Complete a triangulation calculation to measure the distance between actual objects in or near your home. include a well-labeled diagram.
Answers
Triangulation means the measuring of distances in surveys with triangles. If the distance of two objects and the angle between is knwon, the distance between these objects can be calculated.
Given the diagram we have:
So, the distance between both objects will be calculated by:
[tex]c=\sqrt{a^2+b^2-2ab\cdot\cos\theta}[/tex]Where:
Distance to the first object a = 6
Distance to the first object b = 6
Angle between both objects θ = 60°
Substitute the values, we have:
[tex]c=\sqrt{6^2+6^2-2(6)(6)\cdot\cos60}[/tex]Simplify:
[tex]c=\sqrt{36+36-72(0.5)}=\sqrt{72-36}=\sqrt{36}=6[/tex]So, the distance between both objects c = 6 inches
Related Questions
One-third of a number b multiplied by -11 is more than 3 2
Answers
Picture translating A ABC three units to the left and five units up.What are the coordinates of A'?A(2,-2)
Answers
The coordinates of point A are (2, -2)
If the picture is translated 3 units to the left, we need to subtract 3 units to the x coordinate as:
( 2 - 3, -2) = (-1, -2)
Then, if the picture is translated 5 units up, we need to sum 5 units to the y-coordinate as:
( -1 , -2 + 5) = (-1, 3)
So, the coordinates of A' are (-1, 3)
Answer: (-1, 3)
What function makes the HIV virus unique?
Answers
The function which makes the HIV virus unique is: B. It has viral DNA that is transmitted through indirect contact with infected persons.
HIV is an acronym or abbreviation for human immunodeficiency virus and it refers to a type of venereal disease that destabilizes and destroys the immune system of an infected person, thereby, making it impossible for antigens to effectively fight pathogens.
Generally, the high mutation or replication rate of the human immunodeficiency virus (HIV) owing to its enormous genetic diversity (deoxyribonucleic acid - DNA) makes it easily transmittable from an infected person to another.
This ultimately implies that, the HIV virus is unique among other viruses because it can be transmitted without having a direct contact with an infected person such as:
Sharing a hair clipper with him or her.
Using an object that has been infected by a HIV patient.
Additionally, it is extremely difficult to develop an effective and accurate vaccine against the HIV virus because it possesses a high error rate.
Based on the experimental probability, predict the number of times that you will roll a 5 if you roll the number cube 300 timesExperiment result on previews question: The number 5 was rolled 9 times out of 20 on a previous question
Answers
Explanation: To understand this problem we need to know that there are two different types of probability. The experimental probability and the theoretical probability.
- The experimental probability occurs once you conduct the experiment and after the experiment, you calculate the probability using the result of the experiment.
- The theoretical probability occurs before the experiment. Once you have information about the situation so you calculate the probability the get a specific result before trying.
Step 1: For this question, once we have a number cube with faces 1,2,3,4,5 and 6 and we want to know the experimental probability to get a 5 once you roll the cube 300 times you would need to get in real life a number cube and to roll it 300 times. After this experiment we would get all the results of each time we roll it and we would know how many times (from 300 times) we got a number 5. After that, we would use the following formula
[tex]Experimental_{probability}=\frac{number\text{ of times we got a number 5}}{300}[/tex]Once the get this result we finish the question.
The diameter of a circle has endpoints P(-12, -4) and Q(6, 12).
Answers
ANSWER
[tex](x+3)^{2}+(y-4)^{2}=145[/tex]EXPLANATION
The equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) = center of the circle
r = radius of the circle
The center of a circle is the midpoint of the endpoints of the diameter of the circle. Hence, to find the center of the circle, we have to find the midpoint of the diameter:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) and (x2, y2) are the endpoints of the diameter.
