The short leg of a triangle measures 17 and the long leg measures 32. What is the measure of the smaller acute angle of the triangle to the nearest tenth of a degree ? Draw a triangle to represent the problem. Be sure to show the trig equation you used when solving
Answers
The measure of the smaller acute angle of the triangle to the nearest tenth of a degree is 28.3 degrees.
Let's denote the smaller acute angle of the triangle as θ. We can use the tangent function to find the measure of this angle:
tan(θ) = opposite/adjacent
In this case, the opposite side is the length of the short leg (17) and the adjacent side is the length of the long leg (32). So we have:
tan(θ) = 17/32
Using a calculator, we can take the inverse tangent (tan^-1) of both sides to solve for θ:
θ = tan^-1(17/32) ≈ 28.3 degrees
So the measure of the smaller acute angle of the triangle is approximately 28.3 degrees.
Here's a diagram to illustrate the triangle:
/ l
/ l
17 / l opposite
/ l
/ θ l
/_______l
adjacent
32
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Related Questions
Pamela is 6 years younger than Jiri. The sum of their ages is 78 . What is Jiri's age?
Answers
P = Pamela
J = Jiri
J - 6 = P
P + J = 78
We can replace P with J - 6 because they are the same thing.
J - 6 + J = 78
2J - 6 = 78
2J = 84
J = 42
Jiri is 42 years old.
if a round cake has 30 slices how many slices will represent an angle of 216°?
Answers
Answer:18
Step-by-step explanation:360/30=12
216/12=18
Draw yourself a number line. Order the numbers from least to greatest 1/2, 12, 0666666666
6.33333...
-1/10
O -1/10, 1/2, 6666... 12. 6.3333...
O 1/2, -1/10, 0.666..., 6.333., 12
0 -1/10, 1/2, 0.6666..., 6.3333... 12
O 1/2, 1/10, 6.3333..., 0.6666.... 12
Answers
The order of numbers from least to greatest is C. -1/10, 1/2, 0.6666..., 6.3333..., 12
What is a Number Line?A number line is a graphical representation of numbers on a straight line, usually horizontally oriented, with numbers increasing from left to right.
The number line provides a visual representation of the relative size and order of numbers and allows for the estimation and comparison of quantities.
A number line can be extended infinitely in both directions, with negative numbers to the left of zero and positive numbers to the right.
The least number is the negative fraction and the greatest number on the number line is the positive whole number 12.
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HELP PLSSS THIS IS HARD SOMEONE
Answers
Since all the coordinates has been multiplied by 3 for example: (4,8) has become (12,24)
(c) A non-uniform but spherically symmetric charge distribution has a charge density: rho(r)=rho 0
(1−r/R)
rho(r)=0
for r≤R
for r>R
where rho 0
=3Q/πR 3
is a positive constant. Show that the total charge contained in this charge distribution is Q. [4] Show that the electric field in the region r>R is identical to that created by a point charge Q at r=0 [2] Derive an expression for the electric field in the region r≤R. [5]
Answers
To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:
ρ(r) = ρ₀(1 - r/R) for r ≤ R,
ρ(r) = 0 for r > R,
where ρ₀ = 3Q/πR³.
To find the total charge, we integrate ρ(r) over the volume:
Q = ∫ρ(r) dV,
where dV represents the volume element.
Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.
The integral becomes:
Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.
Evaluating this integral gives:
Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.
Simplifying further, we get:
Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].
Simplifying the expression inside the parentheses:
Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].
Simplifying once more:
Q = ρ₀ * π * (R³ - R³/3),
Q = ρ₀ * π * (2R³/3),
Q = (3Q/πR³) * π * (2R³/3),
Q = 2Q.
Therefore, the total charge contained in the charge distribution is Q.
To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.
By Gauss's law, the electric field through a closed surface is given by:
∮E · dA = (1/ε₀) * Qenc,
where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.
Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.
For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².
Plugging these values into Gauss's law:
E * 4πr² = (1/ε₀) * Q,
Simplifying:
E = Q / (4πε₀r²).
This is the same expression as the electric field created by a point charge Q at the origin (r = 0).
To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.
The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.
By Gauss's law, we have:
∮E · dA = (1/ε₀) * Qenc.
Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².
Plugging these values into Gauss's law:
E * 4πr² = (1/ε₀) * Q.
Simplifying:
E = Q / (4πε₀r²).
This expression represents the electric field inside the charge distribution for r ≤ R.
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Derrick needs to sell a minimum of 100 orders each month to make it into the sales winners circle. He has already sold 45 orders this month. He still needs to sell s more orders. Which inequality can be used to find the possible values for s? s−45>100
s−45<100 s+45≤100 s+45≥100
Answers
Answer:
s+45≥100
Step-by-step explanation:
"A minimum of" means either the same amount or more. So, the total amount he sells (s + 45) needs to be greater than or equal to 100.
PLEASE HELP. !!!!!!
the 4th option is “A translation 2 units left and 1 unit up
Answers
Simplify as far as possible. Please include the working in your answer, step by step.
\( \frac{9 {x}^{2} - 4 }{15 {x}^{2} - 13x + 2} \)
Answers
\( \mathfrak{ \huge{SOLUTION}}\)
\( \rm \implies \dfrac{9x - 4}{15 {x}^{2} - 13x + 2} \)
\( \rm \implies = \dfrac{(3x {)}^{2} - {2}^{2} }{ {15x}^{2} 10 - 3x + 2} \)
\( \rm{ \implies \dfrac{(3x + 2)(3x - 2)}{(5x - 1)(3x - 2)} }\)
\(\boxed{ \rm{ \dfrac{3 x + 2}{5x - 1} }}\)
\( \mathfrak{ \huge{ANSWER:}}\)
\(\qquad \bm{ \dfrac{3 x + 2}{5x - 1} } \qquad\)
\( \\ \)
\( \quad \tt{ \green{~Brainly-Philippines}} \quad\)
\(\downarrow\)
i already did 1A) I NEED 1B) HELP BRANILIEST WILL BE GIVNING
Answers
Answer: Turn the box to a 90 degree angle in any possible way to get your answer.
Step-by-step explanation:
Yes it is very likely that i took it off the graph
Solve the literal equation for Y:
4=5x+6y
Answers
Answer:
y=2/3-5x/6
Step-by-step explanation:
The group thought there was enough food for all 5 group members to
complete the trip, with each person getting the required 5600 calories per
day. However, they discover that they are missing 28,800 calories.
Using the map, create a plan a for the rest of the trip that includes taking as
many group members as possible to the South Pole, while sending the rest of
the group members directly back to base camp. Remember that each person
must have 5600 calories of food per day until he or she gets back to base
camp.
Be sure to explain how you came up with your plan. Include all work
necessary to support your answer.
Answers
To create a work plan for the food intake of each person in the group, there needs to be the required 5600 calories and there needs to be a replacement for the caloric deficit.
What is a Work Plan?This refers to the formal roadmap that is created for a project for the purposes of streamlining it.
Based on the fact that a map was not provided, there is insufficient data to solve the problem, so a general overview will be given about a work plan.
Because the group is 28,800 calories short and needs to complete the trip with their five members, then they need to ration their supplies.
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1 Conduct a research based on the topic given to you.
2 Collect data from an organization in Bahrain
3 Prepare the report and complete your presentation once the narrative report is approved.
4 Presentation is 5 minutes per group. Mastery of the topic is important. No reading of the slides. Make a smooth transition of your report.
5 You will report on the scheduled date and time. No changes will be allowed.
6 Complete this cover sheet and attach it to your activity output.
Answers
The given instructions involve conducting research on a specific topic, collecting data from an organization in Bahrain, preparing a report, and delivering a 5-minute presentation. Adherence to the scheduled date and time, mastery of the topic, and smooth transitions in the presentation are crucial.
To fulfill these instructions, the first step is to conduct thorough research on the assigned topic. This may involve gathering information from various credible sources, such as academic journals, reports, and relevant publications. The research should aim to provide a comprehensive understanding of the chosen subject matter.
Next, it is necessary to collect data from an organization in Bahrain. This can be achieved by reaching out to companies or institutions in Bahrain and requesting relevant data or conducting surveys, interviews, or observations to gather the necessary information.
