The trigonometric functions for this angle are sin(0) = -â2/2, cos(0) = -â2/2, and tan(0) = -1. The measure of the reference angle is not 30° or 60°.
The measure of an angle is the amount of rotation from the starting position to the endpoint of the angle. In this problem, the measure of angle is 0 is 7π/4. This means that the angle has rotated 7π/4 radians from the start position, which is equivalent to 360° - (7π/4)*180/π = 315°.
Therefore, the measure of the reference angle is 45°, because the reference angle is the smallest angle that starts at the x-axis and terminates at the terminal side of the angle, which in this case is 315°. The reference angle is equal to the measure of the angle minus the multiple of 360°, so 45° = 315° - 360°.
The trigonometric functions of sine, cosine, and tangent can be used to evaluate the measure of an angle. The sine of an angle is equal to the ratio of the opposite side of the angle over the hypotenuse of the triangle formed by the angle. In this problem, sin(0) = opposite/hypotenuse = -â2/2, since the angle is 7π/4 radians, or 315°.
The cosine of an angle is equal to the ratio of the adjacent side of the angle over the hypotenuse of the triangle formed by the angle. In this problem, cos(0) = adjacent/hypotenuse = -â2/2, since the angle is 7π/4 radians, or 315°.
The tangent of an angle is equal to the ratio of the opposite side of the angle over the adjacent side of the angle. In this problem, tan(0) = opposite/adjacent = -1, since the angle is 7π/4 radians, or 315°.
In conclusion, the measure of angle is 0 is 7π/4, and the measure of the reference angle is 45°. The trigonometric functions for this angle are sin(0) = -â2/2, cos(0) = -â2/2, and tan(0) = -1. The measure of the reference angle is not 30° or 60°.
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Consider two boxes, one containing 3 blue and 2 red marbles, the other contains 3 blue and 5 red marbles. A box is selected at random (i.e. 50:50 chance of selecting either box), and a marble is drawn from it at random. Part a) What is the probability that the selected marble is blue? Do NOT round your answer. Create a variable pB that stores the value of this probability. That is, write your answer as
pb =
Probability of getting a marble is 0.3.
Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.
Two boxes Probability of selecting either of the box = 0.5
Box A contains: 3 blue and 2 red marbles. So, probability of selecting blue marbles,
let p(B1) = [3C1/5C1 ]= 0.6*0.5 = 0.3 (As Probability of selecting box 1 is 50:50 )
Box contains : 3 blue and 5 red marbles,
let p(B2) = [3C2/5C2] = 0.6*0.5 = 0.3 ( As the probability of selecting box 2 is also 50:50 )
So, the final probability of getting a blue ball is 0.3.
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Probability of getting a marble is 0.3.
Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.
Two boxes Probability of selecting either of the box = 0.5
Box A contains: 3 blue and 2 red marbles. So, probability of selecting blue marbles,
let p(B1) = [3C1/5C1 ]= 0.6*0.5 = 0.3 (As Probability of selecting box 1 is 50:50 )
Box contains : 3 blue and 5 red marbles,
let p(B2) = [3C2/5C2] = 0.6*0.5 = 0.3 ( As the probability of selecting box 2 is also 50:50 )
So, the final probability of getting a blue ball is 0.3.
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Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The correct statement for the given diagram are-
m∠5+m∠6=180°m∠2+m∠3=m∠6m∠2+m∠3+m∠5=180°Define the term supplementary angles?Two angles are said to be supplementary if their sums total 180 degrees.
case A: m∠5+m∠3=m∠4 ...eq A
From the definition of supplementary angles
m∠3+m∠4=180°
m∠4=180°-m∠3 ....eq B
Put eq B in eq A
m∠5+m∠3=180°-m∠3
m∠5+m∠3+m∠3=180°
The result is true for m∠2=m∠3
Thus,
The case is not always true.
case B: m∠3+m∠4+m∠5=180° ...eq A
From the definition of supplementary angles
m∠3+m∠4=180°
m∠4=180°-m∠3 ....eq B
Put eq B in eq A
m∠3+(180°-m∠3)+m∠5=180°
m∠5=0°
The case is not true.
case C: m∠5+m∠6=180°
From the definition of supplementary angles
m∠5 and +m∠6 = 180
The case is always true.
case D: m∠2+m∠3=m∠6 ...eq A
From the definition of supplementary angles
m∠5+m∠6 = 180°
m∠6=180°-m∠5 ....eq B
Put eq B in eq A
m∠2+m∠3=180°-m∠5
m∠2+m∠3+m∠5=180°
Sum of interior angles of triangle equals 180 degrees
Thus,
This option will always be true.
case E:
m∠2+m∠3+m∠5=180°
Sum of interior angles of triangle equals 180 degrees
Thus,
This option will always be true.