Hence, the center of the circle is:
[tex]\begin{gathered} M=(\frac{-12+6}{2},\frac{-4+12}{2}) \\ M=(\frac{-6}{2},\frac{8}{2}) \\ M=(-3,4) \end{gathered}[/tex]To find the radius of the circle, we have to find the distance between any endpoint of the circle and the center of the circle.
To do this apply the formula for distance between two points:
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, the radius of the circle is:
[tex]\begin{gathered} r=\sqrt{(6-(-3))^2+(12-4)^2}=\sqrt{9^2+8^2} \\ r=\sqrt{81+64}=\sqrt{145} \end{gathered}[/tex]Hence, the equation of the circle is:
[tex]\begin{gathered} (x+3)^2+(y-4)^2=(\sqrt{145})^2 \\ (x+3)^2+(y-4)^2=145 \end{gathered}[/tex]The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is less than 2". Let B be the event "the outcome is greater than 4". Find P(A or B). Outcome Probability 1 0.15 2 0.31 3 0.35 4 0.08 5 0.11
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The general rule of P(A or B) is given by the formula
[tex]undefined[/tex]Interpreting the whale population on the graph. I think (A).
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The y-intercept is the value in the vertical axis (y-value) when the value on the horizontal axis is zero (x = 0).
Looking at the horizontal axis, the value of x indicates the generation since 2007.
That means x = 0 indicates the generation in year 2007.
The value of y for x = 0 is 240, so the population in year 2007 is 240.
Correct option: A
Suppose that an airline uses a seat width of 16.2 in. Assume men have hip breadths that are normally distributed with a mean of 14 in. and a standard deviation of 1 in. Complete parts (a) through (c) below.
Answers
Given:
population mean (μ) = 14 inches
population standard deviation (σ) = 1 inch
sample size (n) = 126
Find: the probability that a sample mean > 16.2 inches
Solution:
To determine the probability, first, let's convert x = 16.2 to a z-value using the formula below.
[tex]x=\frac{\bar{x}-\mu}{\sigma\div\sqrt{n}}[/tex]Let's plug into the formula above the given information.
[tex]z=\frac{16.2-14}{1\div\sqrt{126}}[/tex]Then, solve.
[tex]z=\frac{2.2}{0.089087}[/tex][tex]z=24.6949[/tex]The equivalent z-value of x = 16.2 is z = 24.6949
Since we are looking for the probability of greater than 16.2 inches, let's find the area under the normal curve to the right of z = 24.6949.
Based on the standard normal distribution table, the area from the center to z = 24.6949 is 0.5
Since we want the area to the right, let's subtract 0.5 from 0.5.
[tex]0.5-0.5=0[/tex]Therefore, the probability that a sample mean of 126 men is greater than 16.2 inches is 0.
A herd of 23 white-tailed deer is introduced to a coastal island where there had been no deer before. Their population is predicted to increase according to A=276/1+11e^(- .35t)where A is the number of deer expected in the herd after t years.(a) How many deer will be present after 3 years? Round your answer to the nearest whole number.(b) How many years will it take for the herd to grow to 50 deer? Round your answer to the nearest whole number.
Answers
Given:
[tex]A=\frac{276}{1+11e^{-0.35t}}[/tex]Where A is the number of deer expected in the herd after t years.
We will find the following:
(a) How many deer will be present after 3 years?
So, substitute t = 3 into the given equation:
[tex]A=\frac{276}{1+11e^{-.35*3}}\approx56.9152[/tex]Rounding to the nearest whole number
So, the answer will be A = 57
=========================================================
(b) How many years will it take for the herd to grow to 50 deer?
substitute A = 50 then solve for t
[tex]\begin{gathered} 50=\frac{276}{1+11e^{-.35t}} \\ 1+11e^{-.35t}=\frac{276}{50} \\ \\ 11e^{-.35t}=\frac{276}{50}-1=4.52 \\ e^{-.35t}=\frac{4.52}{11} \\ -0.35t=ln(\frac{4.52}{11}) \\ \\ t=\frac{ln(\frac{4.52}{11}_)}{-0.35}=2.54 \end{gathered}[/tex]Round your answer to the nearest whole number.