Once the data is collected, it is essential to analyze and synthesize the findings to prepare a comprehensive report. The report should follow a structured format, including an introduction, methodology, data analysis, findings, and conclusions. It is crucial to ensure that the report is well-written, organized, and supported by evidence.
After the report is approved, the next step is to prepare a 5-minute presentation based on the report's key findings and conclusions. It is important to be well-versed in the topic, avoid reading directly from the slides, and ensure a smooth transition between different sections of the presentation.
Lastly, it is necessary to adhere to the scheduled date and time for presenting the findings. Any changes to the presentation schedule may not be allowed, so it is crucial to be prepared and deliver the presentation on the assigned date and time.
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What is the equation in slope-intercept form of the line that passes through the point (5, 0) and is parallel to the line represented by =2.2+1.2
y
=
2.2
x
+
1.2
.
Group of answer choices
=−2.2+11
y
=
−
2.2
x
+
11
=2.2−11
y
=
2.2
x
−
11
=−2.2−5
y
=
−
2.2
x
−
5
=2.2+5
Answers
If a firm permanently borrows
$
100
million at an interest rate of
8
%
, what is the present value of the interest tax shield? (Assume that the tax rate is
30
%
.)
Answers
If a firm permanently borrows $100 million at an interest rate of 8%, the present value of the interest tax shield is $2.4 million.
The following formula can be used to determine the present value of the interest tax shield:
PV(Tax Shield) = Tax Rate × Interest Expense
From the question:
Firm borrows $100 million
Interest rate is 8%
Tax rate is 30%
Let's first determine the interest expense:
Interest Expense = Borrowed Amount × Interest Rate
Interest Expense = $100 million × 8%
Interest Expense = $8 million
Now, we can calculate the present value of the interest tax shield:
PV(Tax Shield) = Tax Rate × Interest Expense
PV(Tax Shield) = 30% × $8 million
PV(Tax Shield) = $2.4 million
Therefore, the present value of the interest tax shield is $2.4 million.
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The complete question is:
If a firm permanently borrows $100 million at an interest rate of 8%, what is the present value of the interest tax shield? (Assume that the tax rate is 30%.)
Worth 10 points
Thank you to whoever does it’s a picture btw
Answers
Answer:
d. 13 inches
Step-by-step explanation:
Right of the bat, we can choose 13 because the two triangle sides must be greater than one. 5+8=13, so the triangle would not be complete.
: A satellite system consists of 4 components and can operate adequately if at least 2 of the 4 components are functional. If each component is, independently, functional with probability 0.6, what is the probability that the system operates adequately
Answers
The probability that the satellite system operates adequately is 0.7056.
The probability that a component is not functional is 0.4. Therefore, the probability that a component is functional is 1-0.4=0.6.
Using the rule of combinations, there are 6 possible combinations of functional and non-functional components:
1. All 4 components are functional: (0.6)^4=0.1296
2. 3 components are functional: (0.6)^3(0.4)=0.3456
3. 2 components are functional: (0.6)^2(0.4)^2=0.2304
4. 1 component is functional: (0.6)(0.4)^3=0.0256
5. No components are functional: (0.4)^4=0.0256
6. At least 2 components are functional: P(2 or 3 or 4) = 0.1296 + 0.3456 + 0.2304 = 0.7056
Therefore, the probability that the satellite system operates adequately is 0.7056.
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For the function f(x) = √4³(x-4), find ƒ−¹(x).
