graph the function f(x)=x^2+6x+4 by starting with the graph of y=x^2 and using transformations

Answers

Answer 1

The following steps we have to follow to make the graph of the given function:

[tex]f(x) = x^2 + 6x + 4[/tex]

Start with the graph of [tex]y = x^2[/tex], which is a parabola that opens upwards and passes through the origin (0, 0).

To shift the parabola to the left by 3 units (since 6/2 = 3), we subtract 3 from x inside the function. This gives us

[tex]y = (x - 3)^2[/tex],

which is the same parabola shifted 3 units to the right.

To shift the parabola up by 4 units, we add 4 to the function. This gives us f(x) = (x - 3)^2 + 4, which is the final function we want to graph.

To graph f(x), we can plot a few points and sketch the resulting parabola. For example, when x = -2, we have

[tex]f(-2) = ( -2 - 3)^2 + 4 = 9[/tex],

so one point on the graph is (-2, 9). Similarly,

when x = -1, we have

[tex]f(-1) = (-1 - 3)^2 + 4 = 8[/tex], so another point on the graph is (-1, 8). We can continue this process to get more points and sketch the parabola.

Here is a rough sketch of the graph of [tex]f(x) = x^2 + 6x + 4:[/tex]

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Graph The Function F(x)=x^2+6x+4 By Starting With The Graph Of Y=x^2 And Using Transformations

Answer 2

The following steps we have to follow to make the graph of the given function:

[tex]f(x) = x^2 + 6x + 4[/tex]

Start with the graph of [tex]y = x^2[/tex], which is a parabola that opens upwards and passes through the origin (0, 0).

To shift the parabola to the left by 3 units (since 6/2 = 3), we subtract 3 from x inside the function. This gives us

[tex]y = (x - 3)^2[/tex],

which is the same parabola shifted 3 units to the right.

To shift the parabola up by 4 units, we add 4 to the function. This gives us f(x) = (x - 3)^2 + 4, which is the final function we want to graph.

To graph f(x), we can plot a few points and sketch the resulting parabola. For example, when x = -2, we have

[tex]f(-2) = ( -2 - 3)^2 + 4 = 9[/tex],

so one point on the graph is (-2, 9). Similarly,

when x = -1, we have

[tex]f(-1) = (-1 - 3)^2 + 4 = 8[/tex], so another point on the graph is (-1, 8). We can continue this process to get more points and sketch the parabola.

Here is a rough sketch of the graph of [tex]f(x) = x^2 + 6x + 4:[/tex]

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Related Questions

Suppose a worker makes $22,000 in wages per year. Find the percent increase in salary the worker can expect if he/she trains to be a teacher and can expect to earn a salary of $42,000.

Answers

The solution is, the percent increase in salary is: 90.9%

Here, we have,

given that,

Suppose a worker makes $22,000 in wages per year.

and, he/she trains to be a teacher and can expect to earn a salary of $42,000.

now, we have to find the percent increase in salary the worker can expect.

so, we have,

previous salary = $22,000

expected salary = $42,000.

so, increase = $ 20000

so, the percent increase in salary is:

20000/22000 * 100

=90.90

so, the percent increase in salary is: 90.9%

Hence, The solution is, the percent increase in salary is: 90.9%.

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Identify the domain and range of the function. y=3√x
A. Domain: x≥3, Range: y≥3
B. Domain: All Real Numbers, Range: All Real Numbers
C. Domain: x≥0, Range: y≥0
D. Domain: x≤0, Range: y≤0

Answers

The domain and range of the function are C. Domain: x≥0, Range: y≥0

Identifying the domain and range of the function

The domain of the function is the set of all possible input values (x) for which the function is defined.

In this case, the function y = 3√x is defined for non-negative real numbers, because the root of a negative number is not a real number.

Therefore, the domain of the function is:

Domain: {x | x ≥ 0}

The range of the function is the set of all possible output values (y) that the function can take.

Since the root of any positive number is also positive, the function y = 3√x will always return a positive number for any positive input value.

Therefore, the range of the function is:

Range: {y | y ≥ 0} or [0, ∞) in interval notation.

Answers

The test statistic based on the information is given by 2.19.

How to calculate the value

This evidence-based test has an available degree of freedom of 11 - being acquired by subtracting 1 from the overall 12. With 11 degrees of freedom in combination with a 0.05 margin of significance, an applicable t-distribution table states that the essential critical value is 1.796.

