The geometric sequence for [tex]a_{1} = -8[/tex], r = 1/2, and n=9 is -1/32.
How to find the geometric sequence?The geometric sequence formula has the general form [tex]a_{n} = a_{1} * r^{n-1}[/tex], where r denotes the common ratio, [tex]a_{1}[/tex] denotes the first term, and n denotes the term's position in the series.
To find the geometric sequence, we can use the formula,
[tex]a_{n} = a_{1} * r^{n-1}[/tex]
where [tex]a_{n}[/tex] is the geometric sequence of n term
[tex]a_{1}[/tex] = first term
n = term number
In given problem [tex]a_{1}[/tex] = -8, r = 1/2, n=9
Put all values in the above equation,
[tex]a_{n} = (-8) * (\frac{1}{2})^{8-1} \\a_{n} = (-8) * (\frac{1}{2})^{7} \\a_{n} = (-8) * \frac{1}{2^{7} } \\a_{n} = (-8) *\frac{1}{128} \\a_{n} = \frac{-1}{32}[/tex]
Therefore the [tex]9^{th}[/tex] term of the geometric sequence is -1/32.
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Solve the inequality: 0.5k < 18.5
A k <9.25
B k> 9.25
C k < 37
D k> 37
a technical engineer is interested in understanding the battery life of two different laptops for student usage at a community college in california. the two models he has are madroid and krapple. he randomly assigned students to one of the laptop models and recorded the number of minutes the students were able to use the computer until the battery ran out. use data file: laptops.csv download laptops.csv does the technical engineer have statistically significant evidence to present to the university budget committee to purchase krapple because it has, on average, a longer battery life? provide the p-value from your analysis.
The conclusion of hypothesis testing through the t-test is that the technical engineer have not statistically significant evidence to present to the university budget committee to purchase Krapple because it has, on average, a longer battery life. The p-value for t-test is equals to the 0.0074.
We have study related to battery life of two different laptops for student usage at a community college in california. There are two models, Krapple and Madroid. Engineer randomly assigned students to one of the laptop models and recorded the number of minutes the students were able to use the computer until the battery ran out. Here we have paired data so paired t test should be used.
Let d = Krapple - Madroid ( Sample sum of difference). Above table shows the calculations, Sample size, n = 15
Sample sum of difference, d = 1243
Sample mean of differences: Σα
= 1243/15 = 82.87
Sample standard deviation = [tex]\sqrt{\frac{488317.73}{15-1}}[/tex]
= 186.76
The Null and alternative Hypotheses are defined as [tex]H_0 : \mu_1- \mu_2 = 0[/tex]
[tex]H_a : \mu_1 - \mu_2 < 0[/tex]
Level of significance, α = 0.05
Test is one tailed (right tailed) df = n- 1
=> Degree of freedom = 14
Using the t - test, [tex]t = \frac{\sum d }{ \sqrt{\frac{n\sum d² - (\sum d)²}{n - 1}}}[/tex]
so, [tex] t = \frac{ 1243}{\sqrt{\frac{15× 488317.73 - (1243)²}{ 15 -1}}}[/tex]
=> [tex]t =\frac{1243}{\sqrt{412836.925}}[/tex]
=> t = 1.93
Now, using distribution table, P- value for t = 1.93, is 0.074. See, p-value > 0.05 , so result is not statistically significant. So, there is no evidence to reject the null hypothesis.
Conclusion: The technical engineer do not have statistically significant evidence to present to the university budget committee to purchase Krapple because it has, on average, a longer battery life.
Hence, required p-value is 0.074.
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Complete question:
the above first figure complete the question.
a technical engineer is interested in understanding the battery life of two different laptops for student usage at a community college in california. the two models he has are madroid and krapple. he randomly assigned students to one of the laptop models and recorded the number of minutes the students were able to use the computer until the battery ran out. use data file: laptops.csv download laptops.csv does the technical engineer have statistically significant evidence to present to the university budget committee to purchase krapple because it has, on average, a longer battery life? provide the p-value from your analysis.
