In Exercises 1-6, describe the transformation of f(x) = x² represented by g.
Then graph each function.
1. g(x) = x² - 2
G=
h=
M=
2. g(x) = (x - 5)²
3. g(x) = (x + 1)² + 3
Answers
The graph of the function after transformation is attached below.
The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system.
The coordinate transformation from polar to Cartesian coordinates is given by the formulas x = r cos and y = r sin, for example, if the polar axis is the positive x axis on the plane and the origins of the Cartesian coordinates (x, y) and polar coordinates (r) are the same.Every bijection from the space to itself can be related to two coordinate transformations.The formulas for the new coordinates of each point's image are constructed in a way that the old coordinates of the original point's image are maintained.In particular, the change of algebraic equations, it is a typical kind of algebraic problem.The graph of the transformed function is attached below. The red graph indicates the parent function f(x) = x² and the blue graph indicated the graph of transformation g(x) = x² - 2
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Related Questions
Graph this.
y=2/3x-4
Answers
Answer:
Step-by-step explanation:
Put the left dot on negative 4, and then put the right dot on positive 6.
Mang Efren is now 5 times as old as his son. Four years ago, the product of their ages was 52. Find Mang Efren's present age in years. (Just type in the numerical value of your answer)
Answers
Mang Efren's present age is 30 years.
Let's assume the present age of Mang Efren's son is x years.
Mang Efren is presently 5 times as old as his son.
So, Mang Efren's present age = 5x years
Four years ago,
Mang Efren's son's age = x - 4 years.
Mang Efren's age = 5x - 4 years
According to the question, four years ago, the product of their ages was 52.
From this information, we will create an equation.
(x - 4)(5x - 4) = 52
5x² - 4x - 20x + 16 = 52
5x² - 24x + 16 - 52 = 0
5x² - 24x - 36 = 0
Solving the quadratic equation to obtain the value of x,
5x² - 30x + 6x - 36 = 0
5x(x -6) + 6(x - 6) = 0
(5x - 6)(x - 6) = 0
x = 6
So, Mang Efren's present age is 5 × 6 = 30 years.
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Clay is flying a helicopter at an altitude of 400 feet in the air. Jason is diving 200 feet below the surface.
How far apart are Clay and Jason?
Explain how to show the distance between Clay and Jason using absolute value.
Answers
Clay and Jason are 600 feet far apart.
When an object goes above the surface, the altitude is measured as +ve and when an object goes below the surface, the altitude is measured as -ve.
Since Clay is flying a helicopter at an altitude of 400 feet in the air,
The Value of altitude of Clay = +400
Since, Jason is diving 200 feet below the surface,
The Value of altitude of Jason = -200
The the distance between Clay and Jason = (The Value of altitude of Clay) - (The Value of altitude of Jason)
= +400 - (-200)
= 400 + 200
= 600 feet
Therefore, the distance between Clay and Jason is 600 feet.
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Melissa rented a Segway, a stand up scooter, in downtown Austin, Tx. The store charges a $3.25 initial charge plus $2.50 per mile. Which equation can be used to find y, the total cost of the rental, if x represents the number of miles Melissa rode on the Segway?
pls it has to be like "y=mx+b"
Answers
Answer:
y = x(2.50)+3.25
Step-by-step explanation:
y (total cost )= x (miles rode) * 2.50 (cost per mile) + 3.25 (initial cost)
I honestly forgot about this lol please revive my brain
Answers
Given:
[tex]y=4x[/tex]To draw the graph:
Let us find the slope as the ratio.
Comparing the given equation with y=mx+c
So, the slope m=4.
In ratio,
[tex]\frac{\text{Change in y}}{\text{change in x}}=\frac{4}{1}\Rightarrow4\colon1[/tex]Let us take two points, (0,0) and (1,4).
So, the graph is,
(Laws of Exponents with Integer Exponents LC) Simplify (34)−1. one over three raised to the fourth power one over three raised to the power of negative four −34 33
Answers
The simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .
In the question ,
the expression is given as (3⁴)⁻¹ ,
the rule of law of exponents states that a⁻ⁿ = 1/aⁿ .
Using the above mentioned law of indices , the expression (3⁴)⁻¹ can be written as ,
(3⁴)⁻¹ = 3⁻⁴ = 1/3⁴
which can be expressed in words as one over three raised to the fourth power .
Therefore , the simplified value of (3⁴)⁻¹ is 1/(3⁴) , which means one over three raised to the fourth power , the correct option is (a) .