Seeing as our experimental statistic of 2.19 surpasses the critical value of 1.796, we must discount the null hypothesis. Consequently, sufficient proof signifies that the average math score population attains a higher mean than its writing counterpart when contemplating a 0.05 level of significance.

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Determine whether the graph of the quadratic function y = –2x^2 – 4x + 4 opens upward or downward. Explain.

Answers

The graph of the quadratic function [tex]y=-2x^2-4x+4[/tex] opens downward.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here the given function is [tex]y=-2x^2-4x+4[/tex]

The general form of the quadratic function is y=[tex]ax^2+bx+c[/tex]

Then, a= -2

Which is negative value.

Then the graph is open downward.

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Felix is purchasing a brownstone townhouse for $2,500,000. To obtain the mortgage, Felix is required to make a 18% down payment. Felix obtains a 30-year mortgage with an interest rate of 6.5%.

a) Determine the amount of the required down payment.
b) Determine the amount of the mortgage.
c) Determine the monthly payment for principal and interest.
quiz

Answers

a) The down payment required would be 18% of the purchase price of the townhouse, which is $2,500,000. Therefore, the down payment required would be:

Down payment = 0.18 x $2,500,000 = $450,000

b) The amount of the mortgage would be the difference between the purchase price of the townhouse and the down payment. Therefore, the amount of the mortgage would be:

Mortgage = $2,500,000 - $450,000 = $2,050,000

c) The monthly payment for principal and interest can be calculated using the loan amount, interest rate and loan term. For a 30-year loan with an interest rate of 6.5%, the monthly payment formula is:

Monthly payment = (P x (r/12)) / (1 - (1 + r/12)^(-n*12))

Where P is the loan amount, r is the interest rate (as a decimal), and n is the number of years. Plugging in the values, we get:

Monthly payment = ($2,050,000 x (0.065/12)) / (1 - (1 + (0.065/12))^(-30*12))
= $12,973.47

Therefore, the monthly payment for principal and interest would be $12,973.47.

The perimeter of a rectangle is 18 X +6 the width of the rectangle is 2X +5 what is an expression for the length of the rectangle

Answers

If perimeter of rectangle is denoted as "18x+6" and width is denoted as "2x+5", then the expression for length of the rectangle will be .

The "Perimeter" of a rectangle is known as the "total-distance" around the outside of rectangle.

Let length of rectangle be denoted by "L". The formula for the "peri-meter" for rectangle is : P = 2(length + width),

The "peri-meter" is = "18x + 6", and "width" is "2x + 5".

Substituting these values into the formula,

We get,

⇒ 18x + 6 = 2(L + 2x + 5),

⇒ 18x + 6 = 2L + 4x + 10,

⇒ 18x - 4x - 10 - 6 = 2L,

⇒ 14x - 16 = 2L,

⇒ 7x - 8 = L,

Therefore, the expression for the length of the rectangle is "7x - 8".

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Find the length of the missing side

Answers

Answer: [tex]b=\sqrt{45}[/tex] or b=6.71 in.

Step-by-step explanation:

Use Pythagorean Theorem

[tex]a^2+b^2=c^2[/tex]

In this case, a=2in and c=7in, and we're solving for b.

[tex](2)^2+b^2= (7)^2\\4+b^2= 49\\b^2=45\\b=\sqrt{45}[/tex]

Therefore, b=6.71 in.

A garden is in the shape of a square with a perimeter of 36 feet. The garden is surrounded by two
fences. One fence is around the perimeter of the garden, whereas the second fence is 2 feet from th
first fence on the outside. If the material used to build the two fences is $1.15 per foot, what was the
total cost of the fences?

Answers

The perimeter of the square garden is 36 feet, which means that each side of the square is 36/4 = 9 feet long. Therefore, the total cost of the fences is $92.

How is Perimeter calculated?

The length of the outer fence, which is 2 feet away from the garden, is equal to the perimeter of a larger square with sides that are 2 feet longer than the sides of the original garden.

So, the length of the outer fence is 4(9+2) = 44 feet.

The length of the inner fence, which is around the perimeter of the garden, is equal to the perimeter of the original square garden, which is 4(9) = 36 feet.

