Line AB is perpendicular to line AC, line CD is congruent to line CE and measurement of angle B is 48° find measurement of angle DEB
Answers
The sum of the interior angles of a triangle adds up to 180°.
Based on this, we can do the following...
0. Finding m∠C:
[tex]m\angle C+m\angle B+m\angle A=180[/tex][tex]m\angle C=180-m\angle B-m\angle A[/tex]With the description of the problem, we know that m∠B = 48° and m∠A = 90°. Replacing these values:
[tex]m\angle C=180-48-90[/tex][tex]m\angle C=42[/tex]With this angle and based on the same logic that the addition of the interior angles of a circle adds up 180°, we can get m∠CED. Also, as CD is congruent to CE, m∠CED = m∠CDE.
[tex]m\angle C+m\angle CED+m\angle CDE=180[/tex][tex]m\angle C+m\angle CED+m\angle CED=180[/tex][tex]m\angle C+2m\angle CED=180[/tex][tex]m\angle CED=\frac{(180-m\angle C)}{2}[/tex]Replacing the value of m∠C previously calculated:
[tex]m\angle CED=\frac{(180-42)}{2}=\frac{138}{2}[/tex][tex]m\angle CED=69[/tex]Finally, as we know segment CB is a straight line, the angle is 180°. Thus...
[tex]m\angle DEB+m\angle CED=180[/tex][tex]m\angle DEB=180-m\angle CED[/tex]Replacing the value previously calculated:
[tex]m\angle DEB=180-69[/tex]Answer:
[tex]m\angle DEB=111[/tex]Related Questions
Solve the following absolute value inequality. Express your answer in interval notation.
Answers
Okay, here we have this:
We need to solve the following inequality, let's do it:
[tex]\begin{gathered} 3\mleft|5-y\mright|\le\: -6 \\ \mleft|5-y\mright|\le\: -2 \end{gathered}[/tex]And considering that the absolute value cannot be less than zero, it means that the inequality has no solution in the set of reals.
Evaluate: 4+8/2 x (6 - 3)163325
Answers
We have to evaluate the expression:
[tex]\begin{gathered} 4+\frac{8\cdot(6-3)}{2}_{} \\ 4+\frac{8\cdot3}{2} \\ 4+\frac{24}{2} \\ 4+12 \\ 16 \end{gathered}[/tex]To solve this, we have to solve the operations in this order:
- First, the operations within the parenthesis.
- Second, the multiplications and quotients.
- Lastly, the additions and substractions.
Answer: 16
hi! I have the answers to A. AND B. which are k=1.243% for a and k= 0.20% for bWhere y is the population after t time, A is the initial population and k is the growth constant.Therefore, for each case, we calculate the value of k:(a)t = 4y = 1375000A = 1309000Solving for k:1375000=1309000⋅ek⋅4e4k=137500013090004k=ln(13750001309000)k=ln(13750001309000)4k=0.01229≅0.0123→1.23%(b)t = 4y = 1386000A = 1375000Solving for k:1386000=1375000⋅ek⋅4e4k=138600013750004k=ln(13860001375000)k=ln(13860001375000)4k=0.00199≅0.002→0.20%(c)To compare we calculate the quotient between both periods:
Answers
Solution
The population growth rate formula is given as
[tex]P=P_0e^{rt}[/tex]Where P is the final population
Po= is the initial population
P is the final population
r is the rate
t is the time taken
If it has been calculated that the growth rate from 2012 to 2016 is 1.23% and from 2016 to 2020 is 0.20%
(c) From these two growth rates, it can be seen that 1.23% is greater than 0.20%, we can conclude that the growth rate from 2012 to 2016 is greater than the growth rate from 2016 to 2020
(d) If the current growth rate continues,, the time it will take for the population to reach 1.5million is as shown below:
[tex]\begin{gathered} P=1500000 \\ P_0=1386000 \\ r=0.20 \\ t=\text{?} \\ P=P_0e^{rt} \\ P=P_0e^{0.2t} \end{gathered}[/tex]This becomes
[tex]\begin{gathered} 1500000=1386000e^{0.2\times t} \\ \frac{1500000}{1386000}=e^{0.2t} \\ 1.08225=e^{0.2t} \\ \ln e^{0.2t}=\ln 1.08225 \\ 0.2t=\ln 1.08225 \end{gathered}[/tex][tex]\begin{gathered} t=\frac{\ln 1.08225}{0.2} \\ t=\frac{0.0790432}{0.2}=0.395 \end{gathered}[/tex]Answer Summary
(a) The growth rate from 2012 to 2016 is 1.23%
(b) The growth rate from 2016 to 2020 is 0.20%
(c) In comparison, the growth rate from 2012 to 2016 is greater than the growth rate from 2016 to 2020
(d) The time it will reach the 1.5 million if the current growth rate continues is 0.395years
Find the measure of each angle in the diagram.