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The correct question is attached.
If I go to the store to buy 6 packages of sausages ( each package has 2 1/2 sausages ) and my dog eats 2 sausages every day in total
How many days until I need to go to the store for sausages again?
The number of days until I need to go to the store for sausages again is
7.5 days.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of packages = 6
Number of sausages in each package = 2(1/2)
Total sausages.
= 6 x 2(1/2)
= 6 x 5/2
= 3 x 5
= 15
Number of sausages the dog eats each day = 2
The number of days the sausages will be used.
= 15/2
= 7.5
Thus,
The number of days is 7.5 days.
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Which one is correct?
A
B
C
D
Answer: C
Step-by-step explanation: TYSM if you give me a brainly... ps love you
Answer:
B.
A trapezoid looks like the following in the image, and B is the same but flipped.
Step-by-step explanation:
Hope it helps! =D
consider a circle of radius 2 centered at the origin. find parameterizations of this curve under the following assumption. clearly state any restriction on the variable of parametrization
As per the given radius, the parameterizations of this curve is 4
The term curve in math is defined as an abstract term used to describe the path of a continuously moving point
Here we have given that consider a circle of radius 2 centered at the origin.
And we have to find the parameterizations of this curve under the following assumption.
Here we have know that we need to find a parameterization for the circle of radius 2 in the xy-plane that one is centered at the origin at the direction of clockwise.
=> x(t) = 2cos(t) ------------------(1)
and
=> y(t) = −2sin(t) -----------------(2)
Here we have to note that the given expression is written as,
=> x²(t) + y²(t)
When we apply the values on it then we get
=4cos²t + 4sin²t
Then it can be written as,
=> 4(cos²t + sin²t)
=> 4
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Two restaurants offer customers large pizzas using different measurements for diameter. Restaurant 1: One large 14-inch pizza for $12.99 Restaurant 2: One large 36.83-centimeter pizza for $12.99 If 1 inch = 2.54 centimeters, what is the length of the crust around the larger pizza, using π = 3.14?
A. 115.65 inches
B. 22.77 inches
C. 43.96 inches
D. 45.53 inches
Answer:
D. 45.53 inches
Step-by-step explanation:
Restaurant 1: diameter = 14 inches
Restaurant 2: diameter = 36.83 inches × (1 inch)/(2.54 cm) = 14.5 inches
The larger pizza is from Restaurant 2, and its diameter is 14.5 inches.
circumference = πd = 3.14 × 14.5 inches = 45.53 inches
Answer: D. 45.53 inches
Answer:it is d 45.53
Step-by-step explanation:becuase I did the test
#17 please help!! I dont know what to do
The distance across the pond is 52 feet.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
In the given diagram, there are two triangles.
If we prove the two triangles are congruent, we will get the distance across the pond as 52 feet.
Already 2 sides of one triangle is given as equal to 2 sides of the other triangle, which are 41 ft and 29 ft.
Also since the lines are intersecting the included angles of the equal sides of both triangle are equal by vertical angle theorem.
So two sides and an included angle of a triangle is equal to corresponding two sides and an included angle of other triangle.
So the triangles are congruent by SAS theorem.
So all the sides of two triangles are equal.
Distance across the pond is 52 feet.
Hence we get the distance across the pond is 52 feet.
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compute the products in exercises 1\[dash]4 using (a) the definition, as in example 1, and (b) the row\[dash]vector rule for computing a x. if a product is undefined, explain why.
1) product is not defined.
2) product is undefined.
3) [ -9 ]
[ 5 ]
[ -11 ]
Explanation:
1) product is not defined.
because no of column of 1st matrix (2) is not same as no of row of second matrix.(3)
2) product is undefined.
because no of column of 1st matrix (1) not same as no of row of second matrix (2).
