An algorithm that converts one number into a different one is called a function.
What are the essentials of functions? A function is an algorithm that transforms one number into another.What the function receives as input is referred to as the independent variable or function's argument.The output of the function is referred to as dependent variables. Functions come in 4 different categories:the return values and arguments of functions.There are arguments and a value returned by this function:arguments-based functions without return values.functions that have both return values and no arguments.the absence of return values and arguments in functions.Chapter 1: Operation Function theory is not particularly difficult, yet students struggle because its fundamentals are unclear.Chapter 1 of Mathematics 2: Function .The human mind developed Function Theory to increase one's capacity for thought.To learn more about functions refer
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Pre Calc work, I need help with writing piece wise functions from graphs. Can anyone help? Giving brainliest
The definition of the piece-wise function is:
[tex]f(x) = 2.5x + 1, -2 \leq x \leq 2[/tex][tex]f(x) = -3, 2 < x < 6[/tex].What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input.
In this problem, for inputs between -2 and 2, the function is a line that goes through (-2,-4) and (2,6). The slope is:
m = (6 - (-4))/(2 - (-2)) = 2.5.
The y-intercept is of b = 1, hence the rule is:
[tex]f(x) = 2.5x + 1, -2 \leq x \leq 2[/tex]
For x greater than 2 and less than 6, the function is constant at -3, hence the rule is:
[tex]f(x) = -3, 2 < x < 6[/tex].
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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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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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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]
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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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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(-11x+3)-2(-11/4x-5/2)= simplify it
Answer:
(+22x^2+16x+11)/(2x)
p% of m change into an algebraic expression.
The expression p% of m changed into an algebraic expression is pm/100
Percentagep% of m
= p% × m
= p/100 × m
= (p × m) / 100
= pm/100
Therefore, the expression p% of m changed into an algebraic expression is pm/100
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Which of the following are identities?
Answer:
A
Step-by-step explanation:
I. False. Consider y = 3 and x = 4.
II. False. Consider x = 1.
III. False. Consider x = -2.
Find the solution of
a(-12 + a) = 0
Answer:
a=0, 12
Step-by-step explanation:
a=0 and –12+a=0===> a=12
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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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}
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
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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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
Which of the following is not a step in finding the area of an unknown figure?
- Calculate the areas of the smaller figures.
- Plug all dimensions into the formula: SA=Ixwxh.
- Divide the figure into smaller, known figures.
- Add up the areas of the smaller figures.
The answer choice which is not a step in finding the area of the unknown figure is; Plug all dimensions into the formula: SA=Ixwxh. option B
Which is not a step in finding the area of an unknown figure?It follows from the task content that all other steps except Plugging all dimensions into the formula; SA = l×w×h are correct steps.
This is due to the fact that, the formula does not work for all shapes and hence, it can't be generalized for all situations.
The step which is not involved in finding the area of an unknown figure is; Plug all dimensions into the formula: SA=Ixwxh.
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Answer:
B) Plug all dimensions into the formula: SA=Ixwxh.
Step-by-step explanation:
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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Approximately how many years will it take for the world’s population to increase to 8,252,000,000 people? Since there will be the original 100% plus an additional 2% each year, the base in the exponential equation is 1.02. Use the equation 8252=(6080)(1.02)x, where x is the number of years. Round to the nearest year.
The number of years it will take for the world’s population to increase to 8,252,000,000 people is 16
How to determine the number of years?This implies that we calculate the value of x
The equation is given as:
8252=(6080)(1.02)^x
Divide both sides by 6080
1.36 = (1.02)^x
Take the logarithm of both sides
log(1.36) = x * log(1.02)
Divide both sides log(1.02)
x = log(1.36)/log(1.02)
Evaluate the quotient
x = 16
Hence, the number of years is 16
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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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write the equivalent of the fraction using a denominator of 52. 2/13
Answer: 8/52
2/13=x/52
(2×52)/13=x
104/13=x
8=x
x=8
8 is the equivalent of the fraction using a denominator of 52. 2/13
Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value. For example, 9/12 and 6/8 are equivalent fractions because both are equal to 3/4 when simplified.
All equivalent fractions get reduced to the same fraction in their simplest form as seen in the example given above. Explore the given lesson to get a better idea of how to find equivalent fractions and how to check if the given fractions are equivalent.