So, the answer will be t = 3
What is the surfacearea of the cone?2A 225π in²B 375m in²C 600T in²D 1000 in 225 in.15 in.
Answers
We are given a cone whose radius is 15 inches and slant height is 25 inches. We need to solve for its surface area.
To find the surface area of a cone, we use the following formula:
[tex]SA=\pi rl+\pi r^2[/tex]where r = radius and l = slant height.
Let's substitute the given.
[tex]\begin{gathered} SA=\pi(15)(25)+\pi(15^2) \\ SA=375\pi+225\pi \\ SA=600\pi \end{gathered}[/tex]The answer is 600 square inches.
Yesterday Ali had n Baseball cards. Today he gave away 6. Using n, Write an expression for the number of cards Ali has left
Answers
Yesterday Ali had n Baseball cards.
Today he gave away 6 cards.
We are asked to write an expression for the number of cards Ali has left.
Ali had a total of n cards and he gave away 6 from them.
So, we have to simply subtract 6 cards from the total n cards.
[tex]n-6[/tex]Therefore, the expression is n - 6 represents the number of cards Ali has left.
Ride 'em Rodeo is a traveling rodeo show. Last night, there were 5 people wearing
boots at the rodeo for every 2 people who were not wearing boots.
If there were 125 people wearing boots at the rodeo last night, how many people were
there altogether?
Answers
The total number of people that were there altogether at the radio show is 175 people.
How to calculate the value?From the information, there were 5 people wearing boots at the rodeo for every 2 people who were not wearing boots.
It was also illustrated that there were 125 people wearing boots at the rodeo last night, those that aren't wearing boots will be illustrated by x.
2/5 = x/125
Collect like terms
5x = 125 × 2
5x = 250
Divide
x = 250/5
x = 50
Those not wearing boots = 50
Total number of people will be:
= Those wearing boots + Those not wearing
= 125 + 50
= 175
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Answer:
175
Step-by-step explanation:
what is the density of a 10g box measuring 10 cm by 5 cm by 5 cm
Answers
Answer:1 g/cm^3
Step-by-step explanation:
35+3(8-4)
(please explain how you did it)
Answers
Answer:47
Step-by-step explanation: First multiply 3x8=24 then subtract 3x4=12 from it. Which will get you 12 then add 35 to 12 which will get you 47.
35 + 3(8-4) = ?
Do the parentheses first : 8 - 4 = 4
= 35 + 3(4)
Then multiply- that's the one that is in parentheses : 3 x 4 = 12
= 35 + 12
Then just straight up add : 35 + 12 = 47
35 + 3(8-4) = 47
So ? = 47
Preston drove to his new college and then back home.Round trip he traveled 642 miles. Preston drives aHonda Civic and gets 38 miles for every gallon of gas. IfPreston needs to make 15 round trips a year how muchwill it cost him in gas assuming the price of gas stays at$2.48 a gallon for all his trips?$Round all answers to the nearest hundredthsDo not put a label, just the numeric value
Answers
1) Gathering the data
Preston
642 miles
38 miles/gallon
15 round trips
1 gallon = $2.48
2) Considering that each round trip consists of 642 miles
So Preston in 15 roundtrips is going to make
15 x 642 miles =9,630 miles
His car gets 38 miles per gallon. So we can write a proportion for that:
38 miles ---------1 gallon
9,630 miles ----- x
Cross multiplying it:
38x = 9,630 Divide by 38
x =9630/38
x=253.42 gallons
Finally, let's set another proportion to find out the cost of it
1 gallon -------------- $2.48
253.42 -------------- y
y= 253.42 x 2.48
y=628.4816
3) Rounding off to the nearest hundredth
$628. 48 That's how much Preston will spend.
can you help me to find midpoint
Answers
First, locate the given points.
