Answer:
Suma= 80 + (4 × 40) + (4 × 20) + (4 × 10) + (4 × 5)
Suma= 80 + 160 + 80 + 40 + 20
Suma= 400
Step-by-step explanation:
The sum of the first five terms of the geometric progression is 1705.
To calculate the sum of the first five terms of a geometric progression, we need to determine the first term and the common ratio. Given that the third term is 80 and the ratio is 4, we can find these values.
In a geometric progression, each term is obtained by multiplying the previous term by the common ratio. Let's denote the first term as "a" and the common ratio as "r."
Given that the third term is 80, we can write the equation:
a * r² = 80
We are also given that the ratio is 4, so we have:
r = 4
Substituting this value of r into the equation, we get:
a * (4)² = 80
a * 16 = 80
16a = 80
a = 5
Now that we have determined the first term (a = 5) and the common ratio (r = 4), we can calculate the sum of the first five terms using the formula for the sum of a geometric series:
Sum = a * (1 - rⁿ) / (1 - r)
Plugging in the values, we have:
Sum = 5 * (1 - 4⁵) / (1 - 4)
Simplifying the calculation:
Sum = 5 * (-1023) / (-3)
Sum = 1705
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An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. The accompanying table shows the number of students who obtained the indicated points for X (rows) and Y (column). The class is composed of 100 students. Y 10 15 6 2 10 15 20 10 10 1 15 14 1 Compute the correlation between the scores of students from the two parts of the quiz.
E(max(X, Y )) = PxPy max(x, y)p(x, y)
= max(0, 0)p(0, 0)+max(0, 5)p(0, 5)+· · ·+max(10, 10)p(10, 10)+max(10, 15)p(10, 15)
= 0 ∗ 0.02 + 5 ∗ 0.06 + · · · + 10 ∗ 0.14 + 15 ∗ 0.01 = 9.6.
fX(x) = R 10(2x + y − 2xy)dy = x +12, 0 ≤ x ≤ 1.
fY (y) = R 10
(2x + y − 2xy)dx = 1, 0 ≤ y ≤ 1.
Since f(x, y) 6= fX(x)fY (y), X and Y are not independent.
Column=A column is a recurring piece or article in a newspaper, magazine or other publication, where a writer expresses their own opinion in few columns allotted to them by the newspaper organisation. Columns are written by columnists.
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c. in cell d63, use the count function in the in-cell dropdown to calculate the number of members using the values in the animal field.
the number of members using the values in the animal field. then the value is 63
1. Application layer: this is the interface that connects a user to a network, the files or data are generated and seek from this layer. Protocols in this layer are FTP, TFTP, DNS, SMTP, SNMP etc.
2. Presentation layer: it is the sixth layer in the OSI model. It is used to present data in a well organized syntax and format to and application and also for document format encryption. Protocols in this layer are XDR, TLS, SSL and MIME.
3. Session layer: this layer is used to create and terminate sessions between the destination and source node, in a network. Protocols in this layer are PPTP, SAP, L2TP and NETBIOS.
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Question 27 of 40
The vertex of the parabola below is at the point (1,-5). Which of the following
could be this parabola's equation?
-10
-20-
20
(1.-5)
10
A. y= (x + 1)² +5
B. y= 2x² +5
O
OC. y=x5
OD. y=(x-1)2-5
The possible equation of the parabola is f(x) = (x - 1)² - 5
How to determine the possible equation of the parabolaFrom the question, we have the following parameters that can be used in our computation:
Vertex = (1, -5)
Rewrite the vertex as follows
So, we have the following representation
(h, k) = (1, -5)
A quadratic function can be represented as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
Substitute the known values in the above equation, so, we have the following representation
f(x) = a(x - 1)² - 5
Set a = 1
f(x) = (x - 1)² - 5
Hence, the function is (d) f(x) = (x - 1)² - 5
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592 × 43 in standard algorithm answer needs to be showed
Answer:
25456
Step-by-step explanation:
MODELING REAL LIFE There are a total of 64 students in a filmmaking club and a yearbook club. The filmmaking club has 14 more students than the yearbook club.
a. Write a system of linear equations that represents this situation. Let x represent the number of students in the filmmaking club and y represent the number of students in the yearbook club.