Answers
Answer:
10y+7x+4+4×-22+3y+11
10y+3y+7x+4x+4-22+11
13y+11x-9
5. Is X-1 a factor of x^5+2x^2-1?No, because f(1) = 2.Yes, because f(1) = 3.No, because f(1) = 0.Yes, because f(1) = 0.
Answers
We want to find if x-1 is a factor of
[tex]f(x)=x^5+2x^2-1[/tex]In order to verify that, we must know the last number of the synthetic division of the polynomial divided by x - 1. If it is zero then it is a factor, and if it is not zero then it is not a factor
If we replace x = 1 in the equation we will find that number:
[tex]\begin{gathered} f(x)=x^5+2x^2-1 \\ f(1)=1^5+2\cdot1^2-1 \\ f(1)=1^{}+2^{}-1 \\ f(1)=2 \end{gathered}[/tex]Then the residual of the polynomial divided by x - 1 is 2, then x - 1 is NOT a factor.
Answer: A No, because f(1) = 2.A Ferris wheel with a 200-foot diameter is spinning at a rate of 10 miles per hour. Find the angular speed of the wheel in radians per minute.
Answers
1) Gathering the data from the question:
Diameter = 200'
Spinning at 10mph
2) Let's convert the units to start working through that:
[tex]\begin{gathered} m------ft \\ 1------5280 \\ -- \\ 1h=60\min \end{gathered}[/tex]So, 1 mile=5280 ft and 1 hour = 60minutes. Then we can convert:
[tex]\frac{10m}{60}=\frac{10\times5280}{60}=\frac{880ft}{\min }[/tex]2.2) Since we have the diameter, then we can state the radius of this Ferris Wheel is 100 ft. Let's plug into the Circumference formula to get the circumference of the Ferris Wheel:
[tex]\begin{gathered} C=2\pi r \\ C=2\pi\cdot100 \\ C=200\pi \end{gathered}[/tex]2.3) We can find the angular velocity since we have the speed and the Circumference. Note that the angular velocity is given as quotient between the speed and the circumference:
[tex]\frac{880}{200\pi}=\frac{22}{5\pi}[/tex]Note that this is given in revolutions per minute. And 1 revolution corresponds to one lap (2π radians). So we need another final conversion for the unit wanted for the question is radians per minute.
[tex]\frac{22}{5\pi}\times2\pi=\frac{44}{5}=8.8[/tex]3) Thus the answer is:
[tex]8.8\: radians\: per\: minute[/tex]Convert the following mixed number to improper fraction10 /2/57 3/20
Answers
The question asks us to convert mixed fractions to improper fraction.
The first Mixed fraction is:
[tex]\begin{gathered} 10\frac{2}{5} \\ \text{whole number = 10} \\ \text{ numerator = 2} \\ \text{ denominator = 5} \end{gathered}[/tex]In order to convert this into an improper fraction, we need to follow some steps:
1. Multiply the denominator by the whole number.
2. Add the result of the multiplication in step 1 to the numerator.
3. The result from step 2 is the new numerator and use the current denominator as the new denominator.
Let us now apply these steps to answer the question
1. Multiply the denominator by the whole number.
[tex]5\times10=50[/tex]2. Add the result of the multiplication in step 1 to the numerator.