3) [ 6 5 ] [ 6 -15 ] [ 9 ]
[ -4 -3 ] X [ 1 ] = [ -4 +9 ] = [ 5 ]
[ 7 6 ] [ -3 ] [ 7 -18 ] [ -11 ]
A matrix is a rectangular array of numbers (or other mathematical objects) that defines operations like addition and multiplication. A matrix over a field F is typically a rectangular array of scalars, each of which is a member of F.
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define the least common multiple of a and b to be the smallest positive number which is divisible by both a and b. prove that the least common multiple of a and b is ab precisely when a and b are coprime 6
The least common multiple(LCM) of two coprime numbers is their product, ab.
Let a and b be two positive integers, and let LCM(a,b) be the least common multiple of a and b.
By definition, LCM(a,b) is the smallest positive number which is divisible by both a and b.
Now, suppose that a and b are coprime, meaning that there are no positive integers other than 1 that divide both a and b.
Since 1 divides both a and b, and 1 is the smallest positive integer, we know that 1 is the only positive integer that divides both a and b.
Therefore, LCM(a,b) must be divisible by both a and b, and 1 is the only positive integer that divides both a and b.
Thus, LCM(a,b) = ab.
This proves that the least common multiple of a and b is ab precisely when a and b are coprime.
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When Mai walks from her new apartment to school and then back home again, her path creates a rectangle. The rectangle measures `400` m in length and `200` m in width. Mai wants to create a scale drawing of this rectangle. Using a scale of `1` cm to `40` m, what would be the length of the rectangle on the scale drawing?
Answer:
10 cm
Step-by-step explanation:
Original measures: 400 m and 200 m
Scale: 1 cm = 40 m
Use proportions.
Length:
1 cm / 40 m = x / 400 m
40 m × x = 400 m × 1 cm
40x = 400 cm
x = 10 cm
length = 10 cm
Answer: 10 cm
Coding languages communicate information that is key to which of the following aspect(s) of the health care system?
code, in communications, a dull rule for replacing a piece of information such as a letter, word, or phrase with a casually selected equivalent.
The term has been frequently exploiting and used as a synonym for cipher, which is a method for transforming a message according to a rule to cover its meaning.
In the past this hazy of the distinction between code and cipher was rather inconsequential; in fact, many historical aught would be more properly classified as codes according to present-day criteria.
In modern communications systems, information is frequently both encoded and encrypted (or enciphered), and so an understanding of the variation between the two is important.
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the liquid-filled prism is placed in a large tank containing a different liquid and sinks to the bottom of the tank. fx is the magnitude of the buoyant force exerted on the prism by the liquid in the tank when the prism is in orientation x . fy and fz are the buoyant forces for orientations y and z . which of the following correctly ranks the three buoyant forces?
The buoyant force is the upward force on an object submerged in a fluid that is caused by the fluid's pressure.
The magnitude of the buoyant force is equal to the weight of the displaced fluid. Therefore, the correct ranking of the three buoyant forces is fx > fy > fz.
The magnitude of the buoyant force can be calculated using the equation Fb = ρgV, where ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of the displaced fluid. For orientation x, the buoyant force fx will be the greatest since the volume of the displaced fluid is the greatest. For orientation y, the buoyant force fy will be the second greatest since the volume of the displaced fluid is second greatest. Finally, for orientation z, the buoyant force fz will be the least since the volume of the displaced fluid is the least.
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Consider the weighted voting system [13: 14, 6, 4, 2]
Are dummies
The number of sequential coalitions is 13!
How to determine the number of sequential coalitions?From the question, we have the following parameters that can be used in our computation:
System = [13: 14, 6, 4, 2]
This means that
n = 13
The number of sequential coalitiions is calculated as
Coalition = n!
substitute the known values in the above equation, so, we have the following representation
Coalition = 13!
Hence, the coalition is 13!
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Complete question
Consider the weighted voting system [13: 14, 6, 4, 2]
How many sequential coalitions are there?
Write the following set as an interval using interval notations. (x|-7
The set |x| < 7 using interval notation is given as follows:
0. < x < 7.
How to obtain the absolute value of a number?The absolute value of a number gives the distance of a number from the origin, hence it basically can be interpreted as the number without the signal.
The expression for this problem is defined as follows:
|x| < 7.
Then the bounds of the open interval are given as follows:
|-7| = 7.|7| = 7.The lowest absolute value is given as follows:
0.
Hence the interval is given as follows:
0 < x < 7.
Missing InformationThe problem asks for the interval notation of:
|x| < 7.
