Answers
===================================
Work Shown:
Through the inscribed angle theorem, we can say that 2 times the inscribed angle gets us the arc that the inscribed angle cuts off.
2*(inscribed angle) = arc measure
2*(2x+2) = 76
4x+4 = 76
4x+4-4 = 76-4 ... subtract 4 from both sides
4x = 72
4x/4 = 72/4 ... divide both sides by 4
x = 18
Answer:
Step-by-step explanation:
2 × inscribed angle = 76
2 × (2x + 2) = 76
Open bracket
4x + 4 = 76
Collect like terms
4x = 76 - 4
4x = 72
Divide both sides by 4
4x/4 = 72/4
X = 18
Therefore X is Equal to 18.
Related Questions
The local deli charges a fee, f, for delivery. On Monday, they delivered two dozen bagels, b, to an office at a total cost of 58. On Tuesday, three dozen bagels were delivered at a total cost of $11. Which system of equations could be used to find the cost of a dozen bagels?
Answers
Answer:
[tex] 2b+f = 8[/tex] (1)
[tex]3b+f=11[/tex] (2)
[tex] b = 11-8=3[/tex]
[tex]f= 8-2(3) = 8-6 =2[/tex]
Step-by-step explanation:
For this case we can put some notation
Let b= dozen bagels and f= delivery fee
And for this case we know that "On Monday, they delivered two dozen bagels, b, to an office at a total cost of $8", so then the total taling in count the delivery fee we have this:
[tex] 2b+f = 8[/tex]
And for the other part "On Tuesday, three dozen bagels were delivered at a total cost of $11", we can write the expression like this:
[tex]3b+f=11[/tex]
And our system of equations would be:
[tex] 2b+f = 8[/tex] (1)
[tex]3b+f=11[/tex] (2)
If we solve for f from equation (1) we got:
[tex]f= 8-2b[/tex]
And if w replace this into equation (2) we got:
[tex]3b+8-2b=11[/tex]
[tex] b = 11-8=3[/tex]
And solving for f we got:
[tex]f= 8-2(3) = 8-6 =2[/tex]
Ivan bought 35 stamps. Some of these stamps cost $0.15 each, and the rest cost $0.40 each. If the total value of the stamps he bought is $7.25, determine the number of $0.15 stamps that Ivan bought.
Answers
Answer:
27
Step-by-step explanation:
Let x represent the number of $0.15 stamps Ivan bought. Then the value of his stamps is ...
0.15x +0.40(35-x) = 7.25
-0.25x +14.00 = 7.25 . . . . . eliminate parentheses, collect terms
-0.25x = -6.75 . . . . . . . . . . . subtract 14.00
x = 27 . . . . . . . . . . . . . . . . . . divide by -0.25
Ivan bought 27 $0.15 stamps.
find the center and radius of the circle that has the equation ( +7)^2 +(−4)^2 = 49
Answers
Answer:
For the given circle, the center is at (-7,4) and radius is 7
Step-by-step explanation:
Given equation of the circle is [tex](x+7)^2+(y-4)^2=49\hfill (1)[/tex]
To find the center and radius of given circle with the help of its equation:
Equation of the circle is of the form
(x-h)^2+(y-k)^2=r^2\hfill (2)[/tex] with center at (h,k) and radius is r.
Given [tex](x+7)^2+(y-4)^2=49[/tex]
The above equation can be written as,
[tex](x-(-7))^2+(y-4)^2=7^2\hfill (3)[/tex]
Now comparing the equations (2) and (3) we get
h=-7, k=4 and r=7
Therefore center at (h,k) is (-7,4) and radius is 7
For the given circle, the center is at (-7,4) and radius is 7
Twenty types of beef hot dogs were tested for calories and sodium content (mg). the hot dogs average 156.85 calories with a standard deviation of 22.64, and the sodium level average 401.15 mg with a standard deviation of 102.43 mg. the correlation given as r = 0.887. the equation of the lsrl predicting sodium level from number of calories is:________
Answers
The equation of the least squares regression line (LSRL) predicting sodium level from the number of calories in beef hot dogs is Sodium Level (mg) = 37.77 mg + 4.077 mg/calories × Calories.