[tex]50+2=52[/tex]3. The result from step 2 is the new numerator and use the current denominator as the new denominator.
[tex]\begin{gathered} \text{new numerator = 52} \\ \text{new denominator = 5} \\ \therefore\frac{52}{5} \end{gathered}[/tex]Therefore, the answer is:
[tex]10\frac{2}{5}=\frac{52}{5}[/tex]Now, let us use the same rules for the next question.
[tex]7\frac{3}{20}[/tex]1. Multiply the denominator by the whole number.
[tex]7\times20=140[/tex]2. Add the result of the multiplication in step 1 to the numerator.
[tex]140+3=143[/tex]3. The result from step 2 is the new numerator and use the current denominator as the new denominator.
[tex]\begin{gathered} \text{new numerator= 143} \\ \text{new denominator = 20} \\ \therefore\frac{143}{20} \end{gathered}[/tex]Therefore, the final answer is:
[tex]7\frac{3}{20}=\frac{143}{20}[/tex]the volume of prism A is 144^3 if the base is 24^2 what is the height of prism A?
Answers
Answer
Height of prism A = 6 units
Explanation
The volume of a prism is given as the product of the area of a face that occurs on two sides of the prism and the distance between the two faces.
In the case of this face being a base, the volume of the prism is given as
Volume = (Area of Base) × (Perpendicular height)
Volume = 144 m³
Area of base = 24 m²
Perpendicular height = h = ?
Volume = (Area of Base) × (Perpendicular height)
144 = (24) × (h)
144 = 24h
We can rewrite this as
24h = 144
Divide both sides by 24
(24h/24) = (144/24)
h = 6 units
Hope this Helps!!!
May 10, 12:38:01 AMA survey was given to a random sample of 195 residents of a town todetermine whether they support a new plan to raise taxes in order toincrease education spending. Of those surveyed, 39 respondents saidthey were in favor of the plan. At the 95% confidence level, what is themargin of error for this survey expressed as a proportion to thenearest thousandth? (Do not write +).Submit AnswerAnswer:
Answers
It is given as,
x= 39.
n= 195.
Estimate for sample proportion= 0.75
Z critical value(using Z table)=1.96
Confidence interval formula is ,
[tex]p\pm Z\times\frac{\sqrt[]{p\times(1-p)}}{\sqrt[]{n}}[/tex][tex]0.75\pm1.96\times\frac{\sqrt[]{0.75\times(1-0.75)}}{\sqrt[]{195}}[/tex][tex]0.75\pm1.96\times\frac{0.433}{1.396}[/tex][tex]1.358\text{ , 0.14206}[/tex]
Lower limit for confidence interval=0.14206
Upper limit for confidence interval= 1.38.
The margin error is determined as,
[tex]1.38-0.14206=\text{ 1.237.}[/tex]Find the surface area of the giving prism round to the nearest 10
Answers
The surface area of the given prism is the sum of areas of all sides.
From the given figure, we have :
2 Triangles with a base of 9 ft and a height of 7.6 ft
1 rectangle with a length of 13 ft and a width of 10 ft
1 rectangle with a length of 13 ft and a width of 8 ft
1 rectangle with a length of 13 ft and a width of 9 ft
The formula for the area of a triangle is :
[tex]A=\frac{1}{2}\times Base\times Height[/tex][tex]A=\frac{1}{2}\times9\times7.6[/tex][tex]A=34.2[/tex]Since there are two triangles, the total area of the triangle is :
[tex]A=2\times34.2=68.4[/tex]The formula for the area of the rectangle is :
We can add the three triangles together.