System of equations: x=?
?x+?y=64
b. How many students are in the filmmaking club? the yearbook club?
There are . students in the filmmaking club and students in the yearbook club.
(a) The System of equations that representing this situation is
x= y+14; x+y = 64
(b) There are 39 students in the film-making club and 25 students in the yearbook club.
In the given question, there are a total of 64 students in a film-making club and a yearbook club.
The film-making club has 14 more students than the yearbook club.
a. We have to write a system of linear equations that represents this situation.
Let x represent the number of students in the film-making club
Let y represent the number of students in the yearbook club.
As given that the film-making club has 14 more students than the yearbook club.
So x = y+14
Total students are 64.
So x+y = 64
System of equations:
x= y+14
x+y = 64
b. Now we have to find how many students are in the film-making club and the yearbook club.
The system of equations are;
x= y+14...................(1)
x+y = 64...................(2)
Now putting the value of x in equation 2.
y+14+y = 64
2y+14 = 64
Subtract 14 on both side, we get;
2y = 50
Divide by 2 on both side, we get;
y = 25
Now putting the value of y in equation 1.
x = 25+14
x = 39
There are 39 students in the film-making club and 25 students in the yearbook club.
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A line passes through the point (9, 1) and has a slope of -4/3
Write an equation in slope-intercept form for this line.
Answer:
Step-by-step explanation:
the answer is y= -4x/3 + 13
A tank is full of water. The tank is a right circular cylinder lying on its side (length is parallel to horizon), with radius 2 m, and length 5 m. Find the work required to pump the water out of a spout that rises 2 m above the tank. Set up the integral, but do NOT evaluate. The base of a solid is a circular disk with radius
W =∫ lower power (-r) to higher power (r + h) (h + r - x) 2pgl [tex]\sqrt{r^2+x^2}[/tex] dx is the integral for the effort needed to pump water out of a spout that is 2 m above the tank.
What is meant by Integral?Integral: In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).
r = 2m
l= 5m
sinθ=x/r
[tex]dv=2l\sqrt{r^2+x^2} dx[/tex]
Let g be the acceleration brought on by gravity, and let p be the density of water.
dm = p dv
dw = dmg (h + r - x)
dw = pg (h + r - x) dx
dw = 2lpg (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
w = ∫dw
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
Therefore, the integral for the work required to pump the water out of a
spout that rises 2 m above the tank is
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^2+x^2}[/tex] dx
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State the domain and range of the following relation: {(2,4), (-1,8), (4,-2), (5,6), (2,-2)}. State whether the relation is a function.
The domain is {2, -1, 4, 5} and the relation is not a function
How to determine the domain?From the question, we have the following parameters that can be used in our computation:
{(2,4), (-1,8), (4,-2), (5,6), (2,-2)}
The domain is the set of the x values
So, we have the following representation
x = {2, -1, 4, 5, 2}
Remove repeated entries
x = {2, -1, 4, 5}
So, the domain is {2, -1, 4, 5}
Also, the relation is not a function
This is because the x value 2 has several y values
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Simplify for all questions
The required simplified solution of the expression is given as,
1. -2√15 2.3c 4. -5
3. √6 5. 2a
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
1.
[tex]=\sqrt{(3 -\sqrt{15} )^2} - \sqrt{(3 +\sqrt{15} )^2} \\=3 -\sqrt{15} - (3 +\sqrt{15})\\=3 -\sqrt{15} -3 -\sqrt{15}\\= -2\sqrt{15}[/tex]
Similarly, the solution of the various expression can be determined.
2.3c
3. √6
4. -5
5. 2a
Thus, the solution of the expression are given above
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figure below to answer the following question.
12.25 cm,
W 48°
T
13.5 cm
13.5 cm
to
55%
U
12.25 cm
The figure is not drawn to scale.
What is the value of x, in degrees?
The value of x, in degrees, is given as follows:
A. 48.
What are similar triangles?Similar triangles are triangles that share these two features given as follows:
Congruent angle measures.Proportional side lengths.The similar triangles in this problem are listed as follows:
WUV and WUT.
