Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.
What is the measured angle C?From the law of cosines;
cosC = ( a² + b² - c² ) / 2ab
Where C is the angle C and a, b, and c are the three sides of the triangle.
Given the data in the question;
Side a = 2Side b = 3Side c = 4Angle C = ?Using law of cosine;
cosC = ( a² + b² - c² ) / 2ab
We substitute the values into the equation.
cosC = ( 2² + 3² - 4² ) / ( 2 × 2 × 3 )
cosC = ( 4 + 9 - 16 ) / ( 12 )
cosC = -3 / 12
cosC = -0.25
We find the inverse of cosine.
C = cos⁻¹( -0.25 )
C = 104.477°
C = 104.5°
Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.
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Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.
A coordinate plane linear graph function shows a line intersecting Y-axis at minus 5 and X-axis at 1.5.
The graph g(x) is the graph of f(x) translated units , and g(x) =
g(x) is a translation of 6 units downwards.
How to identify the translation that generates g(x)?
Here we have the function:
y = f(x) = 3x + 1
Notice that the y-intercept of f(x) is:
f(0) = 3*0 + 1 = 1
The y-intercept of f(x) is y = 1.
Now, we know that the y-intercept of g(x) is -5. then:
g(x) = 3x - 5 = f(x) - 6
Meaning that g(x) is a translation of 6 units downwards.
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Answer:
translated 2
units up
g(x)= f(x-2)
Step-by-step explanation:
just for fun cuz I've heard of different answers.. what's:
6÷2(1+2) = ??
Answer:9
Step-by-step explanation:1+2=3 6/2=3
3x3=9
You can now sell 50 cups of lemonade per week at 39¢ per cup , but demand is dropping at a rate of 5 cups per week each week. Assuming that raising the price does not affect demand , how fast do you have to raise your price if you want to keep your weekly revenue constant.
Answer:
3.9¢ per cup per week
Step-by-step explanation:
Revenue is the product of price and quantity sold. The rate of change in any of these quantities can be found by solving the derivative equation at using the given values.
Relation of rates of changeRevenue (r) is the product of price (p) and quantity sold (q):
r = pq
Differentiating with respect to time, we have ...
r' = p'q +pq'
Given valuesThe values given for the problem are ...
r' = 0p' = rate to be foundp = 39 (cents per cup)q' = -5 (cups per week)q = 50Using the above derivative relation, we have ...
0 = p'(50) +39(-5) . . . . . . fill in given values
Solutionp' = 195/50 = 3.9 . . . . . . add 195, divide by 50
The price must be raised at the rate of 3.9 cents per week to maintain unchanging revenue.
Composition of two functions:Basic
The functions, q(x) and r(x) are defined as 2•x + 1, and -5•x - 3, respectively, therefore;
[tex] \: (q \: \circ \: r) (1)= - 15[/tex]
[tex] \: (r \: \circ \: q) (1)= -18[/tex]
Which method can be used to evaluate the given composite functions?The given functions are;
q(x) = 2•x + 1
r(x) = -5•x - 3
The evaluation of the composite functions can be presented as follows;
[tex](q \: \circ \: r) (x)= q(r(x))[/tex]
Therefore;
[tex](q \: \circ \: r) (1)= q(r(1))[/tex]
r(1) = -5×1 - 3 = -8Which gives;
[tex](q \: \circ \: r) (1)= q( - 8)[/tex]
q(-8) = 2×(-8) + 1 = -15
Therefore;
[tex](q \: \circ \: r) (1)= - 15[/tex]
Similarly, we have;
[tex](r \: \circ \: q) (1)= r(q(1))[/tex]
q(1) = 2×1 + 1 = 3
r(3) = -5×3 - 3 = -18
Which gives;
[tex](r \: \circ \: q) (1)= -18[/tex]
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Any helppppppp??????
First find volume of both the cylinders:
Cylinder Volume Formula: πr²h
(r => radius, h => height)
*Container A:
r = 8
h = 15
πr²h = π(8)²(15) = 960π³
*Container B:
r = 11
h = 13
πr²h = π(11)²(13) = 1573π³
What % of container B is empty after the pumping is complete?