The total length of both fences is the sum of the lengths of the inner and outer fences:

36 + 44 = 80 feet.

The cost of the fences is the total length of both fences multiplied by the cost per foot:

80 x $1.15 = $92.

Therefore, the total cost of the fences is $92.

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math adjacent angles

Answers

Answer: ∠EFA and/or ∠CFB

Step-by-step explanation:

Adjacent: In order to classify adjacent the 2 angles need to have a common side and common vertex

Starting Angle: ∠CFE

Possible Adjacents: ∠ EFA and/or ∠CFB

ap calculus problem
no need full detail solution

Answers

If Limₙ→∞, aₙ ≠ 0 or does not exist, then ∑^∞_{n= 1} (aₙ) diverges.

option C.

What is the solution of the limit function?

The solution of the limit function is calculated as follows;

Limₙ→∞, aₙ ≠ 0 or does not exist, then ∑^∞_{n= 1} (aₙ),

So in this type of function, we will conclude that the function diverges.

This is known as the divergence test, which states that if the limit of the nth term of a series does not approach zero, then the series diverges.

In other words, we can say that if the terms of the series do not approach zero, the series will not converge.

Thus, based on the given option, the correct answer is diverges.

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sin(75°)= sqrt1-cos(150°)/2 true or false

Answers

[tex] \sqrt{ \frac{1 - cos(150)}{2} } = \sqrt{ \frac{1}{2} - \frac{cos(150)}{2} } = \sqrt{ \frac{1}{2} - \frac{ \frac{ - \sqrt{ 3}}{2} }{2} } = \sqrt{ \frac{2}{4} + \frac{ \sqrt{3} }{4} } = \sqrt{ \frac{2 + \sqrt{3} }{4} } [/tex]

[tex]= \frac{ \sqrt{6} + \sqrt{2} }{4} [/tex]

BTW:

[tex]sin(75) = \frac{ \sqrt{6} + \sqrt{2} }{4} [/tex]

[tex] = > sin(75) = \sqrt{ \frac{1 - cos(150)}{2} } [/tex]

Ans: True

Ok done. Thank to me >:33

Can you check if all these answers are correct?
Question 1: The side length c of the triangle is equal to: c 2 =a 2 +b 2 −2abcosC where a and b are the other two side lengths of the triangle, and C is the angle opposite side c. To solve for c, you can plug in the values of a, b, and C into the formula and solve for c. For example, if a=3, b=4, and C=60 ∘ , then you would plug in these values into the formula and solve for c as follows: c 2 =3 2 +4 2 −2⋅3⋅4cos60 ∘ c 2 =25 c= 25 =5 Therefore, the side length c of the triangle is equal to 5. Question 2: The angle C of the triangle is equal to: cosC= 2ab a 2 +b 2 −c 2 where a, b, and c are the other two side lengths of the triangle. To solve for C, you can plug in the values of a, b, and c into the formula and solve for C. For example, if a=3, b=4, and c=5, then you would plug these values into the formula and solve for C as follows: cosC= 2⋅3⋅4 3 2 +4 2 −5 2 =− 4 1 C=cos −1 (− 4 1 )≈109.47 ∘ Therefore, the angle C of the triangle is approximately 109.47 degrees. Question 3: The area of the triangle is equal to A= 2 1 absinC where a and b are the other two side lengths of the triangle, and C is the angle opposite side c. To solve for A, you can plug in the values of a, b, and C into the formula and solve for A. For example, if a=3, b=4, and C=60 ∘ , then you would plug in these values into the formula and solve for A as follows: A= 2 1 ⋅3⋅4sin60 ∘ =6 3 Therefore, the area of the triangle is equal to 6 3 . Question 4: The perimeter of the triangle is equal to: P=a+b+c where a, b, and c are the three side lengths of the triangle. To solve for P, you can simply add up the values of a, b, and c. For example, if a=3, b=4, and c=5, then you would add up these values to get P=12. Therefore, the perimeter of the triangle is equal to 12. Question 5: The centroid of the triangle is located at a point that is: One-third of the way from each vertex to the opposite side. Equidistant from all three vertices. On the medians of the triangle. To find the centroid of the triangle, you can use the following formula: G=( 3 a+b+c , 3 a+b+c , 3 a+b+c ) where (a,b,c) are the coordinates of the three vertices of the triangle.

