Answers
The best option regarding the solutions of the trigonometric equation 2sin(θ) + 1 = 0 in this problem is given as follows:
d. θ = 330º + 360ºn, θ = 210 + 360ºn.
How to solve the trigonometric equation?The trigonometric equation for this problem is defined as follows:
2sin(θ) + 1 = 0
Then, isolating the sine, we have that:
2sin(θ) = -1
sin(θ) = -1/2.
The values of theta for which the sine is of negative 1/2 are given as follows:
θ = 210º, θ = 330º.
(as the sine is negative for the third and fourth quadrant, hence we have to find the equivalent angle to 30º in each of these quadrants).
One entire lap over the unit circle is equivalent to 360º, hence adding 360º n times to any of these solutions is also a solution to the trigonometric equation, meaning that option d is correct.
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Related Questions
Perform the calculation then round to the appropriate number of significant digits
Answers
Answer:
315
Step-by-step explanation:
88.2 × 3.5742 = 315.24444
Answer: 315
The histogram shows the ages of passengers riding in a tour van. How many passengers are under 45 years of age? Enter your answer as a number, like this: 42
Answers
Answer:
12
Step-by-step explanation:
3 + 4 + 5 = 12
Explain the concept of extraneous solutions. Give examples with the different types of functions explored.
Answers
Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.
What is a function ?
Function can be defined as a relation , which relates an input to output is called as function.
In Mathematics, an extraneous solution (or spurious solution) is an solution, consisting of that to an equation, that emerges from the procedure of solving the hassle but isn't always a legitimate strategy to the problem.[1] A missing solution is an answer that is a valid strategy to the hassle,
however disappeared all through the process of solving the problem. each are frequently the consequence of acting operations that are not invertible for a few or all values of the variables, which prevents the chain of logical implications inside the proof from being bidirectional.
Hence , The Extraneous solution, that emerges from the method of solving the hassle but isn't always a valid strategy to the trouble.
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Which linear equation shows a proportional relationship?
y equals two thirds times x
y equals negative 3 times x minus one seventh
y equals three fourths times x minus 5
y equals 3 times x plus 7
Answers
The linear equation that shows a proportional relationship is y equals two thirds times x.
A proportional relationship is a relationship between two variables in which one variable is a constant multiple of the other. In other words, if y is directly proportional to x, then y = kx for some constant k. This can also be written as y/x = k, where k is the constant of proportionality.
The linear equation that shows a proportional relationship is y = 2/3x.
It shows a direct relationship because the coefficient of x (2/3) is constant, and there is no constant term (y-intercept) which breaks the proportionality.
The other equations do not show a proportional relationship because they have a coefficient that varies with x or a constant term.
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Felix's dinner costs $16.49. Felix pays a $20 bill. About how much change did he receive? Show your work.
Answers
Answer: He received $3.51 in change.
Step-by-step explanation:
To get the answer we can subtract the amount Felix paid ($20) by the cost of the dinner ($16.49).
It will look like this:
$20.00 - $16.49 = $3.51
Answer:3 dollars and 51 cents
Step-by-step explanation:
A) y = -0.25x+ 98.75
B) y = -0.25x + 96.25
C) y = -0.75x + 96.25
D) y = -0.75x + 98.75
Answers
Answer:
i think its b
Step-by-step explanation:
In a particular country, the average adult is spending even more time on a mobile device than watching television. From 2014 to 2021, the function y=-9.11x+280x can be used to estimate the average number of minutes per day that an adult spends watching television, and the function y=12.34x + 169.9 can be used to estimate the average number of minutes per day that an adult spends on a mobile device. For both functions, x is the number of years after 2014. a. Based on this information, determine the year in which the time spent watching television is the same as the time spent on a mobile device. b. Use these functions to predict how much time the average adult spends per day watching television and on a mobile device for the year 2021..
Answers
After 0.6412 years the average for mobile device and television usage will coincide.
What are functions?
Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here the equations as y=-9.11x+280x and y=12.34x + 169.9 the period for which the averages are equal will be given by
9.11x+280x=12.34x + 169.9
x = 0.6412 years
Again, after 7 years in 2021 the respective averages will be 9.11 ×7+280×7 = 2023.77 and similarly for mobile device the time spent would be 256.28 minutes
Hence, the answers are After 0.6412 years the average for mobile device and television usage will coincide.