The water pumped from A to B, and we want to know remaining that is empty: A < B: 1573π³- 960π³ = 613π³. Now to find %:
[tex]\frac{613\pi^{3} }{1573\pi ^{3}} * 100 = 0.39 * 100 =[/tex] 39% or 40% (Nearest Tenth)
Hope it helps!
Factorise: a8 - b8
please solve this
Answer:
(a - b)(a + b)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )
Step-by-step explanation:
by repeated use of the difference of squares factorising method, that is
a² - b² = (a - b)(a + b)
given
[tex]a^{8}[/tex] - [tex]b^{8}[/tex]
= ([tex]a^{4}[/tex] )² - ([tex]b^{4}[/tex] )²
= ([tex]a^{4}[/tex] - [tex]b^{4}[/tex] )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis using difference of squares
= ( a² - b²)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis by difference of squares
= (a - b)(a + b)(a² + b² )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )
X
Erica works 30 hours/week for
$10/hour, but she must pay $30 in
taxes. What is her take-home income?
Answer:
$270
Step-by-step explanation:
Find her gross income....then subtract taxes:
30 hr/week * $10/hr - $ 30 = $270
Heyy I just need some help with question 13,17,19 if anyone could help me and show the work that would be amazing thank you!!
Answer:
13. Answer: 0
17. Answer: 3
19. Answer: 2
Step-by-step explanation:
13. f(g(3))
First find g(3) on the right graph.
We see that at x = 3, g(x) = 4
So g(3) = 4
Next find f(g(3)). Since g(3) = 4, that means we have to find f(4) and the from the left graph we see that f(4) = 0 answer
17.f(f(5))
f(5) = 1
f(f(5)) = f(1) = 3 answer
19. g(g(2))
g(2) = 0
g(g(2)) = g(0) = 2 answer
Find the area of circle Y. The image is represented by circle Y with a sector XYZ that has an area of 85.5 square meters. That sector has an arc that measures 117 degrees. The radius of the circle is unknown.
Answer:
263.08 m²
Step-by-step explanation:
The fraction of circle area that a sector represents is proportional to the central angle.
Proportioncircle area/circle angle = sector area/sector angle
circle area / 360° = 85.5 m² / 117°
Multiplying by 360°, we have ...
circle area = (360/117)(85.5 m²) = 263.08 m²
The area of the circle is about 263.08 m².
For the function f(x)=3x²-7, find the value of f(x) when x=3.
Answer:
Step-by-step explanation:
Simply plug in a 3 where you see an x in the function:
[tex]f(3)=3(3)^2-7[/tex] so
f(3) = 3(9) - 7 and
f(3) = 27 - 7 so
f(3) = 20
on a recent trip, the smiths drove at an average speed of 55 miles per hour. if the trip took 5 1/2 hours, how many miles did they drive?
Answer:
302.5
Step-by-step explanation:
5 1/2 = 5.5
55 miles per hour * 5.5 hours
55*5.5
302.5
what is the midpoint of a segment with endpoints (-3, 2) and (7, -5)?
Answer:
[tex](2,-1.5)[/tex]
Step-by-step explanation:
The midpoint formula goes as follows:
[tex](x,y)=(\frac{x1+x2}{2} , \frac{y1+y2}{2})[/tex]
Lets plug in our values, let x1 be -3, x2 be 7, y1 be 2, y2 be -5.
[tex](\frac{-3+7}{2} , \frac{2+-5}{2})[/tex]
Solve numerators
[tex](\frac{4}{2} , \frac{-3}{2})[/tex]
Solve
[tex](2 , -1.5)[/tex]
Therefore the midpoint must be at [tex](2,-1.5)[/tex]
Find the mean and standard deviation for the set of data. {25,16,28,6,30,7,26,20,22}
Answer: 8.7 the mean is 20
Step-by-step explanation:
At Roxas Middle School, every student studies Spanish, Chinese, or both Spanish and Chinese. There are $374$ students enrolled at the school, and $100$ of these students study both Spanish and Chinese. Also, the number of students studying Spanish is twice the number studying Chinese. How many students at Roxas Middle School study Spanish?
Based on the number of students at Roxas Middle School and the number of students studying Chinese and Spanish, the number of students who study Spanish is 182 students.