In triangle UWV, the length of the side adjacent to the angle of 48º has a length of 13.5 cm.
In triangle WUT, the length of the side adjacent to the angle of x has a length of 13.5 cm.
Reminding the two features of similar triangles, namely congruent angle measures and proportional side lengths, the measure of angle x is given as follows:
x = 48º.
(as the equivalent side length is the same, hence the angle measure is also the same).
This means that option A is correct.
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A figure dilated by a factor of 6. By what factor will the perimeter of the figure change.
A piggy bank contains 350 pennies
and nickels worth $11.90. How many
pennies are in the piggy bank?
Answer:
140 pennies
Step-by-step explanation:
Information:
1 penny (cent) = $0.011 nickel = $0.05Define the variables:
Let x be the number of pennies.Let y be the number of nickels.If the piggy bank contains 350 pennies and nickels:
[tex]\implies x+y=350[/tex]
If the piggy bank contains pennies and nickels worth $11.90:
[tex]\implies 0.01x+0.05y=11.90[/tex]
Rearrange the first equation to make y the subject:
[tex]\implies y=350-x[/tex]
Substitute the expression for y into the second equation and solve for x:
[tex]\implies 0.01x+0.05(350-x)=11.90[/tex]
[tex]\implies 0.01x+17.5-0.05x=11.90[/tex]
[tex]\implies -0.04x=-5.6[/tex]
[tex]\implies x=140[/tex]
Therefore, there are 140 pennies in the piggy bank.
Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.The owner of a football team claims that the average attendance at games is over 523 , and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test to support this claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.
Answer:
The statement that the mean attendance is higher than 523 does not have enough facts to stand up.
What is null hypothesis?
A null hypothesis is an educated guess or a prediction of the expected outcome of a particular experiment. It is a statement that assumes there is no difference between two groups or no association between two variables. The null hypothesis is often the opposite of the alternative hypothesis, which is the prediction that the researcher is hoping to prove.
Example 1: In a study of the effectiveness of a new drug for treating depression, the null hypothesis would be that the drug has no effect on depression levels.
Example 2: In a study of the association between smoking and lung cancer, the null hypothesis would be that there is no association between the two variables.
Example 3: In a study of the effect of a new educational program on student performance, the null hypothesis would be that the program has no effect on student performance.
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In this exercise we want to identify primitive elements (generators) of a multiplicative group since they play a big role in the DHKE and many other public-key schemes based on the DL problem. You are given a prime p = 4969 and the corresponding multiplicative group Z*_969. Determine how many generators exist in Z*_969. What is the probability of a randomly chosen element a Z*_969 being a generator? Determine the smallest generator a Z*_969 with a > 1000. What measures can be taken in order to simplify the search for generators for arbitrary groups Z*_p?
1. Number of generators of Z*4969 = 1584
2. Probability of a randomly chosen element a Z*_969 being a generator = [tex]\frac{1584}{4968}[/tex]
3. 1001 is the smallest generator
4. Number of generators
∅(n) = n [tex](1 - \frac{1}{p_{1} } )(1 - \frac{1}{p_{2} } ).........(1 - \frac{1}{p_{n} } )[/tex]
1. Every relative prime of 4968 offers a generation if a is the generation of Z.
4968 = 4 × 1242
= 4 × 3 × 414
= 4 × 3 × 2 ×207
= 4 × 3 × 2× 3× 69
= 4 × 3 × 2 × 3 × 3 ×23
[tex]= 2^{3} * 3^{3} * 23[/tex]
Number of generators ∅ (4968) = 4968[tex](1 - \frac{1}{2} )(1 - \frac{1}{3} )(1 - \frac{1}{23} )[/tex]
Number of generators of Z*4969 = 1584
2. When a Z*4969 value is set, it becomes a generation and belongs to one of the 1584 elements.
The probability that a element is selected from Z*4968 becomes a generation is
= favorable elememt / total element
= [tex]\frac{1584}{4968}[/tex]
= 0.3188
3. To find the smallest generator a Z*_969 with a > 1000.
a > 1000
Every relative prime of 4968 gives a generation of Z*4969
G C D (1001 4968) = 1
Hence, 1001 is the smallest generator
4. Number of generators
∅(n) = n [tex](1 - \frac{1}{p_{1} } )(1 - \frac{1}{p_{2} } ).........(1 - \frac{1}{p_{n} } )[/tex]
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The heights of two different children were recorded in the chart.
a cart of two children's heights from age 0 months to 60 months
Draw a conclusion based on the data provided.
