Two angles are supplementary if their sum is 180. The larger angle measures three degrees more than twice the measure of a smaller angle. If x represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle.The smaller angle measures what?The larger angle measures what?
Answers
We have two angles, x and y, that are supplementary.
x is the smaller angle and y is the larger angle.
If they are supplementary we can write:
\(x+y=180\)The larger angle mesures 3 degrees more than twice the measure of the smaller angle.
Twice the smaller angle is 2x, so we can write:
\(y=2x+3\)We can use the first equation to express y as a function of x and replace it in the second equation:
\(x+y=180\Rightarrow y=180-x\)We can replace y and solve for x as:
\(\begin{gathered} y=2x+3 \\ 180-x=2x+3 \\ 180-3=2x+x \\ 177=3x \\ x=\frac{177}{3} \\ x=59\degree \end{gathered}\)We can then calculate y as:
\(y=180-x=180-59=121\degree\)Answer:
Smaller angle: x = 59°
Larger angle: y = 121°
Related Questions
FIRST ONE TO AWNSER CORRECTLY GETS BRAINLEIST-1.8 + (2.1) Show your work
Answers
Answer:
0.3
Step-by-step explanation:
2.1
-1.8
---------
0.3
What is the slope of the line that is paralell to the line y=3/4 x +2
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Answer:
m (parallel) = 3 /4
Step-by-step explanation:
on the graph Y will start on two
2 5 equals what equals what
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Answer:
25 yeahhhhhhhhhhhhhhhhStep-by-step explanation:
mark me brainliest
Using the present value approach, solve the following:
Tom has $100 in a bank account that pays a guaranteed 5% interest rate each year. How much would Tom have at the end of Year 3?
Answers
Answer:
Step-by-step explanation:
$100x0.5x1=$5
6 = 30 divided by blank
Answers
Answer:30 divided by 5 = 6
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
6 = 30/x
multiply both sides by x
6x = 30
divide both sides by 6
x = 30/6 = 5
pls help me solve this
Answers
The results of operations between vectors are, respectively:
Case A: u + w = <- 3, - 1>
Case B: - 6 · v = <6, 6>
Case C: 3 · v - 6 · w = <- 21, - 15>
Case D: 4 · w + 3 · v - 5 · u = <39, 4>
Case E: |w - v| = √(4² + 3²) = 5
How to determine the operations between vectors
In this problem we must determine the operations between vectors, this can be done by following definitions:
Vector addition
v + u = (x, y) + (x', y') = (x + x', y + y')
Scalar multiplication
α · v = α · (x, y) = (α · x, α · y)
Norm of a vector
|u| = √(x² + y²)
Now we proceed to determine the result of each operation:
Case A:
u + w = <- 6, - 3> + <3, 2>
u + w = <- 3, - 1>
Case B:
- 6 · v = - 6 · <- 1, - 1>
- 6 · v = <6, 6>
Case C:
3 · v - 6 · w = 3 · <- 1, - 1> - 6 · <3, 2>
3 · v - 6 · w = <- 3, - 3> + <- 18, - 12>
3 · v - 6 · w = <- 21, - 15>
Case D:
4 · w + 3 · v - 5 · u = 4 · <3, - 2> + 3 · <- 1, - 1> - 5 · <- 6, - 3>
4 · w + 3 · v - 5 · u = <12, - 8> + <- 3, - 3> + <30, 15>
4 · w + 3 · v - 5 · u = <39, 4>
Case E:
|w - v| = |<3, 2> - <- 1, - 1>|
|w - v| = |<4, 3>|
|w - v| = √(4² + 3²) = 5
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help!! Please !! Thank you if you help
Answers
12. The circle graph represents the jobs at a digital
animation company with 1540 employees
How many more story artists are there
than interns?
