Answer:
Escribir cada expresión en términos de seno. 2. Escribir cada expresión en términos de coseno . 3. Expresar la función dada en términos de la función que se indica en cada literal. 4. Utilizar las identidades fundamentales para escribir una expresión equivalente a la expresión dada. Luego, simplificar. 5. Factorizar las siguientes ...
Step-by-step explanation:
One angle of a triangle measures twice the smallest angle. The third angle measures five more than twice the smallest angle. Find the measure of the smallest angle.
Answer: The smallest angle is 35°
Step-by-step explanation:
1 angle: 2x
smallest angle: x
third angle: 2x + 5
all angles in a triangle add up to 180 degrees. Therefore,
2x+x+2x+5 = 180
5x+5=180
5x+5(-5)=180(-5)
5x = 175
5x/5 = 175/5
x = 35
The smallest angle is 35°
Y=x2+1 ordered pairs
The ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)
How to determine the ordered pairs?The function is given as:
y = x^2 + 1
the ordered pairs are the x and y values of the function
So, we stet x = 0, 1, 2, 3 and 4
y = 0^2 + 1 = 1
y = 1^2 + 1 = 2
y = 2^2 + 1 = 5
y = 3^2 + 1 = 10
y = 4^2 + 1 = 17
Hence, the ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)
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John goes for a jog every third day and every Saturday he goes to the gym. If he goes to the gym and also runs today, how long will it take before there is another day on which he does both?
It will take 21 days before there is another day on which he does both.
What is lowest common multiple (LCM) ?The lowest common multiple (LCM) of two or more numbers is the lowest possible number which is completely divisible by all the given numbers.
Given,
John goes for a jog every third day and every Saturday he goes to the gym.
That means he goes to the gym on every seventh day, and goes for a jog every third day.
Therefore, he goes for both on the days which are LCM of 3 and 7.
But, LCM of 3 and 7 is 21.
Hence, he goes for both in every 21 days.
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Find the sum of the series: 4+8+12+........to 20 term. In (n
Answer:
16
Step-by-step explanation:
4 , 8 , 12 , 16 , 20 , ....................... ans goes on
What is the equation of the line that is perpendicular to the line defined by the equation 2x = 4y – 8 and goes through the point (1, 2)?
The equation of the perpendicular line is y = -2x + 4
How to determine the line equation?The line equation is given as:
2x = 4y - 8
Make y the subject
4y = 2x +8
Divide by 4
y = 0.5x + 2
The slope of the above equation is
m = 0.5
The slopes of perpendicular lines are opposite reciprocals.
This means that, the slope of the perpendicular line is:
n = -1/m
This gives
n = -1/0.5
n = -2
The equation is then calculated as:
y = n(x - x1) + y1
This gives
y = -2(x - 1) + 2
Expand
y = -2x + 2 + 2
Evaluate
y = -2x + 4
Hence, the equation of the perpendicular line is y = -2x + 4
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2. Michelle asks her husband to build a pen for her chickens. Three of the sides will be built with mesh fencing, while the fourth side will back up to the east side of her house. She wants the enclosed area to be 400 square feet. The cost of the fence meshing will be $4.18 per foot and the pen will also need 4 corner posts costing $9.50 each.
a. [6 pts] Let x be the length of the side of the chicken coop that backs up to the east side of the house. Write a function P(x), for the price of the materials for the pen in terms of x. Simplify your answer.
b. [3 pts] Use your calculator to find the dimensions of the pen that costs the least. Set your window with: 0≤x≤80 and 10≤ y ≤400, and round your answer to 2 decimal places. (Insert your graph here. You may hand draw the graph or insert an image of the graph from Desmos)
c. [1 pt] What is the total cost of the pen? Round to dollars and cents.
The function P(x), for the price of the materials for the pen, is 4.18(800/x + x) + 38.
How to illustrate the function?Based on the information, the function P(x), for the price of the materials for the pen will be:
P(x) = 4.18 (2 × 400/x + x) + 38
= 4.18(800/x + x) + 38.
The dimensions will be:
We'll differentiate the function which will give 20✓2. Therefore, the value for x will be 20✓2 which is 28.28 feet and that of y will be 10✓2 which is 14.14 feet.
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Consider the following functions. f=[(-1,1),(1,-2),(3,-4) and g=[(5,0),(-3,4),(1,1),(-4,1)} Find (f-g)(1) =
The difference between the functions give:
(f - g)(1) = f(1) - g(1) = -3
How to find the difference between the functions?
For two functions f(x) and g(x), the difference is defined as:
(f - g)(x) = f(x) - g(x).