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Which set of bowling scores has a median of 149 and a range of 21?
median set:130,140,149,150,159.Range set:10,20,149,159.
Step-by-step explanation:
Median:the value of a set that is arranged from lowest to highest and find the number that is right in between.If there are two numbers in the middle,add them and divide➗by two.Range:the difference between the highest and lowest number in a set.For example,the range for the set 10 20,38 and 50 , the highest and lowest numbers are 50 and 10 so we subtract 50-10 (the highest and lowest numbers) and get 40 as our range.
- Deondra has $32. She buys 4 movie
tickets for $6.25 each. How much money
does she have left to spend on popcorn?
Answer:
Okay so Deondra has a total of $32, and if she buys 4 tickets, and if each costs 6.25, then, you will multiply the amount in which each ticket costs by how many tickets total, and then subtract that quotient by the total amount of money Deondra has.
6.25 times 4 = 25
32 - 25 = 7
She has $7 left to spend on popcorn!
Step-by-step explanation:
Hope it helps! =D
Jim is thinking of buying solar panels. The price of these panels haas decreased by 27% since 2016. Jim would need to pay £4803.40 for the panels now. How much would the panels have cost in 2016? 3 marks.
Answer:
let the price in 2016= Y
Then the price since 2016 ( since the price decreased since 2016)= (1- 27/200)Y= 0.73Y
2016 since 2016
Y 0.73Y
Y now: 4803.40
0.73Y= 4803.40
Y= 4803.40/0.73
= 6580
the cost of the panel in 2016 is 6580
A carnival worker has 380 stuffed animals she buys 6 more boxes with 5 stuffed animals in each box how many stuffed animals does she have now
Jake was golfing and had an incredible day. His scores were "-12,3,-5,2,0" and "-8." What is the sum of his scores?
The sum of his scores is -10
What is sum?A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.
For example, If the value of ages of class is given as 5, 6,7,8,5,6. The sum of of their of ages will be 5+6+7+8+5+6 = 37
The score of jake are -12, 3 ,5 , 2 ,0 and -8. The sum of his scores = -12 + 3 + 5 + 2 + 0 + -8
collecting like terms
-12 + -8 + 3 + 5 + 2 + 0
= -10
Therefore the sum of Jake's score is -10
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a crane is oriented so that the end of the 25-m boom ao lies in the yz plane. at the instant shown, the tension in cable ab is 4.8 kn. determine the moment about each of the coordinate axes of the force exerted on a by cable ab.
Applying Pythagoras theorem, and drawing free body diagram we can measure the moments required.
First of all draw the free body diagram.
Now, in triangle AOC, apply Pythagoras theorem,
Now, write the coordinates of the points,
O (0, 0, 0) m
A (0, 15, 20) m
C (0, 0, 20) m
B (2.5, 0, 20) m
Now, write the position vector from A to B,
Now, write the unit vector rAB
Now, write the tensional force on the point A due to the cable AB,
Now, calculate the force ‘T’ about the origin,
Hence the moments about the coordinate axes are,
Mx = 78.9 kN.m
Mx = 13.15 kN.m
Mx = -9.86 kN.m
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En la frutería “Todo barato”, 2 kg de tomates cuesta $ 38.00. ¿Cuánto debe de pagar Karla si compra 9 kg de tomates
Answer: hi
Step-by-step explanation: hi
s for each matrix below, apply the given row operation(s) to the matrix in order, and give the resulting matrix.
The resulting matrix by applying the given row operations −2R2+3R1 →R1 is given by [tex]\left[\begin{array}{ccc}-25&5&-6\\8&5&6\end{array}\right][/tex] .
Matrix A is equal to :
A = [tex]\left[\begin{array}{ccc}-3&5&2\\8&5&6\end{array}\right][/tex]
Now replace the row R1 by applying the row operations -2R2 + 3R1 on the given matrix we get ,
First element of row 1 is replaced by :
-2(8) + 3(-3)
= -16 -9
= -25
Second element of row 1 is replaced by :
-2(5) + 3(5)
= -10 + 15
= 5
Third element of row1 is replaced by :
-2(6) + 3(2)
= -12 + 6
= 6
Therefore, the resulting matrix after applying the row operation is given by : [tex]\left[\begin{array}{ccc}-25&5&-6\\8&5&6\end{array}\right][/tex] .
The above question is incomplete , the complete question is :
Consider matrix A.
