Answers
The cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]
In triangle ABC, where angle ABC is a right angle (90 degrees) and sides AB, BC, and AC are given as 6, 8, and 10 units respectively, we can use the cosine and cotangent functions to find the cotangent of angle ABC.
The cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse.
In this case,[tex]\(\cos(\angle ABC) = \frac{BC}{AC} = \frac{8}{10} = \frac{4}{5}\).[/tex]
The cotangent [tex](\(\cot\))[/tex] of an angle is the reciprocal of the tangent (tan).
The tangent is the ratio of the opposite side to the adjacent side.
Therefore,[tex]\(\cot(\angle ABC) = \frac{1}{\tan(\angle ABC)}\).[/tex]
Since [tex]\(\tan(\angle ABC) = \frac{AB}{BC} = \frac{6}{8} = \frac{3}{4}\)[/tex], we can find the cotangent:
[tex]\[ \cot(\angle ABC) = \frac{1}{\tan(\angle ABC)} = \frac{1}{\frac{3}{4}} = \frac{4}{3} \][/tex]
Therefore, the cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]
The probable question may be:
The cosine of a certain angle is 4/5. What is the cotangent of the angle?
In triangle ABC , Angle ABC=90 degree, AB=6, BC=8 AC=10
Final answer:
The cosine of an angle being 4/5 means that the ratio of the adjacent side to the hypotenuse in a right triangle is 4/5.
Explanation:
The given question states that the cosine of an angle is 4/5. In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. So, if we have a right triangle with an angle A, and the cosine of A is 4/5, it means that the ratio of the length of the adjacent side to the hypotenuse is 4/5.
Thus, we can say that if the length of the adjacent side is 4 units, then the length of the hypotenuse would be 5 units, assuming the units are consistent. This relationship holds true for any right triangle with an angle whose cosine is 4/5.
For example, if we have a right triangle with an adjacent side of 8 units, then the hypotenuse would be 10 units.
Related Questions
It takes an older employee 13 hours to shovel the snow from a sidewalk, but a younger employee can shovel the same sidewalk in 10 hours. how long will it take them to clear the walk if they work together?
Answers
Time taken by both of the older employee and younger employee is 5.6 hrs
What is Componendo-dividendo rule?Componendo-dividendo rule: A theorem based on the topic of proportions permits a faster way to carry out the calculations and cut down the count of expansions required. It is helpful in situations involving equations with fractions or rational functions. The componendo and dividendo rule are used while studying ratios and proportions. If the ratio of any two given numbers is the same as the ratio of the other 2 numbers, then the ratios of the sum total of the numerator and denominator to the difference of the numerator and denominator of the two rational numbers are equal in nature.
Given, older employee needs 13 hours to shovel the snow.
So in 1 hr the older employee will shovel = 1/13
Younger employee needs 10 hours to shovel the snow.
So in 1 hr the younger employee will shovel = 1/10
Now, when they work together
[tex]1/13+1/10 = 1/x \\(10+13)/130 = 1/x \\3/130 = 1/x\\x = 130/23 = 5.6 hrs[/tex]
Hence, the time taken by both of them together is 5.6 hrs
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Final answer:
Two employees working together can clear the sidewalk in approximately 6 hours and 31 minutes. This is determined by finding the individual work rates, combining them, and then taking the reciprocal of the combined rate to find the total time worked together.
Explanation:
To find out how long it will take two employees to shovel snow together, we need to determine their combined work rate. The older employee takes 13 hours, and the younger employee takes 10 hours. First, we calculate each of their work rates per hour by taking the reciprocal of their time.
So, the older employee's work rate is 1/13 sidewalks per hour and the younger employee's 1/10 sidewalks per hour. To find their combined work rate, we add these two rates together:
Combined work rate = (1/13) + (1/10) = (10 + 13) / (13 × 10) = 23/130 sidewalks per hour
Now, to find the total time taken to shovel the sidewalk when working together, we take the reciprocal of the combined work rate:
Time taken working together = 1 / (23/130) = 130/23 hours
To make this more interpretable, we can convert it into a mixed number:
Time taken working together = 5 hours and (130/23 - 5 × 23/23) hours = 5 hours and 35/23 hours
We can convert 35/23 hours into minutes by multiplying by 60:
Additional minutes = (35/23) × 60 minutes = approximately 91 minutes
Therefore, the time taken working together is roughly 5 hours and 91 minutes, which simplifies to 6 hours and 31 minutes.