Then:
(f - g)(1) = f(1) - g(1)
By looking at the given tables, we know that:
f(1) = -2
g(1) = 1
Replacing that we get:
(f - g)(1) = f(1) - g(1) = -2 - 1 = -3
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b. What is another composition of rigid motions that maps A GHJ to A KLM?
Another rigid motions that maps Δ GHJ to ΔKLM is ΔGHJ winding point J rotates 180° in the counterclockwise direction. It then transits south by 10 units and to the right by two units. See the attached image.
What is Rigid Motion?Rigid Motion is any method of moving all the points in the plane in such a way that.
the relative distance between sites remains constant andthe relative location of the points remains constant.There are four forms of rigid motions:
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Alvin wants to know what his average paddling rate was for a canoe trip to a campsite. On the way there it took him 10 hours against a river current of 3 km/ hr. On the way back, the same distance took him 5 hours with the same 3 km/hr current.
The paddling rate of Alvin is 9km/hr
Given time against the river current is 10 hours , speed is 3km/hr
and time with the river current given is 5 hours and the speed is 3km/hr
We need to calculate the paddling rate of Alvin
Let us assume that
r =Alvin's average paddling rate in km/hour
y = speed of the current in km/hour
we know that
speed= distance/time
∴ distance=speed*time
Now,
To Campsite against the current
Speed=(r-y)
∴ Speed=(r-3) ---- (1)
Time=8 hours
Distance=(r-3)*10------ (2)
10r - 30
From Campsite with the current
Speed=(r+y)
∴Speed=(r+3)*5
Time=3 hours
Distance=(r+3)*5----(1)
Equate equation 1 and equation 2
5r +15
because is the same distance
5r + 15 = 10r - 30
5r = 45
r = 9
Hence ,The rate of the paddling rate is 9km/hr
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Let sets A and B be defined as follows.
A is the set of integers greater than -14 and less than -5.
B={h,i,s,x,z}
a) find the cardinalities of A and B
n(A)=
n(B)=
b) select true or false
-12 ∈ A
-21 ∈ A
s ∈ B
m ∉ B
A is the set of integers greater than -14 and less than -5. B={h, i, s, x, z}. The cardinalities of A and B are, n(A) = 8 and n(B) = 5.
-12 ∈ A, s ∈ B, and m ∉ B are True statements. Since, -21 does not belong to A, 21 ∈ A is a False statement.
Cardinalities of A and B
It is given that,
A = {n : -14 < n < -5, n ∈ Z} ............ (1)
B = {h, i, s, x, z} ......... (2)
Thus, from (1),
A = {-13, -12, -11, -10, -9, -8, -7, -6} ........... (3)
Cardinalities of A and B are the number of members in the set A and B, respectively. Therefore,
n(A) = 8
n(B) =5
Reason Behind True or False
As seen from (3), set A contains the element -12. Thus, -12 ∈ A is True.Again from (3), we can see that -12 does not belong to the set A. Thus, -21 ∈ A is FalseFrom (2), s is present in set B. Hence, s ∈ B is TrueSimilarly, m is not present in set B. Therefore, m ∉ B is TrueLearn more about cardinalities here:
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A lawn can be mowed by 8 people in 6 hours. If 3 people take the day off and do not help mow the grass, how many hours will it take to mow the lawn? Please show me how you figured this out.
A. 6 2/5
B. 9 3/5
C. 2 1/4
D. 5 1/2
If 3 people take the day off, they will need (9 + 3/5) hours to mow the lawn. The correct option is B.
How many hours will it take to mow the lawn?Let's say that each person works at a rate R.
8 people can mow the lawn in 6 hours, then we can write:
(8*R)*6 hours = 1 lawn.
Solving for R:
R = (1/48 lawns per hour).
If 3 people take the day off, then the lawn is mowed by 5 people in a time T, then we need to solve:
(5*R)*T = 1 lawn.
Replacing the value of R:
(5/48 lawns per hour)*T = 1 lawn.
Then we have:
T = (48/5) hours.
We can rewrite that as:
T = (45/5 + 3/5) hours
T = 9 + 3/5 hours.
Then we conclude that the correct option is B.
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Use the distance formula to find the length of the segment C(2, 1) to
D(5,6). Round your answer to two decimal places.
Answer: 5.83
Step-by-step explanation:
[tex]\sqrt{(2-5)^2 + (1-6)^2}=\sqrt{34} \approx 5.83[/tex]
How do i convert the follwing Powers Of Ten into standard numbers?
[tex]10^{7}[/tex]
[tex]10^{5}[/tex]
[tex]10^{8}[/tex]
[tex]10^{12}[/tex]
[tex]10^{6}[/tex]
The standard numbers are obtained from the given numbers as follows;
10⁷ → 1000000010⁵ → 10000010⁸ → 10000000010¹² → 100000000000010⁶ → 1000000Which method can be used to express the numbers in standard form?The standard form of numbers is obtained by expressing the number completely and not using powers of 10
The given numbers in powers of 10 can be expressed in standard form by writing the specified number of zeros next to 1 given by the power of 10 as follows;
Number → Standard form
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Given angle ABC shown on the coordinate plane below.
