Answers
The absolute functions when matched to the respective vertex is as follows;
(-1, -3/7) → f(x) = (1/2)|x + 1| - (3/7)
(5, 2/3) → f(x) = (-3/5)|x - 5| + (2/3)
(0, -4/5) → f(x) = (1/2)|x| - (4/5)
(2/5, 5/3) → f(x) = (-3/2)|x - (2/5)| + (5/3)
What is the absolute value function of the Vertices?
We can solve all of them by writing the equations in a general form;
f(x) = a|x + b| + c
This is a function transformation of f(x) = |x|
where:
a = Factor of vertical stretch
b = Horizontal shift (- shifts right, + shifts left)
c = Vertical shift (+ shifts right, - shifts left)
The original function has its vertex in (0, 0) so the horizontal shift will be the new x coordinate in the new vertex and the vertical shift will be the new y in the new vertex like this:
f(x) = (1/2)|x + 1| - (3/7)
b = 1 horizontal shift of -1
c = -3/7 vertical shift of -3/7
Thus, (-1, -3/7)
f(x) = (-3/5)|x - 5| + (2/3)
b = -5 horizontal shift of 5
c = 2/3 vertical shift of 2/3
Thus, (5, 2/3)
f(x) = (1/2)|x| - (4/5)
b = 0 horizontal shift of 0
c = -4/5 vertical shift of -4/5
Thus, (0, -4/5)
f(x) = (-3/2)|x - (2/5)| + (5/3)
b = -2/5 horizontal shift of 2/5
c = 5/3 vertical shift of 5/3
Thus, (2/5, 5/3)
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Related Questions
What does it mean to have a slope of “0”. Provide an equation as an example
Answers
When a line has a slope of 0, it means that the line is a horizontal line that is parallel to the x-axis. An equation that shows this is y = 0x + 2.
What is the meaning of a slope of 0?The slope of a line shows the change in the line and how it is shaped on the graph. If the slope of a line is 0, what it means is that the line has not slanting shape and is instead simply straight on the horizontal axis.
As a result of the line being a straight horizontal line, it will be parallel to the x-axis which is also a horizontal line.
Take the equation:
y = 0x + 2
y = 2
Y will be a horizontal line on y=2.
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…Ajavsbyhsbwdujdnwiowbeuhsbwb
Answers
Answer:
alphabet
Step-by-step explanation:
Name three collinear point in plane E.
Name the intersection of plane & and
line EN.
Name the intersection of plane and
line EN.
Name the intersection of line BW and
line EN
Name three planes.
Name a point that is coplanar with
M and F
Name the intersection of plane and
plane FDM.
Name the intersection of plane MKJ and
plane FDJ.
Answers
For purposes of description, lines, planes, and points are crucial in geometry. The correct answer is as follows:
A. 9 points (Points - M, N, O, P, Q, R, S, T, U)
B. 3 lines (Lines - MO, PQ, RS)
C. 2 planes (Planes - K and L)
D. (P, N, Q) , (M, N, O), (R, N, S)
E. (M, P, S, T)
F. M, O
G. N
H. S
I. Horizontal plane
J. Line D
What is meant by Collinearity?Collinearity in geometry is the quality of a set of points being on a single line. Collinear points are a group of points that share this characteristic. The phrase has been used more broadly to refer to aligned objects, i.e., things that are "in a line" or "in a row."
The subject of geometry involves points, planes, and lines. A plane is a flat surface that can be either horizontal or vertical, whereas a line is a straight path that links two locations.
Understanding the offered figure and interpreting each question in light of the terminologies in it are necessary in order to answer the questions. As an illustration, collinear points are those that can be joined by a straight line, but non-collinear points cannot be connected by a straight line.
The correct answers is as follows:
A. 9 points (Points - M, N, O, P, Q, R, S, T, U)
B. 3 lines (Lines - MO, PQ, RS)
C. 2 planes (Planes - K and L)
D. (P, N, Q) , (M, N, O), (R, N, S)
E. (M, P, S, T)
F. M, O
G. N
H. S
I. Horizontal plane
J. Line D
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Answer:
Step-by-step explanation:
A. 9 points (Points - M, N, O, P, Q, R, S, T, U)B. 3 lines (Lines - MO, PQ, RS)C. 2 planes (Planes - K and L)D. (P, N, Q) , (M, N, O), (R, N, S)E. (M, P, S, T)F. M, OG. NH. SI. Horizontal planeJ. Line D
profit is defined as earnings less expenses (earnings - expenses). At the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each. They also paid $50 to the festival's organizers for a vendor permit. Use the expression m=2p - 0.75p - 50 to answer the following questions.