Answers

Answer:

All of the answers appear to be correct based on the given formulas and values.

What is the solution to 2|1-x|+1>3

Answers

Answer:

x < 0, x > 2

Step-by-step explanation:

|1-x| > 1

(x-1)^2 > 1

x^2 -2x + 1 > 1

x^2 - 2x > 0

x(x-2) > 0

Using the graph of y=x(x-2), x(x-2)> 0 when

x < 0, x > 2

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Find WX. Assume that segments that appear to be tangent are tangent.

WX =

(50 POINTs will give BRAINIEST FOR EFFORT)

Answers

Answer:

WX = 34 units

---------------------

WX and YX are tangents drawn from point X to circle Z.

Tangent segments drawn to the same circle from the same point are equal:

WX = YX

Substitute values for side lengths and solve for x:

7x - 29 = 2x + 167x - 2x = 16 + 295x = 45x = 9

Substitute 9 for x and find the length of tangent WX:

WX = 7*9 - 29 = 63 - 29 = 34

Δ XYZ, shown below, is a 30° - 60° - 90° triangle.

8). Which leg is the shorter leg?
9). In a 30° - 60° - 90° triangle, the shorter leg is always opposite the _____° angle.
10). Which leg is the longer leg?
11). In a 30° - 60° - 90° triangle, the longer leg is always opposite the ____° angle.

12). If YZ = 5, then XY = ____ and XZ = _______.
13). If YZ = 6, then XY = ____ and XZ = _______.
14). If XY = 8, then YZ = _____ and XZ = _______.
15). If XY = 6, then YZ = _____ and XZ = _______.

Answers

Answer:

8). YZ

9). 30°

10). XY

11). 90°

12). XY=10 and XZ=5√3

13). XY=12 and XZ=6√3

14). YZ=4 and XZ=4√3

15). YZ=3 and XZ=3√3

Mrs. Brown records the rainfall in Seattle, Washington during each month of 2021. (8.75, 4.68, 2.61, 1.03, 1.12, 1.91, 0.00, 0.11, 3.02, 5.76, 10.62, 4.38} Mrs. Brown wants to use a graphical representation that will allow her students to see the overall shape of the data and provide enough information to determine the 5-number summary Which representations should Mrs. Brown consider? Select all that apply.

Answers

Answer:

Its line plot and box plot

Step-by-step explanation:

Final Examination O
7
Consider the following information from a company's unadjusted trial balance at December 31, 2020. All accounts have normal balances.
Accounts Receivable.
Accounts Payable
Cash
Service Revenue
Common Stock
Equipment
Insurance Expense
Multiple Choice
$ 5,100
680
1,760
6,280
4,600
5,500
430
Land
Notes Payable, Due 2023
Notes Receivable, Matures 2021
Prepaid Insurance
Rent Expense
Retained Earnings, January 1, 2020
Salaries and Wages Expense
What is the total of the debit side of the unadjusted trial balance?
$18.790
4,400
4,600
1,260
430
Saved
1,430
7,910
3,760

Answers

The value of total of the debit side of the unadjusted trial balance is,

⇒ $24,350

We have to given that;

Consider the following information from a company's unadjusted trial balance at December 31, 2020.

Hence, We get;

The computation of the total of debit side is shown below;

= Accounts Receivable + Cash + Equipment + Insurance Expense + Land + Notes Receivable + Prepaid Insurance + Rent Expense + Salaries and Wages Expense

= 5100 + 680 + 1760 + 6280 + 4600 + 5500 + 430

= $24350

Thus, The value of total of the debit side of the unadjusted trial balance is,

⇒ $24,350

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Total Time Slept
Individual Total Time Slept
(hours)
Individual Total Time Slept
(hours)
Mike 8
1
2
Gina 10
John 10 Elisabeth 9
Susan 8
1
2
Alexis 9
1
2
Linda 8
1
2
Drake 8
1
2
Frankie 6
1
2
Vincent 8
1
2
Bob 7
1
2
Herbert 9
Kim 7
1
2
John 10
Louie 9
1
2
Chrissy 7
1
2
Pamela 8
1
2
Liam 10
Heather 8 Julian 8
1
2
© 2017 Connections Education LLC. All rights reserved. 2
1. What was the most common amount of sleep?
2. Is there an outlier in the data? If so, what is it? Explain how you know.
3. What is the difference in hours between the longest night’s sleep and the
shortest night’s sleep?
4. How many people slept longer than 8 hours?
3
Part 2
Directions: The next day, Molly asked 5 more people how long they slept the night
before. Below is a chart of their answers. Add their times to the line plot you
created in Part 1.
Total Time Slept
Name Total Time Slept
(hours)
Zaria
7
LaDajia
12
Devonte
7
Leon
8
Kylie
7
1. Describe how the new data has changed the line plot.
2. Is there an outlier in the data? If so, is it the same as the outlier before the
new data was added? Explain.
3. How many total people slept less than 8 hours? How do you know?