A car's cruise control function should keep the car within 2.5 mph of the set speed. Shala sets her cruise control for 65 mph. A. create a compound inequality to represent the speed Shala's car should go and graph the inequality on the number line. B. Shala is driving on a road with a speed limit of 60 mph. It is possible for her to get a ticket if she goes more than 7mph over the speed limit. is it possible for Shala to get a ticket while she is on cruise control.
Part A: compound inequality for the speed Shala's car: | x - 65 | ≤ 2.5
Part B: 67 mph < 67.5 (maximum value) Thus, she will not get the ticket.
Explain about the compound inequality:Two or more inequalities are connected together with or or and to form a compound inequality (also described as a combined inequality). A value must only make one aspect of an inequality true in order to be the solution to an or inequality. An inequality's solution must make both portions true in order to succeed.
Speed limit set by car's cruise control function = 2.5 mph.
Speed limit set by Shala = 65 mph.
Thus,
Maximum speed of car = 65 + 2.5
Minimum speed of car = 65 - 2.5
Let x represents the current speed of car,
x ≤ 65 + 2.5 or x ≥ 65 - 2.5
x - 65 ≤ 2.5 or x - 65 ≥ - 2.5
x - 65 ≤ 2.5 or - (x-65) ≤ 2.5
| x - 65 | ≤ 2.5 ( required compound inequality)
Now,
65 - 2.5 ≤ x ≤ 65 + 2.5
62.5 ≤ x ≤ 67.5
In interval notation; [62.5, 67.5]
The inequality on the number is drawn.
If Shala goes with 7 mph over the speed limit.
60 + 7 = 67 mph < 67.5 (maximum value)
Thus, she will not get the ticket.
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fifty (50) soc390 students from the spring scored an average of 80 on exam 1, with a standard deviation of 12. fifty-two (52) soc 390 students from the fall scored an average of 81 on exam 1, with a standard deviation of 6. what can we conclude?
There is no significant difference in the average scores of two groups of SOC 390 students who took Exam 1 in the spring and fall semesters, respectively, as per the two-sample t-test with a p-value of 0.388.
The average score of the spring group of 50 students in SOC 390 on Exam 1 was 80, with a standard deviation of 12, while the average score of the fall group of 52 students was 81, with a standard deviation of 6. To determine if the difference in the means of the two groups is statistically significant, we can use a two-sample t-test.
Assuming unequal variances, the t-value for the two groups is 0.87, with a corresponding p-value of 0.388. Since the p-value is greater than the standard alpha level of 0.05, we fail to reject the null hypothesis that the two groups have equal means.
Therefore, we can conclude that there is no significant difference in the average scores of the two groups of SOC 390 students who took Exam 1 in the spring and fall semesters, respectively.
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The complete question is :
What is the difference between the average scores of two groups of students who took Exam 1 in SOC 390 in the spring and fall semesters, respectively, given that the spring group consisted of 50 students who scored an average of 80 with a standard deviation of 12, and the fall group consisted of 52 students who scored an average of 81 with a standard deviation of 6?
Find the value of x.
please answer
Answer:
x =107+88 =195, 360 -195 =165
Answer:
73°
Step-by-step explanation:
In an inscribed quadrilateral opposite angles are supplementary( they add up to 180) so angle x and its opposite angle( which is 107°) are equal to 180.
x + 107 = 180
Subtract 107 from both sides to isolate the x
x = 73
104°
X what does that equal if it’s a vertical angel?
Answer:If 104° is a measure of one of the vertical angles formed by the intersection of two straight lines, then the measure of the other vertical angle would also be 104°. This is because vertical angles are always congruent, which means they have the same measure.
Step-by-step explanation:
please help me with this !!