Answers
The amount that will be made by the local festival given the expression m=2p - 0.75p - 50 is 225.
How to calculate the profit?From the information, at the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each.
The expression given was illustrated as:
m=2p - 0.75p - 50
Therefore since we are given the value of p as 220. This will be:
m=2p - 0.75p - 50
m = 2(220) - 0.75(220) - 50
m = 440 - 165 - 50
m = 440 - 215
m = 225
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At the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each. They also paid $50 to the festival's organizers for a vendor permit. Use the expression m=2p - 0.75p - 50 to answer the following questions.
Find the profit when the number of the ice cream pops represented by p is 220.
How do you do multiplication? Give complete reasons and complete answers please.
Answers
Answer:
Step-by-step explanation:
Multiply like this
2 x 2
How to do this
Just double 2
Answer:
multiplication is like doing repeated addition so let’s try doing 5x5
In repeated addition form it would be 5+5+5+5+5 which equals 25
I don’t know how to really explain it but I hope this helps!
Step-by-step explanation:
fill in the blanks with perfect squares to approximate the square root of 112.
A. 121
B. 81
C. 100
D. 64
Answers
Answer:
[tex]100 < 112 < 121[/tex]
[tex] \sqrt{100} < \sqrt{112} < \sqrt{121} [/tex]
[tex]10 < \sqrt{112} < 11[/tex]
A and C are the desired numbers.
Can someone help me?
Answers
The midpoint of the fourth class interval is 0.51
The range of the fourth class is 0.48-0.54
So, to find the middle point of the class we use the following formula:
The average of the top and lower values of a specific class interval is referred to as the class midpoint (also known as the class mark). The class midpoint substitutes a range of values with a single value in a frequency distribution table. We can create a line graph for our data using the frequency and the class midpoint.
Midpoint = Upper limit+Lower limit/2
Upper limit = 0.54
Lower limit = 0.48
Substituting the values in the formula we get:
Midpoint = (0.54+0.48)/2
= 0.51
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Do exactly what it says and make sure u make the table of values
Answers
olution
2a.
The graph of as described is given below (showing at least five points)
The (clear) graph that has the dashed line of asymptotes
The table will be
Bb.
o write the equation
We start from
[tex]f(x)=2^x[/tex]Translate the graph up by 3 units
[tex]f(x)=2^x+3[/tex]Translate the graph 4 units to the left
[tex]f(x)=2^{x+4}+3[/tex]2c.
o get the equation of asymptotes
[tex]\begin{gathered} \lim _{x\to-\infty}f(x)=\lim _{x\to-\infty}(2^{x+4}+3)=0+3=3 \\ \text{The equation of asymptotes} \\ y=3 \end{gathered}[/tex]Sidney has $85,450 in a savings account. The interest rate is 12% per year and is not
compounded. How much will she have in total in 1 year?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r
is the interest rate expressed as a decimal, and t is the time in years.
Answers
The amount that Sidney will have in her account in 1 year is $ 95,704.
Given that:-
Principal amount = $85,450
Interest Rate = 12 % per annum
i = prt
Where,
i represents interest,
p represents the principal,
r represents the interest rate, and
t represents the time (in years)
Hence, putting the values in the formula of simple interest, we get,
i = 85450*(12/100)*1 = $ 10,254
Hence, the amount that Sidney will have in her account in 1 year is
85450 + 10254 = $ 95,704
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Several members of a running club would like to survey the rest of the members to determine which 5K races the club should enter. They decide to use a random number table to sample 10 of the 78 members. The members are assigned the numbers 01–78. Refer to the given line from a random number table. Which numbers represent the first 5 members selected?
24000 75983 62200 91518 11198 88936
(A)24, 07, 59, 62, 20
(B)24, 00, 07, 59, 83
(C)24, 75, 36, 22, 51
(D)24, 75, 98, 36, 22
Answers
The numbers that represent the first 5 members selected is A. 24, 07, 59, 62, 20.
How to illustrate the information?From the information, the members of a running club would like to survey the rest of the members to determine which 5K races the club should enter.
In this case, they decide to use a random number table to sample 10 of the 78 members. The numbers illustrated are 24000 75983 62200 91518 11198 88936.
Therefore, the appropriate numbers chosen will be (24) 000 (7) (59) 83 (62)(20)0.