Then, draw the line that connects them
Next, add the two x-coordinates of the endpoints and divide by 2. In this case, (1 + 4)/2 = 5/2 = 2.5
Then, draw a line perpendicular to the x-axis that passes through x = 2.5, until it intersects the other line. The intersecting point is the midpoint.
In this case, the coordinates of the midpoint are (2.5, 0.5), as can be seen in the figure
Which points are on the graph of y = cot x? (Select all that apply)A. (/3 , √3/2)B. (/2 , 0)C. (0 , )D. (/4 , 1)E. ( , 0)
Answers
Solution:
The graph function is given below as
[tex]y=cotx[/tex]The graph is given below as
Therefore,
The points on the graph are
[tex]\begin{gathered} \Rightarrow(\frac{\pi}{4},1) \\ \Rightarrow(\frac{\pi}{2},0) \end{gathered}[/tex]OPTION B AND option D are the right answers
Today's high temperature is 72°F. If yesterday's high temperature was 87"F, what was the change in high temperatures?
Answers
To find the change in temperature we have to do a subtraction:
Highest temperature-lowest temperature-
87-72= 15F
The change in high temperatures was 15 F .
If he paints 1/2 of the wall blue, hoy many square feet will be blue?
Answers
To determine how much of the wall is blue we first need to find its area. The wall is a rectangle, then its area is the product of its height and length:
[tex]\begin{gathered} A=(8\frac{2}{5})(16\frac{2}{3}) \\ A=(\frac{42}{5})(\frac{50}{3}) \\ A=(14)(10) \\ A=140 \end{gathered}[/tex]Hence, the area of the wall is 140 square ft. To determine how much of the wall is already painted we multiply this by 1/2, then:
[tex](140)(\frac{1}{2})=70[/tex]Therefore, 70 square ft are blue.
In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equation x^2+ y^2= 5, and the path of the bean bag canbe represented by y = -0.5x^2 -1.5x + 4. To which points could she have tossed her bean bag?(-1,-2) or (-2, 1)(1.-2) or (2,1)(-1,2) or (-2,-1)(1, 2) or (2, -1)
Answers
We have two equations, the first is a circle, which we can identify by the characteristic form of the equation:
[tex]x^2+y^2=5[/tex]The second is a quadratic equation:
[tex]y=-0.5x^2-1.5x+4[/tex]We know that Sasha got the bag to land in the edge of the circle defined by the hole, equation 1.
So, to know the points at which the bag landed, we can look for th eintersection of the two equations, which is the same as solving a system of equations:
[tex]\begin{gathered} x^2+y^2=5 \\ y=-0.5x^2-1.5x+4 \end{gathered}[/tex]Since we have been given alternatives, we can check them to get the correct answer.
The first option is (-1,-2) or (-2,1). Since the sign of the alternatives are the only thing that change and the circle equation doesn't differenciate the signs, the best equation to test first is the second one. Let's try that for (-1,-2).
[tex]\begin{gathered} y=-0.5(-1)^2-1.5(-1)+4 \\ y=-0.5+1.5+4=5 \end{gathered}[/tex]We got y = 5, which is not -2, so this alternative is incorrect.
Let's got for the second alternative, (1.-2) or (2,1):
[tex]y=-0.5(1)^2-1.5\cdot1+4=2[/tex]This is also incorrect.
The third alternative is (-1,2) or (-2,-1), we already saw that for x = -1, y = 5, which makes this alternative also incorrect.
Let's check if the last one will be correct, (1, 2) or (2, -1). We already saw that for x = 1, y = 2 in the second equation, let's check if this is also correct for the first:
[tex]\begin{gathered} (1)^2+y^2=5 \\ y^2=5-1=4 \\ y=\pm2 \end{gathered}[/tex]One of the results is y = 2, so this also checks out.