Step-by-step explanation:
This is an ordinary annuity type of question :
FV = C [ ((1+i)^n) -1 )/i ] plug in the numbers
FV = 25 000 [ (1+.08)^9 -1 ]/ .08 = ~ $ 312 189
What is a formula for the nth term of the given sequence? 13,15,17…
Answer: [tex]a_n = 2n+11[/tex]
======================================
Explanation:
The gap between adjacent terms is 2.
15-13 = 217-15 = 2We add 2 to each term to get the next. Therefore, d = 2 is the common difference.
The first term is [tex]a_1 = 13[/tex]
Use that and the value of d to determine the nth term formula of this arithmetic sequence.
[tex]a_n = a_1 + d(n-1)\\\\a_n = 13 + 2(n-1)\\\\a_n = 13 + 2n-2\\\\a_n = 2n+11 \textbf{ is the final answer}\\\\[/tex]
---------------
Check:
Plug in n = 1
[tex]a_n = 2n+11\\\\a_1 = 2*1+11\\\\a_1 = 2+11\\\\a_1 = 13\\\\[/tex]
That confirms 13 being the 1st term.
Now use n = 2
[tex]a_n = 2n+11\\\\a_2 = 2*2+11\\\\a_2 = 4+11\\\\a_2 = 15\\\\[/tex]
That matches with the fact 15 is the 2nd term.
I'll let you check the third term.
what is the area of triangle ABC
A 6√3
B 18√3
C 36√3
D 72√3
Answer:
B 18√3
Step-by-step explanation: 1. Calculate the base and height of the triangle.
2. Multiply the base and height of the triangle.
3. Divide the result by 2.
4. Multiply the result by the square root of 3.
5. The answer is 18√3.
finding the final amount in a word problem on compound...
When $2,000 is loaned for 5 years at 15% interest compounded monthly, the final amount (or future value) is $4,214.36.
How is the final amount determined?The final amount is the future value of the present value investment.
The future value can be computed using the FV formula or an online finance calculator as follows:
N (# of periods) = 60 months (5 years x 12)
I/Y (Interest per year) = 15%
PV (Present Value) = $2,000
PMT (Periodic Payment) = $0
Results:
Future Value (Final amount)) $4,214.36
Total Interest = $2,214.36
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There are 28 more butterflies than snails. There are 9 snails. How many butterflies are there?
Answer:
Step-by-step explanation:
Step 1:
Butterflies is greater than Snails
More=addition
GP: 28+9=B
Step 2:
28+2=30
30+7=37
Answer: 37 Butterflies
Hope this helps!
Given that,
Total butterflies = 28
Total snails = 9
More butterflies than snails are = butterflies + snails
[tex]\implies28+9[/tex]
[tex]\implies 37[/tex]
Therefore, there are 37 butterflies.
There are 4 bikes and 12 children what is the ratio of bikes to children
Answer:1:3
Step-by-step explanation:
we can show this as 4:12=1:3
so ratio of bikes to children is 1:3
How many times can 3 go into 64
Answer:
How many times can 3 go into 64?
21 times
3 x 21
= 63Step-by-step explanation:
You're welcome.
Answer: 21.3333333333
Step-by-step explanation:
64 / (Divided by) 3 equals 21.3333333...(Recurring, Meaning to go on for infinity)
Fast for 100 points
One interior angle of a triangle is 35°, and the other two angles are congruent. Choose the equation that could be used to determine the degree measure of one of the congruent angles.
2x + 35 = 180
2x − 35 = 90
x + 35 = 180
x − 35 = 90
2x + 35 = 180 is the correct equation that could be used to determine the degree measure of one of the congruent angles.
What are congruent angles?
Congruent angles are angles that have the same measure. Two angles are said to be congruent if they have the same degree measurement.
2x + 35 = 180 can be used to determine the degree measure of one of the congruent angles.
Let x be the degree measure of each of the two congruent angles.
Then, the sum of the interior angles of a triangle is 180 degrees, so we can set up the equation:
35 + x + x = 180
Simplifying and solving for x, we get:
2x + 35 = 180
Therefore, 2x + 35 = 180 is the correct equation that could be used to determine the degree measure of one of the congruent angles.