The correct option is A.
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Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form. 3, 4+i
(Please answer soon as possible thank you)
Answers
By algebra properties, the standard form with rational coefficients is the polynomial x³ - 11 · x² + 7 · x + 51, whose lead coefficient is 1 and comprise the roots 3 and 4 + i.
How to determine a polynomial of least degree
A polynomials of least degrees includes all the roots and the given lead coefficient, which can used in the following formula:
p = a · Π (x - rₐ)
Where:
a - Lead coefficientrₐ - a-th root of the polynomial.If we know polynomial has rational coefficients, then the complex root 4 + i has a "twin" equal to 4 - i in accordance with the quadratic formula, otherwise the polynomial will have at least an irrational coefficient. Then, the least degree polynomial is introduced below:
p = 1 · (x - 3) · (x - 4 - i) · (x - 4 + i)
Then, we expand the expression by algebra properties:
p = (x - 3) · [x² - 8 · x - (16 - i²)]
p = (x - 3) · (x² - 8 · x - 17)
p = x³ - 8 · x² - 17 · x - 3 · x² + 24 · x + 51
p = x³ - 11 · x² + 7 · x + 51
The standard form is the polynomial p = x³ - 11 · x² + 7 · x + 51.
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find the equation of the line shown
Answers
Answer: The equation is (y=x+6)
Step-by-step explanation:
Lets assume the equation to be y=mx+c,
where,
m=slope of the line
c=constant
Since we know that,
slope=m=tanx
where x is the angle between x-axis and line
tanx=
[tex]tanx= \frac{perpendicular}{base}[/tex]
so here it will be,
[tex]tanx=\frac{10-6}{4-0} \\= > tanx=1\\= > m=1[/tex]
Also, c=6 as we can clearly see from the graph
Therefore the equation of line is => y= x +6
Use a graph of a polynomial G(x) to determine its zeros and the multiplicity of each zero. List the zeros from smallest to largest.
Answers
Zeros of a Polynomial
When a polynomial has a zero at x = a, then its graph 'touches' or 'crosses' the x-axis. If the zero has an even multiplicity (2, 4, 6, etc.), the graph 'bounces' off the x-axis.
We can see the graph crosses the x-axis 4 times and no bouncing occurs, so each zero has a multiplicity of 1.
From left to right, the zeros are:
x = -4 with a multiplicity of 1.
x = -2 with a multiplicity of 1.
x = 1 with a multiplicity of 1.
x = 3 with a multiplicity of 1.
For the function f(x)=x2−8x+11, find x when f(x)=−4.(Use a comma to separate multiple solutions.)
Answers
Given function:
[tex]f(x)=x^2-8x+11[/tex]Finding x when f(x) = -4
[tex]x^2-8x+11=-4[/tex][tex]\begin{gathered} x^2-8x+15=0 \\ x^2-5x-3x+15=0 \end{gathered}[/tex][tex]\begin{gathered} x(x-5)-3(x-5)=0 \\ (x-3)(x-5)=0 \\ x=3,5 \end{gathered}[/tex]Thus, the value of x is 3 and 5.
The graph of the derivative of a function, f, is shown. Use the graph to determine the interval on which f is increasing.
A. (-∞, 2)
B. (2, ∞)
C. (-∞, ∞)
D. (-1, ∞)
E. (-∞, 1)
Answers
Answer:
B) [tex](2,\infty)[/tex]
Step-by-step explanation:
Since we are given the graph of [tex]f'(x)[/tex], this gives us the value of the derivative, or the rate of change, of [tex]f(x)[/tex] given an x-value. For [tex]f(x)[/tex] to be increasing, then [tex]f'(x) > 0[/tex], which is a positive rate of change. As you may have noticed, when [tex]x > 2[/tex], the value of [tex]f'(x)[/tex] is positive. This means that f increases on the interval [tex](2,\infty)[/tex], or answer B.
Matthew drew a scale drawing of a summer camp. The sand volleyball court, which is 18 meters long in real life, is 27 millimeters long in the drawing. What is the scale of the drawing?
Answers
Answer:
3 millimeters : 2 meters
There ya go, happy to help! :)
Answer:
The scale of the drawing is 3 millimeters : 2 meters.
Step-by-step explanation:
lessons cost $3 for members and $5 for non-members if twice as many members as non-members takes lessons and the total fees collected are $132 how many non-members take lessons?
Answers
The number of non-members is 12 and the number of members is 24.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let x be the number of members, and the number of non-members.
