For the given data, ∅ is the given angle in standard position, terminal side passes through (21, -20) then the exact value of cot ∅= ( - √41/ 20 ) in simplest radical form.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
For the given angle ∅ (theta) in standard position:
Terminal side of ∅ is passes through the point ( 21, -20 )
( 21, -20) represents ∅ is in the second quadrant.
In second quadrant sine in positive and cosine is negative.
Base is negative and altitude is positive.
Base = 21
Altitude = -20
Using Pythagoras theorem,
Hypotenuse² = (21)² + (-20)²
⇒ Hypotenuse = √41
Cot ∅ = - √41/20 ( simplest radical form )
Then the exact value of
Cot ∅ = ( - √41/ 20 ) in simplest radical form.
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A car is valued at $35400 at the start of the year, and at $25700 at the end of that year. During that year, the car travelled 25000kms.
a) Find the total depreciation of the car in that year in dollars
b) Find the depreciation per kilometre for this car
c) Using (initial value) -> V₀ = 35400, write down a rule for the value of the car Vₙ after ₙ kilometres
d) How many kilometres are travelled when the value of the car is $6688?
e) Including the first year of travel, how many kilometres in total is this car expected to drive before it has a value of 0?
a. Total depreciation = $9700
b. Depreciation per kilometer = $0. 388 per kilometer
c. Vₙ = $35400 + ₙt
d. Distance = 4723. 16 kilometers
e. Total distance = 29723. 16 kilometers.
How to determine the depreciation
i. The formula for total depreciation is given as;
Total depreciation = Cost of asset - Residual value
Cost of car = $ 35400
Residual value = $25700
Total depreciation = $35400 - $25700
Total depreciation = $9700
b. Depreciation per kilometer = Total depreciation/ distance travelled in kilometers
Depreciation per kilometer = $ [tex]\frac{9700}{25000}[/tex]
Depreciation per kilometer = $0. 388 per kilometer
c. Vₙ = V₀ + ₙt
t = time of depreciation
V₀ = $35400
Vₙ = $35400 + ₙt
d. When the car costs $35400, it travelled 25000 kilometers
It costs $6688, it would travel 'x' kilometers
Cross multiply
$35400 × x = $ 6688 × 25000 kilometers
Make 'x' subject
x = [tex]\frac{6688 * 25000}{35400}[/tex]
x = [tex]\frac{167200000}{35400}[/tex]
x = [tex]4723. 16[/tex] kilometers
The car would travel 4723. 16 kilometers
e. To find the total distance
Total distance = 25000 + 4723. 16
Total distance = 29723. 16 kilometers.
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Which choices are equivalent to the quotient below? Check all that apply. √16 √8
The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2
How to find the equivalent of a quotient?We want to find the equivalent quotient of the given expression; √16 / √8
Now, we know that the square root of 16 is equal to 4 i.e. √16 = 4
Thus, applying that to our expression gives;
√16/√8 = 4/√8
Now, square root of 8 which is √8 can also be expressed as; 2√2
Thus;
4/√8 = 4/2√2 = 2/√2
The steps to rationalize the denominator, to get rid of all radicals that are in the denominator are as follows;
Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.
Step 2: Make sure all radicals are simplified.
Step 3: Simplify the fraction if needed.
If we rationalize the denominator of our expression, we have;
2/√2 × √2/√2 = 2√2/ 2 = √2
Also, 2/√2 can be expressed as √4 /√2
Therefore, The equivalent quotient of the expression √16/√8 are: √2 and √4 / √2
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In a year of 365 days Paul skipped school for the months of January and February.
He had summer vacations for the months June to August. How many days of the
year (excluding Sundays) did he attend school?