Answers
Answer:
231
Step-by-step explanation:
From the pie chart we see that the story artists constitute 20% of the total employee strength of 1540 employees and the interns constitute only 5% of that number
In actual values
Number of story artists = 1540 x 20% = 1540 x 20/100 = 308
Number of interns = 1540 x 5% = 1540 x 5/100 = 77
Difference = 308 - 77 = 231
write an equivalent expression
Answers
Answer:
\(3^{-9}\)or \(\frac{1}{3^{9} }\)
Step-by-step explanation:
3^3/3^12 = 3^3 * 3^(-12) = 3 ^(3-12) = 3^(-9) or 1/3^9
y = 5 x + 4
slope=
Its worth it
Answers
Answer:
5
Step-by-step explanation:
Given, y=5x+4
It is in the form, y=mx+c, m is the slope
Slope m = 5
Follow the process of completing the square to solve x = 4x +3.
x -
Which of the following equations is used in this process?
(2x - 42.19
(2x4,2= 12
(2x 42-28
Answers
9514 1404 393
Answer:
the correct choice is marked
Step-by-step explanation:
The process for completing the square would generally put x-terms on one side of the equal sign and the constant term on the other side:
x^2 +4x = 3
Then the square of half the x-coefficient would be added to both sides. Here, that is (4/2)^2 = 4.
x^2 +4x +4 = 7
In order to make this match one of the answer choices, we must multiply both sides by 4.
4x^2 +16x +16 = 28
Now, we can factor the left side to see a match to the last answer choice.
(2x +4)^2 = 28
_____
Additional comment
As you can see, we had to deviate from the "complete the square" process to arrive at an equation that matches an answer choice. It cannot be said that the chosen equation "is used in the process." It might be useful to discuss this question with your teacher.
Which person earns a living wage?
A. Paulo earns $350 per week, and his weekly costs are $400.
B. DeMarcus earns $350 per week, and his weekly costs are
$300.
c. Vivienne earns $250 per week, and her weekly costs are
$400.
D. Claudia earns $250 per week, and her weekly costs are
$300.
Answers
Answer:
B becouse he earns 350 and spends 300 so he is earning 50 extra
Step-by-step explanation:
Answer:
B. DeMarcus earns $350 per week, and his weekly costs are $300.
Step-by-step explanation:
What is a living wage?The minimum income necessary for a worker to meet their cost-of-living expenses and to provide some discretionary income.
Therefore, a person earns a living wage if their earnings are greater than their weekly costs.
The only person who earns more than their weekly costs is DeMarcus.
Since DeMarcus earns $350 per week and his weekly costs are $300, his income is enough to meet his basic needs with $50 left over.
pls help me pls 00000000000000000000
Answers
Answer:
7b - 3 ≤ -22
Step-by-step explanation:
7b - 3 ≤ -22
Hope that helps!
5h-6-8+7h what’s the answer ?
Answers
Calvin estimated he would need 8 hours to
complete his science project. It actually took
him 12 1/2 hours to get everything done. What
was his percent error?
Answers
Answer:45%
Step-by-step explanation:
Hope this helps.
I’m not really good at percentages but I’m sorry I couldn’t give you the full answer. You got this though! <3
Domain answers:
-The set of all real numbers from 0-60
-The set of all real numbers from 500-2000
-The set of all real numbers from 25-500
-{0,1,2,3...,500}
-{25,50,75,100,...}
-{60,61,62,63,...,2000}
Range answers:
The set of all real numbers from 0-60
-The set of all real numbers from 500-2000
-The set of all real numbers from 25-500
-{0,1,2,3...,500}
-{25,50,75,100,...}
-{60,61,62,63,...,2000}
Answers
Domain= "number of minutes water has been added" and the set of all real numbers would be from 0-60
Range= "amount of water in the pond(in liters) and the set of all real numbers from 500-2000
I hope this helps
I'm terribly sorry if this is wrong
there was 506 tickets sold for the school play they were either student tickets or adult tickets there was 56 more student tickets sold than adult tickets sold how many adult tickets were sold
Answers
Answer:
A = 228 tickets
Step-by-step explanation:
We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.
Because the number of adult and student tickets together equals 506, we have A + S = 506.