3x + 5y = 132
x = 2y
After solving the above two linear equations:
6y + 5y = 132
11y = 132
y = 132/11
y = 12 non-members
x = 24 members
Thus, the number of non-members is 12 and the number of members is 24.
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Plot function h on the graph.
H(x) = {-4, x<-3
x>-3
x+5,
Answers
Given the function is plotted on the graph and attached below.
You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.
To: Determine whether a graph reflects a function using the vertical line test. Check the graph to check if any vertical lines that were generated would repeatedly cross the curve. If such a line exists, the graph does not depict a function.
Hence the required graph is created .
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The area of the triangle is 85m2. if the base of the triangle is 5m, what is the height of the triangle?
A = bh/2
Answers
Answer:
Height = 36m
Step-by-step explanation:
As per the given data: Area of the triangle = 85m2
Base of the triangle = 5m
Height of the triangle = ? (x)
As we know, A = bh/2
by substituting the given values in the above equation, we get
85 = 5 * x/2
5x = 170
x = 36
date : 09-10-2022
TRUE OR FALSE?
For two setsA and B, (A U B)' = A' n B'.
Answers
The statement that for two sets A and B, (A ∪ B)' = A' ∩ B' is true.
Let us check it with the help of an example.
Let A = {1,2,3,4,5,6} ,
B = {5,6,7,8,9,10} and ,
A universal set S = {1,2,3,4,....,15}
Now, we can write,
A ∪ B = {1,2,3,4,5,6,7,8,9,10}
LHS = (A ∪ B)' = {11,12,13,14,15}
A' = {7,8,9,10,11,12,13,14,15}
B' = {1,2,3,4,5,11,12,13,14,15}
RHS = A' ∩ B' = {7,8,9,10,11,12,13,14,15} ∩ {1,2,3,4,5,11,12,13,14,15} = {11,12,13,14,15}
As we can observe from above,
LHS = RHS
Hence, the statement that for two sets A and B, (A ∪ B)' = A' ∩ B' is true.
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Please help me I’m miserable because I was sick.It’s 2:00AM and this is due at 8 somebody please help me and x does not equal 12 and D isn’t 95?
Answers
Here are some tips that may help you feel better:
1. Rest: Get plenty of sleep and rest as much as possible to allow your body to recover.
2. Hydration: Drink lots of fluids to stay hydrated and help flush out any toxins in your body.
3. Nutrition: Eat healthy foods that are easy to digest, such as soups, broths, and fruits.
4. Medication: Take any prescribed medication as directed and follow the instructions on the label.
5. Warmth: Use warm blankets and a hot water bottle to soothe aches and pains.
6. Avoiding stress: Stay away from stress as much as possible since it can interfere with your immune system's functioning.
7. Humidifier: Use a humidifier to help ease congestion and dryness in the air.It's also essential to see a doctor if your symptoms persist or worsen. Don't hesitate to seek medical attention if necessary.
Furthermore, the information given in the question, "x does not equal 12 and D isn't 95," seems unrelated to the context of the problem. It's unclear what information the question is asking for, so please provide more details if you have any.
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A) There are two parallel lines and a line that goes through them in this diagram. The line that goes through them causes perpendicular lines to form.
What are perpendicular lines?
Perpendicular lines are lines that intersect and create 90° angles. The two angles in this diagram are 90° due to this intersection.
B) There are two types of angles: supplementary and complementary: complementary angles are angles whose measurements add up to 90°. Supplementary angles are angles whose measurements add up to 180°. As you can see in this problem, the two angles (7x+11 and -1+8x) are 90°. When added they would equal 180°. These angles are supplementary.
C) Now that you know what supplementary angles are, you can use its characteristics to solve for x:
Since the two angles added up equal 180, write an equation that represents this: (7x+11) + (-1+8x) = 180Now, combine like terms: 10 +15x= 180Subtract both sides by 10: 15x= 170Divide both sides by 15 and you have your answer: x= 11.33D) Now, solve for the two equations by plugging in x [you final answers should be 90]:
(7x+11) = 7(11.33) +11 = 90.31 ≈ 90(-1+8x) = -1 + 8(11.33) = 89.65 ≈ 90
The point at which a company's costs equal its revenues is the break-even point. C represents the cost, in dollars, of x
units of a product and R represents the revenue, in dollars, from the sale of x units. Find the number of units that must
be produced and sold in order to break even. That is, find the value of x for which C = R.