The days of the year (excluding Sundays) paul attends school is 183 days
CalendarTotal days in a year = 365
Months Paul skipped school = January, February, June, July August
= 31 + 28 + 30 + 31 + 31
= 151 days
Days he attend school excluding Sunday = Total days in a year - (Months Paul skipped school + Sundays)
= 365 - (151 + 31)
= 365 - 182
= 183 days
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more math i need help in please nd thank u
The value of x when y = 1.728 and z = 5 in the inverse variation y = (k × x²) / z³ is 36
Inverse variationThe types of variation are;
Inverse variationDirect variationJoint variationy = (k × x²) / z³
where,
k = constant of proportionalityIf y = 12, x = 4 and z = 2
y = (k × x²) / z³
12 = (k × 4²) / 2³
12 × 2³ = k × 4²
12 × 8 = k × 16
96 = 16k
k = 6
Find x when y = 1.728 and z = 5
y = (k × x²) / z³
1.728 = (6 × x) / 5³
1.728 × 5³ = 6x
1.728 × 125 = 6x
216 = 6x
x = 216/6
x = 36
Therefore, value of x when y = 1.728 and z = 5 in the inverse variation y = (k × x²) / z³ is 36
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Someone help me please
Answer: 12
Step-by-step explanation:
Let's say that the length needed to be found is x
As the two lengths of both triangles are parallel to one another, we can use the equation to find x
6/x = (6+4)/20
6/x = 1/2
x = 12
The function f(x) = 200 × (1.098)x represents a village's population while it is growing at the rate of 9.8% per year.
Create a table to show the village's population at 0, 2, 4, 6, 8, and 10 years from now.
Use your table to create a graph that represents the village's population growth.
When the population doubles from its current size, the village will need to dig a new water well. To the nearest half of a year, about how long before it is time for the village to dig the new well?
The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.
How to graph a function?For a function f(x) = y, the steps to draw a graph for the given function are as follows:
Consider certain values of x Substitute x values in the given function to obtain y valuesPlot the x and y values in the graphJoin the points to know the variation.Calculation:It is given that,
f(x) = 200 × [tex](1.098)^x[/tex]
Village's population growing rate = 9.8%
Creating a table for x and f(x) values:
x: 0 2 4 6 8 10
f(x = 0) = f(0) = 200 × [tex](1.098)^0[/tex] = 200
f(x = 2) = f(2) = 200 × [tex](1.098)^2[/tex] = 241
f(x = 4) = f(4) = 200 × [tex](1.098)^4[/tex] = 291
f(x = 6) = f(6) = 200 × [tex](1.098)^6[/tex] = 350
f(x = 8) = f(8) = 200 × [tex](1.098)^8[/tex] = 423
f(x = 10) = f(10) = 200 × [tex](1.098)^1^0[/tex] = 509
So,
(x, f(x)): (0, 200) (2, 241) (4, 291) (6, 350) (8, 423) (10, 509)
Plotting these points in the graph and joining the points, the graph is shown below.
Finding the time for the village to dig a new well:
It is given that the population doubled from its current size, the village will need to dig new water well.
The current size of the village = 200
If it doubles for a certain time 't' = 400
So,
400 = 200 × [tex](1.098)^t[/tex]
⇒ [tex](1.098)^t[/tex] = 2
⇒ log[tex](1.098)^t[/tex] = log 2
⇒ t log(1.098) = 0.301
⇒ t × 0.04 = 0.301
∴ t = 7.525 years
Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.
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A fair six sided die is rolled twice what is the probability it will end on one and then six
Answer:
2.78%
Step-by-step explanation:
Probability Formula
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
We are told that the six-sided dice is fair. This means that each of the faces has the same probability of being rolled.
Therefore, the probability of rolling one is:
[tex]\implies \sf P(x = 1)=\dfrac{1}{6}[/tex]
The probability of rolling six is:
[tex]\implies \sf P(x = 6)=\dfrac{1}{6}[/tex]
Therefore, the probability of rolling one and then six is:
[tex]\begin{aligned}\implies \sf P(x=1)\:and\:P(x=6) & = \sf \dfrac{1}{6} \times \dfrac{1}{6}\\& =\sf \dfrac{1}{36}\\& = \sf 0.0278\:(3\:s.f.)\\& = \sf 2.78\%\:(3\:s.f.)\end{aligned}[/tex]
Total elements in sample space=6
P(1)
1/6P(6)
1/6P(1 and 6)
(1/6)²1/362.78%Evaluate the expression 21 ÷ 3 + 8 − 4.
A) 19
B) 17
C) 15
D) 11
Answer:
D
Step-by-step explanation:
We will use the order of operations to evaluate the expression.
From left to right , Multiplication/Division followed by Addition/Subtraction.