○ ƒ˜¹(x) = log₁ (2¹+4)
3
○ ƒ˜¹(x) = [1084(2+4)]*
Of
log4
O f-¹(x) = ¹081 (2¹) +
+4
3
O f-¹(x) = (log₁2)¹ +4
3
![For the function f(x) = 4(x-4), find (x). (x) = log (2+4)3 (x) = [1084(2+4)]*Oflog4O f-(x) = 081 (2)](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/9MM4izhTBxIcL3KeqgMaSRm6pnntFkQv.png)
Answers
The inverse of the function is f⁻¹(x) = 4 + log(x³)/log(4³)
How to determine the inverse functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = ∛[4³⁽ˣ⁻⁴⁾]
Swap x and y
So, we have
x = ∛[4³⁽y⁻⁴⁾]
Take teh cube of both sides
So, we have the following representation
4³⁽y⁻⁴⁾ = x³
Take the logarithm of both sides
(y - 4)log(4³) = log(x³)
So, we have
y - 4 = log(x³)/log(4³)
Add 4 to both sides
y = 4 + log(x³)/log(4³)
So, we have
f⁻¹(x) = 4 + log(x³)/log(4³)
Hence, the inverse is f⁻¹(x) = 4 + log(x³)/log(4³)
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If a random variable X has the gamma distribution with α=2 and β=1, find P(2.2 P = (2.2 < X < 2.9)
Answers
The probability that 2.2 < X < 2.9 for a random variable X with a gamma distribution with α = 2 and β = 1 is approximately 0.0862
Given that X has the gamma distribution with α = 2 and β = 1, we are to find the value of P(2.2 < X < 2.9)
Using the gamma distribution, the pdf can be given as\(\[f(x) = \frac{1}{{\beta ^\alpha }\Gamma (\alpha )}x^{\alpha - 1}{e^{ - x/\beta }}\]\)
Where α = 2 and β = 1.
Substituting these values in the above pdf, we get\(\[f(x) = \frac{1}{{{\text{e}}\Gamma (2)}}{x^1}{e^{ - x}} = xe^{ - x}\]\)
Therefore, P(2.2 < X < 2.9) can be found using the cumulative distribution function as
P(2.2 < X < 2.9) = F(2.9) - F(2.2)
The cumulative distribution function can be given as\(\[F(x) = \int\limits_0^x {f(t)} dt = \int\limits_0^x {te^{ - t} dt} \]\)
Integrating by parts, we get
\(\[\begin{array}{l} u = t\hspace{0.33em}\Rightarrow du = dt \\ dv = {e^{ - t}}\hspace{0.33em}\Rightarrow v = - {e^{ - t}} \end{array}\]\)
Therefore, the integration of F(x) will be\(\[\begin{array}{l} F(x) = - xe^{ - x} - \int { - {e^{ - x}}dt} = - xe^{ - x} + {e^{ - x}} \\ F(x) = (1 - x){e^{ - x}} \end{array}\]\)
Putting the values of 2.2 and 2.9 in F(x), we get
\(\[\begin{array}{l} P(2.2 < X < 2.9) = F(2.9) - F(2.2) \\ P(2.2 < X < 2.9) = (1 - 2.9){e^{ - 2.9}} - (1 - 2.2){e^{ - 2.2}} \\ P(2.2 < X < 2.9) \approx 0.0862 \end{array}\]\)
Hence, the required probability is approximately equal to 0.0862.
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if a multiple choice test consists of questions, each of which with of which only 1 is correct, (a) in how many different ways can a student check off one answer to each question?
Answers
In a multiple-choice test consisting of n questions, each of which has k answer choices, a student can check off one answer to each question in k^n different ways.
The number of different ways in which a student can check off one answer to each question in a multiple-choice test depends on the number of questions and the number of answer choices for each question.
For instance, if there are 3 questions, and each question has 4 answer choices, then the total number of ways the student can answer the test is 4x4x4=64.
In general, if there are n questions and each question has k answer choices, then the total number of ways the student can answer the test is k^n. This is because there are k choices for the first question, k choices for the second question, and so on, up to the nth question.
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Which of the following three goods is most likely to be classified as a luxury good?a. Kang b. Lafgar c. Welk
Answers
Welk is most likely to be classified as a luxury good. A luxury good is a good for which demand increases more than proportionally with income.
This means that as people's incomes increase, they are more likely to spend a larger proportion of their income on luxury goods.
The income elasticity of demand for a good is a measure of how responsive demand is to changes in income. A positive income elasticity of demand indicates that demand increases as income increases, while a negative income elasticity of demand indicates that demand decreases as income increases.
The income elasticity of demand for Welk is 4.667, which is much higher than the income elasticities of demand for Kang (-3) and Lafgar (1.667). This indicates that demand for Welk is much more responsive to changes in income than demand for Kang or Lafgar.
Therefore, Welk is most likely to be classified as a luxury good.
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PLEASE HURRY!!!!!!!!!!!!