[tex]A=(13\times10)+(13\times8)+(13\times9)[/tex][tex]A=130+104+117[/tex][tex]A=351[/tex]Now we have the areas of the sides, take the sum of these areas to find the surface area.
[tex]\text{Surface Area = 68.4 + 351}[/tex][tex]\text{Surface Area = 419.4 ft\textasciicircum{}2}[/tex]Six office desks that are 7 1/12 feet long are to be placed together on a wall that is 42 7/12 feet long. Will they fit on the wall? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Yes, if no more than a total of foot is needed for spacing between desks. (Type an integer or a simplified fraction.) B. No, they do not all fit along the wall.
Answers
Answer:
[tex]\text{Yes, If no more than a total of }\frac{1}{12}foot\text{ is needed for spacing between desks}[/tex]Explanation:
Given that six office desks that are 7 1/12 feet long are to be placed together.
The length of the six desks is;
[tex]\begin{gathered} 6\times7\frac{1}{12} \\ =6\times7+6\times\frac{1}{12} \\ =42\frac{6}{12} \end{gathered}[/tex]Given that the wall is 42 7/12 feet long.
Then the length of the six desks is shorter than the length of the wall.
[tex]42\frac{7}{12}-42\frac{6}{12}=\frac{1}{12}[/tex]Therefore, it will fit on the wall if no more than a total of 1/12 foot is needed for spacing between desks.
[tex]\text{Yes, If no more than a total of }\frac{1}{12}foot\text{ is needed for spacing between desks}[/tex]Write the following Equation as a EXPONENTIAL equation do not simplify your answer
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Answer:
[tex]V=14^5[/tex]Explanation:
Given the logarithmic equation:
[tex]\log_{14}(V)=5[/tex]The relationship between the logarithm and exponential forms is given below:
[tex]\log_ba=c\implies b^c=a[/tex]That is:
• The base (b) in the logarithmic form becomes the base of the exponent.
,• The answer (c) in the logarithmic form becomes the exponential form.
Thus, the given equation in exponential equation is:
[tex]V=14^5[/tex]Evaluate the following expression.x³ when x = 5
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Given x^3, set x=5 and find the corresponding value, as shown below
[tex]\begin{gathered} x=5 \\ \Rightarrow x^3=5^3=5*5*5=25*5=125 \end{gathered}[/tex]Thus, the answer is 125which table represents points on the graph of h (x) = 3 root -x+2
Answers
Given the function :
[tex]h(x)=\sqrt[3]{-x+2}[/tex]To find which table represents the given function, let x with the numbers given in the table and find the corresponding value of h(x)
So, when x = 0
[tex]h(0)=\sqrt[3]{0+2}=\sqrt[3]{2}[/tex]Now look to the tables which table has y = 3root of 2
We can deduce that the first two tables are wrong
Now, substitute with x = 2
[tex]h(2)=\sqrt[3]{-2+2}=\sqrt[3]{0}=0[/tex]So, this result will be agreed with the third table
so, the answer is: Table 3
-Solve the system of equations – X – 8y = 49 and —x – 2y = 7 by combining theequations.
Answers
ANSWER
x = 7
y = -7
EXPLANATION
Given:
- x - 8y = 49 ..........(equ 1)
- x - 2y = 7 ............(equ 2)
Desired Outcome
The values of x and y.
Multiply Equation 2 by -1
[tex]equ\text{ 2}\times-1\Rightarrow x+2y\text{ = -7 ............}(equ\text{ 3})[/tex]Add Equation 1 with Equation 3
[tex]\begin{gathered} -\text{ x - 8y = 49} \\ x\text{ + 2y = -7} \\ ------ \\ -6y\text{ = 42} \\ y\text{ = }\frac{42}{-6} \\ y\text{ = -7} \end{gathered}[/tex]Solve for x from equation 3
[tex]\begin{gathered} x\text{ + 2y = -7} \\ x\text{ + 2}(-7)\text{ = -7} \\ x\text{ - 14 = -7} \\ x\text{ = -7 + 14} \\ \text{x = 7} \end{gathered}[/tex]Hence, the values of x and y are 7 and -7 respectively.