21 / 3 + 8 - 4
= 7 + 8 - 4
= 15 - 4
= 11
Therefore, the answer is D
Answer:
D) 11
Step-by-step explanation:
Division and multiplication always comes first in an equation. Since there is no multiplication in the expression, we can divde first.
21 / 3 = 7
Our new expression will be: 7 + 8 - 4
Now we can just add (7) , (8), and (-4) not caring about the order, since they are all addition or subtraction.
I'll do the addition first, but order does not matter.
7 + 8 = 15
15 - 4 = 11
So 11 is our final answer.
Looking at the answer choices, D has 11, so D is our answer for this question.
Find the surface.area of the composite.figure...
11 in.
3 in.
6 in.
3 in.
H
8 in.
SA =
3 in.
6 in.
11 in.
[?] in.2
If you'd like,
you can use a
calculator.
Enter
URGENT!!! Write a compound interest function to model the following situation. Then, find the balance after the given number of years.
Answer:
The answer to our question is A = 16,100(1.001)12t; $17,510
Step-by-step explanation:
I hope this helps and have a good day!
What's the value of this python expression: (2**2) == 4?
Answer:
Python will return:
True
Step-by-step explanation:
The math function ** is an exponent indicator.
The equation you made was:
[tex]2^2 =4[/tex]
When you run this in python, it will return as true.
It is run as a Boolean expression because you have already provided the answer to the expression with the "==" statement.
If you had provided an incorrect answer (setting it equal to any number other than 4), it would return False.
Whats the solution √x-6-x-12
Determine the present value of quarterly payments of $450 for 6 years at 7.5% annual interest, compounded quarterly. PV= R[(1+i)^-n]/i
Using it's formula, the present value of the amount is: $288.
What is the present value formula?The present value formula is:
[tex]PV = \frac{R}{(1 + r)^n}[/tex]
In which the parameters are:
R is the future value.r is the interest rate.n is the number of periods.Considering quarterly compounding, the parameters for this problem are as follows:
R = 450, r = 0.075/4 = 0.01875, n = 6 x 4 = 24.
Hence the present value is:
[tex]PV = \frac{R}{(1 + r)^n}[/tex]
[tex]PV = \frac{450}{(1.01875)^{24}}[/tex]
PV = $288
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Solve 3[-x + (2 x +1)]=x-1
Question :
Solve 3 [-x + (2x + 1) ] = x - 1Solution :
⇒ 3 [-x + 2x + 1] = x - 1
⇒ 3 [x + 1] = x - 1
⇒ 3 × [x + 1] = x - 1
⇒ 3x + 3 = x - 1
⇒ 3x - x + 3 = -1
⇒ 2x + 3 = -1
⇒ 2x = -1 - 3
⇒ 2x = -4
⇒ x = -4 / 2
⇒ x = -2
Simplifying
3[-1x + (2x + 1)] = x + -1
Reorder the terms:
3[-1x + (1 + 2x)] = x + -1Remove parentheses around (1 + 2x)
3[-1x + 1 + 2x] = x + -1Reorder the terms:
3[1 + -1x + 2x] = x + -1Combine like terms: -1x + 2x = 1x
3[1 + 1x] = x + -1[1 * 3 + 1x * 3] = x + -1[3 + 3x] = x + -1Reorder the terms:
3 + 3x = -1 + xSolving
3 + 3x = -1 + xSolving for the variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1x' to each side of the equation.
3 + 3x + -1x = -1 + x + -1xCombine like terms: 3x + -1x = 2x
3 + 2x = -1 + x + -1xCombine like terms: x + -1x = 0
3 + 2x = -1 + 03 + 2x = -1Add '-3' to each side of the equation.
3 + -3 + 2x = -1 + -3
Combine like terms: 3 + -3 = 0
0 + 2x = -1 + -32x = -1 + -3Combine like terms: -1 + -3 = -4
2x = -4Divide each side by '2'.
x = -2Simplifying
x = -2let n be a natural number such that GCF(n, 70)= 10, and LCM(n, 70)=210. Find N. (Hint: Do you remember that LCM(A,B) x GCF(A, B)= A x B?)