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Answer:
2x + 35 = 180 is the correct equation that could be used to determine the degree measure of one of the congruent angles.
Step-by-step explanation:
working on notes right now also the other guy is error free.
What is the mean in the set of data below:
Data: 2.25, 4.5, 3.75, 1.5, 5.25 (hint: do not round your answer)
Answer: 3.45
Step-by-step explanation:
Answer:
aswer will be 11.25 hope this helps
Anita Beasley
The cylinder shown has a radius of 7 inches and a volume of 2772 cubic inches.
What is the approximate heighth of the cylinder? (Use for)
With the help of the volume and radius of the cylinder, we know that the height is 18.01 in.
What is a cylinder?A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been solid in three dimensions.
In elementary geometry, it is regarded as a prism with a circle as its basis.
A cylinder can instead be described as an infinitely curved surface in a number of modern domains of geometry and topology.
So, in the given situation use the formula:
V=πr²h
Now, calculate as follows:
V=πr²h
h = V/πr²
h = 2772/π7²
h = 18.00724in
Rounding off: h = 18.01 in
Therefore, with the help of the volume and radius of the cylinder, we know that the height is 18.01 in.
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Solve the inequality
x^2-2x<35
From the sign chart, we can see that the solution set is x < -5 or -5 < x < 7. Therefore, the solution to the original inequality is:
x < -5 or -5 < x < 7
How to solve inequality?In order to solve an inequality, you need to isolate the variable on one side of the inequality symbol (i.e., <, >, ≤, ≥) and determine the range of values for which the inequality holds true.
The process for solving an inequality depends on the specific type of inequality. Here are the general steps for solving different types of inequalities:
Solving linear inequalities:
a. Move all variable terms to one side of the inequality and all constant terms to the other side.
b. Divide or multiply both sides by a positive constant (i.e. not zero) to isolate the variable.
c. If you multiply or divide by a negative constant, flip the inequality symbol to maintain the inequality.
Solving quadratic inequalities:So, the inequality can be written as:
[tex](x - 7) (x + 5) < 0[/tex]
To solve this inequality, we need to consider the sign of the expression on the left-hand side for different values of x. We can do this by creating a sign table:
x | x - 7 | x + 5 | (x - 7) (x + 5)
----------|-----------|-----------|----------------
-6 | -13 | -1 | +13
-4 | -11 | +1 | -11
-1 | -8 | +4 | -32
6 | -1 | +11 | -11
8 | +1 | +13 | +13
From the sign table, we can see that the expression (x - 7)(x + 5) is negative (i.e., less than zero) for values of x between -5 and 7. Therefore, the solution to the inequality is:
[tex]-5 < x < 7[/tex]
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An artist was able to draw one-eighth of a picture every hour. If he needed to paint 9 pictures for an art show, how many hours would it take him?
According to the question we can say that it will take the artist 72 hours to paint 9 pictures for the art show.
If the artist can draw one-eighth of a picture in one hour, then he can draw one complete picture in 8 hours (since 8 x 1/8 = 1).
Therefore, to draw 9 pictures, the artist will need 9 x 8 = <<9*8=72>>72 hours.
So, it will take the artist 72 hours to paint 9 pictures for the art show.
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Find the area of the triangle.
5 km
143°
7 km
The area of the triangle is approximately 11.524 km²
What is an area?
We can find the area of the triangle using the formula:
Area = (1/2) * a * b * sin(C)
where a and b are the lengths of the two sides and C is the angle between them.
In this case, a = 5 km, b = 7 km, and C = 143°. However, before we can use this formula, we need to convert the angle to radians. We can do this by multiplying by pi/180:
C = 143 * pi/180
C ≈ 2.495 radians
Now we can substitute the values into the formula and calculate the area:
Area = (1/2) * 5 km * 7 km * sin(2.495)
Area ≈ 11.524 km²
Therefore, the area of the triangle is approximately 11.524 km².