Answers

The most common amount of sleep: is 8 hours (6 individuals).

Outlier: Frankie (slept for 6 hours), as there is a significant difference between his sleep time and the rest of the individuals in the dataset (range of 4 hours).

How to solve

The predominant resting time among the subjects is 8 hours.

Nonetheless, it's worth noting that an outlier exists within the dataset; Frankie spent a mere 6 hours sleeping - which amounts to two hours less than the sleep duration recorded by the second least rested individual (8 hours).

This information can be extracted from analyzing the figures and noticing the conspicuous discrepancy between Frankie's slumbering span and that of the other participants in the pool of data and this is the outlier.

Answers

Step-by-step explanation:

Arrange this equation into y = mx + b form.....m is the slope

9x+3y =11

3y = -9x + 11

y = -9/3 x + 11/3

y = -3 x + 11/3 m = slope = - 3

Help me please with this question, been stuck on it for a couple days

Answers

Answer:

-4.01, -4, -7,

Step-by-step explanation:

It's as simple as substituting and solving. However, this one isnt so simple. The problem tries to trick you because each of the numbers that is provided is supposed to be substituted for x. For example, one of the numbers is 4, which means the equation would be -(4)+6[tex]\geq[/tex]10. But in this problem, the 4 would become a negative four due to the negative sign next to the x. In contrast, the negative numbers in the list provided would then become positive because negative times a negative is positive.

For each function below, identify and enter the percent rate of change per unit, t. Round to the nearest tenth of a percent.
Then use the drop-down menus to classify each as exponential growth or decay.

Answers

The percent rate of each function given is:

[tex]f(t) = 1.18^t:16.99\%\\\\g(t) = 2^{-2t}:-9.1\%\\\\h(t) = 1.19^{\frac{t}{10} }:8.5\%\\\\k(t) = 0.13^t:-19.5\%[/tex]

What is percent rate of change?

A measure known as the percent rate of change quantifies the amount of change in a quantity over time and is given as a percentage of the initial number. It is frequently used to keep tabs on population growth, shifts in the financial markets, and other occurrences.

You must first determine the amount of change in the quantity (often done by deducting the beginning value from the final value) in order to compute the percent rate of change. To calculate the percent rate of change, divide this amount of change by the starting value, multiply the result by 100, and add a percent sign.

[tex]f(t) = 1.18^t:[/tex] 16.99% is the percent rate of change per unit (t). This increase is exponential.

[tex]g(t) = 2^{-2t}:[/tex] Approximately -9.1% of a percent rate of change per unit, t. The decline is exponential.

[tex]h(t) = 1.19^{\frac{t}{10} }:[/tex] The average percent rate of change for unit t is around 8.5 percent. This increase is exponential.

[tex]k(t) = 0.13^t:[/tex] t represents the percent rate of change, which is around -19.5% per unit. The decline is exponential.

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What are the factors of m2 – 6m + 6m – 36?

Answers

Answer:

6 and -6

Step-by-step explanation:

M^2-6m+6m-36

m^2-36

(m-6)(m+6)

Draw a pie chart to show the periods of sunshine cloudiness and darkness during the day

Answers

The procedure for creating a pie chart based on a given set of data involves a number of steps such as.

Create a circular shape with a non-specific measurement for its radius. Begin by drawing radii that correspond to the values of each respective component, using the horizontal radius as a starting point and ensuring that the central angles match. Apply the same procedure to all element of the given information.

What is the pie chart?

The Steps to draw a pie chart for weather conditions in Kaduna:

1. Draw a circle to represent 24-hour period.

2. Divide circle into sections for sunshine, cloudiness, and darkness.

Lastly, Use the weather duration to find section size.