Use the Intermediate Value Theorem to show that the polynomial function has a zero in the given interval.
Answers
Given:
[tex]f(x)=10x^4-4x^2+5x-1;\lbrack-2,0\rbrack[/tex]Using the intermediate value theorem,
[tex]\begin{gathered} f(x)=10x^4-4x^2+5x-1 \\ f(-2)=10(-2)^4-4(-2)^2+5(-2)-1 \\ f(-2)=160-16-10-1=133 \\ \text{and} \\ f(0)=10(0)^4-4(0)^2+5(0)-1=-1 \end{gathered}[/tex]So, we have find value c between [-2,0].
[tex]\begin{gathered} f(x)=0 \\ 10x^4-4x^2+5x-1=0 \\ \Rightarrow x=-1\text{ it satisfies the equation} \\ \text{Also, -1}\in\lbrack-2,0\rbrack \end{gathered}[/tex]It shows that, the above polynomial function has zero in the given interval.
Also, the value of f(-2) = 133
9. You want to be able to withdraw the specified amount periodically from a payout annuity with the given terms. Find how much the account needs to hold to make this possible. Round your answer to the nearest dollar. Regular withdrawal: $4500 Interest rate: 4.5% Frequency quarterly Time: 24 years Account balance: $
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This is a question on Future Value of Annuity. There is a present sum from which withdrawals will be made. We therefore employ the formulae thus:
[tex]PVA=\text{PMT(}\frac{1-(1+\frac{i}{m})^{-mn}}{\frac{i}{m}}\text{)}[/tex]Where:
PVA = Present Value of Annuity
PMT = Periodic sum
i = Interest Rate
n = Number of interest periods
m = Compunding frequency
Substituting, we have:
[tex]\begin{gathered} P\text{VA}=4500(\frac{1-(1+\frac{0.045}{4})^{-(4\times24)}}{\frac{0.045}{4}}) \\ P\text{VA}=263,340 \end{gathered}[/tex]PVA = $263,340
What is the length of side s of the square shown below?45°6S90°A. 2.B. 6C. 3D. 5.2E. 3.2F. .6
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The diagram shows a square with one side marked as s, while the diagonal that cuts across measures 6 units.
The diagonal results in a right angled triangle with two sides measuring 45 degrees and one side measuring 90 degrees. Now that we have a right angled with one angle, and two sides (one is given as 6, and one is unknown), we now calculate side s as follows;
[tex]\begin{gathered} \cos 45=\frac{\text{adj}}{\text{hyp}} \\ We\text{ use the ratio for cosine because the sides shown are the} \\ \text{adjacent (between the right angle and the reference angle) and} \\ \text{hypotenuse (facing the right angle)} \\ \cos 45=\frac{s}{6} \\ \cos 45=\frac{1}{\sqrt[]{2}} \\ \text{Therefore,} \\ \frac{1}{\sqrt[]{2}}=\frac{s}{6} \\ \text{Cross multiply and you have} \\ \frac{6}{\sqrt[]{2}}=s \\ \text{Rationalize the expression and you have} \\ 3\sqrt[]{2}=s \\ \text{Therefore} \\ s=3\sqrt[]{2} \end{gathered}[/tex]The correct answer is option E
What is the first step to solve this equation: 5m + 10= 7m + 4A: subtract 5m to both sides B: add 5m to both sides C: divide by 5 to both sides D: multiply by 5 to both sides
Answers
We are given the linear equation
[tex]5m+10=7m+4[/tex]If we subtract 5m to both sides we get
[tex]5m+10-5m=7m+4-5m[/tex]Simplifying
[tex]10=2m+4[/tex]which is one step closer to the solution, therefore the answer is A.