Graph the solution to this inequality on the number line.
−5+x≥−3
Answers
Answer: 2
Step-by-step explanation:
To graph the solution to the inequality -5 + x ≥ -3 on the number line, we first need to isolate x.
Adding 5 to both sides of the inequality, we get:
x ≥ 2
This means that any value of x greater than or equal to 2 will satisfy the inequality. To graph this solution on a number line, we draw a closed circle at the point 2 and shade all the points to the right of 2, including the point 2 itself.
The resulting graph looks like this:
------•-------------------------------->
2
The shaded region on the right of 2 represents all the values of x that make the inequality true.
equivalent of it is not true that the test is today or the party is tonight
Answers
This is a logical statement, of the form
\(\urcorner(p\lor q)\)where p is the statement "the test is today" and q is the statement "the party is tonight". The DeMorgan's Law indicates that:
\(\urcorner(p\lor q)\equiv\urcorner p\wedge\urcorner q\)Therefore the equivalent statement is " the test is not today and the party is not tonight".
if this trapezoid is moved through the translation (x+3,y-2) what will the coordinates of B` be
Answers
Answer:
-2, 2
Step-by-step explanation:
Wright (3+4i)+(8+2i) as a complex number in standard form
Answers
Answer:
11 +6i
Step-by-step explanation:
(3+4i)+(8+2i)
Add the real portions
3+8 = 11
Add the imaginary portions
4i+2i = 6i
The complex number in a+bi form is
11 +6i
Answer:
\( = 11 + 6i\)
Step-by-step explanation:
\((3 + 4i) + (8 + 2i) \\ 3 + 4i + 8 + 2i \\ = 11 + 6i\)
hope this helps
brainliest appreciated
good luck! have a nice day!
In ΔQRS, s = 3.1 cm,
�
m∠Q=62° and
�
m∠R=114°. Find the length of q, to the nearest 10th of a centimeter.
Answers
The length of q is 5.4 cm, to the nearest 10th of a centimeter. In order to find the length of q, we can use the law of sines.
What is The law of sines?The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all sides and angles of the triangle.
In this case, we have:
q/sin 62° = s/sin 114°
Rearranging the equation and solving for q, we get:
q = (s*sin 114°)/sin 62°
Plugging in the given values, we get:
q = (3.1*sin 114°)/sin 62°
= 3.1*1.53/0.876
= 5.41 cm
Rounding this off to the nearest 10th of a centimeter, we get q = 5.4 cm.
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To the closest tenth of a centimeter, the length of q is 5.4 cm. We can use the rule of sines to calculate the length of q.
What is the purpose of law of sines?The law of sines is commonly used to find a triangle's elusive side or angle. If exact triangle measurement combinations are provided, this law can be used. ASA Given two angles as well as an included side, the goal is to determine the unknown side.
According to the rule of sines, the ratio of a triangle side's length to the sine of its opposing angle is identical for all triangle sides and angles.
In this instance, we have:
q/sin 62° = s/sin 114°
When we rearrange the equation and solve for q, we get:
q = (s*sin 114°)/sin 62°
With the provided values, we get:
q = (3.1*sin 114°)/sin 62°
= 3.1*1.53/0.876
= 5.41 cm
If we round this to the closest tenth of a centimeter, we get q = 5.4 cm.
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Refer to the image below,
il change facility follows the uniform probability distribution between 21 and 38 minutes. What is the probability that a randomly selected car will require exactly 30 minutes to service
Answers
The probability that a randomly selected car will require exactly 30 minutes to service is approximately 0.0588 or 5.88%.
To find the probability that a randomly selected car will require exactly 30 minutes to service, we need to determine the probability density function (PDF) of the uniform distribution.
In a uniform distribution, the PDF is constant within the given interval and zero outside of it. The interval for this problem is between 21 and 38 minutes.
Since the distribution is uniform, the PDF is given by:
f(x) = 1 / (b - a)
where a is the lower bound of the interval (21 minutes) and b is the upper bound of the interval (38 minutes).
Plugging in the values:
f(x) = 1 / (38 - 21) = 1 / 17
Now, to find the probability that a randomly selected car will require exactly 30 minutes, we need to calculate the area under the PDF curve at x = 30.