Because there are 56 more student tickets than adult tickets we have A + 56 = S
And the way the system is already set up allows us to use substitution.
Thus, we have:
\(A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S\)
The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.
Locust Software sells computer training packages to its business customers at a price of $102. The cost of production (in present value terms) is $96. Locust sells its packages on terms of net 30 and estimates that about 5% of all orders will be uncollectible. An order comes in for 20 units. The interest rate is 1.5% per month.
Required:
a-1. Calculate the profit or loss if this is a one-time order and sale will not be made unless credit is extended
a-2. Should the firm extend credit if this is a one-time order?
b. What is the break-even probability of collection?
c-1. Now suppose that if the customer pays this month's bill, they will place an identical order in each month indefinitely and can be safely assumed to pose no risk of default.Calculate the present value of the sale.
c-2. Should credit be extended?
d. What is the break-even probability of collection in the repeat-sales case?
Answers
Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise.
Find the following sums without using a calculator or a formula. Hint: Apply the procedure used by Gauss. (See the Math Matters on page 31.)
+393 +394 + 395
(a) 1+2+3+4+...+392
(b) 1+2+3+4
x
546 + 547 +548 + 549
(c) 2+4+6+8+...+76 + 78 + 80 +82
Answers
(a) The sum of the series 1+2+3+4+...+392 is 77,028.
(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).
(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.
To solve the exercise using Polya's four-step problem-solving strategy, we will apply the procedures presented in the lesson.
(a) For the series 1+2+3+4+...+392:
Using the arithmetic series formula Sn = (n/2)(a + l), where n is the number of terms, a is the first term, and l is the last term, we can substitute the values: Sn = (392/2)(1 + 392) = 196(393) = 77,028.
(b) For the series 1+2+3+4...x:
To find the sum of this series, we need to know the number of terms (n) based on the value of x. Since the series follows a consecutive pattern, the number of terms will be equal to x itself. Thus, the sum of the series would be Sn = (x/2)(1 + x).
(c) For the series 546 + 547 + 548 + 549:
Using the arithmetic series formula Sn = (n/2)(a + l), we can determine the number of terms (n) by subtracting 546 from 549 and then adding 1: n = 549 - 546 + 1 = 4. Substituting the values into the formula: Sn = (4/2)(546 + 549) = 2(1095) = 2,190.
The final answer for each part is:
(a) The sum of the series 1+2+3+4+...+392 is 77,028.
(b) The sum of the series 1+2+3+4...x is (x/2)(1 + x).
(c) The sum of the series 546 + 547 + 548 + 549 is 2,190.
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HELP WILL GIVE BRAINLIEST
The graphs of the functions f(x)-40¹, 6x-4(1-0).
400-4 (1+1)
are shown below.
Answers
If the graph of \(f(x) = 4e^{0.1x}\) is blue, then the graph of \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\) is: C. red.
What is an exponential function?In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:
\(f(x) = a(b)^x\)
Where:
a represents the initial value or y-intercept.x represents x-variable.b represents the rate of change, common ratio, decay rate, or growth rate.For the rate of change of the blue exponential function \(f(x) = 4e^{0.1x}\), we have the following:
b = \(e^{0.1}\)
b = 1.11
For the rate of change of this exponential function \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\), we have the following:
b = 1 + 0.1/0.5
b = 1.2
Therefore, this exponential function \(f(x) = 4(1+\frac{0.1}{0.5} )^{0.5x}\) is represented by the red line on the graph.
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Help me please!!!!!!!