Answer:
based on the data i can draw a conclusion that child two and child one both grow taller as their time (months) increases. child 2 grows at a faster rate than child 1.
Step-by-step explanation:
Write the equation of each line in slope-intercept form.
Answer:
24. y= -1/3x+1
25. y= -2/-1x+3
James received total scholarships of $30,000 to pursue his accounting degree at State University. He spent $15,000 of the money on tuition, $1,000 on books, and $14,000 on rent for his off-campus apartment. James must include _______ in gross income on his tax return.
14000
James received total scholarships of $30,000 to pursue his accounting degree at State University. He spent $15,000 of the money on tuition, $1,000 on books, and $14,000 on rent for his off-campus apartment. James must include 14000 in gross income on his tax return.
Your wages, dividends, capital gains, business income, and retirement distributions are all included in your gross income. Acclimations to Pay incorporate such things as Instructor costs, Understudy loan revenue, Provision installments or commitments to a retirement account.
Where can I find my tax return's gross revenue?The total amount of your earnings and income for the tax year minus certain income adjustments is your adjusted gross income (AGI). Your AGI is listed on Line 11 of Forms 1040, 1040-SR, and 1040NR for the tax year 2022.
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solving systems using substitution 4y=x ; 3x-y=70
Answer:
x= 56/3
y= 14/3
Step-by-step explanation:
for process look at provided image
What values of u and v make ΔHIJ ≅ ΔCDE?
u= ?
v= ?
Answer:
u = 8 ; v = 7
Step-by-step explanation:
5u = u + 32
5u - u = 32
4u = 32
4/4 u = 32/4
u = 8
v + 7 = 2v
2v - v = 7
v = 7
Which statement is true about the functions f(x)=-15x^2+32 and g(x)=-17x^2+5x+32? a. f(x) and g(x) have the same zeros. b. f(x) has a higher maximum than g(x). c. f(x) and g(x) have the same y intercept. d. f(x) and g(x) are odd functions.
None of the options are valid because the specified functions are both parabolic.
Explain about the Functions?Functions represent the connection between two groups of values. For instance, if y=f(x), each value of x has a corresponding value in the set of y. The dependent variable is Y, and the independent variable is x.
An example of a rule is a function, which produces one output for a single input. Alex Federspiel is the picture's author. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. The fact that x is the input value leads us to say that y is a function of x. In mathematics and the sciences, functions are fundamental for constructing physical relationships.
Given functions in this case are
f(x)=-15x2+32
g(x)=-17x2+5x+32.
The functions' zeros are
x = 1.461, -1.233, and 1.527.
When g(x) has a higher maximum than f(x), f(x)intercept exceeds g. (x).
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Noah went into a movie theater and bought 9 drinks and 4 candies, costing a total of $60. Nachelle went into the same movie theater and bought 10 drinks and 2 candies, costing a total of $57.50. Determine the price of each drink and the price of each candy.
Answer:
Drink: $5
Candy : $3.75
Step-by-step explanation:
Let d = the cost of a drink
Let c = the cost of a candy
9d + 4c = 60
10d + 2c = 57.50 ⇒ Mult. by -2 ⇒ -20d -4c = -115 Add this to the first equation
-20d - 4c = -115
9d + 4c = 60
-11d = -55 Divide both sides by -11
d = 5
A drink costs $5.00.
Plug in 5 for d in either of the two equations to solve for c
9d + 4c = 60
9(5) + 4x = 60
45 + 4c = 60 Subtract 45 from both sides
4c = 15 Divide both sides by 4
x = 3.75
A candy costs $3.75
Cliff (W-2 wages: $16,228) and Deb (W-2 wages: $2,600) send their daughter Julia (born 10-1-2010) to daycare while they both worked. They paid $250 per month for daycare. They are filing MFJ. They can claim the credit for child and dependent care expenses. What is their eligible amount of work-related daycare expenses?