The probability is equal to the value of the PDF at x = 30:
P(X = 30) = f(30) = 1 / 17 ≈ 0.0588
Therefore, the probability that a randomly selected car will require exactly 30 minutes to service is approximately 0.0588 or 5.88%.
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help me ...Given △ABC≅△EFG, which congruency statement is true?
(A.) EC¯¯¯¯¯≅BF¯¯¯¯¯
segment E C is congruent to segment B F
(B.) CB¯¯¯¯¯≅GE¯¯¯¯¯
segment C B is congruent to segment G E
(C.) AC¯¯¯¯¯≅EG¯¯¯¯¯
segment A C is congruent to segment E G
(D.) BA¯¯¯¯¯≅EF¯¯¯¯¯
Answers
Answer:
(C.) AC¯¯¯¯¯≅EG¯¯¯¯¯ is true
Step-by-step explanation:
The positions of the letters in naming the triangles in the statement of congruent tells you which sides are congruent.
△ABC≅△EFG
Sides AB and EF are congruent
△ABC≅△EFG
Sides BC and FG are congruent
△ABC≅△EFG
Sides AC and EG are congruent
Look at the choices:
(C.) AC¯¯¯¯¯≅EG¯¯¯¯¯ is true
find the points (x,y) at which the curve x(t)=4cos(t),y(t)=4sin(2t) has a horizontal tangent.
Answers
The curve has horizontal tangents at the points (0,0) for all values of t. To find the points at which the curve has a horizontal tangent, we need to find the values of t that make the derivative of y(t) equal to zero.
First, we need to find the derivative of y(t):
y'(t) = 8cos(t)
Next, we set y'(t) equal to zero and solve for t:
8cos(t) = 0
cos(t) = 0
This occurs when t = π/2 or 3π/2.
Now, we can plug these values of t back into the original equations to find the corresponding points:
When t = π/2,
x(π/2) = 4cos(π/2) = 0
y(π/2) = 4sin(2(π/2)) = 0
So the point is (0,0).
When t = 3π/2,
x(3π/2) = 4cos(3π/2) = 0
y(3π/2) = 4sin(2(3π/2)) = 0
So the point is also (0,0).
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Use Algorithm 1 to find the transitive closures of these relations on {1, 2, 3, 4}.
a. {(1,2), (2,1), (2,3), (3,4), (4,1)}
b. {(2,1), (2, 3), (3,1), (3,4), (4,1), (4, 3)}
c. {(1,2), (1,3), (1,4), (2,3), (2,4), (3, 4)}
d. {(1, 1), (1,4), (2,1), (2,3), (3, 1), (3, 2), (3,4), (4, 2)}
Answers
To find the transitive closures of the given relations, we can use Algorithm 1, also known as the Warshall's algorithm. Here are the transitive closures for each relation:
a. Relation: {(1,2), (2,1), (2,3), (3,4), (4,1)}
Transitive Closure: {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}
b. Relation: {(2,1), (2, 3), (3,1), (3,4), (4,1), (4, 3)}
Transitive Closure: {(2,1), (2,3), (2,4), (3,1), (3,3), (3,4), (4,1), (4,3), (4,4)}
c. Relation: {(1,2), (1,3), (1,4), (2,3), (2,4), (3,4)}
Transitive Closure: {(1,2), (1,3), (1,4), (2,3), (2,4), (3,4)}
d. Relation: {(1, 1), (1,4), (2,1), (2,3), (3, 1), (3, 2), (3,4), (4, 2)}
Transitive Closure: {(1,1), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}
In the transitive closure, every pair (i, j) represents a directed edge from i to j in the transitive closure graph.
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Answers
Answer: The slope is 1.5. The equation of the line is y=1.5x+3
Step-by-step explanation:
Slope is the "Rise" over the "Run" of a line. The rise is the change in y. The run is the cange in x. Take any two points. I picked (0,3) and (4,9) since they were clearly on whokle number lines. The rise is (9-3) or 6. The run is (4-0) or 4. Rise/Run = 6/4 or 1.5. The y intercept is at 3 (the value of y when x=0). The full line equation is thus y = 1.5x+3.