Answers
Answer:
Yes, one gallon is enough
Step-by-step explanation:
16ft x 12ft = 192ft
If one gallon covers 250 square feet then she will have enough for another 58ft remaining
Help me by tonight please ! Thank you
Answers
B
B
A
C
I think it’s this
0.86÷2 y. 0.91÷7
ayudaaaaaaaaaaa(lo escriben en español no hablo ingles)
Answers
Answer:
yes get that one 0.78.10
Step-by-step explanation:
A seat in Section A of the stadium is chosen at random. The fan sitting in that seat receives two free tickets to next week's game. Find the probability that a person in each color seat would receive the free tickets. 1. P(yellow) = 2. P(red) = 3. P(blue) = 4. P(blue or yellow) = 5. P(red or blue) = Red Blue Blue Blue Seats in Section A Red Red Blue Blue Red Red Blue Blue Red Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Answers
The probabilities are:
1. P(yellow) = 2/5
2. P(red) = 3/10
3. P(blue) = 3/10
4. P(blue or yellow) = 7/10
5. P(red or blue) = 3/5
To find the probability that a person in each color seat would receive the free tickets, we need to calculate the probabilities of each event.
1. P(yellow): There are 8 yellow seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a yellow seat at random is P(yellow) = 8/20 = 2/5.
2. P(red): There are 6 red seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a red seat at random is P(red) = 6/20 = 3/10.
3. P(blue): There are 6 blue seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a blue seat at random is P(blue) = 6/20 = 3/10.
4. P(blue or yellow): To calculate the probability of selecting a blue or yellow seat, we add the individual probabilities of selecting a blue seat and a yellow seat: P(blue or yellow) = P(blue) + P(yellow) = 3/10 + 2/5 = 7/10.
5. P(red or blue): To calculate the probability of selecting a red or blue seat, we add the individual probabilities of selecting a red seat and a blue seat: P(red or blue) = P(red) + P(blue) = 3/10 + 3/10 = 6/10 = 3/5.
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Which of the following proves ABC DEF?
A.
SAS
B.
SSS
C.
SSA
D.
ASA
Answers
Answer:
SAS
Step-by-step explanation:
SAS
two side 1 angle
if not that try SSA
Answer:
SAS
Step-by-step explanation:
We have two sides are equal and the angle between the two sides are equal so we can use the side angle side
change 6 1/3 to a percent
Answers
hope this helps!
Help would be appreciated
Answers
EASY POINTS!
Winter has just begun. After one week, the temperature decreased by 46.8° with a
percent change of 72%. What was the temperature at the beginning of the week and
what is the temperature now?
Answers
Answer:Can somebody also help me with this. i'm confused please hurry!
Step-by-step explanation:
-2x (-3x²y)(2y) = _______.
Answers
Answer:
12x³y²
Step-by-step explanation:
You want the product -2x (-3x²y)(2y).
ExponentAn exponent is a means of telling the number of times the base is a factor in a product. For example, the exponent 2 means the base is a factor twice in the product:
x² = x·x
ApplicationWhen the same factor appears a number of times in a product, an exponent can be used to represent that number.
(-2x)(-3x²y)(2y) = (-2)(-3)(2)(x·x²)(y·y)
The factor x appears 3 times in the product, and the factor y appears twice. The numerical product can be simplified, so the result is ...
12x³y²
Makayla wants to make 200 mL of a 18% saline solution but only has access to 8% and 24% saline mixtures.
Which of the following system of equations correctly describes this situation if x represents the amount of the 8% solution used, and y represents the amount of the 24% solution used?
Answers
Answer:
x + y = 200
0.08x + 0.24y = 0.18(200)
Step-by-step explanation:
x + y = 200
0.08x + 0.24y = 0.18(200)
The equations which describes the amount of 8% solution used and the amount of 24% solution used are: x+ y=200 and x+3y=450.
What is equation?An equation is a relationship between two or more variables. They are mostly present in equal to form and are equated to find the value of variables present in them.
How to form equation?let the amount of 8% solution used be x and the amount of 24% solution used be y.
According to question the amount of total solution will be 200ml, So, the equation will be:
x +y=200
Now we have been said that the solution will be 18% saline and 8% saline mixture and 24% saline mixtures are used, So the next equation will be:
0.08x+ 0.24y=0.18*200
8x/100+24/100=18/100*200
8x+24y=3600
8(x+3y)=3600
x+3y=450
Hence the equations which shows the amount of solutions will be x+y=200 and x+3y=450.
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