The eligible amount of work-related daycare expenses will be $2600
What is MFJ?Married filing jointly is a filing status for married couples, allowing them to file joint tax returns. When filing taxes under married filing jointly status, a married couple can record their respective incomes, deductions, credits, and exemptions on the same tax return.
Given here wages of the cliff are $16,228 and if the deb is $2,600
now the mfj is 35% hence cliffs credit is 35% × $16,228 = $5679.8
and daycare yearly expenses are = $250×12
= $3000
but deb's income is $2600 and thus credit cannot exceed deb's wages therefore the revised credit would be $2600
Hence, the eligible amount of work-related daycare expenses will be $2600
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A husband and wife plan to save money for their daughter's college education in 5 years. They decide to purchase an annuity with a semiannual payment earning 10.5% compounded semiannually. Find the future value of the annuity in 5years if the semiannual payment is $3150. Round your answer to the nearest cent.
The future value of the annuity is ?
Answer:
$40,601.92
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 1.5/100
r = 0.015 per year,
Then, solve the equation for P
P = I / ((1 + r/n)nt - 1)
P = 3150 / ((1 + 0.015/2)(2)(5) - 1)
P = 3150 / ((1 + 0.0075)(10) - 1)
P = $40,601.92
Summary:
The principal investment required to get a total interest of $3150 from compound interest at a rate of 1.5% per year compounded 2 times per year over 5 years is $40,601.92.
Joan
made 3 quarts of soup. She
ate 1/7 of the soup each day for
a week. How much soup did she
eat each day?
Answer:
21 quarts of soup
Step-by-step explanation: I take . as a mutiply
This is easy you just need to take [tex]3 : \frac{1}{7} = \frac{3}{1} : \frac{1}{7} = \frac{3}{1} . \frac{7}{1} = \frac{3 . 7 }{1 . 1} = \frac{21}{1} = 21[/tex] quarts of soup
when approximating the area below a curve, using midpoint rectangles always produces the best approximation.
The statement given is true. When approximating the area below a curve, using midpoint rectangles always produces the best approximation.
A good way to estimate areas with rectangles is to make each rectangle cross the curve at the midpoint of that rectangle's top side. Midpoints always the best approximate for the area under the curve using a finite number of rectangles.
What to use the midpoint rule?The midpoint rule, also known as the rectangle method or mid-ordinate rule, is used to estimate the area under a simple curve. There are other methods to estimate the area, such as the left rectangle or right rectangle sum, but the midpoint rule gives the better approximate compared to the two methods.
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The fox population in 2001 was measured to be 340. By 2005, the population was measured again to be 285. The population changes linearly. Let the input be years since 2001.
a) Find a formula for the fox population, P. Let the input be years since 2001.
I think it's P=-13.75(x-2001)+340, but I'm not sure.
b) What does your model predict the fox population to be in 2010?
If the above is correct, then it's P=216.25
The model of the function is y = -13.75x + 27853.75 and the estimated population in 2010 is 216.25
Linear FunctionA linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0.
In this problem, we can take the two points to find the slope and y-intercept of the function.
using a linear function model;
y = mx + c
m = slopec = y - interceptslope (m) = y₂ - y₁ / x₂ - x₁
m = 285 - 340 / 2005 - 2001
m = -13.75
Using the slope, we can find the y-intercept
y = mx + c
Taking one point;
285 = -13.75(2005) + c
c = 27853.75
The model of the function is y = -13.75x + 27853.75
b) The population in 2010 will be
y = -13.75(2010) + 27853.75
y = 216.25
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how would you explain finding the slope to classmate
Answer/Step-by-step explanation:
Since the axes are labelled and there are nice points marked on the line, you can practically SEE the slope here without any calculating, just by counting. Start with a point and find the directions to the next point. To get from one point to the next, go UP2 and OVER3.
"UP2 and OVER3" is the slope 2/3. Double check that you get a slope that is positive because the line is going up to the right, it should have positive slope.