Explanation:The equation of the least squares regression line (LSRL) predicting sodium level from the number of calories in beef hot dogs can be determined using the given statistics and the formula for the slope (b) of the LSRL:
b = r (sy/sx)
Where r is the correlation coefficient, sy is the standard deviation of the y-values (sodium levels), and sx is the standard deviation of the x-values (calories).
Given that r = 0.887, sy = 102.43 mg, and sx = 22.64 calories, we can calculate the slope (b):
b = 0.887 (102.43 mg / 22.64 calories) = 4.077 mg/calories
Then, we can use the y-intercept (a) in the equation y = a + bx, where a = y-bar - b*x-bar.
Given that the average sodium level y-bar = 401.15 mg and the average number of calories x-bar = 156.85 calories, the y-intercept (a) will be:
a = 401.15 mg - (4.077 mg/calories * 156.85 calories) = 37.77 mg
Therefore, the equation of the LSRL is:
Sodium Level (mg) = 37.77 mg + 4.077 mg/calories × Calories
Can someone please help me with how to do this?? I am lost
The question is, "Find intersections and unions of the following given sets.
Thank you.
Answers
Answer:
The answer to your question is below
Step-by-step explanation:
See the picture below
G ∩ M = { Max, Anael}
G ∪ S = { Max, Acel, Carl, Anael, Acton, Dario, Kai, Barek, Carlin}
When you multiply fractions and the first number is a whole number is you answer a whole or fraction?
Answers
Answer:
whole numbers can be written in fraction form. But fraction can or cannot be whole number.
Answer is fraction.
Step-by-step explanation:
As, the fraction number is in the form of [tex]\frac{p}{q}[/tex] and the first number is whole number [tex](a)[/tex].
when fraction multiply by whole number,
[tex]\frac{p}{q} \times a=\frac{a \times p}{q}[/tex] is fraction.
For example, [tex]p=2,q=3 \ and \ a=4[/tex]
[tex]\frac{p}{q} \times a=\frac{4 \times 2}{3}[/tex]
[tex]\frac{p}{q} \times a=\frac{8}{3} \Rightarrow \ fraction[/tex]
For example, [tex]p=3,q=5 \ and \ a=5[/tex]
[tex]\frac{p}{q} \times a=\frac{5 \times 3}{5}[/tex]
[tex]\frac{p}{q} \times a=\frac{3}{1} \Rightarrow \ whole \ number[/tex]
Fill in the code to complete the following function for computing a Fibonacci number. public static int fib(int index) { if (index == 0 || index == 1) // Base case ________ else // Reduction and recursive calls return fib(index - 1) + fib(index - 2); }
Answers
Final answer:
The student asked for the completion of a Java function to compute the nth Fibonacci number using recursion. The base case for the function is missing, which should return the index when it is either 0 or 1. Two alternatives to improve runtime are memoization and dynamic programming, with an example provided for the latter technique.
Explanation:
The student is asking for the missing code in a recursive Java function to compute the nth Fibonacci number. To complete the base case of the provided function, we should return the index itself because the 0th and 1st Fibonacci numbers are defined as 0 and 1, respectively.
The function should look as follows:
public static int fib(int index) {
if (index == 0) return 0; // Base case for 0
if (index == 1) return 1; // Base case for 1
else // Reduction and recursive calls
return fib(index - 1) + fib(index - 2);
}
Using this recursive algorithm is inefficient due to its exponential time complexity, represented by O(2^n). To illustrate the concept of reducing computation time, two alternative approaches can be used: memoization and dynamic programming. Memoization stores the results of expensive function calls and reuses them when the same inputs occur again, thus avoiding the need to recompute them. Dynamic programming approaches the problem from a bottom-up perspective, computing and storing the result of smaller subproblems first, which then are used to compute larger ones.
An example of a dynamic programming approach is to use a loop to calculate the sequence iteratively:
public static int fib_loop(int index) {
if (index == 0) return 0;
if (index == 1) return 1;
int a = 0, b = 1, sum;
for (int i = 2; i <= index; i++) {
sum = a + b;
a = b;
b = sum;
}
return b;
}
The time complexity for the iterative solution is O(n), which is significantly faster than the recursive approach. Therefore, fib_loop() can compute Fibonacci numbers much quicker than the recursive fib(). For example, calculating fib(40) using the recursive method can take a significant amount of time, while fib_loop(40) will complete in a fraction of the time due to its linear time complexity.
Assuming you start with just one microbe that divides every 30 minutes, how many microbes would you have after 8 hours?