The other point is (2,-1), let's check in both equations:
[tex]\begin{gathered} (2)^2+y^2=5 \\ 4+y^2=5 \\ y^2=1 \\ y=\pm1 \end{gathered}[/tex]Checks out, and:
[tex]\begin{gathered} y=-0.5(2)^2-1.5\cdot2+4 \\ y=-2-3+4=-1 \end{gathered}[/tex]And the "y" checks out too.
So, the correct alternative is the last one: (1, 2) or (2, -1).
Using pH=-log{H3O+}, what is pH for 3.4 X 10^-4 ?
Answers
The value of the pH for pH=-log{H3O+} is found as 3.47.
What is defined as the pH?The pH of aqueous or some other liquid solutions is a quantitative measure of their acidity or basicity. The concentration of hydrogen ion, which normally ranges between around 1 and 10∧14 gram-equivalents per litre, is converted into a number between 0 and 14. The concentration of hydrogen ion in pure water, which really is neutral (nor acidic and neither alkaline), is 10∧7 gram-equivalents per litre, corresponding to a pH of 7. A solution with such a pH less than 7 is classified as acidic, while one with pH greater than 7 is classified as basic, or alkaline.For the given equation,
pH = - log [H3O+]
and , H3O+ = 3.4 X 10^-4
The, the pH will be estimated as;
pH = - log [ H3O+]
pH = - log [ 3.4 x10 ^-4]
pH = - [log 3.4 + log 10^-4]
pH = - [0.53 + (-4)]
pH = -[-3.47]
pH = 3.47
Thus, the value of the pH is found as 3.47.
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2) through: (-2,5), perp. to 1 = 7 1 1 LU perp m 1 2 b Sub y, m, and
Answers
Answer:
y = (-7/2)x - 2
Step-by-step explanation:
Equation of a line:
The equation of a line is given by:
y = mx + b
In which m is the slope and b is the intercept.
We want the equation of a line perpendicular to y = (2/7)x - 4.
This slope is 2/7.
When two lines are perpendicular, the multiplication of their slopes is -1.
We want to find m. So
(2/7)*m = -1
2m = -7
m = (-7/2)
So
y = (-7/2)x + b
Through the point (-2,5):
This means that when x = -2, y = 5. So
y = (-7/2)x + b
5 = (-7/2)*(-2) + b
7 + b = 5
b = 5 - 7
b = -2
So, the equation is:
y = (-7/2)x - 2
You invent a game that is played on a perfect 12 foot by 12 foot square. What is the longest distance between any two points on the square? A. 12 feetB. 15 feetC. 17 feetD. None of the aboveI will really appreciate the help on this problem.
Answers
The given figure is a square that measures 12 foot by 12 foot. please see illustration below;
The square in the sketch above shows the longest distance between two opposite diagonals, and that is the hypotenuse, labelled as a.
In the triangle ADC, using Pythagoras' theorem;
[tex]\begin{gathered} AD^2+DC^2=AC^2 \\ 12^2+12^2=a^2 \\ 144+144=a^2 \\ 288=a^2 \\ \sqrt[]{288}=a \\ a=16.97 \end{gathered}[/tex]The longest distance which is a (that is AC) is approximately 17 ft as shown above (16.97 ft).
P. The Shah family basement floor is shaped like a trapezoid. The basement has sides of and 24 feet and two sides of 21 feet. They are going to carpet the basement. The carpeting will cost $35 per square yard. A. What is the area, in square feet, of the basement foor? Show your work. B. What is the cost to carpet the basement floor? Explain how you found your answer
Answers
A.
In order to calculate the area of the trapezoid, we need to calculate its height:
Using the Pythagorean Theorem, we have:
[tex]\begin{gathered} 21^2=h^2+6^2 \\ 441=h^2+36 \\ h^2=441-36 \\ h^2=405 \\ h=20.12 \end{gathered}[/tex]Now, calculating the area:
[tex]\begin{gathered} A=\frac{(B+b)h}{2} \\ A=\frac{(36+24)20.12}{2} \\ A=60\cdot10.06 \\ A=603.6 \end{gathered}[/tex]B.