"It was you who awoke me last summer out of a life-long stupid dream" write the conclusion for this quote
Answers
hope this helps
Which Act protects consumers against inaccurate and unfair practices from credit card companies and lenders? The ______ in Lending Act protects consumers against inaccurate and unfair practices from credit card companies and lenders.
Answers
Hope this helped!
Answer:
Truth
Step-by-step explanation:
The graph shows the location of Jacob's, Kent's, and Hakim's houses. Each unit on the graph represents 1 kilometer. A coordinate plane is shown. Hakims house is located at negative 3, 1, Jacobs house is located at 1, 5, and Kents house is located at 1, 1. Line segments connect the points to form a right triangle.
Answers
d^2=(x2-x1)^2+(y2-y1)^2 so in this case we have:
d^2=(5-1)^2+(1-3)^2, d^2=(1-5)^2+(1-1)^2, d^2=(1-3)^2+(1-1)^2
d^2=(16+4), d^2=16, d^2=4
So the total distance or perimeter, p, is:
p=√20+√16+√4
p=√20+4+2
p=6+√20 km (exact)
p≈10.47 km (to nearest hundredth of a kilometer)
Answer:
14 km
Step-by-step explanation:
I did FLVS
3/5x+19−3/20x−7/35x+19−3/20x−7 simplified is
Answers
Final answer:
To simplify the expression, combine like terms and then simplify to get (1/4)x+24.
Explanation:
To simplify the expression, 3/5x+19−3/20x−7/35x+19−3/20x−7, we can combine like terms and then simplify:
Combine 3/5x−3/20x−7/35x to get (3/5−3/20−7/35)x = (12/20−3/20−4/20)x = (5/20)x = (1/4)x.Combine 19+19 to get 38.Combine −7−7 to get −14.Combine the results: (1/4)x+38−14 = (1/4)x+24.So, the simplified expression is (1/4)x+24.
Felicia put $175 into a CD that pays 4% interest, compounded semiannually. According to the rule of 72, approximately how long will it take for her money to double?
Answers
A=p(1+r/100)^n
where;
A=amount
p=principle
r=rate
n=time
therefore the time taken for Felicia's money to double will be:
350=175(1+4/100)^n
350/175=1.04^n
2=1.04^n
therefore introducing natural longs we get:
ln2=nln1.04
n=(ln2)/(ln1.04)
n=17.7 years
The answer is 17.7 years
Answer:
the answer is 18 years
Step-by-step explanation:
i just did this on 12/8/18 good luck to cheaters
In a horse race, how many different finishes among the first 33 places are possible if 20 horses20 horses are running? (exclude ties)
Answers
To solve this problem, let us break this down one by one.
There are 20 possible
horses that could win in first place. Therefore this means that for each of
these possibilities, there are now 19 horses that could come in second. So
meaning there are 20 x 19 possible combinations for the first 2 places.
20 x 19 = 380. And for each of those combinations, there are also
18 possible horses that could come in the third place. So
20 x 19 x 18 = 6,840
There are 6,840 possible horse combinations for the first 3
places in the race.
"if the price of mints was raised from 5 cents each to 15 cents for two, what was the increase in price per mint?"
Answers
7.5 cents is an increase of 2.5 cents from the previous price 5 cents for one mint and it is a 50% increase
Answer:
Increase in price per mint is 2.5 cents .
Step-by-step explanation:
The price of mints is raised from 5 cents each to 15 cents for two.15 cents is the rice in price for two mints .Hence rise in price for each mint is 15÷2=7.2 cents.
Rise in price for each mint = 7.2-5=2.5cents.
Percent increase = [tex]\frac{2.5}{5} (100)=50[/tex]
There is 50% increase in price per mint.
Where are the x-intercepts for f(x) = −4cos(x − pi over 2) from x = 0 to x = 2π? (?
Answers
the x-intercepts of the graph of f, are the zeros of f, that is the solutions of f(x)=0.
so we solve
[tex]-4cos(x- \frac{ \pi }{2})=0[/tex]
[tex]cos(x- \frac{ \pi }{2})=0[/tex]
at this point we ask ourselves, keeping the unit circle in mind, "cosine of what is 0?"
In the unit circle, from 0 to 2π radians,
cos 90° = cos (π/2) rad = 0
and
cos 270° = cos (3π/2) rad = 0
this means that
i)
[tex]x- \frac{ \pi }{2}= \frac{ \pi }{2}[/tex]
[tex]x= \pi [/tex]
and
ii)
[tex]x- \frac{ \pi }{2}= 3\frac{ \pi }{2} [/tex]
[tex]x=3\frac{ \pi }{2} +\frac{ \pi }{2}=2 \pi [/tex]
ii) also, check that [tex]f(0)=-4cos(0- \frac{ \pi }{2})=-4cos(-\frac{ \pi }{2})[/tex] is also 0, because cos (-pi/2)= cos (-90°)=cos 270°=0
Answer:
x=0, x=π, and x=2π
I NEED THIS ANSWER NOWWWW PICTURE ATTACHED
Which system of inequalities is represented by the graph?
y ≤ 3x
y > –2x – 1
y > 3x
y ≤ –2x – 1
y < –3x
y ≥ 2x – 1
y > –3x
y ≤ 2x – 1
Answers
For the purple area, let's choose a point (1,0), which is in the area.
For y = 2x -> 2 >0, so the inequality will be y ≤2x
For y = -2x - 1 -> -3 < 0, so the inequality will be y ≥ -2x - 1
You can use the similar approach to find other area representations
True or False? The distribution whose five-number summary is shown below has at least one outlier. 21.7, 55.3, 73.4, 89.3, 142.2 A. True B. False
Answers
Answer:
True
Step-by-step explanation:
Apex approved
Answer:
this answer is true
Step-by-step explanation:
i say this because 142.2 is an outlier.
What is the factorization of the polynomial below?
x^3-4x^2+45x
Answers
x³-4x²+45x = x(x² - 4x + 45)
If you solve the quadratic equation inside the parenthesis using the quadratic formula, the roots are imaginary. Therefore, the quadratic equation is already a prime polynomial.
The final answer is x(x² - 4x + 45).
Lukas graphed the system of equations shown. 2x + 3y = 2 y = x + 3 What is the solution to the system of equations? (–2, 2) (0, 0.67) (0, 3) (1, 0)
Answers
The solution to the given system of linear equations is (-1.4, 1.6).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given system of equations are 2x+3y=2 -----(i) and y=x+3 -----(ii)
Substitute, equation (ii) in equation (i), we get
2x+3(x+3)=2
2x+3x+9=2
5x=-7
x=-7/5
x=-1.4
Substitute x=-1.4 in equation (ii), we get
2(-1.4)+3y=2
-2.8+3y=2
3y=2+2.8
3y=4.8/3
y=1.6
So, the solution is (-1.4, 1.6)
Therefore, the solution to the given system of linear equations is (-1.4, 1.6).
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[tex]-2y + y - 3 = 6
[/tex]
Answers
The formula for the nth term of an arithmetic sequence can be found using the formula a(n)=a (1)+(n-1)d. Which of the following is equivalent to this equation?
a. n=a(n)
b. n=a(n)+a(1)-d/d
c. n=a(n)-a(1)
d. n=a(n)-a(1)+d/d
Answers
[tex] a_{n} = a_{1}+(n-1)d [/tex] , multiplying out the bracket gives
[tex]a_{n}= a_{1}+nd-d [/tex], rearranging to make [tex]n[/tex] the subject
[tex] a_{n}- a_{1}+d=nd [/tex]
[tex] \frac{ a_{n}- a_{1}+d }{d}=n [/tex]
Hence, the correct answer is option d
Answer:
D.
Step-by-step explanation:
:)
If the problem is 7+(-5) how many spaces do you move to the right or left
Answers
Addition of a negative is the same as subtraction.
A card is drawn from a standard deck of 52 cards. what is the probability that it is a heart? type in your answer to two decimal places!
Answers
1 suit is a heart
so the probablity is 1 out of 4 or 25% or 0.25
the price of a television decreased from 1000.00 to 800.00.what is the percent of decrease.
Answers
So....
100((800 - 1000) / 1000)
= 100(-1/5) = -20%
Considering the question asks what is the percentage 'decrease' and thus has mentioned that the price is decreasing, you should just give the answer as 20%. If it was not mentioned that the value increases or decreases, it would be correct to put it as -20%
Answer:
The decrease is 20%
Step-by-step explanation:
If a weighted score for a project is based on just two criteria, fit with strategy, weighted 70% and roi, weighted 30%, what would be the weighted score for a project with scores of 80 on fit with strategy and 50 on roi?
Answers
Final answer:
To calculate the weighted score for a project, apply the weights to the scores for each criterion and sum the results. The calculated weighted score for a project with scores of 80 on 'fit with strategy' (70% weight) and 50 on 'ROI' (30% weight) is 71.
