8 \\\\\\ \stackrel{\textit{radius is half the diameter}}{r=\cfrac{8}{2}}\implies r=4 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=4\\ h=15 \end{cases}\implies V=\pi (4)^2(15)\implies V\approx 754~cm^3[/tex]

So, the standard deviation of the probability distribution is approximately 2.780.

To find the standard deviation for the probability distribution, we first need to find the mean (or expected value) of the distribution.

The mean is given by:

μ = ∑(x * P(x))

where x is the number of adults with a college degree and P(x) is the corresponding probability from the table.

μ = (00.0081) + (10.0756) + (20.2646) + (30.4116) + (4*0.2401)

μ = 2.8

So, the mean number of adults with a college degree in a sample of 4 is 2.8.

Next, we can use the formula for the standard deviation of a probability distribution:

σ = √∑[(x - μ)² * P(x)]

where x is the number of adults with a college degree, μ is the mean we just calculated, and P(x) is the corresponding probability from the table.

σ = √ [(0-2.8) ²0.0081 + (1-2.8) ²0.0756 + (2-2.8) ²0.2646 + (3-2.8) ²0.4116 + (4-2.8) ²*0.2401]

σ = √ [7.72404]

σ = 2.780

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The solution has a pH of 2.13, which is a measurement of a solution's acidity or alkalinity.

An aqueous solution's pH is a measure of how basic or acidic it is. The negative logarithm of the concentration of hydronium ions (H₃O⁺) is what this term, which means "power of hydrogen," is defined as. The pH scale goes from 0 to 14, where 0 is the most acidic and 14 is the most basic (or alkaline).

Since the concentration of hydronium and hydroxide ions in a solution with a pH of 7 is equal, this value is regarded as neutral. In contrast to bases, which have a pH above 7, acids have a pH below 7. The difference in the concentration of hydronium ions is represented by each full number on the pH scale.

The pH of a solution can be determined using the formula:

pH = -log[H⁺]

where [H⁺] is the concentration of hydronium ions in moles per liter.

In this case, [H⁺] = 7.4×10⁻³ moles/liter.

Substituting into the formula:

pH = -log(7.4×10⁻³) = 2.13

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Required true statements are f and d are vertical, d and e supplementary, g and are adjacent, d and g are complementary and f and e are linear pair.

What is the value of d?

Here d is the opposite angle of f.

We know opposite angles are always equal.

So, according to question f = 71° then d = 71°.

Now we need to check given statements are true or false.

1) Given d and f are adjacent.

We know, adjacent angles always have same vertex.

But angle f and d don't have any common vertex.

So, we can say d and f are not adjacent.

2) Given d and e are complementary.

From the picture, sum of d and e is 180°.

We know, sum of two complementary angles is 90° always.

So, this statement is also not true.

3) f and d are vertical.

Vertical angles are always opposite each other where two line cross.

Here it is clear f and d are opposite and they made by two line cross.

So, f and d are vertical is a true statement.

4) d and e supplementary.

Already said sum of d and e is 180°.

We sum of two supplementary angles is 180° always.

So, This is the true statement.

5) Here g and f have common vertex.

So, g and f are adjacent is the true statement.

6) Here value of g is (90-71) = 29°

So, sum of g and d is 90°.

Therefore, g and d are complementary.

7) Here d and g are not opposite.

So, they are not vertical.

8) Linear pair means, two hands of two common line

Here, f and e have two hands of two common line.

So, they are a linear pair.

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The expected value is calculated by multiplying the probability of each outcome by its corresponding value and then summing up all the values. In this case, the possible outcomes are either the man dies and the insurance company pays out the death benefit of $100,000, or he does not die and the insurance company keeps the premium of $260.

Expected value = (probability of death x death benefit) + (probability of no death x premium)

Expected value = (0.00248 x $100,000) + (0.99752 x $260)

Expected value = $248 + $259.38

Expected value = $507.38

Therefore, the expected value for the person buying the insurance is $507.38, rounded to the nearest dollar.

One of the function that satisfies all four statements is f(x) = 2 - [tex]e^{3-x}[/tex] , for x ≤ 3.