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Mr. Klimek made his wife a rectangular vegetable garden. The width is 5 3/4 ft, and the length is 9 4/5 ft. Mr. Klimek calculated his garden to be 15 11/20 square feet. Is Mr. Klimek correct with his calculations? If he is, what did he do to find his answer. If he is incorrect, what did he specifically do wrong, what is the correct answer? Show and Explain.
Answers
Answer:
He is wrong. The right answer is 56.35. Or 56 7/20
Step-by-step explanation:
So lets go over what we know.
The width is 5 3/4ft.
The length is 9 4/5 ft.
The square feet is l*w, otherwise known as area.
So in this, we multiply 5 3/4 by 9 4/5.
Before we multiply however, lets put this into decimal form. Its easier to think of it this way.
3/4, or 3 divided by 4, is 0.75 So 5 3/4 is actually 5.75
4/5, or 4 divided by 5, is 0.80. So 9 4/5 is actually 9.8
Now lets multiply:
5.75*9.8
This might seem a bit confusing, but here is a step by step way of how I multiplied:
5*9 is 45. 5 times 8 is 40. Move the decimal since we used 8 instead of .8 its now:
45 and 4.0
Which is 49.
Now lets multiply 9.8 by the 0.75
3/4ths of 9 is 6.75. 3/4 of 8 is 6. Again, move over the decimal since we used 8 instead of .8 its now:
6.75 and .6
This is 7.35
Add that to 49:
56.35
So this is your answer.
Now, this is not what Mr.Klimek got.
So he is wrong.
The real answer is 56.35
To find the fractional form of this, we can take the decimal 35 and put it over 100:
35/100
Then simplfy. In this case 5 goes into both numbers. So:
7/20
So we have 56 7/20.
Now, the final question, what did Mr.Klimek do wrong?
Well, he added his length and width, instead of multiplying.
We already know what our two numbers equal: 9.8 and 5.75.
Lets add these:
9 plus 5 is 14. 0.8+0.75 is 1.55.
14+1.55=15.55
Using the method of transfering fractions I spoke of above:
55/100
5 goes into both numbers:
11/20
So adding the lenght and width, we got 15 11/20. This is what Mr.Klimek did.
So to sum up each answer:
The answer is 56.35 or 56 7/20Mr.Klimek is incorrect.Mr.Klimek added the length and Width, instead of multiplying.Hope this helps! :D
Determine if the sequence below is arithmetic or geometric and determine the
common difference / ratio in simplest form.
9, 3, 1, ...
Answers
Answer: This is a geometric sequence and the common ratio is equal to 1/3.
Step-by-step explanation:
The given sequence is a geometric sequence with the common ratio 1/3.
What is Geometric Progression?Geometric progression is a sequence of numbers such that the ratio of two consecutive numbers is the same for whole sequence.
This ratio is common ratio.
The given sequence is 9, 3, 1, .......
Arithmetic sequence is a sequence where the numbers are arranged in an order such that the difference of two consecutive numbers, called common difference, is a constant.
3 - 9 = -6
1 - 3 = -2
Difference is not constant, so not an arithmetic sequence.
3/9 = 1/3
1/3 = 1/3
Ratio is constant.
So the sequence is geometric sequence.
And the common ratio in the simplest form is 1/3.
Hence the sequence is geometric with common ratio 1/3.
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Answer the questions about the following polynomial.
8x³+6x-1
The expression represents a
term is
the leading term is
polynomial with
terms. The constant
, and the leading coefficient is
Answers
The expression represents a polynomial with three terms.
What is polynomial?A polynomial is an expression consisting of variables (often denoted by x, y, z, etc.) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. Polynomials can be used to express a wide range of algebraic equations, from simple linear equations to more complex equations. Polynomials can also be used to construct functions with properties that are useful for solving real-world problems.
The expression represents a polynomial with three terms.
The constant term is -1, and the leading coefficient is 8. The leading term is 8x³.
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The sun produces 3.9 ⋅ 1033 ergs of radiant energy per second. How many ergs of radiant energy does the sun produce in 1.55 ⋅ 107 seconds?