C = 13x +250 and R = 15.5x.
How many units must be produced and sold in order to break even?
4
Answers
The number of units that must be produced and sold in order to break even will be 100.
What is the break-even point?At the break-even point, the cost of the revenue is equal to the cost of the manufacturing.
The break-even point is the point at which a business's costs and revenues are equal. R stands for the revenue, in dollars, from the sale of x units, and C stands for the cost, in dollars, of x units of a product.
C = 13x + 250 and R = 15.5x
By the definition of the break-even point, then the equation is given as,
13x + 250 = 15.5x
15.5x - 13x = 250
2.5x = 250
x = 250 / 2.5
x = 100
The number of units that must be produced and sold in order to break even will be 100.
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the 4 winning numbers in a swimming club lottery were called out as follows the 1st number is the square root of 576 the 2nd number is a multiple of 8 between 30 and 39 the 3rd number is the cube of 3 the 4th number is the largest prime number less than 40 what we’re the 4 winning numbers?
Answers
The four winning numbers are 24, 32, 27 and 37 respectively
How to determine the numbersIt is important to note the following;
A prime number is a number than is divisible by 1 and itselfA square root is defined as the factor of a number which when multiplied by itself would give back the original numberThe cube of a number is that number to the exponent or power of 3A multiple is defined as the product of an integer, element or quantityFrom the information given;
a. First number = square root of 576
This is represented as
First number = √576
First number = 24
b. Second number = multiple of 8 between 30 and 39
Second number = 32
c. Third number = cube of 3
This is represented as;
Third number = 3³
Third number = 37
d. largest prime number less than 40
Fourth number = 37
Hence, the numbers are 24, 32, 27 and 37
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Help I don’t know how to solve these it’s about functions pls give me an answer with an explanation. f(x)=-x+2;Solve for x when f(x)=1
Answers
For the function f(x) = x + 2, the value of x when f(x) = 1, gives x = -1
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
Given that:
f(x) = x + 2
When f(x) = 1, substituting:
1 = x + 2
x = -1
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the digram shows a triangle
Answers
Answer:
30 cm²Step-by-step explanation:
Area of triangle = 1/2 (base × height)
1/2(12*5)=
1/2*60=
30 cm²
The angle of elevation of the top of a building from a point 80m away on level ground
is 25 0 . Calculate the height of the building to the nearest metre.
Answers
The height of the building to the nearest meter is 38 m.
In the question ,
it is given that
distance between the point and building is 80m
and the angle of elevation from the point to the top of the building is 25°
the figure formed from the data is shown below ,
where AB (h)is the height of the building .
So , From triangle ABC
tan25° = AB/BC
tan25° = h/80
simplifying further
we get ,
h = 80*tan25°
h = 80*(0.466)
h = 37.28
h ≈ 38
Therefore , The height of the building to the nearest meter is 38 m.
The given question is incomplete , the complete question is
The angle of elevation of the top of a building from a point 80m away on level ground is 25° . Calculate the height of the building to the nearest meter.
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in a residential neighborhood, the distribution of house valies is Unimodal and skewed to the right, with a median of $200,000 and an IQR of $100,000. for which of the following sample sizes is the sample median most likely to be above $250,000?A. n=10B. n=50C. n=100D. n=1000E. impossible to determine without more information
Answers
The smaller the sample size the greater the variability and higher the chance of getting an overestimate
From the given data
Median = $200,000
IQR = $100,000
The sample size for the median above to $250,000 is n =10
Because n=10 shows a sample with the fewest values, it is most likely that the sample median will be farther from the true median.
Answer : A) n = 10
any number to the zero power
Answers
Answer:
1
The answer is 1
The answer to this question is 1
Out of 250 racers who started the marathon, 217 completed the race, 24 gave up, and 9 were disqualified. What percentage did not complete the marathon? Round your answer to the nearest tenth of a percent.
Answers
Answer:
209 out of 230 completed that is 209/230 x 100% = 90.869 % the rest did NOT complete 100% - 90.8% = 9.13 %
Find the missing side length.Assume that all intersecting sides meet at right angles.Be sure to include the correct unit in your answer.4 yd8 yd14 yd12 yd?16 yd
Answers
For the given figure, all the intersecting sides meet at right angles
The lengths of the vertical sides are 14, 8, and ?
Let the missing side = x
So,
[tex]14=8+x[/tex]so,
[tex]x=14-8=6[/tex]so, the answer will be the length of the missing side = 6 yd