Answers
Answer: 1/16,384 microbes
Step-by-step explanation:
Since the microbes divides every 30minutes, if the microbes divides by half every 30minutes, then after an hour it will divides by another half that is (1/2)of 1/2 to give 1/4.
Subsequently after another hour, the microbes will reduces to 1/4 of its remains (i.e 1/4) to give 1/16.
Since the denominator is increasing geometrically each hour.
Looking at the trend;
After 1hr = 1/4 of the original microbe = 1/4
After 2 hrs = 1/4 of the remaining microbe = 1/4 of 1/4 = 1/16
Generalizing, we will let the number of hours be n
According to the progression, 1, 1/4,1/16,...n
Since its a Geometric Progression, nth term = ar^n-1
Where a is the first term = 1
r is the common ratio = 1/4
n is the number of hours of decay
After 8hours, the microbes will have been divided by
(1)(1/4)^8-1
= (1/4)^7
= 1/16,384 microbes
Answer:
1/2^16 or 0.0000152588 microbes
Step-by-step explanation:
Assuming you start with just one microbe that divides every 30 minutes.
This means that the half life of the microbe is 30 minutes or 0.5hours
The interpretation of this half life is that after every half-life, which in this case is 30 minutes, half of the microbe will be gone, and half will remain.
It follows that after another half hour the amount remaining will be
1/2 of 1/2= 1/4 microbes
Thus after 8 hours, there would have been (8/0.5)=16 half lives.
Therefore the amount of microbes remaining will be 1/2^16 of 1 = 0.0625
Alternatively, we could solve the differential equation
dM/dt=kM, where dM/dt is the rate of decay, and M is the amount at any time t, k is the decay constant
Solution of this first order differential equation by separating the variables and integrating yields {dM/M={kt+c, lnM=kt+c, and ......
M=Moexp(-kt)
The initial value Mo=1, when t=0, and given value M=0.5, t=0.5h yields the value of k as follows
0.5=exp(-k*0.5)
ln(0.5)=-k*0.5
k=1.386
After any time time, thus the given expression holds
M=exp(-1.386t)
Thus after 8 hours, the microbes remaining will be
M=exp(-1.386t)=exp(-1.386*8)=0.000152588 microbes.
A charity organization had a fundraiser where they sold each ticket for a fixed price. After selling 200 tickets, they had a net profit of 12,000. They had to sell a few tickets just to cover necessary production costs of 1,200.
Answers
Answer:
Y = 66x - 1200 will be the equation.
Step-by-step explanation:
This question is incomplete; Here is the complete question.
A charity organization had a fundraiser where they sold each ticket for a fixed price. After selling 200 tickets, they had a net profit of $12,000. They had to sell a few tickets just to cover necessary production costs of $1200.
Let Y represent the net profit (in dollars) when they have sold c tickets. Complete the equation for the relationship between the net profit and the number of tickets sold.
If the selling price of one ticket is $x, then selling price of 200 tickets
= $200x
Since production cost of the tickets = $1200 and profit earned is $12000
Therefore, Profit = Selling price of x tickets - production cost
12000 = 200x - 1200
200x = 13200
x = $66
Now we can rewrite the equation for c tickets sold and profit earned $Y
Y = 66c - 1200
Karl and Pete produce cars and trucks. Karl can produce 10 cars per hour or 5 trucks per hour. Pete can produce 12 cars per hour or 4 trucks per hour.Based on the scenario, Pete’s opportunity cost of one truck is:a. 6 cars.b. 4 cars.
c. 1 1/3 cars.d. 3 cars.e. 3/4 car.
Answers
Answer:
The opportunity cost will be 3 cars
So option (d) will be correct answer
Step-by-step explanation:
The opportunity is cost is best characterized as the following best action done without, it is something we give up to gain another.
For instance the opportunity cost of going to class can be the pleasure from watching movie, or spending time with companions or something different. The opportunity cost can be determined by isolating what you forgone by what you gain.
So opportunity cost [tex]=\frac{12}{4}=3cars[/tex]
So option (d) will be the correct answer
Final answer:
Pete's opportunity cost of producing one truck is 3 cars, which is found by dividing Pete's car production rate by his truck production rate (12 cars per hour / 4 trucks per hour).