Draw angle A”B””C” = Ro 90(T<-4,3>(ABC))
The attached image shows the image of A"B"C" after the transformation
What is the transformation of the triangle about?The transformation rule states:
A"B"C" = Ro90° (T(-4,3)(ABC))
This implies that one need to rotate the triangle in a 90⁰ clockwise direction, and then one need to translate the triangle.
Using the image shown, the coordinates of ABC are;
A = (-1, 2)
B = (1, 4)
C = (3, -1)
The 90⁰ rule clockwise rotation will be:
(x,y) -- (y,-x)
So, when translated, it will be:
A' = (2, 1)
B' = (4, -1)
C' = (-1, -3)
Then the translation of the triangle using T(-4,3):
(x, y) - (x - 4, y + 3)
So, there is:
A'' = (-2, 4)
B'' = (0, 2)
C'' = (-5, 0)
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Find DE
3x - 28
3x - 30
D
G
E
F
33
Answer:
11 units
Step-by-step explanation:
We first need to solve for x
3x -28 +3x -30 + x = 33 Combine the x's
7x - 28 -30 = 33 Combine -28 and -30
7x - 58 = 33 Add 58 to both sides
7x = 91 Divide both sides by 7
x = 13 Now plug 13 into the expression for DE
3x - 28
3(13) - 28
39 -28
11
Which of the following sets shows all the numbers from the set {1, 2.5, 3, 4.5, 5} that make the inequality 3a + 4 ≥ 13 true?
{2.5, 3, 4.5}
{1, 2.5}
{3, 4.5, 5}
{4.5, 5}
(-11x+3)-2(-11/4x-5/2)= simplify it
Answer:
(+22x^2+16x+11)/(2x)
If
C(x) = 12000 + 400x − 2.6x2 + 0.004x3
is the cost function and
p(x) = 1600 − 8x
is the demand function, find the production level that will maximize profit. (Hint: If the profit is maximized, then the marginal revenue equals the marginal cost.)
Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.
How to find the production level that'll maximize profit?The cost function, C(x) is given by 12000 + 400x − 2.6x² + 0.004x³ while the demand function, P(x) is given by 1600 − 8x.
Next, we would differentiate the cost function, C(x) to derive the marginal cost:
C(x) = 12000 + 400x − 2.6x² + 0.004x³
C'(x) = 400 − 5.2x + 0.012x².
Also, revenue, R(x) = x × P(x)
Revenue, R(x) = x(1600 − 8x)
Revenue, R(x) = 1600x − 8x²
Next, we would differentiate the revenue function to derive the marginal revenue:
R'(x) = 1600 - 8x
At maximum profit, the marginal revenue is equal to the marginal cost:
1600 - 8x = 400 − 5.2x + 0.012x
1600 - 8x - 400 + 5.2x - 0.012x² = 0
1200 - 2.8x - 0.012x² = 0
0.012x² + 2.8x - 1200 = 0
Solving by using the quadratic equation, we have:
x = 220.40 or x = -453.73.
Since profit can't be negative, the production level that'll maximize profit is approximately equal to 220.
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Solve for xxx in the diagram below.
x=x=x, equals
^\circ
∘please help
Answer:
x = 34
Step-by-step explanation:
The angles x + 12, 100, and x add up to a straight angle, so the sum of their measures is 180°.
(x + 12) + (100) + (x) = 180
x + 12 + 100 + x = 180
2x + 112 = 180
2x = 68
x = 34
If np>5 and nq>5, estimate P (at least 10) with n=13 and p=0.5 by using the normal distribution as approximation for the binomial distribution, if np, or nq,5, then state that the normal approximation is not suitable.
Using the normal distribution, the probability is given as follows:
[tex]P(X \geq 10) = 0.0485[/tex].
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution are:
p = 0.5, n = 13.
Hence the mean and the standard deviation are:
[tex]\mu = np = 13 \times 0.5 = 6.5[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{13 \times 0.5 \times 0.5} = 1.8028[/tex]Using continuity correction, the desired probability is P(X > 9.5), which is one subtracted by the p-value of Z when X = 9.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.5 - 6.5}{1.8028}[/tex]
Z = 1.66
Z = 1.66 has a p-value of 0.9515.
1 - 0.9515 = 0.0485, then:
[tex]P(X \geq 10) = 0.0485[/tex].