Explanation:
To calculate the weighted score for a project based on the provided criteria, you need to apply the weights to the scores for each criterion and then sum the results. In this case, the criteria are 'fit with strategy' which has a weight of 70% and 'ROI' which has a weight of 30%.
The weighted score for 'fit with strategy' is calculated as follows:
(Score for 'fit with strategy' × Weight of 'fit with strategy') = (80 × 0.7) = 56.
The weighted score for 'ROI' is calculated as follows:
(Score for 'ROI' × Weight of 'ROI') = (50 × 0.3) = 15.
To find the total weighted score for the project, you add these two results together: 56 (from fit with strategy) + 15 (from ROI) = 71.
Therefore, the total weighted score for the project is 71.
PLEASE HELP NEED ASAP! 10 PTS!
Solve each system by elimination.
1. -9x+2y= -1.
18x-7y=17
2. 4x+18y= -28
2x+9y= -14
3. 20x+y= -11
-10x-3y= -17
4. -3x+y=7
-6x+2y=12
Thank you!
Answers
-9x + 2y = -1 (1)
18x - 7y = 17 (2)
To eliminate x, multiply (1) by 2 to obtain
-18x + 4y = -2
18x - 7y = 17
Add the two equations.
-3y = 15
y = -5
From (2), obtain
18x = 17 + 7y = 17 + 7*(-5) = -18
x = -1
Answer: x= -1, y = -5
Problem 2.
4x + 18y = -28 (1)
2x + 9y = -14 (2)
Divide (1) by 2 to obtain the system of equations
2x + 9y = -14
2x + 9y = -14
These two equations re identical.
Therefore there are an infinite number of solutions.
Answer:
There is no unique set of solutions.
Problem 3.
20x + y = -11 (1)
-10x - 3y = -17 (2)
Multiply (2) by 2 to obtain
20x + y = -11
-20x - 6y = -34
Add the two equations to eliminate x.
-5y = -45
y = 9
From (1), obtain
20x = -11 - y = -11 - 9 = -20
x = -1
Answer: x = -1, y = 9
Problem 4
-3x + y = 7 (1)
-6x + 2y = 12 (2)
Divide (2) to obtain the system of equations
-3x + y = 7
-3x + y = 6
Because 7 ≠ 6, th set of equations is nonsensical (inconsistent).
Answer:
The set of equations is invalid, and it has no solution.
Manuel and rita bought cds at the music store. rita's cds originally cost three times more than manuel's cds, but she received a $9 discount. if rita spent $21 total, which equation can be used to find the amount manuel spent
Answers
3m = 21 + 9
3m = 30
m = 30/3
m = 10 <== ur solution
Answer with Step-by-step explanation:
Let cost of Manuel's cds=m
Rita's cds originally cost three times more than Manuel's cds, but she received a $9 discount.
i.e. Rita's cds cost=3m-9
Rita spent $21 total.
i.e. 3m-9=21
Adding 9 on both sides, we get
3m=30
Dividing both sides by 3, we get
m=10
Hence, equation which can be used to find the amount Manuel spent is:
3m-9=21
a ratio is a rate, sometimes,never, or always?
Answers
Ratio can be rate but rate can never be ratio. In essence, rate is comparison between ratios. While ratio is comparison between two or more numbers. Further, ratio on one hand, involves numbers either in amount, size, measurement, degrees, percentages or fractions with the absence of specific unit of measurement. On the contrary, rate is comparing quantities, amounts or unit of events happened expressed in a specific measurement or expressed under time. Take for instance, an example, Joe eats 2 while John eats 4 meals in a day. The ratio can be Joe: John, 2:4 meals. While the rate, is Joe eats 2 meals/day and John 4 meals/day.
Can some one please help me with this question answer What is 40%of 320
Answers
320 * 0.4 = 128 ← answer
Final answer: 128
Explain 2 other ways other than rotating 180 degrees counterclockwise or clockwise, that would allow the point to find it’s way to the same place from its original position. Hint: You may combine transformations.