What is triangle?
A triangle is a 2-dimensional geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and is used in various fields such as mathematics, engineering, architecture, and art. Triangles can be classified into different types based on their sides and angles, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. The area of a triangle is calculated by using the formula A = 1/2 * base * height, where the base is the length of one of its sides and the height is the perpendicular distance between the base and the opposite vertex.
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Complete question is: The area of the triangle is approximately 11.524 km²
how many integers between 100 and 999, inclusive, have the property that some permutation of its digits is a multiple of 11 between 100 and 999? for example, both 121 and 211 have this property. (2017amc10a problem 25)
226 integers are present between 100 and 999, inclusive, and have the property that some permutation of its digits is a multiple of 11 between 100 and 999.
Here, we have,
The problem statement is to find the number of multiples of 11 between 100 and 999 inclusive, where some multiples may have digits repeated twice and some may not.
To solve this problem, we can first count the number of multiples of 11 between 100 and 999 inclusive, which is 81.
Some of these multiples may have digits repeated twice, and each of these can be arranged in 3 permutations.
Other multiples of 11 have no repeated digits, and each of these can be arranged in 6 permutations.
However, we must account for the fact that switching the hundreds and units digits of these multiples also yields a multiple of 11, so we must divide by 2, giving us 3 permutations for each of these multiples.
Thus, we have a total of 81 × 3 = 243 permutations.
However, we have overcounted because some multiples of 11 have 0 as a digit.
Since 0 cannot be the digit of the hundreds place, we must subtract a permutation for each of these multiples.
There are 9 such multiples (110, 220, 330, ..., 990), yielding 9 extra permutations.
Additionally, there are 8 multiples (209, 308, 407, ..., 902) that also have 0 as a digit, yielding 8 more permutations.
Therefore, we must subtract these 17 extra permutations from the total of 243, giving us 226 permutations in total.
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a gym knows that each member, on average, spends 70 minutes at the gym per week, with a standard deviation of 20 minutes. assume the amount of time each customer spends at the gym is normally distributed. a. what is the probability that a randomly selected customer spends less than 65 minutes at the gym? b. suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. what are the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym?
(a) The probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013. (b) The expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes
a) The probability that a randomly selected customer spends less than 65 minutes at the gym is calculated using the standard normal distribution formula.
z = (x - μ) / σ
where,μ = 70 minutes, σ = 20 minutes, x = 65 minutes
Substituting the given values, we get
z = (65 - 70) / 20
z = -0.25
Using a standard normal table or calculator, the probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013.
b) The standard deviation (standard error) of the sample mean can be calculated using the formula:
SE = σ/√n
where,σ = 20 minutes, n = 49
Substituting the given values, we get
SE = 20/√49
SE = 2.857 minutes
Therefore, the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes, respectively.
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I need Helpppp my teacher sucks at teaching
The missing value in the given figure is 120 degree.
What is an isosceles trapezoid?An isosceles trapezoid is a trapezoid where the non-parallel sides are congruent.
What is angle theorem of trapezoid?The base angles of an isosceles trapezoid are congruent.
The converse is also true: If a trapezoid has congruent base angles, then it is an isosceles trapezoid.
Equation:In CFED,
As it is and isosceles trapezoid,
m∠C=m∠F
m∠D=m∠E
∴m∠F = 60 degrees
Now
m∠D+m∠E+m∠F+m∠C = 360 degree
2m∠D+120=360
m∠D=(360-120)/2
∴m∠D=120 degree
Thus the value of missing angle is 120 degree.
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PLESEEE I NEEDDD HELPP OR ILL FAIL PLEASEEE!!
Thus, the measure of the minor arc CG for the given chord for the circle is found as: arc CG = 30°.
Explain about the minor arc:The shortest arc that connects two points on a circle is called a minor arc.