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f(x)=- x ^ 2 - 1,x ne5\\ -3,x=5 lim x -> 5 f(x) = lim x -> 5 f(x) Find if
Answer:
the answer to the question is 1
Answer:
-26 Is the correct answer
Step-by-step explanation:
A car’s purchase for $27,000 after each year the resale value decreases by 35% what will the resale be after four years
The resale value of the car after four years is $4820
How to determine the resale value?The given parameters are:
initial value, a = $27,000
Rate, r = 35%
The value of the car each year is represented as:
Value = a *(1 - r)^t
So, we have:
Value = 27000 *(1 - 35%)^t
After four years, we have:
Value = 27000 *(1 - 35%)^4
Evaluate
Value = 4820
Hence, the resale value of the car after four years is $4820
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evaluate f(x)=4|x|+3 for x=-5
A man ordered 4 times as many boxes of ballpoint pens as boxes of felt-tip pens. Ballpoint pens cost $4.41 per box, and felt-tip pens cost $3.44. If the man's order of pens totaled $63.24, how many boxes of each type of pen did he buy?
How many boxes of felt-tip pens did he buy?
Answer:
3
Step-by-step explanation:
Let x = # of boxes of felt-tip pens.
(x)(3.44)+(4x)(4.41) = 63.24
21.08x = 63.24
x = 3
Because x = 3, the man bought 3 boxes of felt-tip pens and 12 boxes of ballpoint pens.
help with this question please !
Answer:
angle 8 is congruent to angles 3, 6, and 1
Step-by-step explanation:
If n and q are parallel then corresponding and vertical angles would be congruent. So: angle 8 is congruent to angles 3, 6, and 1.
Write an equation for this word
sentence: one fifth of a number
equals 16.
Answer: x / 5 = 16
x = 80
Solve log (3x + 4) = log (x – 2) + 3 log 2
Answer:
x + 4
Step-by-step explanation:
Sine the bases are all the same, I can write the equation:
3x+4 = (x-2) 2^3 When we are adding with logs, that means to multiple. Also, when we have 3 log 2, that can be written as 2^3 or 8 (2x2x2)
3x+4=(x-2)8
3x+4 = 8x-16
4=5x-16
20 = 5x
4=x
Find the solution of
a(-12 + a) = 0
Answer:
a=0, 12
Step-by-step explanation:
a=0 and –12+a=0===> a=12
3 On Saturday Keisha ran 35
she ran 41 kilometers. How much farther did she run on
Saturday than on Sunday?
By subtracting decimals, how much farther she ran on Saturday than on Sunday is determined as: 1.078 kilometers.
How to Subtract Decimals?When subtracting decimals, the number value is taken into consideration.
Distance ran by Keisha on Saturday = 3.218 kilometers.
Distance ran by Keisha on Sunday = 2.41 kilometers.
Subtract both decimals to determine how much farther she run on Saturday than on Sunday.
3.218 - 2.14 = 1.078 kilometers.
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One yellow daisy and two pink carnations tied with ribbon will be used for corsages at a Mother's Day banquet. Each corsage takes 6 inches of ribbon. The daises are $0.85 each, the carnations are $0.50 each, and the ribbon is $0.24 per foot. There will be 24 corsages. What is the total cost?
Answer:
$47.28
Step-by-step explanation:
The total cost is found by adding the costs of the components.
Component costThere is one daisy, at $0.85 each.
There are to carnations at $0.50 each, for a total of 2×$0.50 = $1.00.
The is 6 inches of ribbon. That amount is 1/2 foot, so its cost is ...
(1/2 ft)×$0.24/ft) = $0.12.
Total costThe total cost of the components of one corsage is ...
daisy cost + carnation cost + ribbon cost = $0.85 +1.00 +0.12 = $1.97
There are 24 corsages, so their total cost will be 24 times this amount, or ...
24 × $1.97 = $47.28
The total cost of the 24 corsages is $47.28. All the costs of the components required for making a corsage are added to get the total cost of the corsage.
How to calculate the total cost?Total cost is the sum of all the individual component costs.Consider a and b are the two components with a cost K of each. Then the total cost = aK + bKCalculation:It is given that,
The components and their costs:
The cost of each daise = $0.85
The cost of each carnation = $0.50
The cost of the ribbon per foot = $0.24 (1 foot = 12 inches)
The components for making one single corsage:
One yellow daisy + two pink carnations + 6 inches of ribbon = 1 corsage
Then, calculating the price for one single corsage,
1 × $0.85 + 2 × $0.50 + (1/2) × $0.24 = cost of 1 corsage
⇒ $0.85 + $1 + $0.12
⇒ $1.97
For 24 corsages, the total cost = 24 × $1.97 = $47.28
Therefore, the total cost of the 24 corsages is $47.28.
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