The given question is incomplete , the complete question is
The Simplified value of (3⁴)⁻¹ is
(a) one over three raised to the fourth power
(b) one over three raised to the power of negative four
(c) −3 to the power of 4
(d) 3 to the power of 3
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The Jules Server Scholarship Fund gives a graduation award of
$250.00 to a graduating senior at North End High School. Currently the
fund has a balance of $8300.00 in an account that pays 2.2% interest
compounded annually. Will the amount earned in annual interest be enough
to pay for the award?
Answers
The compound interest of $182.60 will not be enough to pay for the award.
What is compounding?Compounding is the process by which interest is added to both the principal balance already in place and the interest that has already been paid. Thus, compounding can be thought of as interest on interest, with the result that returns to interest are magnified over time, or the so-called "miracle of compounding." For instance, if you deposit $1,000 in an account that offers 1% yearly interest, after a year you would have received $10 in interest.So, annual interest will be sufficient to serve the award:
Compound interest of $83020.00 at the annual interest of 2.2% for 1 year will be $182.60.The total amount after 1 year will be $8482.60.(Refer to the compound chart given below)
Interest will be $182.6 and the graduation award is $250.00, so the interest will not be enough to pay for the award.Therefore, the compound interest of $182.60 will not be enough to pay for the award.
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Which of the following is equivalent to 2.76?
2.76%
27.6%
two and nineteen twenty fifths
twenty five over nineteen
Answers
The equivalent number to 2.76 is the mixed number 2 + 19/25.
Which of the following is equivalent to 2.76?
Here we need to see which option is equivalent to the given number, which is 2.76.
We can rewrite this as a mixed number.
2 + a/b
Such that:
a/b = 0.76
By looking at the options, we can see:
19/25 = 0.76
Then the correct option is:
2 + 19/25
So the third option is the correct one.
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12. Adam didn't sleep well the night before a big trip. He only slept 4 ½ hours. This is 3/5
of what he usually sleeps. How many hours does he usually sleep?
Answers
Answer:
seven and a half hours
Step-by-step explanation:
aa
what is the value of n?
Answers
Answer: Sorry for the late answer, I was already answering it by the time someone else answered
Step-by-step explanation:
Since two angles on a straight line add up to 180, I used the angles given to find the adjacent angles to it by subtracting those angles from 180. Then, since the angles of a triangle add up to 180, I used the angles I just solved for to find the angle that is adjacent to n. I did the same thing I did to the first two angles by subtracting it from 180 to find n, which was 69 degrees
|-4/3x-5|>19
Solve with work please. ;)
Answers
The inequality expression given as |-4/3x - 5| > 19 has a solution of 10.5 < x < -18
How to solve the inequality?From the question, the inequality is given as
|-4/3x-5|>19
Rewrite properly as
|-4/3x - 5| > 19
Remove the absolute bracket
So, we have the following representation
-19 > -4/3x - 5 > 19
Add 5 to all sides of the inequality
So, we have
-14 > -4/3x > 24
Multiply through by -3/4
So, we have
10.5 < x < -18
Hence, the solution to the expression is 10.5 < x < -18
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Evaluate the expression for x=-1,0, 1, 2
-3x + 4
X=0
X=-1
x = 1
X=2
Answers
Answer:
-3(-1) + 4 = 3 + 4 = 7
-3(0) + 4 = 0 + 4 = 4
-3(1) + 4 = -3 + 4 = 1
-3(2) + 4 = -6 + 4 = -2
Growing linearly, the balance owed on your credit card triples from $500 to $1500 in 9 months. If the balance were growing according to the exponential function f(x)=500(1+0.13)x where x represents the number of months, what would the balance be after 9 months? Round your answer to the nearest cent.
Answers
If the balance were growing according to the exponential function, the balance owed on your credit card after 9 months is equal to $1,502.02.
What is an exponential function?In Mathematics, an exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of an argument.
From the information provided, an exponential function that models or represents the rate at which the balance owed on your credit card triples is given by:
f(x) = 500(1 + 0.13)^x
Where:
f(x) represents the balance owed on your credit card.x represents the number of months.After 9 months, the balance owed on your credit card would be calculated by substituting the value of x with 9 as follows:
Balance owed, f(x) = 500(1 + 0.13)^9
Balance owed, f(x) = 500(1.13)^9
Balance owed, f(x) = 500 × 3.0040419380
Balance owed, f(x) = $1,502.02.