Explanation:
Pete's opportunity cost of producing one truck can be determined by looking at the alternative production of cars he could have achieved in the same amount of time. Since Pete can produce 12 cars per hour or 4 trucks per hour, we can set up a ratio of cars to trucks based on his production abilities. To find the opportunity cost of one truck, we divide the number of cars Pete can make by the number of trucks, which is 12/4, giving us 3. Hence, Pete's opportunity cost of one truck is 3 cars. This calculation is similar to how opportunity cost is determined in examples such as the production possibility frontier, where the slope shows the trade-off between two different products.
The members of a singing group agree to buy at least 250 tickets for a concert. The group buys 20 fewer lawn tickets than balcony tickets. What is the least number of balcony tickets bought?
Answers
Answer:
Members of Singing group will buy minimum 135 number of balcony tickets.
Step-by-step explanation:
Given:
Minimum of tickets will be bought =250
Let number of lawn tickets be 'l'.
Also Let number of balcony tickets be 'b'
Now given
The group buys 20 fewer lawn tickets than balcony tickets.
Framing in equation form we get;
[tex]l=b-20[/tex]
Now The Sum of Number of balcony tickets and Number of lawn tickets should be greater than or equal to Minimum of tickets will be bought by the group.
Framing in equation form we get;
[tex]l+b\geq 250[/tex]
Now substituting the value of 'l' in above equation we get;
[tex](b-20)+b\geq 250\\\\b-20+b\geq 250\\\\2b-20\geq 250\\\\2b\geq 250+20\\\\2b\geq 270\\\\b\geq \frac{270}{2}\\\\b\geq 135[/tex]
Now we know the value of b which is 135 we will substitute in equation [tex]l=b-20[/tex] to find the value of l we get;
[tex]l=135-20 = 115[/tex]
Hence Members of singing group will buy minimum 135 number of balcony tickets.
Solve the system of equations. \begin{aligned} &6x-5y = -32 \\\\ &-7x+8y=46 \end{aligned} 6x−5y=−32 −7x+8y=46 x=x=x, equals y=y=y, equals
Answers
Answer:
The solution is x=-2, y=4
Step-by-step explanation:
we have
[tex]6x-5y=-32[/tex] ----> equation A
[tex]-7x+8y=46[/tex] ----> equation B
Solve the system by graphing
Remember that
The solution of the system of equations is the intersection point both graphs
using a graphing tool
The intersection point is (-2,4)
see the attached figure
therefore
The solution is x=-2, y=4
Answer:
The solution is x=-2, y=4
Step-by-step explanation:
A plastic storage box in the shape of a rectangular prism has a length of x+3, a width of x-4 and a height of 5. Represent the surface area of the box as a trinomial in terms of x
Answers
Answer:surface area = 2x^2 + 18x - 34
Step-by-step explanation:
The formula for determining the surface area of a rectangular prism is expressed as
Surface area = 2lh + 2wh + 2wl
Where
l represents the length of the rectangular prism.
h represents the height of the rectangular prism.
w represents the width of the rectangular prism
From the information given,
l = x+3
h = 5
w = x - 4
Surface area = 2 × 5 × (x+3) + 2 × (x - 4) × 5 + 2 × (x - 4) × (x + 3)
= 2(5x + 15) + 10(x - 4) + 2[x^2 + 3x - 4x - 12]
= 10x + 30 + 10x - 40 + 2x^2 - 2x - 24
= 2x^2 + 18x - 34
If a data point has a corresponding z-score of -1.5, then it is one and a half standard deviations above the mean value. 1. True 2. False
Answers
Answer: False.
Step-by-step explanation:
For any random variable x,
Formula to calculate the z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
, where [tex]\mu[/tex] = Mean
[tex]\sigma[/tex] = Standard deviation
Let x be the data point has a corresponding z-score of -1.5.
Then , we have
[tex]-1.5=\dfrac{x-\mu}{\sigma}[/tex]
[tex]-1.5\sigma=x-\mu[/tex]
[tex]\mu-1.5\sigma=x[/tex]
i.e. x is one and a half standard deviations below the mean value.
( one and a half =[tex]1+\dfrac{1}{2}=1.5[/tex] )
Therefore , the given statement is false.
Sophie earns $12.80 per hour babysitting. She has to repay a loan to her parents in the amount of $100. After repaying the loan, she wants to have at least enough money to buy herself a pair of sneakers costing $130.40. Write an inequality modeling the number of hours, x, Sophie needs to work to have enough money to buy the sneaker
Answers
Answer:
She would have to work 11 hours to get enough money to buy the sneakers
But if you want the hours included for the time she needs to work to pay off the loan she would have to work 8 hours, so all together 19 hours.
Answer:
It would be x ≥ 18
Step-by-step explanation:
A metalworker has a metal alloy that is 15% copper and another alloy that is 60% copper. How many kilograms of each alloy should the metalworker combine to create 90 kg of a 51% copper alloy?
Answers
18 kg of 15% copper and 72 kg of 60% copper should be combined by the metalworker to create 90 kg of 51% copper alloy.
Step-by-step explanation:
Let x = kg of 15% copper alloy
Let y = kg of 60% copper alloy
Since we need to create 90 kg of alloy we know:
x + y = 90
51% of 90 kg = 45.9 kg of copper
So we're interested in creating 45.9 kg of copper
We need some amount of 15% copper and some amount of 60% copper to create 45.9 kg of copper:
0.15x + 0.60y = 45.9
but
x + y = 90
x= 90 - y
substituting that value in for x
0.15(90 - y) + 0.60y = 45.9
13.5 - 0.15y + 0.60y = 45.9
0.45y = 32.4
y = 72
Substituting this y value to solve for x gives:
x + y = 90
x= 90-72
x=18
Therefore, in order to create 90kg of 51% alloy, we'd need 18 kg of 15% copper and 72 kg of 60% copper.
The marginal cost of providing 25 neighborhood street lamps is $2000. There are 3 people living in the neighborhood. Person 1 is willing to pay $800 for the 25 lamps and person 2 is willing to pay $300 for the 25 street lamps. Efficiency requires that 25 lamps be provided. What is the minimum amount person 3 is willing to pay for 25 street lamps?
Answers
Answer:
Person 3 needs to pay $900.
Step-by-step explanation:
Consider the provided information.
The marginal cost of providing 25 neighborhood street lamps is $2000.
Person 1 is willing to pay $800 for the 25 lamps.
person 2 is willing to pay $300 for the 25 street lamps.
We need to find the minimum amount person 3 is willing to pay for 25 street lamps?
Let person 3 need to pay x amount.
Therefore, the sum of the amount should be equal to $2000.
$2000=$800+$300+x
$2000=$1100+x
x=$2000-$1100
x=$900
Hence, person 3 needs to pay $900.
Person 3 must be willing to pay at least $900 for 25 street lamps to meet the marginal cost of $2000 for efficient provision, considering person 1 and person 2 are contributing a total of $1100.
To determine the minimum amount person 3 must be willing to pay for the 25 street lamps, we need to consider the total cost of providing the lamps and the amount the other two people are willing to pay. The marginal cost for providing the 25 lamps is $2000. Person 1 is willing to pay $800, and person 2 is willing to pay $300. The sum paid by person 1 and person 2 is $800 + $300 = $1100.
Since the total cost is $2000, for efficiency, the total amount paid by all three people should at least match this cost. Therefore, the minimum amount that person 3 must be willing to pay is the difference between the total cost and the sum paid by the first two persons:
Total cost - Sum paid by person 1 and person 2 = Minimum amount person 3 must pay
$2000 - $1100 = $900
Thus, person 3 must be willing to pay at least $900 for the efficient provision of the 25 street lamps.
Explain how to find n, the number of copies the machine can print in one minute. I need an algebraic expression for the answer.
Once the first part is done, I need help with this question.
Working at the same rate, how long will it take the machine to print 5,200 copies? Explain how you found your answer.
Answers
Answer:
Step-by-step explanation:
From the table, the number of copies can be plotted on the y axis and against the number of minutes on x axis. The slope of the straight line graph that would be formed would represent the become n, the number of copies the machine can print in one minute.
n = (y2-y1)/(x2-x1)
Picking points from the table,
y2 = 650
y1 = 325
x2 = 10
x1 = 5
Slope, n = (650 - 325)/(10 - 5)
n = 325/5 = 65 copies per minute
Working at the same rate, the time that it will take the machine to print 5,200 copies would be
65 copies = 1 minute
5200 copies would take
5200/65 = 80 minutes
A person can pay $7 for a membership to the history museum and then go to the museum for just $1 per visit. What is the maximum number of visits a member of the history museum can make for a total of $45.