Answers
Answer:
the answer to this problem is 165.85.
Step-by-step explanation:
Freddy is helping buy ingredients for salads for the school spaghetti dinner he bought 10 pounds of onions at $0.69 per pound 100 pounds of tomatoes at $0.99 pound 1,000 pounds of break cumbs at $0.09 per pound and 100 pounds of lettuce at $0.69 per pound which of the items he bought cost the most?
Answers
Answer:
Answer: Tomatoes If you multiply 10 x 0.69 (for onions) it would be 6.9If you multiply 100 x 0.99 (for tomatoes) it would be 99Lastly, if you multiply 100 x 0.69 (for lettuce) if would be 69Which are the most? Tomatoes.~ Hope this helps
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a map drawn move to the scale 2 cm : 100 mi. on the map b is 3.5 centimeters from town a and town c is 2 centimeters past town b how many miles apart town a and town b
Answers
The distance between town a and b is 175 mi.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.
Given that, a map drawn move to the scale 2 cm : 100 mi. on the map town b is 3.5 centimeters from town a and town c is 2 centimeters past town b
Since, 2 cm = 100 mi
1 cm = 50 mi
Therefore, 3.5 cm = 50×3.5 = 175 mi
Hence, the distance between town a and b is 175 mi.
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The hanger image below represents a balanced equation.
Write an equation to represent the image.
Answers
Each side is equal so just set them equal to one another in an equation
Your friend has read 6 more than twice as many pages as your
sister has read. Let 4
be the number of pages that your sister has
read. Write an expression for the number of pages that your friend
has read
Answers
Answer:
Expression: 2s + 6
# of Pages Friend Read: 14 pages
Step-by-step explanation:
Let's call the number of pages your sister has read, s, and the number of pages your friend has read, f. We will make our equation first. If your friend has read 6 more than twice as many pages as your sister has, your equation would look like this:
f = 2s + 6
That is your equation for how many pages your friend read, your expression would be just 2s + 6. Now, we will substitute in 4 for s, and we get:
f = 2 * 4 + 6
Multiplying gives:
f = 8 + 6 = 14
So your friend has read 14 pages.
Hope this helped!
According to the 2000 U.S. Census, 7 out of every 25 homes are heated by electricity. At this rate, predict how many homes in a community of 12,000 would be heated by electricity.a.6,725 homesb.3,100 homesc.3,360 homesd.4,020 homes
Answers
In 7/25 households, electricity is used for heating. By multiplying by 20,000. You'll receive 3,360. In light of this, the 2000 census indicates that 3,360 out of 12,000 houses use electricity for heating.
How many homes use electricity for heating in U.S. Census?Because we've already done it 7 out of every 25 residences are heated by electricity, according to the 2000 U.S. census.At this rate, we must determine how many residences in a 12000-person neighbourhood would be heated by electricity.Let x be the number of homes in a neighbourhood that would be heated by electricity.There being a direct variation
The result is that , A neighbourhood of 12000 people with 3360 dwellings that use electricity for heating. In 7/25 households, electricity is used for heating. By multiplying by 20,000. You'll receive 3,360. According to the 2000 Census, 3,360 dwellings out of 12,000 are heated by electricity.
[tex]$\frac{7}{25}=\frac{x}{12000}$[/tex]
[tex]$x={7 \times 12000}/{25}$$x=3360$[/tex]
As a result, 3360 households out of the 12000 in the community use electricity for heating.
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A plane intersects a sphere with a volume of about 44.6 cubic meters through the center of the sphere. What is the area of the cross section to the
nearest tenth?
Answers
Solve for x, it’s confusing me because of how it’s split
Answers
Answer:
x=30m
Step-by-step explanation:
Smaller triangle of sizes 26m and 10m...
using Pythagoras rule...let the middle line that so the triangle be y...
26² = 10²+y²
26²-10²=y²
y²=676-100
y²=576
y=√576
y=24m
the middle line is now 24m
now the larger triangle of sizes 18m, 24m and x...
using Pythagoras rule...
x²=24²+18²
x²=576+324
x²=900
x=√900
x=30m
Given that startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half, complete the statements to show that △abc ~ △def by the sas similarity theorem. horizontal and vertical lines are . so, angles are right angles by definition of perpendicular lines. all right angles are . therefore, △abc ~ △def by the sas similarity theorem.