If each square yard is $35, first let's convert the area from ft² to yd² (1 yard = 3 feet, 1 yd² = 9 ft²):
[tex]A=603.6\text{ ft}^2=\frac{603.6}{9}\text{ yd}^2=67.07[/tex]So the total cost is:
[tex]\text{cost}=67.07\cdot35=2347.45[/tex]So the cost is approximately $2347.45.
A restaurant serving 150 side dishes of skinless mashed potatoes each day produces two orders of mashed potatoes from each 8 ounce potato. when the skins are discarded, the potatoes have a yield percentage of 90%. However, to reduce waste and promote sales, the potato skins are instead used as an appetizer. what is the edible portion of the potato skins in ounces?
Answers
The edible portion of the potato skins in ounces is = 0.8%
What are potatoes?Potatoes are vegetable tubers that can be eaten with the skin when properly cooked.
The number of side dishes of skinless mashed potatoes= 150
Two orders of mashed potatoes = 8 ounce potato.
The potatoes with discarded skin = 90% yield
The potatoe skin= 10% of the 8 ounces
That is;
= 10/100×8
= 80/100 = 0.8 ounce
Therefore, the portion of the potatoes that consists of the skin in ounce is = 0.8 ounce
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The population of Canada, as estimated every five years since 1960, is shown in the table. 1. . Calculate the finite differences for the data set.
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data set
STEP 2: Find the finite difference
We first find the differences in the output values which is the population as seen below
[tex]\begin{gathered} 19.68-17.91=1.77 \\ 21.32-19.68=1.64 \\ 23.21-21.32=1.89 \\ 24.59-23.21=1.38 \\ 25.94-24.59=1.35 \\ 27.79-25.94=1.85 \\ 29.35-27.79=1.56 \\ 30.77-29.35=1.42 \\ 32.31-30.77=1.54 \\ 34.01-32.31=1.70 \\ 35.75-34.01=1.74 \end{gathered}[/tex]STEP 3: Find the second order difference
[tex]\begin{gathered} 1.64-1.77=-0.13 \\ 1.89-1.64=0.25 \\ 1.38-1.89=-0.51 \\ 1.35-1.38=-0.03 \\ 1.85-1.38=0.47 \\ 1.56-1.85=-0.29 \\ 1.42-1.56=-0.14 \\ 1.54-1.42=0.12 \\ 1.70-1.54=0.16 \\ 1.74-1.70=0.04 \end{gathered}[/tex]STEP 4: Find the third order difference
[tex]undefined[/tex]5. Find the arclength that subtends a central angle of 175° in a circle with radius 3 feet.
Answers
As given by the question
There are given that the central angle is 175 degrees and the radius is 3 feet.
Now,
The length of an arc given it subtends a known angle at the centre is:
[tex]\text{arc length=2}\times\pi\times r\times\frac{175}{360}[/tex]Then,
[tex]\begin{gathered} \text{arc length=2}\times\pi\times r\times\frac{175}{360} \\ \text{arc length=2}\times3.14\times3\times\frac{175}{360} \\ \text{arc length=}9.16 \end{gathered}[/tex]Hence, the arclength is 9.16.
call Scott's is collecting canned food for food drive is class collects 3 and 2/3 pounds on the first day in 4 and 1/4 lb on second day how many pounds of food has they collected so far
Answers
The food collected on first day,
[tex]\begin{gathered} 3\frac{2}{3} \\ =\frac{3\times3+2}{3} \\ =\frac{9+2}{3} \\ =\frac{11}{3} \end{gathered}[/tex]The food collected on second day,
[tex]\begin{gathered} 4\frac{1}{4} \\ =\frac{4\times4+1}{4} \\ =\frac{16+1}{4} \\ =\frac{17}{4} \end{gathered}[/tex]The total amount of food collected can be calculated as,
[tex]\begin{gathered} T=\frac{11}{3}+\frac{17}{4} \\ =\frac{11\times4+17\times3}{3\times4} \\ =\frac{44+51}{12} \\ =\frac{95}{12} \\ =7\frac{11}{12} \end{gathered}[/tex]Therefore, the total amount of food collected so far is 7 11/12 pounds.