⇒[tex]\frac{2}{13} =\frac{x}{52}[/tex]
⇒[tex]\frac{2(52)}{13} = x[/tex]
⇒[tex]x = 8[/tex]
therefore, 8 is the equivalent of the fraction using a denominator of 52. 2/13
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Simplify the following expression.x-[tex]\frac{2}{3}[/tex] x[tex]\frac{6}{7}[/tex]
Keeping the bases and adding the exponents, the simplified expression is:
[tex]x^{\frac{4}{21}}[/tex]
How to solve a product of two terms with the same base and different exponents?We keep the bases and add the exponents.
Hence:
[tex]x^{-\frac{2}{3}} \times x^{\frac{6}{7}} = x^{-\frac{2}{3} + \frac{6}{7}} = x^{\frac{-14 + 18}{21}} = x^{\frac{4}{21}}[/tex]
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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.
6. Evaluate x³ = -8 *
find m+n
pls help !!!
Answer:
m + n = 140===============
GivenTwo parallel lines,Included triangle between the parallel lines,Two interior angles of the triangle are m and n,Another angle of 40°.To find The sum of angles m and nSolutionAs per given, the missing interior angle is corresponding with 40° angle.
Since corresponding angles are equal, the third interior angle of the triangle is 40°.
Sum of three interior angles is 180°:
m + n + 40 = 180m + n = 180 - 40m + n = 140Apply angle sum property
m+n+40=180m+n=180-40m+n=140The answer is 140
Jada is solving the equation shown below.
Negative one-half (x + 4) = 6
Which is a possible first step to begin to simplify the equation? Select two options.
Divide both sides of the equation by –2.
Subtract 4 from both sides of the equation.
Multiply both sides of the equation by –2.
Distribute –2 over (x + 4).
Distribute Negative one-half over (x + 4).
Answer:
Distribute -1/2 over (x+4)
Step-by-step explanation:
-0.5(x+4) = 6
-0.5x - 2 = 6
-0.5x = 8
x = -16
Answer:
Multiple both sides by -2 or Distribute negative one-half over (x+4)
Step-by-step explanation:
-1/2(x+4) = 6
If I multiple both sides by -2, I am clearing the fraction:
(-2)(-1/2)(x+4) = 6(-2)
x+4 = -12
x = -16
OR
-1/2(x + 4) = 6
-1/2x -2 = 6 Remember, a negative times a positive is a negative.
-x - 4 = 12 multiply both sides by 2
-x = 16
x = -16
I need help with question in photo
Answer:
14
Step-by-step explanation:
[tex] {x}^{2} = {4}^{2} \\ = 16\\ 4y = 4 \times - 3 \\ 4 \times - 3 = - 12 \\ 16 - - 12 =16 + 12 \\ - \times - = + \\ 16 + 12 = 28 \\ 28 \div 2 = 14[/tex]
Examine the Scatterplot and Identify Characteristics of the data that are ignored by the regression line.
x 10 8 13 9 11 14 6 4 12 7 5
y 7.46 6.77 12.74 7.11 7.81 8.84 6.08 5.39 8.5 6.42 5.73
The regression equation is y = 3.002 + 0.5x and the scatterplot is illustrated.
What is a scatterplot?It should be noted that a scatterplot simply means a type of data that shows the relationship between two numerical variables.
From the information, summation is X is 99, summation Y is 82.5, summation XY is 797.47, and summation X² is 1001.
Now the value of a will be:
= 82.5 - 1001 - 99 - 797.47/(11.1001 - 99²)
= 3.002
b = (11 × 797.47 - 99 × 82.5)/11.1001 - 99²
= 0.5
The regression equation will be:
y = a + bx.
y = 3.002 + 0.5x
There's positive linear correlation between x and y.
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Here are two steps from the derivation of the quadratic formula (image w question below)
Answer:
B. Completing the square
Step-by-step explanation:
Between the first and second steps shown, the square of half the x-term coefficient was added to both sides. That is a value that makes the polynomial on the left be a "perfect square trinomial."
The process of adding the value required to make the left side a perfect square is called "completing the square."
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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a display at an aquarium has sea stars to wolf eels in a ratio 4 : 5. It also has 5/8 as many rockfish as sea stars. there are 40 more wolf eels than rock fish. How many sea stars are there?
The number of sea stars is 64.
What is a ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other.
In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."
This ratio is expressed in fraction form as a/b. We utilize the same method for further simplifying a ratio as we use for further simplifying a fraction.
According to the question,
Ratio of sea stars to wolf eels = 4:5
Number of rock fish= 5/8 (Number of sea stars)
Number of wolf eels - Number of rock fish = 40
Using the given information, we get,
Number of sea stars = 8/5 (Number of rock fish)
On simplification,
Number of wolf eels = 80
So, number of sea stars = (4/5)*80
= 64
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