Sunlight: 10/24 = 42% of circle. Cloudy for 3 hours = (3/24) or 12.5% of circle. 11 hours for darkness = (11/24) or 45.8% of circle.

Thus, Label pie chart sections attached as "Sunshine", "Cloudiness", and "Darkness".

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See text below

b Discuss the performance with your teach During a 24-hour period in Kaduna, the sun shone for 10 hours, it was cloudy for 3 hours and it was dark for the remainder of the time. Draw a pie chart to show the periods of sunshi cloudiness and darkness during the day.

Please Help me with this math problem ASAP? x=?

Answers

The value of x in the expression is

x = -4.24

How to find x

To solve for x in the the equation e^(3x+10) = 13^(x/4) we can take the natural logarithm (ln) of both sides

ln(e^(3x+10)) = ln(13^(x/4))

3x + 10 = (x/4) * ln(13)

Isolating x by collecting like terms

3x - (x/4) * ln(13) = -10

factor out x as a common factor:

x * (3 - ln(13)/4) = -10

x = -10 / (3 - ln(13)/4)

x = -4.2395

x = -4.24 to 2 decimal place

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Me pueden ayudar a realizar este ejercicio con método de sustitución, reducción e igualación, por favor

Answers

The solution of the system of equations is x = -5/17 and y = -16/17.

To do this, we can use a method called substitution. In this method, we solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation. This results in a new equation with only one variable, which can be solved to find the value of that variable. Once we know the value of one variable, we can substitute it into either equation to find the value of the other variable.

Let's apply this method to your system of equations:

5x - y/2 = -1 (Equation 1)

3x - 2y = 1 (Equation 2)

First, we'll solve Equation 1 for y in terms of x:

5x - y/2 = -1

y/2 = 5x + 1 (Add y/2 to both sides)

y = 10x + 2 (Multiply both sides by 2)

Now we substitute this expression for y into Equation 2:

3x - 2(10x + 2) = 1 (Substitute y = 10x + 2)

3x - 20x - 4 = 1

-17x = 5

x = -5/17

Now that we know the value of x, we can substitute it into either Equation 1 or Equation 2 to find the value of y. Let's use Equation 1:

5x - y/2 = -1

5(-5/17) - y/2 = -1

-25/17 - y/2 = -1

y/2 = -1 + 25/17

y/2 = -8/17

y = -16/17

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Complete Question:

What is the solution of the system of equations:

5x - y/2 = -1

3x - 2y = 1

You invest $1800 in an account paying 6.3% interest compounded daily. What is the account's effective annual yield? You invest $1800 in an account paying 6.3% interest compounded daily. What is the account's effective annual yield?

Answers

The account's effective annual yield if you invest $1800 and it pays 6.3% interest compounded daily, is calculated as: 6.53%.

How to Find the Effective Annual Yield?

In order to find the effective annual yield of an account, the formula to apply is expressed as:

Effective annual yield = (1 + r/n)^n - 1

where:

r represents the annual interest rate (as a decimal)

n represents the number of times the interest is compounded per year

In this case, we are given the following:

Annual interest rate = 6.3% = 0.063

The interest is compounded daily, so n = 365 (days in a year)

Plugging in the variables we have:

Effective annual yield = (1 + 0.063/365)^365 - 1

Effective annual yield = 0.0653 or 6.53%

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A triangle has two sides of length 3.2 cm and 8.5 cm.

Which value could be the length of the third side of the triangle?

Answers

Any value between 5.3 cm and 11.7 cm (exclusive) could be the length of the third side of the triangle which is 6.7cm in the given options.

What is the triangle inequality theorem?

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with sides a, b, and c, where c is the longest side, the following inequality holds:

a + b > c

This means that the length of any side of a triangle must be less than the sum of the lengths of the other two sides. This theorem is fundamental in geometry and is used in many proofs and applications.

According to the given information

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, the length of the third side must be greater than the difference between the other two sides and less than their sum.

Let's apply this rule to the given triangle. We have two sides of length 3.2 cm and 8.5 cm.

To be a valid triangle, the length of the third side must satisfy the following inequality:

8.5 cm - 3.2 cm < third side < 8.5 cm + 3.2 cm

5.3 cm < third side < 11.7 cm

Therefore, any value between 5.3 cm and 11.7 cm (exclusive) could be the length of the third side of the triangle. So it's 6.7cm.