What number of students study Spanish?The first thing to do is to find out the number of students who are studying either Spanish or Chinese:
= Total number of students - Students studying both Spanish and Chinese
= 374 - 100
= 274 students
Then, assuming the number of students studying Chinese alone is x, the expression to find them would be:
274 = 2x + x
Solving gives:
2x + x = 274
3x = 274
x = 274 / 3
x = 91 students
The number studying Spanish is twice this number so will be:
= 91 x 2
= 182 students
In conclusion, there are 182 student studying Spanish.
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Let f(r) = 6,
find f-¹(r)
There is no answer because there cannot be one to one function inverse.
PLEASE HELP, TIMED
University students in an Iowa town have a mean hourly wage of $11.75, with a standard deviation of $1.25. The distribution of hourly wages is not assumed to be symmetric.
Between what two-hourly wages does Chebyshev's Theorem guarantee that we will find at least 75% of the people?
Round your answers to the nearest hundredth.
The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages between $9.25 and $14.25.
What does Chebyshev’s Theorem state?When the distribution is not normal, Chebyshev's Theorem is used. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.At least 89% of the measures are within 3 standard deviations of the mean.An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].The Chebyshev Theorem guarantees that we will find at least 75% of the people with wages within 2 standard deviations of the mean, hence the bounds are:
11.75 - 2 x 1.25 = $9.25.11.75 + 2 x 1.25 = $14.25.More can be learned about the Chebyshev Theorem at https://brainly.com/question/25303620
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What is the following quotient?
√120 divided by √30
02
4
O 2√10
O 3√10
Step-by-step explanation:
sqrt(120) / sqrt(30) = sqrt(120/30) = sqrt(4) = 2
The quotient of √120 divided by √30 is 2.
What is Square Root?Square root of a number is the value such that the value when multiplied to itself two times gives the original number.
It is denoted by the symbol √.
For example, square root of 16 is 4 since 4 × 4 = 16
The given numbers are √120 and √30.
We have to find the quotient when √120 is divided by √30.
Try to write each of the number as a product of perfect squares if possible.
√120 = √(4 × 30)
We know that √(ab) = √a √b
So, √120 = √4 × √30 = 2√30 (∵√4 =2)
√120 /√30 = 2√30 / √30 = 2
Hence the required quotient is 2.
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I need help ASAP PLS HELP MEE I'll mark brainlist if correct and ill add 50 points I NeED The answer 5 mins AFTER PLS DO IT BEFORE 5 MIn (with explanation)
On which number line do the points represent negative seven and one over two and +1?
Answer list (below)
Answer:
Second number line
Step-by-step explanation:
This second line is the only line on which
[tex]-7\frac{1}{2} \text{ appears to the left of } 0 \text{ on the line (Point R)}\\+1 \text{ appears to the right of } 0 \text{ on this number line (Point T) }\\[/tex]
Answer:
○B (second option)
Step-by-step explanation:
In the second option, we can see that the point T is at +1. The point R is between -7 and -8, therefore we understand that it is at a value of [tex]\bf -7\frac{1}{2}[/tex].
All the other options have the points R and T at values not asked for in the question.
The intersection point of an angle bisectors of a triangle
Answer: The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter . The incircle touches each side of the triangle
832 x156 show your work
Answer:
129792
Step-by-step explanation:
156
× 832
----------
312
468
+ 1248
---------------
129792
Determine a solution to system of linear inequalities graphed and justify your answer.
Michael Wittry has been investing in his Roth IRA retirement account for 20 years. Two years ago, his account was worth $215,658. After losing of its original value, it then gained of its new value back. What is the current value of his Roth IRA?
The current value of his Roth IRA is $215,658.00
What is Roth IRA retirement account?
Roth IRA retirement account is a retirement account where the contributions to the account are invested after taxes after have been deducted.
In other words, when the individual make contributions, taxes are first of all, deducted so as to invest the after-tax contribution into the Roth IRA account
The account lost 1/3 of its original value of $215,658
balance after the loss=$215,658-(1/3*$215,658)
balance after the loss=$ 143,772.00
Now the account regained 1/2 of its new balance of $ 143,772.00
balance now=$143,772.00+(1/2*$143,772.00)
balance now=$215,658.00
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Complete with the missing fractions:
michael wittry has been investing in his roth IRA retirement account for 20 years. Two years ago his account was worth $215,658. after losing 1/3 of its origiInal value, it then gained 1/2 of its new value back, what is the current value of his roth IRA?