A minor arc's measure is equal to the angle's central measure and is less than 180 degrees.The longer arc that joins two circle ends is known as a major arc.A major arc's measure is greater than 180 degrees and equal to 360 degrees less the diameter of a small arc with the same ends.A semicircle is an arc that is exactly 180 degrees in length.For the given figure:
Using the intersecting chord theorem:
m∠FED = 1/2(arc CG - arcFD)
39 = 1/2(arc CG - 48)
arc CG - 48 = 39*2
arc CG = 78 - 48
arc CG = 30°
Thus, the measure of the minor arc CG for the given chord for the circle is found as: arc CG = 30°.
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Complete question:
Find the measure of minor arc CG for the attached figure.
Which expression is the simplest form of 4(3x + y) + 2(x-5y) +x2?
Answer:
Step-by-step explanation:4(3x+y)+2(x-5y)+x²=12x+4y+2x-10y+x²
=14x-6y+x²
=x²+14x-6y
Mrs. Hernandez’s class sold fruit pies for $5 each and Mr. Kane’s class sold bottles of fruit juice for $2 each. Together, the classes sold 29 items and earned $94 for their school. Write and solve a system of equations that models this problem. SHOW ALL YOUR WORK! Mrs. Hernandez's class sold fruit pies and Mr. Kane's class sold bottles of fruit juice.
Mrs. Hernandez's section has sold 12 fruit pies and Mr. Kane's class had sold 17 bottles of fruit juice.
Let's use the variables 'x' and 'y' to represent the number of fruit pies sold by Mrs. Hernandez's class and the number of bottles of fruit juice sold by Mr. Kane's class, respectively.
From the problem, we know that:
Each fruit pie sold for $5, so the revenue from Mrs. Hernandez's class is 5x.
Each bottle of fruit juice sold for $2, so the revenue from Mr. Kane's class is 2y.
The total number of items sold is 29, so x + y = 29.
The total revenue earned is $94, so 5x + 2y = 94.
Our system of equations is:
x + y = 29
5x + 2y = 94
To solve the system, we can use the substitution method. Solving the first equation for y, we get:
y = 29 - x
Substituting this expression for y into the second equation, we get:
5x + 2(29 - x) = 94
Simplifying and solving for x, we get:
3x = 36
x = 12
Substituting x = 12 into the equation y = 29 - x, we get:
y = 29 - 12 = 17
Therefore, it can be concluded that Mrs. Hernandez's class sold 12 fruit pies and Mr. Kane's class sold 17 bottles of fruit juice.
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Need help finding the missing coefficient
Answer:
- 40
Hope this helps!
Step-by-step explanation:
( 4d - 6 )( 4d - 4 ) : Cross Multiply
( 4d × 4d ) + ( 4d × (-4)) + ((-6) × 4d ) + ((-6) × (-4))
[tex]16d^{2}[/tex] - 16d - 24d + 24 : ( Combine like terms )
[tex]16d^{2}[/tex] - 40d + 24
charlie's teacher claims that he does not study and just guesses on exams. on an exam with 201 true-falsequestions, charlie answered 53.7% of the questions correctly. calculations using these results show that if hewere really just guessing, there would be roughly 1 chance in 7 that he would do this well. is there statisticallysignificant evidence against the teacher's claim that charlie is just guessing? why or why not?4
There is No statisti-cally signi-ficant evidence against the teacher's-claim that Charlie is just guessing because the probability is very low.
The total number of True-false questions are = n = 201.
The probability of getting a correct answer by guessing is = p = 0.5,
Charlie answered 53.7% = 0.537 of the questions correctly,
So, P(p' ≥ 0.537)
⇒ P(z ≥ (0.537 - 0.5)/√(0.5×0.5)/201,
⇒ P(z ≥ 1.05) = 1 - P(z < 1.05)
⇒ 0.1469
Since, the probability is very low,
Therefore, there is not any significant evidence against the teachers claim.