If the teacher is insisting that you use the slope formula, then name two of the points, such as (0, 4) and (3, 6). First subtract the y's, 6 - 4 is 2, put that on top of a fraction. Then subtract the x's, 3 - 0 is 3, put that on the bottom of a fraction. You get 2/3 again. Doesn't matter what points you use, since they are all on the same line it will come out the same.
using traditional methods it takes 90 hours to receive an advanced driving license. a new training technique using computer aided instruction (cai) has been proposed. a researcher believes the new technique may lengthen training time and decides to perform a hypothesis test. after performing the test on 190 students, the researcher fails to reject the null hypothesis at a 0.02 level of significance.
The conclusion is that there is no sufficient evidence at the 0.02 level of significance that the new technique lengthens the training time.
Given,
The mean time taken to receive advanced driving license, through traditional methods [tex]\mu = 90[/tex] hours
The researcher believes the new technique may lengthen the training time
Researcher conducts hypothesis test of n = 190 students
The researcher fails to reject the null hypothesis at significance level, [tex]\alpha = 0.02[/tex]
Test hypothesis :-
[tex]H_0[/tex] :The mean time it takes for the new technique to receive an advanced driving license is 90 hours, i.e. [tex]\mu = 90[/tex].
[tex]H_a[/tex]: The mean time it takes for the new technique to receive an advanced driving license is greater than 90 hours, i.e. [tex]\mu > 90[/tex].
Failure to reject the null hypothesis means that our sample did not provide enough evidence to conclude that the effect exists. However, the lack of evidence does not prove that the effect does not exist.
As a result, the average time for the new technique to obtain an advanced driving licence is less than 90 hours.
Thus,, the researcher's belief that the new technique would lengthen training time was incorrect.
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group consisting of anne, bert, carl, and diana is about to select one out of five possible alternatives, a, b, c, d, e. the true utilities of the four individuals for the five alternatives are as follows:
a) U(6) UC) Ud) U(e) Anne 0.9 0.8 0.6 0.5 0.4 Bert 0.6 1.0 0.5 0.3 0.4 Carl 0.4 0.3 0.7 0.9 0.2 Diana 0.7 0.6 0.5 0.2 0.1 Which alternative will be selected if the following decision making methods are used: (i) the decision is based on the traditional voting procedure (each voter gets one vote). (ii) each person is asked for their top two choices, and the alternative that is chosen by the maximum number of people is selected. (iii) the group uses the Borda count with 5 points for the most preferred alternative, and 1 point for the least preferred alternative. (iv) the group follows a dot-voting scheme, where each person gets 10 "dots", and they assign the number of dots to each alternative that are roughly proportional to their Utility. (v) the group uses the "maximin rule" which prescribes that the group should prefer the alternative in which the worse-off person is as well-off as possible.
(vi) the sum of individual utilities is maximized for the group. Discuss the pros and cons of the group decision making methods listed above.
(ii) each person is asked for their top two choices, and the alternative that is chosen by the maximum number of people is selected
the best is always to look for points on the line that are exactly corner points of grid squares.
the true utilities of the four individuals for the five alternatives
(0.3, 0.4) and (0.6, 0.8)
so, the linear equation is
y = ax + b
0.4 = a×0.3 + b
0.8 = a×0.6 + b
let's subtract the second from the first equation :
-0.4 = a×-0.3 + 0
a = -0.4/-0.3 = 0.4/0.3 = 4/3
so, the equation is
y = (4/3)x
learn more about of equation here
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6. If A and B are supplementary angles
and mA = 8m ZB, find m2 A and m2 B.
[A] 78.75, 11.25
[C] 160, 20
[B] 80, 10
(D) 157.5, 22.5
Answer:
C) 160, 20-----------------------
Given:Angles A and B are supplementary,Angle A is 8 times the angle B.Find the angle measures:We know supplementary angles sum to 180 deg:
m∠A + m∠B = 180,And we are given:
m∠A = 8 m∠BSubstitute the second equation into the first one and solve for m∠B:
8m∠B + m∠B = 1809m∠B = 180m∠B = 180/9m∠B = 20Find m∠A:
m∠A = 8*20m∠A = 160Correct choice is C.