What is the definition of function?Hos inputs andoutputsInputs haveEvery input hosonly ONE outputxrches andy-wolvesdifferent outputsevery time
Answers
The definition of function is
vertex, domain and range, and zeros in this parabola, could you tell me them?
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The vertex, domain, range and zeros of the parabola are -2, (-∞, +∞), (-2,+∞) and -0.5 and 2.5 respectively.
What is parabola ?Parabola is a curve like shape, in which any point is equal distance from a fix point.
The vertex of the parabola in the given graph is -2.
The domain of parabola is all the possible values of x,
in the given graph, the value of x is from -∞ to +∞
So the domain of parabola is (-∞, +∞)
The range of parabolas is all the values of y corresponding to values of x,
in the graph, the value of y≥-2
The range of parabola is (-2,+∞)
Zeros are values on the x-axis, which are 0.
So there are two zeros, -0.5 and 2.5.
To know more about Parabola on:
https://brainly.com/question/4074088
#SPJ1
train moves at a constant speed of 8 miles every 6 minutes. Fill in the table below to show how far the train travels according to differentmounts of time.Time (minutes)Distance (miles)31560
Answers
we have the following:
speed 8 miles every 6 minutes:
[tex]s=\frac{8}{6}=1.34[/tex]therefore, the speed is 1.34 mi/m, now to complete it would be:
[tex]\begin{gathered} d=s\cdot t \\ d1=1.34\cdot3=4 \\ d2=1.34\cdot15=20 \\ d3=1.34\cdot60=80 \end{gathered}[/tex]therefore, the answer is:
Time (minutes) Distance (miles)
3 4
15 20
60 80
Hi I just wanted you to check over my work to let me know if I did it correct
Answers
Answer:
Hello, Which part would you like to have checked?
I can't seem to make out your work from that of the assignment.
Step-by-step explanation:
Just let me know, here to help!
A triangle has angles that are 38º and 47º. Find the measure of the third angle. 177 ° 95° 133 °85 °
Answers
hello,
As we know, a triangule has 3 angles and the sum of them must be equal to 180º. So, let's calculate the question:
38 + 47 + x = 180
85 + x = 180
x = 180 - 85
x = 95º
As smart phones have grown in popularity, regular cell phones have fallen out of favor. As aresult, one electronics retailer estimates that 20% fewer regular cell phones will be sold everyyear. If the retailer sells 605,390 regular cell phones this year, how many will be sold 3 yearsfrom now?If necessary, round your answer to the nearest whole number.
Answers
309960
Explanation
exponential decay function is a function that shrinks at a constant percent decay rate. The equation can be written in the form
[tex]\begin{gathered} y=a(1-b)^x \\ \text{where a is the initial cost} \\ b\text{ is the decrease percnetage ( in decimal)} \\ x\text{ is the time} \end{gathered}[/tex]so
Step 1
Let
[tex]\begin{gathered} a=605390 \\ b=20\text{ = 0.2} \\ x=\text{ 3 ( years)} \end{gathered}[/tex]replace
[tex]\begin{gathered} y=a(1-b)^x \\ y=605390(1-0.2)^3 \\ y=605390(0.8)^3 \\ y=605390(0.512) \\ y=309959.68 \\ \text{rounded to the whole number} \\ y=309960 \end{gathered}[/tex]therefore, the answer is
309960
I hope this helps you
According to the diagram, an 8-foot-tall statue casts a shadow on the ground that is 15 feet in length. Based on this information, which trigonometric ratio has the value 8/15 ?A. cos CB. tan BC. cos BD. tan C
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the right optio is tan C because...