Answers
Lines running horizontally and vertically are parallel. So, angles A, B, and C are right angles by definition of perpendicular lines. All right angles are equal. Therefore, △ABC ~ △DEF by the SAS similarity theorem.
Given that startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half
Step 1: Multiply both sides of the equation by de:
a/b * de = bc/ef * de
Step 2: Simplify the left side of the equation:
ade = bcde
Step 3: Divide both sides of the equation by ad:
a/d = b/e
Step 4: Multiply both sides of the equation by be:
ab/d = be/e
Step 5: Simplify the left side of the equation:
ab = be
Step 6: Divide both sides of the equation by be:
a/b = 1/e
Step 7: Multiply both sides of the equation by ef:
a/b * ef = 1/e * ef
Step 8: Simplify the left side of the equation:
aef = ef
Step 9: Divide both sides of the equation by ef:
a/b = 1/e
Conclusion: startfraction a b over d e endfraction = startfraction b c over e f endfraction = one-half
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Answer:
perpendicular
b and e
congruent
What is the perimeter?
Help plz..
And No links!! I repeat No links!!
Answers
Answer:
32
Step-by-step explanation:
I'm good at math hehe ggggggrhdgcdg
Answer:
24 ft
Step-by-step explanation:
10^2 = 100
6^2 = 36
100 - 36 = 64
[tex]\sqrt{64}[/tex] = 8
b = 8 ft
10+6+8 = 24
which of the following is the solution set of the equation below:
Answers
Answer:
D
Step-by-step explanation:
i think you know this already but it's D!
At a coffee shop, the first 100 customers' orders were as follows. Small Medium Large Hot 5 48 22 Cold 8 12 5 If we choose a customer at random, what is the probability that his or her drink will be a medium?
Answers
Answer:
60%
Step-by-step explanation:
48 + 12 = 60
There is a 60% chance you randomly choose a medium out of 100 customers.
Explanation:
Each of the students in class writes a different 2 digit number on the whiteboard. The teacher claims that no matter what the students write there will be at least three numbers on the white board whose digits have the same sum what is the smallest number of students in the calls for the teacher to be correct?
Answers
Answer: The teacher's claim is that there will be at least three numbers on the whiteboard whose digits have the same sum, no matter what the students write. To see if this claim is true, we can consider different cases for the number of students in the class.
If there are only two students in the class, the teacher's claim is not true. The two students can write any two different two-digit numbers, and it's not guaranteed that the digits in those numbers will have the same sum.
If there are three students in the class, the teacher's claim is true. The three students can write any three different two-digit numbers, and at least one of those numbers is guaranteed to have digits that have the same sum as one of the other numbers.
If there are more than three students in the class, the teacher's claim is true. No matter what numbers the students write, there will always be at least three numbers whose digits have the same sum.
Therefore, the smallest number of students for the teacher's claim to be true is three students.
It's worth mentioning that the teacher's claim is not necessarily true for all cases, it's only true that any three numbers picked out of the two-digit numbers set, will have digits with the same sum.
Step-by-step explanation:
How can you tell if a linear system has infinitely many solutions?
Answers
A linear system has infinite solutions if it consists of exactly the same equations.
The 3 possible solutions of a linear system are:
- Unique or one solution
- Infinite solutions
- No solution
- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.
Example:
3x + 2y = -4 ..... (equation 1)
6x = -4y - 8 ..... (equation 2)
Add 4y to both sides of equation 2:
6x + 4y = -8
Divide both sides by 3:
3x + 2y = -4
Hence, equation 2 is exactly the same as equation 1. If we plot their graphs, they will share the same graph. Any solution of equation 1 is also solution of equation 2. Therefore, this linear system has infinite solutions.
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using multiple properties of exponents simplify the expression
2a^3b^-4/3a^5b^-2
Answers
2a³b⁻⁴/3a⁵b⁻² = 2/3(ab)²
What are exponents?The exponent of a number shows how many times the number is multiplied by itself.
Example: 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power."