Answers
Answer: the maximum number of visits would be 38
Step-by-step explanation:
A person can pay $7 for a membership to the history museum and then go to the museum for just $1 per visit.
Let x represent the number of visits that the person makes to the museum after paying for the membership. This means that if the person makes x visits to the history museum, the total cost would be
7 + x
If a member of the history museum pays a total of $45. It means that the number of visits that he can make to the history museum would be
7 + x = 45
x = 45 - 7 = 38
It is estimated that almost ___% of collisions involving a vehicle and a train were at crossings where warning devices such as lights, gates and bells were in working order.
Answers
Answer: 50%
Step-by-step explanation:
It is estimated that almost 50% of collisions involving a vehicle and a train were at crossings where warning devices such as lights, gates and bells were in working order. This high percentage may be as a result of malfunction of warning devices, because when warning devices malfunction they give wrong signals that could lead to accidents. It could also be as a result of violation or ignorance of traffic rules and warning signals which can also lead to collision.
The question discusses the number of accidents happening at railway crossings despite working warning systems, akin to a problematic intersection at Clay Street and Eagle Avenue that saw many accidents despite traffic rules. While specific statistics aren't given, such cases highlight the importance of adhering to traffic signals and safety measures for both drivers and pedestrians.
Explanation:The question seems to be related to railroad crossing safety, specifically the effectiveness of warning devices like bells, lights, and gates. While the exact percentage is not provided, studies show that a significant proportion of vehicle-train collisions occur at crossings where these warning systems are fully functional. Like the traffic signal installed at the intersection of Clay Street and Eagle Avenue to prevent the high number of accidents, these warning devices aim to control vehicular and pedestrian traffic. Unfortunately, they may not always be heeded, and thus accidents occur.
Similar to the situation in the Clay Street and Eagle Avenue intersection, safety measures only work if they're respected. A traffic signal might reduce accidents, but only if drivers and pedestrians heed it. Unfortunately, despite railroad crossing warnings, accidents still occur, often due to negligence, recklessness, or distraction.
It emphasizes the importance of traffic rules and safety measures in our day to day life. Be it the students crossing the road or vehicles moving in traffic, the role of traffic signals and warning signs is critical. We must remember these are not there to restrict us, but to ensure everyone's safety.
Learn more about road safety here:https://brainly.com/question/33417376
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Find sin(a)&cos(B), tan(a)&cot(B), and sec(a)&csc(B).
Answers
Answer:
Part A) [tex]sin(\alpha)=\frac{4}{7},\ cos(\beta)=\frac{4}{7}[/tex]
Part B) [tex]tan(\alpha)=\frac{4}{\sqrt{33}},\ tan(\beta)=\frac{4}{\sqrt{33}}[/tex]
Part C) [tex]sec(\alpha)=\frac{7}{\sqrt{33}},\ csc(\beta)=\frac{7}{\sqrt{33}}[/tex]
Step-by-step explanation:
Part A) Find [tex]sin(\alpha)\ and\ cos(\beta)[/tex]
we know that
If two angles are complementary, then the value of sine of one angle is equal to the cosine of the other angle
In this problem
[tex]\alpha+\beta=90^o[/tex] ---> by complementary angles
so
[tex]sin(\alpha)=cos(\beta)[/tex]
Find the value of [tex]sin(\alpha)[/tex] in the right triangle of the figure
[tex]sin(\alpha)=\frac{8}{14}[/tex] ---> opposite side divided by the hypotenuse
simplify
[tex]sin(\alpha)=\frac{4}{7}[/tex]
therefore
[tex]sin(\alpha)=\frac{4}{7}[/tex]
[tex]cos(\beta)=\frac{4}{7}[/tex]
Part B) Find [tex]tan(\alpha)\ and\ cot(\beta)[/tex]