Answers
Notice that a 180° rotation clockwise or counterclockwise (around the origin) send any point P(a, b) to a point with coordinates (-a, -b).
this means the number values of the respective x and y coordinates are the same, but the signs are different.
for example rotating point P(-3, 17) 180 degrees results in point (3, -17)
check picture 2.
reflecting point P(a, b) with respect to :
the y-axis results in point (-a, b)
the x-axis results in point (a, -b)
for example , consider point P(-3, 17)
reflecting this point with respect to the y axis, results in (3, 17)
reflecting (3, 17) with respect to the x-axis results in (3, -17)
So the effect of reflecting with respect to the y axis, the x axis (the other way around is the same) results in the same point as rotating 180 degrees.
Answer:
1) reflect with respect to the y-axis, then reflect this last point with respect to the x-axis
2) reflect with respect to the x-axis, then reflect this last point with respect to the y-axis
Identify the standard form of the equation by completing the square
Answers
[tex]4 x^{2} -8x-(9 y^{2} +36y)-68=0[/tex]
[tex](2x)^{2} -2*(2x)*2-((3y)^{2} +2*(3y)*6)-68=0[/tex]
add and subtract 2^ to the x-expression and 6^ to the second expression to complete the square.
[tex][(2x)^{2} -2*(2x)*2+4]-4-((3y)^{2} +2*(3y)*6+36-36)-68=0[/tex]
[tex](2x-2)^{2} -4-((3y+6)^{2} -36)-68=0[/tex]
[tex](2x-2)^{2} -(3y+6)^{2} -4+36-68=0[/tex]
[tex](2x-2)^{2} -(3y+6)^{2} -36=0[/tex]
[tex](2x-2)^{2} -(3y+6)^{2} = 6^{2} [/tex]
divide by 6 squared
[tex]( \frac{2x-2 }{6} )^{2} -( \frac{3y+6}{6} )^{2} =1[/tex]
[tex]( \frac{x-1 }{3} )^{2} -( \frac{y+2}{2} )^{2} =1[/tex]
[tex] \frac{ (x-1)^{2} }{9} - \frac{(y+2)^{2}}{4} =1[/tex]
Answer: A
How to divide fractions with whole numbers
Answers
Hope this helps.
Conjectures and Postulates are accepted as true without formally proving they are true.
True or False
Answers
Answer:
False; only true for postulates!!!
Step-by-step explanation:
On BYU :)
Will give brainliest!
What is the x-coordinate at the point of intersection of y1= 2(5x + 3) and y2= x2 − 15? Consider only the positive value of x, and round the value to nearest hundredth.
Answers
at
2 (5x + 3) = (x2 -15)
solve and advise answer in comments and will assist further
Solution
The equation of two curves are
[tex]y_{1}=y=2 \times (5 x+3)\\\\y_{2}=y=x^2-15[/tex]
Equating the two curves that is y values, to find their point of Intersection
→ 2 × (5 x+3)=x²-15
→10 x +6=x²-15⇒⇒Used distributive property of multiplication with respect to addition
→x² -10 x -15 -6=0
→x² -10 x-21=0
For a Quadratic equation of the type
[tex]\rightarrow ax^2+b x +c=0\\\\x=\frac{-b \pm \sqrt{D}}{2 a}\\\\D=b^2-4ac[/tex]
Using discriminant method to solve the problem
[tex]x=\frac{-(-10)\pm\sqrt{(-10)^2-4 \times 1 \times (-21)}}{2 \times 1}\\\\x=\frac{10 \pm \sqrt{100+84}}{2}\\\\x=\frac{10 \pm \sqrt{184}}{2}\\\\x=5 \pm \sqrt{46}\\\\x_{1}=5+6.78\\\\x_{1}=11.78\\\\x_{2}=5-6.78\\\\x_{2}=-1.78[/tex]
The x coordinate of point of intersection are, 11.78 and -1.78.
A geometric sequence has a common ratio of 2/9 and the first term is 729 what is the 8th term?
Answers
an=ar(n-1)
where;
a=first term
r=common ratio
n=nth term
thus the 8th term will be:
8th=728*(2/9)^(8-1)
=728*(2/9)^7
=128/6561
The graph represents a person's heart rate in beats per minute during 30 minutes of exercise.
Which statement best describes the relationship between heart rate and time doing exercise?
Answers
Looking at the graph closely we can see that the heart rate increases from 0 to 6 min then became steady from 6 to 25 min then finally decreases from 25 to 30 min. Therefore the correct answer is:
“The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes.”
In real life cardiac exercises, we can interpret that the period from 0 to 6 min is the period where the person is still warming up thus leading to an increase in heart rate. At 6 min, the person is fully warmed up hence reaching a stable heart rate. Then at 25 min, the person starts cooling down which means that the exercise is ending soon.