The function that satisfies all four statements is a decreasing function with a horizontal asymptote y = 0 that intersects the x-axis at x = 3. One possible function that satisfies all four statements is:

f(x) = 2 - [tex]e^{3-x}[/tex], for x ≤ 3

Explanation:

Statement 1, The domain of the function is x ≤ 3 because the expression [tex]e^{3-x}[/tex] becomes undefined for x > 3.

Statement 2, The range of the function is y ≥ 0 because the exponential term [tex]e^{3-x}[/tex] is always positive and subtracting it from 2 will always result in a non-negative value.

Statement 3, The x-intercept of the function is 3 because f(3) = 0, which means the graph intersects the x-axis at x = 3.

Statement 4, When x decreases, the function increases because the exponential term [tex]e^{3-x}[/tex] becomes smaller and smaller as x decreases, which causes the entire expression 2 - [tex]e^{3-x}[/tex] to increase.

Correct Question :

Write a function for which all four statements are true.

Statement 1: The domain of the function is x ≤ 3.

Statement 2: The range of the function is y ≥ 0.

Statement 3: The x-intercept of the function is 3.

Statement 4: When x decreases, the function increases.

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The expression that gives the surface area of a sphere with radius as r would be =4πr². That is option A.

A sphere is defined as the shape whose surface is made up of all the points that are an equal distance from the point that is the shape's center.

The formula that can be used to calculate the surface area of a sphere is given as;

S.A = 4πr²

Since the radius given is in terms of r, therefore, the expression that shows the surface area of a sphere would be = 4πr².

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Answer:

Step-by-step explanation:

1. -Growth because its increasing

  -asymptote y=0  boundary

  -domain (-∞,+∞)  where does x exist

  -range (0, +∞)    where does y exist

  - y-int (0,2)   plug x into equation or look where it hits y-axis

2.  Decay because its decreasing

   - asymptote y=4

   - domain  (-∞,+∞)

   -range (4, +∞)

   y-int (0,7)

3.  growth

y=-3

domain: (-∞,+∞)

range: (-3, +∞)

(0, -2.25)

4.  decay

y=3

domain  (-∞,+∞)

range (3, ∞)

y-int (0,5)

Answer:

x = 9

Step-by-step explanation:

The measure of angle M is half of the sum of the big arc minus the little arc it intersects.

We also know ∠M = 4x +4

∠M= 1/2(mArc CK - mArc LN)

Substitute in values

4x +4 = 1/2(15x + 12 - 67)

Combine like terms

4x + 4 = 1/2(15x - 55)

Multiply (what's in side the parenthesis by 1/2)

4x + 4 = 7.5x - 27.5

Isolate the x. Add 27.5 to both sides

4x + 31.5 = 7.5x

Subtract 4x from both sides

31.5 = 3.5x

Divide both sides by 3.5

9 = x

The number of homeruns Luis Gonzales will have after 100 games can be expected using probability as 55.

Given that,

Luis Gonzales plays baseball for the Arizona Diamondbacks.

Number of games played in a season = 20

Number of games he had homeruns = 11

So there is a chance to get 11 homeruns from 20 games.

Probability of having homeruns = 11/20 = 0.55

If he played 100 games,

Expected number of homeruns he would get = 100 × 0.55 = 55

Hence the expected number of homeruns he has in 100 games is 55.

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The critical value is at x = -3/4, and the solution set is  ( -3/4, ∞)

We can define the critical values as the problematic values. For example, we can't divide by zero, so the value of x that makes the denominator equal to zero is a critical value.

4x + 3 = 0

4x = -3

x = -3/4

That is the critical value.

Now let's solve the inequality.

-5/(4x + 3) < 0

That is true as long as the denominator is positive, so:

4x + 3 > 0

x > -3/4

The solutions et is ( -3/4, ∞)

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The map shown the western lands that Georgia ceded to the federal government. The Option A is correct.

Georgia ceded its western land to federal government because of financial struggles faced after the American Revolutionary War.

The state had accumulated debts and lacked the financial resources to manage and develop the western lands within its borders which were inhabited by Native American tribes.  Also, there were concerns about potential conflicts with Native American tribes and the need for federal protection.

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