we know that
If two angles are complementary, then the value of tangent of one angle is equal to the cotangent of the other angle
In this problem
[tex]\alpha+\beta=90^o[/tex] ---> by complementary angles
so
[tex]tan(\alpha)=cot(\beta)[/tex]
Find the value of the length side adjacent to the angle alpha
Applying the Pythagorean Theorem
Let
x ----> length side adjacent to angle alpha
[tex]14^2=x^2+8^2\\x^2=14^2-8^2\\x^2=132[/tex]
[tex]x=\sqrt{132}\ units[/tex]
simplify
[tex]x=2\sqrt{33}\ units[/tex]
Find the value of [tex]tan(\alpha)[/tex] in the right triangle of the figure
[tex]tan(\alpha)=\frac{8}{2\sqrt{33}}[/tex] ---> opposite side divided by the adjacent side angle alpha
simplify
[tex]tan(\alpha)=\frac{4}{\sqrt{33}}[/tex]
therefore
[tex]tan(\alpha)=\frac{4}{\sqrt{33}}[/tex]
[tex]tan(\beta)=\frac{4}{\sqrt{33}}[/tex]
Part C) Find [tex]sec(\alpha)\ and\ csc(\beta)[/tex]
we know that
If two angles are complementary, then the value of secant of one angle is equal to the cosecant of the other angle
In this problem
[tex]\alpha+\beta=90^o[/tex] ---> by complementary angles
so
[tex]sec(\alpha)=csc(\beta)[/tex]
Find the value of [tex]sec(\alpha)[/tex] in the right triangle of the figure
[tex]sec(\alpha)=\frac{1}{cos(\alpha)}[/tex]
Find the value of [tex]cos(\alpha)[/tex]
[tex]cos(\alpha)=\frac{2\sqrt{33}}{14}[/tex] ---> adjacent side divided by the hypotenuse
simplify
[tex]cos(\alpha)=\frac{\sqrt{33}}{7}[/tex]
therefore
[tex]sec(\alpha)=\frac{7}{\sqrt{33}}[/tex]
[tex]csc(\beta)=\frac{7}{\sqrt{33}}[/tex]
To find the values of sin(a)&cos(B), tan(a)&cot(B), and sec(a)&csc(B), use trigonometric identities and the reciprocal identities of trigonometric functions.
Explanation:The question is asking to find the values of sin(a)&cos(B), tan(a)&cot(B), and sec(a)&csc(B). To solve these trigonometric expressions, you need to recall the definitions and relationships between trigonometric functions. Here are the step-by-step calculations:
sin(a)&cos(B): Use the trigonometric identity sin(A)cos(B) = (1/2)(sin(A+B) + sin(A-B)) to find the value.tan(a)&cot(B): Use the reciprocal identities of tan and cot to find the values.sec(a)&csc(B): Use the reciprocal identities of sec and csc to find the values.what is the measure of this angle ? I think 180 or i’m completely wrong
Answers
Answer:
It is an obtuse angle.
Step-by-step explanation:
It is not a 180° angle. Because 180° angle forms a straight line.
The given angle is an obtuse angle which means it is greater than 90° and less than 180°
Note that 90° angle is perpendicular angle(interior angles of a rectangle)
That angle can be measured using a protractor.
A small island has a roughly rectangular shape. It is 18.2 kilometers wide and 28.5 kilometers long. Rising water levels are reducing the width by 1.2%each year and the length by 0.8% each year.
Answers
Answer:
2% area reduction
Step-by-step explanation:
The original area is 18.2*28.5=518.7 sq km
1.2% reduction of 18.2 km is 17.9816 km (18.2-18.2*1.2/100)
0.8% reduction of 28.5 km is 28.272 km (28.5-28.5*0.8/100)
The new are is 17.9816*28.272=508.3757 sq km (98 % of the original area)
Another way is (100-1.2)*(100-0.8) LW/(100*100)=0.98LW (98 % of the original area)
Answer:
Here's the answer ;)
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Simplify each expression and match it with the equivalent value.
Answers
Answer:
log base 6 of the cube root of 6 matches with 1/3
-3 log 5 of 25 matches with -6
log base 2 of the 4th root of 8 matches with 3/4
log base 3 of 1/81 matches with -4
Answer:
Step-by-step explanation:
Let's simplify all the possible answers:
[tex]log_{6} \sqrt[3]{6}[/tex] = [tex]log_{6} (6\frac{1}{3} ) = \frac{1}{3}[/tex] [tex]log_{3} \frac{1}{81} = log_{3} (3^{-4} )[/tex] = -4 [tex]-3log_{5} 25 \\[/tex] = [tex]-3log_{5} (5^{2} )[/tex] = -3*2 = -6 [tex]log_{2} \sqrt[4]{8}[/tex] = [tex]log_{2} \(2^{\frac{3}{4} }[/tex] = [tex]\frac{3}{4}[/tex]Hope it will find you well.