Devon is young and has just graduated college with her associate’s degree. She plans to start saving money for retirement as soon as she starts her new job. By taking 10% of her monthly gross income, Devon is able
to contribute (a) $__________ each month to a retirement plan. The account is expected to earn interest with an APR of 5.25% compounded monthly. Round answers to two decimal places.
a. How much money will be in Devon’s retirement account if she continues to make the same monthly
.
investment for 40 years?
b. Overall, Devon contributed how much of her own money into the retirement account?
c. What percent of the final balance in Devon’s retirement account was interest?
You may not ask for help from others or give help to others on specific project questions.
Part 1: Continued
2. Later in life, Devon convinces her friend Taylor to start saving for retirement as well. Even though Taylor is the same age as Devon, she hasn’t started saving for retirement yet. With only 20 years left until they both plan to retire, Taylor decides she needs to invest at least twice as much as Devon each month to try to catch up to Devon’s retirement plan. Taylor opens a similar retirement account to Devon’s that also has an APR
5.25% compounded monthly. She will invest (b) $__________ per month. Round answers to two decimal places.
a. How much money will be in Taylor’s retirement account if she continues to make the same monthly
investment for 20 years?
b. By the time she retires, Taylor will have contributed how much of her own money overall?
c. What percent of the final balance in Taylor’s retirement account will be interest?
3. Write complete sentences that identify which person had the higher amount and by how much. Round answers to two decimal places.
a. Who had more money in their retirement account when they planned to retire? How much more?
b. Who contributed more to their retirement account? How much more?
Part 1: Devon is able to contribute (a) $450 each month to a retirement plan.
a. The amount in Devon's retirement account if she makes the same monthly investment for 40 years is $733,253.26.
b. Overall, Devon's total contribution of her own money into the retirement account is $216,000.
c. The percent of the final balance in Devon's retirement account that was interest was 70.5%.
Part 2: Taylor will invest (b) $1,733.00 per month.
a. The amount that will be in Taylor's retirement account if she makes the same monthly investment for 20 years is $733,253.26.
b. By the time that Taylor retires, she will have contributed $415,920 of her own money into the account.
c. The percent of the final balance in Taylor's retirement account that will be interest is 43.3%.
3. Both Devon and Taylor had the same amount, $733,253.26, in their retirement accounts when they planned to retire.
a. None had more money at their retirement.
b. Taylor contributed more to her retirement account by $199,920 ($414,920 - $216,000).
Data and Calculations:Devon's Investments:Gross monthly income = $4,500
APR = 5.25% compounded monthly
N (# of periods) = 480 months (12 x 40 years)
I/Y (Interest per year) = 5.25%
PV (Present Value) = $0
PMT (Periodic Payment) = $450 ($4,500 x 10%)
Results:
FV = $733,253.26 ($517,253.26 + $216,000)
Sum of all periodic payments = $216,000 ($450 x 480)
Total Interest = $517,253.26
Percentage of interest out of the FV = 70.5% ($517,253.26/$733,253.26 x 100)
Taylor's Investment:N (# of periods) = 240 months (12 x 20 years)
I/Y (Interest per year) = 5.25%
PV (Present Value) = $0
FV (Future Value) = $733,253.26
Results:
PMT = $1,733.00
Sum of all periodic payments = $415,920 ($1,733 x 240
Total Interest = $317,333.26
Percentage of interest out of the FV = 43.3% ($317,333.26/$733,253.26 x 100)
Thus, based on the time value of money of investments, it is more profitable to start investing early.
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How many numbers are in the list 433, 429, 425, ... -103, -107?
Answer:
135
Step-by-step explanation:
The number is in descending order by 4.Then add the first and last number i.e.
433+107===> 540
divide 540 by 4
540/4
= 135
Answer:
134
Step-by-step explanation:
-107/4 = -26.75
429/4 = 107.25
107.25 - (-26.75)
107.25 + 26.75 = 134
1. You have learned several techniques for solving quadratic equations. Create an equation that would be best for each technique listed below. Then explain why that technique would be best for each equation that you created.
2.What is the discriminant and what happens if you are solving and the discriminant turns out to be negative?
The techniques that can be used to best explain for each equation that I have created are:
What are the techniques?A) For graphing - This is often used in checking if your answer is correct, if the math is known to be a little tedious, graphing is recommended
(b) For factoring: x^2 -3x +4 '
Where: (x-4)(x+1)=0
Then x=-1, 4
(c) For square root method: x^2 = 64
Therefore x = + or - [tex]-\sqrt{64}[/tex] = + or - 8
(d) For completing the square: x^2 + 4x = 11 and x^2 +4x + 4
Note that: x^2 +4x + 4
= x^2 + 4x = -4
= x^2 +4x + 4 = -4 + 4
= (x+2)^2 = 0
So, x = -2
(e) For quadratic formula: 6x² + 7x -19 =0
x= [-b + or - sqr(b² - 4ac)]/2a
Note that b=7
a=6
c=-19
Therefore
x= [-7+ or - sqr(49+4(6)(9)]/2
2. if the discriminant is said to be negative, then the equation is one that is made up of two imaginary or complex solutions.
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See full question below
You have learned several techniques for solving quadratic equations. Create an equation that would be best for each technique listed below. Then explain why that technique would be best for each equation that you created.
a. graphing
b. factoring
c. square root method
d. completing the square
e. quadratic formula
2. What is the discriminant and what happens if you are solving and the discriminant turns out to be negative?
Find one possible missing coordinate so that the point becomes a solution to the given inequality. (x, 8) is a solution to 3x - 4 < y. X =
Answer:
x = 0
Step-by-step explanation:
Substituting the given "point" into the equation gives the possibilities for x.
SubstitutionUsing (x, y) = (x, 8), the inequality becomes ...
3x -4 < 8
Solving for x gives ...
3x < 12 . . . . . . . add 4
x < 4 . . . . . . . divide by 3
Any value of x less than 4 will make (x, 8) a solution to the inequality. For example, ...
x = 0 . . . . . . (0, 8) is a solution to the inequality
Explain why organization was important in your thought process and calculation for an accurate solution. You should also reflect on how correct organization of a problem can help you in everyday life. Include real-world examples to support your response.
It should be noted that organization was important in the thought process and calculation for an accurate solution.
What is problem solving?It should be noted that problem-solving enables us to identify and exploit opportunities in the environment and exert control over the future.
In this case, problem solving skills and the problem-solving process are a critical part of daily life both as individuals and organizations
Also, good problem solving activities provide an entry point that allows all students to be working on the same problem.
In this case, the open-ended nature of problem solving allows high achieving students to extend the ideas involved to challenge their greater knowledge and understanding and problem solving develops mathematical power.
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In a certain school 70% of the students in first-year chemistry have had algebra. If there are 290 students in first-year chemistry, how many of them have had algebra?
The number of the students in the school that have had algebra is 203
How to determine the number of students?The given parameters in the question are
Proportion of students taking algebra, p = 70%Number of students in the school, n = 290The number of students that had algebra in the school is calculated as:
Algebra = Proportion of students taking algebra * Number of students in the school
The above equation can be represented as:
Algebra = np
Substitute values for n and p in the above equation
So, we have
Algebra = 290 * 70%
Express 70% as decimal i.e. 0.70
So, we have
Algebra = 290 * 0.70
Evaluate the product i.e. multiply 290 and 0.70
So, we have
Algebra = 203
Hence, the number of the students in the school that have had algebra is 203
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Question 3 of 10
If a circle has a diameter of 24 inches, which expression gives its area in
square inches?
OA. 12. T
OB. 242. T
O C. 122. T
OD. 24. T
SUBMIT
Answer:
OB:.242.T gives it's area in square inches
i need help with these 2
Answer:
Step-by-step explanation: Hey for the second one I got y = -3/4x -0.5 I'm not sure if its correct though sorry if not
ill try my best to explain my solution though
1. From the parallel equation (3x + 4y = 12) all we need to do is find the slope
So the easiest way to do so is to put the said equation in y-intercept form
y=mx +b
m= slope
b= y intercept
so 1. 3x + 4y = 12
=
4y = 12-3x
divide that by 4 to get only y
y=3-3/4x
-3/4 is our slope
y=-3/4x+b
than we have a point -2, -2
if we put -2 for y
-2=-3/4x+b
and then we put our -2 for x
-2 = -3/4 * -2 + b
=
-2 = -1.5 +b
b=-0.5
Answer : y=-3/4x-0.5