A Snack company can pack 15 granola bars in a box how many boxes are needed for 600 granola bars ?
Answers
Answer:40
Step-by-step explanation: 15 bars to a box.
600 bars in total.
600/15= 40
40 boxes of granola bars
f(x) = log 2(x+3) and g(x) = log 2(3x + 1).(a) Solve f(x) = 4. What point is on the graph of f?(b) Solve g(x) = 4. What point is on the graph of g?(c) Solve f(x) = g(x). Do the graphs off and g intersect? If so, where?(d) Solve (f+g)(x) = 7.(e) Solve (f-g)(x) = 3.
Answers
Given
[tex]\begin{gathered} f(x)=log_2(x+3) \\ and \\ g(x)=log_2(3x+1) \end{gathered}[/tex]a)
[tex]\begin{gathered} f(x)=4 \\ \Rightarrow log_2(x+3)=4 \\ \Leftrightarrow x+3=2^4 \\ \Rightarrow x+3=16 \\ \Rightarrow x=13 \end{gathered}[/tex]The answer to part a) is x=13. The point on the graph is (13,4)
b)
[tex]\begin{gathered} g(x)=4 \\ \Rightarrow log_2(3x+1)=4 \\ \Leftrightarrow3x+1=2^4 \\ \Rightarrow3x+1=16 \\ \Rightarrow3x=15 \\ \Rightarrow x=5 \end{gathered}[/tex]The answer to part b) is x=5, and the point on the graph is (5,4).
c)
[tex]\begin{gathered} f(x)=g(x) \\ \Rightarrow log_2(x+3)=log_2(3x+1) \\ \Rightarrow\frac{ln(x+3)}{ln(2)}=\frac{ln(3x+1)}{ln(2)}] \\ \Rightarrow ln(x+3)=ln(3x+1) \\ \Rightarrow x+3=3x+1 \\ \Rightarrow2x=2 \\ \Rightarrow x=1 \\ and \\ log_2(1+3)=log_2(4)=2 \end{gathered}[/tex]The answer to part c) is x=1 and graphs intersect at (1,2).
d)
[tex]\begin{gathered} (f+g)(x)=7 \\ \Rightarrow log_2(x+3)+log_2(3x+1)=7 \\ \Rightarrow log_2((x+3)(3x+1))=7 \\ \Leftrightarrow(x+3)(3x+1)=2^7 \\ \Rightarrow3x^2+10x+3=128 \\ \Rightarrow3x^2+10x-125=0 \end{gathered}[/tex]Solving the quadratic equation using the quadratic formula,
[tex]\begin{gathered} \Rightarrow x=\frac{-10\pm\sqrt{10^2-4*3*-125}}{3*2} \\ \Rightarrow x=-\frac{25}{3},5 \end{gathered}[/tex]However, notice that if x=-25/3,
[tex]log_2(x+3)=log_2(-\frac{25}{3}+3)=log_2(-\frac{16}{3})\rightarrow\text{ not a real number}[/tex]Therefore, x=-25/3 is not a valid answer.
The answer to part d) is x=5.
e)
[tex]\begin{gathered} log_2(x+3)-log_2(3x+1)=3 \\ log_2(\frac{x+3}{3x+1})=3 \\ \Leftrightarrow\frac{x+3}{3x+1}=2^3=8 \\ \Rightarrow x+3=24x+8 \\ \Rightarrow23x=-5 \\ \Rightarrow x=-\frac{5}{23} \end{gathered}[/tex]The answer to part e) is x=-5/23