In general, xⁿ means that x is multiplied by itself for n times.
Properties of exponents:
Law of Product: a ^m × a ^n = a ^(m + n)
Law of Quotient: a ^m/a ^n = a ^(m - n)
Law of Negative Exponent: a^-m = 1/a ^m
Law of Power of a Product: (ab)^m = a ^m . b ^m
Law of Power of a Quotient: (a/b) ^m = a ^m/b ^m
Given expression
2a³b⁻⁴/3a⁵b⁻²
= 2/3 . a³/a⁵ . b⁻⁴/b⁻²
Law of Negative Exponent: [tex]a^{-m} = 1/a^{m}[/tex]
= 2/3 . a³/a⁵ . b²/b⁴
Law of Quotient: [tex]a^{m} /a^{n} = a^{m-n}[/tex]
= 2/3 . a³⁻⁵ . b²⁻⁴
= 2/3 . a⁻² .b⁻²
Law of Power of a Product: [tex]a^{m} .b^{m}= (ab)^{m}[/tex]
= 2/3 . (ab)⁻²
Law of Negative Exponent: [tex]a^{-m} = 1/a^{m}[/tex]
= 2/3 . 1/(ab)²
= 2/3(ab)²
Hence the simplified expression of 2a³b⁻⁴/3a⁵b⁻² is 2/3(ab)².
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The radius $r$ of a circle inscribed within three mutually externally tangent circles of radii $a$, $b$ and $c$ is given by \[\frac{1}{r}
Answers
The formula yields the radius $r$ of a circle that is inscribed within three circles with radii $a$, $b$, and $c$ that are mutually external tangents.
[tex][\frac{1}{r} = \frac{1}{a} + \frac{1}{b} + \frac{1}{c}][/tex]
The radius of the inscribed circle is related to the radii of the three mutually externally tangent circles using a method known as the radical centre formula. According to this equation, the reciprocals of the radii of the three externally tangent circles add up to the radius of the circle that is inscribed.
The power of point theorem states that the product of the distance between the point and the three points of tangency is equal to the product of the distance between the point and the centres of the circles. This formula is based on the fact that the circles are mutually externally tangent and their centres are collinear. It is crucial to note that the formula can only be used if the circles are mutually externally tangent; otherwise, it is invalid.
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A survey was conducted to determine whether a group of 11th graders and 12th graders preferred to go to the amusement park or to the zoo for a class
trip. The results are shown in the table.
Amusement Park Zoo
11th Graders
32
18
12th Graders
24
26
Based on the table, what is the probability that a student preferred a class trip to the zoo given they are in 11th grade?
Answers
Answer:
36%
Step-by-step explanation:
18/50 = 0.36 --> 36%
The probability that a student preferred a class trip to the zoo given they are in 11th grade is; 0.36
What is the probability?
Total number of eleventh graders is; 32 + 18 = 50
Number of class trip to the zoo given they are in the 11th grade = 18
Thus, probability that a student preferred a class trip to the zoo given they are in 11th grade is;
P(11th grade trip to zoo) = 18/50
P(11th grade trip to zoo) = 0.36
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Julie needs to buy some new pencils for school. Each pencil cost 0.39. If she has 5.00 dollars now, what is the maximum number of pencils she can purchase. There is no tax in this purchase.
Answers
Answer:
At max, Julie can buy 12 pencils. She will have 32 cents left.
Step-by-step explanation:
I did 0.39x10=3.90. Next, I did 0.30x13=5.07. I went down by one and ended up with 0.39x12=4.68.
I did 0.39 times 12 and my answer was 4.68
27/3 TO A WHOLE
NUMBER
Answers
Answer:
9, after being converted to a mixed number
Step-by-step explanation:
Just divide 27 by 3, it’ll equal 9
yw :)
hope i helped, reach out if it’s wrong (it’s not lol)
Have a great day :3
Answer: 9
Step-by-step explanation:
since fraction means we divide the numerator by denominator, we divide 27 by 3
⇒27/3
⇒27 ÷ 3
⇒9 answer
hope that helps ...
PLEASE HELP QUICK!!!
Answers
Answer:
I believe the answer is C. -10 < x <2
Step-by-step explanation: