Answers
CF= 28.8675…cm
CA^2= 50^2 +70^2
CA= 86.02325…cm
Angle CAF= tan-1(28.8675/86.02325)
= 18.6 (3 s.f.)
Related Questions
Table for a linear equation
Fill in the table using this function rule.
y = -10x + 1
x y
-5
-1
0
1
Answers
Answer:
x: y :
-5 | 51
-1 | 11
0 | 1
1 | 11
Step-by-step explanation:
y = 10x + 1
(Table)
x: y:
-5 |
-1 |
0 |
1 |
Lets begin plugging in our (x) into the function(x = -5)y = -10(-5) + 1
y = 50 + 1 (if you multiply a negative by a negative it will be positive)
y = 51
(x = -1)y = -10(-1) + 1
y = 10 + 1
y = 11
(x = 0)y = -10(0) + 1
y = 0 + 1
y = 1
(x = 1)y = -10(1) + 1
y = 10 + 1
y = 11
Plug into the table
(table)
x: y :
-5 | 51
-1 | 11
0 | 1
1 | 11
If you have any questions feel free to ask:)Later on in this module, you will learn how to model events by writing trigonometric functions. for now, do some research on events that are cyclical or periodic. write a discussion post about one of those events. be sure to describe the event and the period.
Answers
The events that are cyclical are:
The change of seasons each yearEarth Rotation.Moon Phases.Tides.The events that are periodic are:
Pendulum OscillationSimple harmonic motionstuning fork,, etc.What are Cyclical events?Cyclical events are known to be event that occurs in a specific order e.g. Changes in the economy.
The Events that take place only after a regular interval of time are known to be periodic event.
Therefore, the events that are cyclical are:
The change of seasons each yearEarth Rotation.Moon Phases.Tides.The events that are periodic are:
Pendulum OscillationSimple harmonic motionstuning fork,, etc.Learn more about Cyclical events from
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Jamal has run 7 miles from point a to point b of a race. the entire race from point a to point c is 26 miles. how many
more miles will he run to complete the race?
Answers
The number of more miles he needs to run to complete the race is 19 miles.
How to find distance in miles?He has run 7 miles from point a to point b of a race.
The entire race from point a to point c is 26 miles.
Therefore, the number of more miles he needs to run to complete the race is as follows:
let
x = the more miles he needs to run
Hence,
x = 26 - 7
x = 19 miles
Therefore, he needs to run 19 more miles to complete the race.
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which of the following is the equation of a line in sloep intercept form for a line with slope = 1/3 and y intercept at 0,-4
Answers
Answer:
Step-by-step explanation:
y + 4 = 1/3(x - 0)
y + 4 = 1/3x - 0
y = 1/3x - 4
explanation/proof why the lines are parallel and insights
Answers
Answer:
The lines are parallel is the will never touch.
Step-by-step explanation:
Which line is perpendicular to the line: y − 4 = 25(x +1)?
Answers
Find the x-intercept and y-intercept of each linear function
Answers
y-int=-2
2)x-int=2
y-int=4
Keiko surveyed people with cell phones.
Age in years=a
Texts they send per day=t
He drew a best-fit line and determined its equation.
Student
Keiko
Trend Line
t -1.63a + 92.14
Evaluate how many texts a 15 year old would send each day according to Keiko's trend line equation.
Answers
Using the line of best fit, the amount of texts a 15-year old would send in a day is of 67.69.
What does the line of best fit gives?It gives the expected number of texts a person of an age a would send in a day, according to the following function:
t = -1.63a + 92.14.
For a person that is 15 years old, we have that a = 15, hence the expected number is given by:
t = -1.63 x 15 + 92.14 = 67.69 texts.
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what is pi times squared
Answers
Answe
Step-by-step explanation:
cuanto es 3,072 en fraccion ?
Find the volume of the rectangular prism in cubic feet. 3.4 ft 0.8ft 0.6ft "these are not the answers these are the ft of the prism
Answers
Answer:
A
Step-by-step explanation:
becaauss im smart and trust me im smart
Given that p(x) = 2(x - 12)2 + 5, what is the value p(3)
Answers
Answer:
p(3) = 25
Step-by-step explanation:
p(3) = 2(3 - 12)2+5
p(3) = 6 - 24 + 2 + 5
p(3) = 25
Can I get help with this pls
Answers
Answer:
2 [tex]\leq[/tex] x [tex]\leq[/tex] 7
Step-by-step explanation:
See attachment.
Find the volume of the rectangular prism using the formula v = bh.
the area of the base, b, equals
___ cm2.
the volume of the prism is
___cm3.
Answers
Answer:
v=bh cm3 cm2 is not answer is 903cm2 23
#24. you and your friends go to the county fair the cost to get in is $8 and the tickets per game to my cost $0.25 each. Write an equation to create a table of reasonable values and identify the domain and range for the scenario.
Answers
The equation of the scenario is y = 8 + 0.25x and the domain is x ≥ 0 and the range is y ≥ 8
How to determine the equation?The given parameters are:
Entrance fee = $8Rate = $0.25 per personLet the total cost be y, and the number of people be x.
The equation would be:
y = Entrance + Rate * x
This gives
y = 8 + 0.25x
Hence, the equation of the scenario is y = 8 + 0.25x
The table of valuesSet x = 0 to 5, and calculate the function values
y = 8 + 0.25 * 0 = 8
y = 8 + 0.25 * 1 = 8.25
y = 8 + 0.25 * 2 = 8.50
y = 8 + 0.25 * 3 = 8.75
y = 8 + 0.25 * 4 = 9.00
y = 8 + 0.25 * 5 = 9.25
So, the table of values is:
x y
0 8
1 8.25
2 8.50
3 8.75
4 9.00
5 9.25
The domain and the rangeThe domain is the set of people that can get in (i.e. at least 0), while the range is the total amount (i.e. at least the entrance fee)
Hence, the domain is x ≥ 0 and the range is y ≥ 8
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The NUK Energy Company is designing a new logo, as shown in the accompanying
diagram, with mNK-130 and mNK-m.NU.
N
K
What is the measure of ZKNU?
1) 80°
2) 65°
3) 50°
4) 100°
U
Answers
The measure of the angle KNU (∠KNU) of the cyclic quadrilateral is; Option 3: 50°
How to find the angle in a quadrilateral?
From the attached cyclic quadrilateral of NUK Energy Company's new logo, we can say that equal angles intercept equal arcs and as such, the measure of angle KNU will be;
∠KNU 1/2 * 100 = 50°
This is because If two inscribed angles of a circle intercept the same arc or arcs of equal measure, then the inscribed angles have equal measure.
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the picture below illustrates a special type of comic section called a circle. which of the following offers the best description of how a circle is formed?
Answers
From the diagram, a circle is formed because D. The plane passes through only one nappe of a circular one and is parallel to its base.
How does the diagram show the formation of a circle?The plane given only passes through one nappe instead of the two nappes.
The angle that the plane passes the nappe is parallel and not perpendicular to the base of the nappe as shown in the diagram.
The plane does not pass through the vertex which is the point where the planes.
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PLEASE HELP!!! 50 POINTS!!!
Answers
Answer:
Part A:
In order to find a coterminal angle, or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible.
Part B:Simply put, coterminal angles start at 0° and end at the same place, though in different directions and multiple times around (you're probably going to want to make that sound a little more formal). Since each time around is 360°, boom
Part C: 75° is in Quadrant II, right? If I go one more time around, 75 + 360 = 435°. I can also go "backward. Starting at 0 and going clockwise, I'm going 75 fewer degrees than all the way around, so 360-75 = 285° but since I'm going "backward" 75 - 360 = -285°. One more is on you.
Step-by-step explanation:
For some △MNP: P = 38°, N = 90°, and m = 12 cm. Solve the triangle. Hint: Sketch the
triangle and label all unknown parameters.
Answers
Angle M = 52°, n = 15.2cm, p = 9.4cm
What is a triangle?A triangle is a plane shape with three sides and three angles.
To define the triangle completely we have to know the measure of the three angles and three sides.
Analysis:
The triangle is a right-angled triangle
we need to find the remaining angle M and two sides n and p
M + N + P = 180
M + 90 + 38 = 180
M = 180 - 128 = 52°
sin 52 = m/n
m = n sin 52
n = m/sin 52 where m = 12cm
n = 12/0.788 = 15.2cm
sin 38 = p/n
p = n sin 38
p = 15.2 x 0.615 = 9.4cm
In conclusion, solving the triangle means finding M, n and p which are 52°, 15.2cm and 9.4cm respectively.
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plss help, ill give brainiest
Answers
Answer:
A
Step-by-step explanation:
Cylinder volume= V = π r ^2 h
So you times Pie by the radius (diametre divided by two- 3.5) you then square this. After that, times it by the height (10)
So the volume is 384.85.
You then find 30% of this, so times 384.85 by 30%.
You then get an answer of 115.455, and this is equal to A.
I hope this helps, have a lovely day.
Martin wants to use coordinate geometry to prove that the opposite sides of
a rectangle are congruent. He places parallelogram ABCD in the coordinate
plane so that A is (0, 0), B is (a,0), C is (a, b), and D is (0, b).
What formula can he use to determine the distance from point D to point A?
A. 0-0)2+(b-0)² = √√b² = b
B. (a-a)2+(b-0)² = 6²
C. (0-0)² + (b-0)² = 6²
OD. √(-a)2+(b-0)²-√√b² = b
Answers
The correct answer is option A which is the distance between A and D will be AD = [tex]\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b[/tex].
What is coordinate geometry?A coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
The formula utilised to find the distance between two points is;-
X = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
We have the coordinates of the point A = (0, 0) and D is (0, b).By applying the formula to find the distance between A and D.
AD = [tex]\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b[/tex].
Therefore the correct answer is option A which is the distance between A and D will be AD = [tex]\sqrt{(0-0)^2-(b-0)^2}=\sqrt{b^2}=b[/tex].
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Please help!
The price of products may increase due to inflation and decrease due to depreciation. Derek is studying the change in the price of two products, A and B, over time.
The price f(x), in dollars, of product A after x years is represented by the function below:
f(x) = 72(1.25)x
Part A: Is the price of product A increasing or decreasing and by what percentage per year? Justify your answer. (5 points)
Part B: The table below shows the price f(t), in dollars, of product B after t years:
t (number of years)
1 2 3 4
f(t) (price in dollars)
65 84.5 109.85 142.81
Which product recorded a greater percentage change in price over the previous year? Justify your answer. (5 points)
Answers
Answer:
A)25% B)Product B
Step-by-step explanation:
A) To find whether product A price is increasing or decreasing, we will find the difference in price between year 0 and 1 year after.
When x = 0,
f(0) [tex]72(1.25)^{0}\\= 72*1\\= 72[/tex]
when x = 1,
f(1) = [tex]72(1.25)^{1}\\= 72*1.25\\= 90[/tex]
From here we can already see the price is increasing.
% increase = (Difference in price / Original Price) * 100
= [tex]\frac{90-72}{72} *100\\=\frac{18}{72} *100\\=0.25*100\\=25percent[/tex]
Therefore the price is increasing by 25% per year.
B) Same concept as Part A, we will find the price difference between year 1 and 2.
% increase = (Difference in price / Original Price) * 100
[tex]\frac{84.5-65}{65} * 100\\= \frac{19.5}{65} * 100\\= 0.3*100\\= 30 percent[/tex]
Therefore we can see here Product B has a higher increase than Product A.
Step-by-step explanation:
A
f(x) = 72 × 1.25 × x
so, the price is $90 after 1 year (72×1.25×1).
$180 after 2 years (72×1.25×2)
$270 after 3 years (72×1.25×3)
and so on.
or did you mean
f(x) = 72 × (1.25)^x
so, still, the price is $90 after 1 year (72×1.25^1).
$112.50 after 2 years (72×1.25^2).
$140.625 = $140.63 after 3 years (72×1.25^3)
that makes more sense. I will continue with that assumption.
so, the price is increasing, as every factor of the multiplication is positive and larger than 1. therefore, it only goes up.
and due to the formula, the price of every year is the price of the previous year multiplied by 1.25.
a multiplication by 1.25 is an increase of 25% (compared to a constant multiplication by 1).
so, the price increases every year by 25%.
B
year 1
price $65
year 2
price $84.50 difference $19.50
100% = 65
1% = 65/100 = 0.65
19.5/0.65 = 30% difference
year 3
price $109.85 difference $25.35
100% = 84.5
1% = 84.5/100 = 0.845
25.35/0.845 = 30% difference
year 4
price $142.81 difference $32.96
100% = 109.85
1% = 109.85/100 = 1.0985
32.96/1.0985 = 30% difference
so, product B has the greater percentage increase in the price (30% vs. 25%).
A biologist hypothesizes that the mean life expectancy of a mosquito is 14 days. Researchers believe the true mean is less than 14 days and they plan a hypothesis test at the 5% significance level on a random sample of 60 of these mosquitos. If the alternative hypothesis is correct, for which of the following values of μ is the power of the test greatest?
μ = 9
μ = 7
μ = 10
μ = 14
μ = 18
Answers
Based on the alternative hypothesis, the value of μ that will have the greatest test power is μ = 7.
Which value of μ will have the greatest power of test?The alternative hypothesis is that Hₐ : μ < 14.
For the alternative hypothesis to be right, μ will have to be less than 1.4.
μ will also give a greater test power the lower it is below 14. From the options therefore, μ with the greatest test power would be 7.
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Answer:
μ = 7
Step-by-step explanation:
Got this right on the segment exam. Good luck, my FLVS fellows!
Julia surveyed twenty households on her street to determine the average number of children living in each household. the tables below represent the collected data and a randomly selected sample from the population. compare the mean of the population with the mean of the sample. population data 0 3 3 1 3 2 2 2 5 4 3 3 3 0 1 2 0 2 3 3 sample data 5 3 0 2 4 what is the difference between the mean of the sample and the mean of the population? 0.55 1.25 2.25 2.80
Answers
The difference between the mean of the sample and the mean of the population is A. 0.55
Calculations and Parameters:Given the population data is:
0 3 3 1 3 2 2 2 5 4 3 3 3 0 1 2 0 2 3 3
The sample data is:
5 3 0 2 4
The mean of the population data is:
45/20= 2.25
The mean of the sample data is:
14/5= 2.8
Therefore, the difference between the mean of the sample and the population is:
2.8-2.25= 0.55
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does someone mind helping me with this question? Thank you!
Answers
Answer:
70
Step-by-step explanation:
ok so we just plug 4 for x in the expression:
5 (2*4 + 6 )
5 ( 8 + 6 )
5*14 = 70
Have a good day! :)
A car used of a gallon of gas to drive of a mile. At this rate, how many miles
can the car travel using 1 gallon of gas?
Answers
• 29
^ 3.5
Step-by-step explanation:
Since 1/4 * 4 = 1
We just have to multiply 1/64 times 4 to get the
answer
1/64 * 4 = 4/64
What critical value of t* should be used for a 95% confidence interval for the population mean based upon a random sample of 20 observations
Answers
Using a calculator, the critical value of the t-distribution that should be used for a 95% confidence interval with 20 observations is of t* = 2.0930.
How to find the critical value of the t-distribution?A calculator is used, with two inputs:
The confidence level.The number of degrees of freedom, which is one less than the sample size.In this problem, we have a 95% confidence interval, with 20 - 1 = 19 df, hence the critical value is of t* = 2.0930.
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help solve these algebraic fractions please, with explanation would be great
Answers
Step-by-step explanation:
i answered it , and tried to give explanation too...
hope its helpful ,
GRADE 11 MATH
PLEASE HELP!
Nelson received $10,000 on his 17th birthday. This is the accumulated amount of an
investment his parents made on the day he was born. The investment earned 9.5%/a,
compounded semi-annually.
a) Determine the amount that Danny’s parents invested 17 years ago. [3 marks]
b) How much interest did the investment earn? [1 mark]
Answers
The amount that was invested 17 years ago is $2064.25.
The interest earned is $7935.75.
What is the amount invested 17 years ago?The formula that would used to determine the amount that was invested 17 years ago is:
P = FV / (1 + r)^nm
Where:
FV = Future value = 10,000P = Present value R = interest rate = 9.5 / 2 = 4.75%m = number of compounding = 2 N = number of years = 1710,000 / (1.0475)^(17 x 2) = $2064.25
Interest earned = 10,000 - 2064.25 = $7935.75
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If ab = 10 ft, ac = 14 ft, and bc = 20 ft, what is rs? 10 ft 14 ft 20 ft 24 ft
Answers
The side |rs| is congruent to side |ac| which is 14 ft.
What are congruent triangles?Congruent triangles are two similar triangles that have corresponding sides and angles and they are of equal measure.
The figures from the textbook illustrate that following rotation, the two triangles are congruent.
This signifies that the angles and sides of the first triangle are equal to the angles and sides of the other triangle.
Therefore:
ab = tr = 10 ftac = rs = 14 ftbd = ts = 20 ftLearn more about congruent triangles here:
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(-2,4) on cordinate plane
Answers
The coordinate -2, 4 implies -2 is the value on the x or horizontal axis and 4 is the value on the y or vertical axis.
What is a coordinate plane?This a plane used for graphs or points that is based on a vertical axis (y) and a horizontal axis (x).
How does -2,4 look on a coordinate plate?The first number, -2 indicates the value in x or the horizontal axis, while the second number 4 indicates the position on y or the vertical axis. You can see this in the imaged attached (red dot).
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The coordinate -2, 4 implies -2 is the value on the x or horizontal axis and 4 is the value on the y or vertical axis.
What is a coordinate plane?
This a plane used for graphs or points that is based on a vertical axis (y) and a horizontal axis (x).
How does -2,4 look on a coordinate plate?
The first number, -2 indicates the value in x or the horizontal axis, while the second number 4 indicates the position on y or the vertical axis. You can see this in the imaged attached (red dot).
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