The natural number , n is 30
How to determine the value
Given;
GCF(n, 70) = 10
LCM(n, 70) = 210
We have that;
LCM(A,B) x GCF(A, B)= A x B
Then,
(n, 70) = n × 70 = 70n
10 × 210 = 2100
Equate the two expressions
70n = 2100
n = [tex]\frac{2100}{70}[/tex]
n = [tex]30[/tex]
Thus, the natural number , n is 30
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Consider triangle DEF. The legs have a length of 36 units each. What is the length of the hypotenuse of the triangle 18 units units 36 units units
Answer:
(っ◔◡◔)っ ♥ 36 square root 2 ♥
Step-by-step explanation:
The length of the hypotenuse of the triangle is approximately 48.99 units.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
We can use the Pythagorean theorem to find the length of the hypotenuse of the triangle:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs.
Substituting the values given in the problem.
c² = 18² + 36²
c² = 324 + 1296
c² = 1620
Taking the square root of both sides.
c = √(1620)
Simplifying.
c = 6 √(90) or approximately 48.99
Therefore,
The length of the hypotenuse of the triangle is approximately 48.99 units.
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The price of the product decreased by 10%and then decreased by 20% . calculate total percentage change between the final and initial prices
What is percentage change?
By quantifying the difference between two numbers and expressing it as an increase or decrease, the Percentage Change Calculator (percent change calculator) may determine the percentage change.
The initial price [tex]V_{1}[/tex] (100%) was decreased by 10%., then this reduced price is reduced more by 20% that becomes the final price [tex]V_{2}[/tex] which is 72.
Calculate percentage change from [tex]$V_{1}=100$[/tex] to [tex]$V_{2}=72$[/tex].
=[tex]& \frac{\left(V_{2}-V_{1}\right)}{\left|V_{1}\right|} \times 100 \\[/tex]
[tex]=& \frac{(72-100)}{|100|} \times 100 \\[/tex]
[tex]=& \frac{-28}{100} \times 100 \\[/tex]
[tex]=&-0.28 \times 100 \\[/tex]
[tex]=&-28 \% \text { change } \\[/tex]
[tex]=& 28 \% \text { decrease }[/tex]
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A couple quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
By the way the 2nd and 3rd attachments (or the ones with the chart filled out already) are my first 2 attempts, but I got both of them mostly all wrong. So please use those as what not to do lol. And the first attachment (without the chart filled out) is the actual question and the one I need to get answers for, tysm!
All the relevant transformations are as shown in the explanations below.
How to Interpret Transformations?We are given the original function as y = x and told the transformation is as follows;
1) y = x + 5; This means that the function was shifted 5 units to the left.
2) y = ³/₈x; This means that the function was vertically stretched by a scale factor of ³/₈.
3) y = -x - 2 or y = -(x + 2); This means that the function was first shifted by 2 units to the left before being reflected over the x-axis.
4) y = 6x + 1; This means that the function was stretched by a factor of 6 and then shifted 1 unit to the left.
5) y = x - 11; This means that the function was shifted 11 units to the right.
6) y = 8x; This means that the function was vertically stretched by a scale factor of 8.
7) y = -1/3x; This means that the function was horizontally stretched by a scale factor of 1/3.
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what is the height of figure 1?
Answer:
4
Step-by-step explanation:
What is the value of the expression below when w = 9 and x = 5?
10w + 4x
Answer:
110
Step-by-step explanation:
10w + 4x
10 (9) + 4 (5)
90 + 20
110
The answer is 110.
Hope it helps!
Have a nice day:)
I SHOULD ALREADY KNOW THIS
[tex]t \geqslant 35[/tex]
Since there are at least 35 tic tacs, there has to be 35 tic tacs or more in the box.D is the centroid of triangle abc. what is the value of x when bd=2x+40 and bf=18x
The value of x= 20 units
BD = BF
BD =2x + 40
BF = 18x
Equate the expressions thus:
2x + 40 = 2/3(18x)
2x + 40 = 12x
Collect like terms
2x - 12x = - 40
-2x = - 40
Divide both sides by - 2
x = 20
Hence, x = 20 units
The centroid is the center point of the item. The factor in which the 3 medians of the triangle intersect is known as the centroid of a triangle. it is also defined because of the point of intersection of all the 3 medians. The median is a line that joins the midpoint of a facet and the opposite vertex of the triangle.