Julia pays a flat rate of $106 for her cell phone and is charged $0.12 for every text she sends. Julia spends at least $142 on her phone bill each month. Which of the following describes the number of texts she sends?
a. a minimum of 300
b. a maximum of300
c. more than 300
d. fewer than 300
Answers
Answer:
a. A minimum of 300
Step-by-step explanation:
If her bill is $142 then it is a sum of the flat rate plus the money she pays for all the smses she sent. As an equation, it can be expressed this way
106 + 0.12x = 142 where x is the number of smses
0.12x = 36
x = 300 smses
So if we were told that she pays $142 per month, we'd know that she sends 300 smses. But we are told she pays AT LEAST $142 so there is a possibility that she sends even more than 300 smses
Convert y = x^2 + 2x - 5 into the form y-k = a( x- h)^2
Answers
Answer:
[tex]y+6=(x+1)^{2}[/tex]
Step-by-step explanation:
we have
[tex]y=x^{2}+2x-5[/tex]
This is the equation of a vertical parabola open upward (because the leading coefficient is positive)
The vertex is a minimum
The equation of a vertical parabola into vertex form is
[tex]y-k=a(x-h)^2[/tex]
where
(h,k) is the vertex of the parabola
Convert the equation into vertex form
Move the constant term to the left side
[tex]y+5=x^{2}+2x[/tex]
Complete the square
[tex]y+5+1=x^{2}+2x+1[/tex]
[tex]y+6=x^{2}+2x+1[/tex]
Rewrite as perfect squares
[tex]y+6=(x+1)^{2}[/tex]
therefore
[tex]a=1\\h=-1\\k=-6[/tex]
The vertex is the point (-1,-6)
A garage floor measures 150 feet by 120 feet. A scale drawing of the floor on grid paper uses a scale of 1 unit and 15 feet.What are the dimensions of the drawing
Answers
Answer:
The dimensions of the drawing are 10 units by 8 units
Step-by-step explanation:
we know that
The scale drawing is [tex]\frac{1}{15}\ \frac{unit}{feet}[/tex]
That means ---> 1 unit in the drawing represent 15 feet in the actual
To find out the dimensions of the drawing, multiply the actual dimensions by the scale drawing
so
[tex]150\ ft=150(\frac{1}{15})=10\ units[/tex]
[tex]120\ ft=120(\frac{1}{15})=8\ units[/tex]
therefore
The dimensions of the drawing are 10 units by 8 units
You are buying fruit to make fruit baskets apples come in bags of 20. Ornages come in bags of 16. And bananas come in bags of 32. You have one bag of each fruit each fruit basket must be identical. A) what is the greates t number of fruit baskets that you can make using all fruit ?
Answers
Answer:
160 basket of each fruit baskets we can make using all fruit.
Step-by-step explanation:
Given:
Oranges comes in bags = 16
Apples comes in bags = 20
bananas come in bags = 32
We need to find the greatest number of fruit baskets that you can make using all fruit.
Also Given:
You have one bag of each fruit basket must be identical.
So we will first find the least common multiple of all the numbers we get;
20 = 20,40,60,80,100,120,140,160
16 = 16,32,48,64,80,96,112,128,144,160
32 = 32,64,96,128,160
The least common multiple is 160.
Hence we can say that, 160 basket of each fruit baskets we can make using all fruit.
what is the difference of (-3x^3+5x^2+4x-7)-(6x^3-2x+3)
Answers
Good evening ,
Answer:
(-3x^3+5x^2+4x-7)-(6x^3-2x+3) = -9x³+5x²+6x−10
Step-by-step explanation:
(-3x^3+5x^2+4x-7)-(6x^3-2x+3) = -3x³+5x²+4x-7-6x³+2x−3
= -9x³+5x²+6x−10.
:)
Two identical rubber balls are dropped from different heights. Ballroom is dropped from a height of 154 feet, and ball to is dropped from a height of 271 feet. Use the function f(t) = -16t^2 + h to determine the current height, f(t), of a ball dropped from a height h, over the given time t.
Write a function for the height of ball 1.
h_1(t) = _____
Answers
Answer:
[tex]h_1(t)=-16t^2+154[/tex]
Step-by-step explanation:
Put the initial height of ball 1 into the given formula:
[tex]h_1(t)=-16t^2+154[/tex]