What matrix results apply the given row operation(s) R1 to the matrix in order, and give the resulting matrix represented by −2R2+3R1?
A = [tex]\left[\begin{array}{ccc}-3&5&2\\8&5&6\end{array}\right][/tex]
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NO LINKS!!
Write a function given the conditions noted below.
Answer:
[tex]\textsf{36)} \quad f(x)=\dfrac{7x}{x-12}[/tex]
[tex]\textsf{37)} \quad g(x)=\dfrac{1}{x+2}[/tex]
[tex]\textsf{38)} \quad h(x)=\dfrac{x-2}{(x-2)(x+3)}[/tex]
Step-by-step explanation:
Vertical AsymptotesEquation: x = aA vertical asymptote occurs at the x-value(s) that make the denominator of a rational function zero.Horizontal AsymptotesEquation: y = bIf the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote (but there is a slant asymptote).If the degree of the numerator is equal to the degree of the denominator, the asymptote is the result of dividing the highest degree term of the numerator by the highest degree term of the denominator.Question 36Given that the function has a horizontal asymptote at y = 7, the degree of the numerator must be equal to the degree of the denominator.
Also, 7 will be the result of dividing the highest degree term of the numerator by the highest degree term of the denominator.
Given that the function has a vertical asymptote at x = 12, the denominator must equal zero when x = 12.
Therefore, a rational function that meets these conditions is:
[tex]f(x)=\dfrac{7x}{x-12}[/tex]
Question 37Given limits:
[tex]\displaystyle \lim_{x \to\infty} k(x)=0[/tex]
[tex]\displaystyle \lim_{x \to-2^+} k(x)=\infty[/tex]
The first limit means that as x approaches positive infinity, the function equals zero. Therefore, the rational function has a horizontal asymptote at y = 0. So the degree of the numerator should be less than the degree of the denominator.
The second limit means that as x approaches -2 from the positive side, the function equals positive infinity. Therefore, the rational function has a vertical asymptote at x = -2.
Therefore, a rational function that meets these conditions is:
[tex]g(x)=\dfrac{1}{x+2}[/tex]
Question 38A removable discontinuity (hole) exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal.
Therefore, a rational function that meets these conditions is:
[tex]h(x)=\dfrac{x-2}{(x-2)(x+3)}[/tex]
For this rational function the hole is at (2, ¹/₅), as when x = 2, the numerator and denominator are both zero.
The functions can be represented as y = 7x/(x - 7), y = 1/(x + 2) and y = (x - 3)/[(x - 3)(x + 1)]
How to determine the functionsConditions #1
From the question, we have the following parameters that can be used in our computation:
Vertical asymptote, x = 12
Horizontal asymptote, y = 7
A function with the following features
Vertical asymptote, x = a
Horizontal asymptote, y = b
Can be represented as
y = bx/x - a
So, we have
y = 7x/(x - 12)
Conditions #2
Here, we have the following limits
lim x⇒∝ k(x) = 0 and lim x⇒2⁺ k(x) = ∝
This means that:
Vertical asymptote, x = -2
Using the rule in (1), we have
y = 1/(x + 2)
Condition #3
Here, we have
Function with a hole
This implies that the denominator and the numerator have a common factor
An instance of this is
y = (x - 3)/[(x - 3)(x + 1)]
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Here is a number line from 0 to 1
0--------0.2A
a) Write a fraction with a denominator of 10 that could go after B on the number line. b) Write a fraction with a denominator of 100 that could go before A on the number line. c) Write three fractions that could be in between A and B on the number line. 0 Compare answers with a partner.
Answer:
0.1 ,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9, 1
(a) show that f is one-to-one. (b) use theorem 7 to find s (f ^-1) d9sad. (c) calculate f 21 sxd and state the domain and range of f 21 . (d) calculate s f 21 d9sad from the formula in part (c) and check that it agrees with the result of part (b). (e) sketch the graphs of f and f 21 on the same axes.
The function f(x) = 9 - x² is a one to one function and the value of f⁻¹(x) = √9 - x.
The graph of the function is attached below.
In math the term graph is defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Here we have the function f(x) = 9 - x² and here we also know that on the interval 0≤x≤3 and a=8.
Now, we have to check the given function is one to one or not, for that we have to plot the function on the graph then we get the graph like the following.
While we looking into the graph we have identified that each input value has exactly only one output, therefore it is said to be one to one function.