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if at least one child in a family with 2 children is a boy, what is the probability that both children are boys?

Answers

Answer:

The probability of both children being boys in a family with 2 children is

There are 3 possible outcomes for the gender of each child: boy, girl, or unknown. There are 2 children, so there are 3

=9 possible combinations of genders for the 2 children.

Of these 9 combinations, 3 of them have both children being boys: BB, BG, and GB. So the probability of both children being boys is

However, this is only the probability if we don't know the gender of the first child. If we know that the first child is a boy, then the probability of both children being boys is

. This is because there are only 2 possible outcomes for the gender of the second child: boy or girl. If the first child is a boy, then the second child must be a boy in order for both children to be boys. So the probability is

Step-by-step explanation:

Let's use the following notation for the children:

B: Boy G: Girl

There are 4 possible combinations for a family with 2 children:

1. BB (Both children are boys)

2. BG (First child is a boy, second child is a girl)

3. GB (First child is a girl, second child is a boy)

4. GG (Both children are girls)

Since we know that at least one child is a boy, we can eliminate the 4th combination (GG) as it doesn't meet the condition. Now we have 3 possible combinations left:

1. BB

2. BG

3. GB

Now, to find the probability that both children are boys (BB) from the remaining combinations, we can calculate it as follows:

Probability = (Number of favorable outcomes) / (Total possible outcomes)

Probability = 1 (BB) / 3 (BB, BG, GB)

Probability = 1/3

So, the probability that both children are boys is 1/3.

uppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 1600 bacteria selected from this population reached the size of 1838 bacteria in four hours. Find the hourly growth rate parameter.

Answers

Answer:

Below.

Step-by-step explanation:

Exponential growth equation is

Nt = No e^kt where No is initial quantity , Nt is quantity after time t and k is some constant.

Here we have:

1838 = 1600 e^4k

e^4k = 1838/1600 = 1.14875

4k = ln 1.14875 = 0.138674

k = 0.034669

Find x, y, and z. If necessary, round to the tenths place. A. x = 23, y = 44.5, z = 116 B. x = 23, y = 89, z = 116 C. x = 44.5, y = 44.5, z = 116 D. x = 66, y = 89, z = 116

Answers

The measure of angle x is 23⁰.

The value of arc angle y is 45.5⁰.

The value of arc angle z is 116⁰.

What is the value of x, y and z?

The measure of angle x, y and z is calculated as follows;

∠mEGF = ¹/₂ (arc EF - arc DC ) (intersecting chord theorem)

33 = ¹/₂ (89 - x )

2(33) = 89 - x

66 = 89 - x

x = 89 - 66

x = 23⁰

The value of arc angle z is calculated as follows;

89 + 132 + 23 + z = 360 (sum of angles of a circle)

244 + z = 360

z = 360 - 244

z = 116⁰

The value of angle y is calculated as follows;

∠mGEF = ¹/₂(z) (intersecting chord theorem)

∠mGEF = ¹/₂(116)

∠mGEF = 58⁰

∠mEFG = 180 - (58 + 33) = 89

y + 89 + y = 180 (sum of angles on a straight line)

2y + 89 = 180

2y = 91

y = 91/2

y = 45.5⁰

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The measure of angle x is 23⁰.

The value of arc angle y is 45.5⁰.

The value of arc angle z is 116⁰.

What is the value of x, y and z?

The measure of angle x, y and z is calculated as follows;

∠mEGF = ¹/₂ (arc EF - arc DC ) (intersecting chord theorem)

33 = ¹/₂ (89 - x )

2(33) = 89 - x

66 = 89 - x

x = 89 - 66

x = 23⁰

The value of arc angle z is calculated as follows;

89 + 132 + 23 + z = 360 (sum of angles of a circle)

244 + z = 360

z = 360 - 244

z = 116⁰

The value of angle y is calculated as follows;

∠mGEF = ¹/₂(z) (intersecting chord theorem)

∠mGEF = ¹/₂(116)

∠mGEF = 58⁰

∠mEFG = 180 - (58 + 33) = 89

y + 89 + y = 180 (sum of angles on a straight line)

2y + 89 = 180

2y = 91

y = 91/2

y = 45.5⁰

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