Then, we can calculate the centroid of the triangle by means of taking the common of the x coordinates and the y coordinates of all of the three vertices. So, the centroid method can be mathematically expressed as G(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/three).
The centroid of a triangle is the point at which the 3 medians coincide. The centroid theorem states that the centroid is 23 of the space from each vertex to the midpoint of the opposite aspect.
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what is the mode of 250 100 75 200 150 100?
[tex]\textbf{Heya !}[/tex]
the mode is the number that occurs the most
All numbers here occur once, except [tex]\sf{100}[/tex].
so 100 is the mode.
`hope it was helpful to u ~
Describe a relationship that can be modeled by the function represented by the graph, and explain how the function models the relationship. Identify and interpret the key features of the function in the context of the situation you described in part A.
The graph is a decreasing exponential graph.
How to illustrate the information?Part A: The given graph is decreasing the exponential graph since the graph is decreasing rapidly as the value of x is increasing the value of y is decreasing very rapidly.
Part B: The graph shown here is maybe the case of any electric appliance which is of cheap quality. The time when it is brought then its performance and its life is awesome after that its life is decreasing rapidly.
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Last week, Layla's Ice Cream Shoppe sold 11 sundaes with nuts and 39 without. what is the ratio of the number of sundaes without nuts
The ratio of the number of sundaes with nuts to the number of sundaes without nuts is; 11:39
How to find the sharing ratio?We are given;
Number of sundaes with nuts sold = 11
Number of sundaes without nuts sold = 39
Thus, the ratio of the number of sundaes with nuts to the number of sundaes without nuts is;
11:39
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Each element in a population has an equal chance of being chosen for inclusion in the sample independent of any other event in the process. This is known as _________.
Each element in a population has an equal chance of being chosen is Random selection.
Given that each element in a population has an equal chance of being chosen for inclusion in the sample independent of any other event in the process.
Sampling is an umbrella term for all methods used to take samples from populations. The main purpose of sampling is to ensure that a chosen sample reflects the desired characteristics of a population so that a statistical study can produce accurate and reasonable results. Sampling techniques include random sampling, stratified sampling and many others.
As we know, random selection is the process of selecting a small group of people from a larger group to participate in a study. Each person has an equal chance of being selected, giving each person in the group an equal chance to participate.
Hence, Each element in a population has an equal chance of being chosen for inclusion in the sample independent of any other event in the process is known as random selection.
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There are 15 unmatched socks in your drawer. 9 are black, 5 are white, and 1 is brown. What is the probability that if you already randomly choose one of the black socks, that you will choose another black sock?
Answer: 4/7
Step-by-step explanation:
You pick one black sock, meaning there are 14 socks remaining in the drawer, 8 of which are black. Thus, the probability is 8/14, which simplifies to 4/7.
If a truck traveled 75 miles in 3 hours, how many miles would the truck have traveled per minute?
The truck travelled 0.42 miles per minute
How to determine the miles per minute?The given parameters are:
Distance = 75 miles
Time = 3 hours
Convert time to minutes
Time = 3 * 60 minutes
Time = 180 minutes
The speed is calculated as:
Speed = Distance/Time
This gives
Speed = 75 miles/180 minutes
Evaluate
Speed = 0.42 miles per minutes
Hence, the truck travelled 0.42 miles per minute
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Mia invests $5000 in an index fund after 1 year the funds share price has increased by 8% how much did mia gain
A year later, Mia gained $400.
Calculation of interestMia invests in an index fund= $5000
The share price of the fund has grown by 8% after a year.
So, one year later Mia's investment would also increase by 8% since her invested share value has grown by 8%.
Hence, the amount of share would be = ($5000 + 8% of $5000) =($5000+$5000*8/100) = ($5000+$400) = $ 5400
Therefore, Mia's gain is $400.
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need help with the y value
Answer: 12x
Step-by-step explanation:
The question is asking what equation models the table above. You have to make an equation that when any of the times on the left column are plugged in, the value on the right column are outputted.
For 1, the equation should output 12. For 2, the equation should output 24. For 3, the equation should output 36, and so on.
Here, we see a pattern: for every value we input as the number of seconds, the height is 12 times more than that. Assuming x is the time and y is the height,
[tex]y=12x[/tex]
If we use any x on the left, it's corresponding height will be the y.