And the inverse of the function is calculated by rewritten the function as,
=> f⁻¹(x) = √9 - x.
And the graph of f⁻¹(x) is plotted as follows,
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3x + 2y=4 3x + 6x=-28
The solution to the equations is x = 20/3 and y = -8
How to determine the solution to the equation?From the question, we have the following parameters that can be used in our computation:
3x + 2y=4
3x + 6y=-28
The above equations is a system of linear equations
So, we can subtract them to eliminate x as follows
4y = -32
Divide both sides by 4
y = -8
Substitute y = -8 in the equation 3x + 2y=4
3x - 16 =4
Evaluate the like terms
3x = 20
So we have
x = 20/3
Hence, the soluton is x = 20/3 and y = -8
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A scientist records the temperature of three different mixtures as -33.625℉, -33 5/6℉, and -33 6/25℉. What is the order from least to greatest temperature of the mixtures?
Answer: To determine the order of the temperature of the mixtures from least to greatest, we need to compare the values of the temperatures in their simplified fractional forms.
-33.625℉ = -33 5/8℉
-33 5/6℉ = -33 5/6℉
-33 6/25℉ = -33 24/100℉
We can compare the fractions by comparing the numerators, if they are the same we can compare the denominators.
So, the order from least to greatest temperature of the mixtures is:
-33 6/25℉ < -33 5/6℉ < -33 5/8℉
It's important to notice that these temperatures are negative.
Step-by-step explanation:
Give two reasons. why this shape is a square when x = 6
The two reasons why the shape is a square when x = 6 are:
i. It's length of sides are equal.
ii. The measure of it's internal angles are right angle.
Properties of a square.A figure that is bounded by four straight sides on a 2 dimensional plane can be categorize as a quadrilateral. Examples are; rectangle, trapezium, rhombus, square etc.
A square is a shape which has an equal length of sides, and other distinguishing properties.
Considering the given question, when x = 6;
a. (3x - 7) = 3(6) - 7
= 18 - 7
= 11
b. (x + 5) = 6 + 5
= 11
Therefore its sides are congruent.
Thus, the two reasons why the shape is a square are:
i. It has equal length of sides.
ii. It can be observed that each angle of the figure is a right angle.
So that the figure is a square.
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Draw the graph of y=f(x) and y= 1/f(x) on the same axes.
f) f(x) = -(x+4)²+1
are there any specific steps to get the answers here?
Answer: To graph y = f(x) and y = 1/f(x) on the same axes, you can follow these steps:
First, graph y = f(x) by plotting a few points, such as (-5, -19), (-3, -1), (0, 1) and (5, 19), and then connecting them with a smooth curve.
Then, graph y = 1/f(x) by finding the inverse function of f(x) which will be
1/f(x) = -1/(x+4)²+1
Next, plot a few points on this new function, such as (-5, -1/19), (-3, -1), (0, 1) and (5, 1/19), and then connecting them with a smooth curve.
Finally, make sure that the same x and y scales are used for both graphs, and label the axes and the functions clearly.
It is important to note that as f(x) = -(x+4)²+1, the domain of f(x) is all real numbers but the range is (1, infinity) so the reciprocal will be defined only for the range of f(x) and the domain of 1/f(x) will be (1, infinity)
Also, the graph of y = f(x) will be a parabola opening upwards and y = 1/f(x) will be a parabola opening downwards, both with vertex (-4,1)
The graph of y = -(x+4)²+1 will be a parabola opening upwards and the graph of y = -1/(x+4)²+1 will be a parabola opening downwards.
Step-by-step explanation:
All the questions answered
The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 = (x+7)(x+7)
What is Quadratic equation?Any equation using the formula ax² + bx + c = 0 is a quadratic equation.
where a, b and c are constants, and x is an unknown variable.
It is called "quadratic" because the variable is squared (in other words, raised to the power of 2).
The most common way to solve a quadratic equation is to factor it into two linear equations, which can then be solved using the methods of linear algebra.
Another way is to use the quadratic formula, which expresses the roots of the equation in terms of the coefficients a, b and c.
It is called a quadratic equation because it can be written in the form
ax² + bx + c = 0
which is the standard form for a quadratic equation.
Examples:
1) x² + 4x – 5 = 0
2) 4x² – 7x + 3 = 0
3) 2x² + 3x – 4 = 0
Therefore , The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 = (x+7)(x+7)
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