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Write the equation of each circle
On solving the provided question we can say that
1. circle centered at the origin with a radius of 10 is:
[tex]x^{2} +y^{2} =100[/tex]
2. circle with center R(-1, 8) and a radius of 5 is:
[tex](x + 1)^2 + (y - 8)^2 = 25[/tex]
3. center P(8, -5) and a radius of 24.5 is:
[tex](x -8)^2 + (y +5)^2 = 24.5[/tex]
4. the origin and passing through the point (9, -2) is:
[tex]x^{2} +y^{2} -18x+4y+85=0[/tex]
5. center B(0, -2) and passing through the point (-6, 0) is:
[tex](x )^2 + (y +2)^2 = 40[/tex]
6. center F(11, 4) and passing through the point (-2, 5) is:
[tex](x -11)^2 + (y - 4)^2 = 1708[/tex]
What is circle?A circle seems to be a two-dimensional component that is defined as the collection of all places in a jet that are equidistant from the hub. A circle is typically shown with a capital "O" for the centre and a lower portion "r" for the radius, which represents the distance from the origin to any point on the circle. The formula 2r gives the girth (the distance from the centre of the circle), where (pi) is a proportionality constant about equal to 3.14159. The formula r2 computes the circumference of a circle, which relates to the amount of space inside the circle.
circle centered at the origin with a radius of 10 is:
[tex]x^{2} +y^{2} =100[/tex]
circle with center R(-1, 8) and a radius of 5 is:
[tex](x + 1)^2 + (y - 8)^2 = 25[/tex]
center P(8, -5) and a radius of 24.5 is:
[tex](x -8)^2 + (y +5)^2 = 24.5[/tex]
the origin and passing through the point (9, -2) is:
[tex]x^{2} +y^{2} -18x+4y+85=0[/tex]
center B(0, -2) and passing through the point (-6, 0) is:
[tex](x )^2 + (y +2)^2 = 40[/tex]
center F(11, 4) and passing through the point (-2, 5) is:
[tex](x -11)^2 + (y - 4)^2 = 1708[/tex]
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What is the length of one leg of the triangle?
64 cm
64 StartRoot 2 EndRoot cm
128 cm
128 StartRoot 2 EndRoot cm
The length of other leg of the triangle is 64√2 cm.
What is Pythagoras theorem?
For right angle triangle,
Hypotenuse² = Base²+Height ²
Here we have a right angle triangle.
It is given that height and base of the triangle is 8 cm.
Now we want to find other leg of the triangle.
It is clear that other leg means hypotenuse here because this is a right angle triangle.
We know,
Hypotenuse ²= Base²+Height ²
[tex] = {64}^{2} + {64}^{2} \\ = 4096+ 4096 \\ = 2 \times 4096[/tex]
So,
[tex]hypotenuse = \sqrt{2 \times 4096} \\ = \sqrt{64 \times 64 \times2 } \\ = 64\sqrt{2} [/tex]
Therefore, length of the third leg is 64√2 cm.
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Correct question is " There is a right angle triangle. Height and base of the triangle is 8 cm.What is the length of other leg of the triangle?
64 cm
64√2 cm
128 cm
128√2 cm"
I need help with this question
The equilateral triangle ABC have the value for x as 4√3, the measure of angle B is equal to 60° and the area is derived to be equal to 16√3.
How to evaluate for the required values of the equilateral triangle ABCAn equilateral triangle have all its sides and angle to be equal, and each interior angles is equal to 60°
using the trigonometric ratio of sin for the angle C;
recall sin 60° = √3/2
sin 60° = x/8 {opposite/hypotenuse}
√3/2 = x/8
x = 4√3 {cross multiplication}
angle B = 60° {one interior angle of an equilateral triangle}
area of triangle = 1/2 × base × height
area of triangle ABC = 1/2 × 8 × 4√3
area of triangle ABC = 16√3.
Therefore, the equilateral triangle ABC have the value for x as 4√3, the measure of angle B is equal to 60° and the area is derived to be equal to 16√3.
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