[tex]undefined[/tex]find the exact value of cosine Pi / 3 express your answer with a rational denominator
Answers
it is given that,
the expression is
cosine Pi/3
we know that
so,
[tex]\cos \frac{\pi}{3}=\cos \frac{180}{3}=\cos 60=\frac{1}{2}[/tex]thus, the answer is 1/2
m = y2-yi=X2-X1Find the slope of the line that passesthrough these two points.(6,4)m = [?](2, -4)-
Answers
The slope between two points (x1,y1) and (x2,y2) is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case we have the points (2,-4) and (6,4), then:
[tex]\begin{gathered} m=\frac{4-(-4)}{6-2} \\ m=\frac{4+4}{4} \\ m=\frac{8}{4} \\ m=2 \end{gathered}[/tex]Therefore, the slope is 2
This is a practice assessment that will not be graded! Just need help finding this answer to understand it overall
Answers
The general structure of the equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
h is the x-coordinate of the center of the circle
k is the y-coordinate of the center of the circle
r is the radius of the circle.
Note that the equation has minus signs inside the parentheses, this means that the sign of the coordinates is the opposite as the one shows on the equation.
The first step is to identify the coordinates of the center of the circle in each equation as well as the radius:
Equation 1:
[tex](x-3)^2+(y+2)^2=9[/tex]The x-coordinate of the center is the value inside the first parentheses: h= 3
The y-coordinate of the center is the value inside the second parentheses: k= -2
[tex]center\colon(3,-2)[/tex]To determine the radius you have to calculate the square root of the last number of the equation:
[tex]\begin{gathered} r^2=9 \\ r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]Use the same logic for the other three equations:
Equation 2:
[tex](x-3)^2+(y-2)^2=16[/tex]h=3
k=2
[tex]\text{center:(3,2)}[/tex]Radius:
[tex]\begin{gathered} r^2=16 \\ r=\sqrt[]{16} \\ r=4 \end{gathered}[/tex]Equation 3
[tex](x+3)^2+(y+2)^2=16[/tex]h=-3
k=-2
[tex]\text{center:(-3,-2)}[/tex]Radius:
[tex]\begin{gathered} r^2=16 \\ r=\sqrt[]{16} \\ r=4 \end{gathered}[/tex]Equation 4
[tex](x-3)^2+(y-2)^2=9[/tex]h=3
k=2
[tex]\text{center:(3,2)}[/tex]Radius:
[tex]\begin{gathered} r^2=9 \\ r=\sqrt[]{9} \\ r=3 \end{gathered}[/tex]Next, you have to determine the center and the radius of each graph:
Circle 1:
Has a radius with a length of 4 units and center (3,2), the equation that corresponds to this circle is the second equation.
Circle 2:
Has a radius with a length of 4 units and the center at (-3,-2), the equation that corresponds to this circle is the third equation.
Circle 3:
Has a radius with a length of 3 units and a center at (3,2), the equation that corresponds to this circle is the fourth equation.
Circle 4:
Has a radius with a length of 3 units and center at (3,-2), the equation that corresponds to this graph is the first equation.
Hello, May I please get some assistance with this homework question? I posted an image below Q2
Answers
Solving (a)
The two functions we have are:
[tex]\begin{gathered} f(x)=3x+3 \\ g(x)=x^2 \end{gathered}[/tex]We are asked to find the composite function:
[tex](f\circ g)(x)[/tex]Step 1. The definition of a composite function is:
[tex](h\circ k)(x)=h(k(x))[/tex]In this case:
[tex](f\circ g)(x)=f(g(x))[/tex]This means to plug the g(x) expression into the value of x of the f(x) function.
Step 2. Substituitng g(x) as the value for x in f(x):
[tex](f\circ g)(x)=f(g(x))=4(x^2)+3[/tex]Simplifying:
[tex](f\circ g)(x)=\boxed{4x^2+3}[/tex]Step 3. We also need to find the domain of this composite function.
The domain of a function is the possible values that the x-variable can take. In this case, there would be no issues with any x value that we plug as the x-value. Therefore, the domain is all real numbers.
The domain of fog is all real numbers.
Answer:
[tex](f\circ g)(x)=\boxed{4x^2+3}[/tex]The domain of fog is all real numbers.