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Complete Question:
Growing linearly, the balance owed on your credit card triples from $500 to $1500 in 9 months. If the balance were growing according to the exponential function f(x) = 500(1 + 0.13)^x, where x represents the number of months, what would the balance be after 9 months? Round your answer to the nearest cent.
Answer:
$1502.02
Step-by-step explanation:
f(x)=500(1+0.13)^x
f(9) = 500(1.13)^9
f(9) = 500(3.004041938)
f(9) = 1502.02
Answer: $1502.02
Solve 7x − 2(x + 1) = 6x + 14
A. x = −12
B. x = 12
C. x = −16
D. x = 16
I don't know what to do here.
Answers
1. Distribute -2
7x-2(x+1)=6x+14
7x-2x-2=6x+14
2.combine like terms
7x-2x-2=6x+14
5x-2=6x+14
3.add 2 to isolate x on one side
5x-2=6x+14
5x=6x+16
4. Subtract 6x from both sides to isolate the number
5x=6x+16
-x=16
5. Divide by -1 on both sides to make x positive
-x=16
X=-16
Answer: C, x = -16
Step-by-step explanation:
1. Distribute
7x-2(x+1)=6x+14
7x-2x-2=6x+14
2. Combine like terms
7x-2x-2=6x+14
5x-2=6x+14
3. Add 2 to both sides
5x-2+2=6x+14+2
4. Simplify
Add the numbers
5x=6x+16
5. Subtract 6x from both sides
5x-6x=6x+16-6x
6. Simplify
Combine like terms
-x=16
7. Divide both sides by the same factor
-x/-1=16/-1
8. Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
HELP I’LL MARK BRAINLIEST AND ITS 100 POINTS
p: a month begins with the letter M; q: it has 31 days
match the statements
1) conditional
2) converse
3) inverse
4) contrapositive
if a month does not begin with the letter M then it does not have 31 days
if a month does not have 31 days then it does not begin with the letter
if a month begins with the letter M then it has 31 days if a month has 31 days then it begins with the letter M
Answers
Answer:
1) Conditional
If a month begins with letter M, then it has 31 days.
2) Converse
If a month has 31 days, then it begins with letter M.
3) Inverse
If a month does not begin with the letter M, then it does not have 31 days.
4) Contrapositive
If a month does not have 31 days, then it does not begin with the letter M.
Step-by-step explanation:
1) Conditional
If a month begins with letter M, then it has 31 days.
2) Converse
If a month has 31 days, then it begins with letter M.
3) Inverse
If a month does not begin with the letter M, then it does not have 31 days.
4) Contrapositive
If a month does not have 31 days, then it does not begin with the letter M.
Conditional statement states the original statement. If 'p' , then 'q'
Converse statement switch positions in the original if --then statement. If 'q', then 'p'
Inverse statement states the opposite of the original statement. If not 'p', then not 'q'.
Contrapositive if not 'q' , then not 'q'.
Help! I don’t know if this is correct
Answers
Answer:
can you turn it to the carma I can see it that good
what two numbers multiply to 2400 and add up to -16?
Answers
Based on the fact that the two numbers multiply to 2,400 and add up to -16, the numbers are undefined.
How to find the numbers?Assume that one of the numbers is x and the other number is y, the system of equations to represent this is given that the two numbers add up to -16 and multiplying to 2,400:
x + y = -16
xy = 2,400
Expressing y in terms of x :
xy = 2,400
y = 2,400 / x
Solving for x gives:
x + y = -16
x + (2,400 / x) = -16
x = 0
y = 0
The problem given in the question is wrong because the results of x and y are undefined.
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If someone could help me with these two problems please. ( will mark brainliest if correct )
Answers
The value of t for the angles of the given triangle will be 30.67.
What are the angles of triangle?The straight angle is equal to the total of the angles of a triangle. Three angles, one at each vertex and bounded by two neighbouring sides, make up a triangle. For a very long period, it was unknown if there were any alternative geometries for which the total is different.
The triangle has three sides and is a two-dimensional figure having the sum of the angles of 180 degrees.
In the given image the three angles are 2t, t + 8, and t - 12. The value of t will be calculated as:-
2t + t + 8 + t - 12 = 180
4t - 4 = 180
4t = 184
t = 184 / 4
t = 30.67
Therefore, the value of t for the angles of the given triangle will be 30.67.
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If Maggie corrected her mistake, what would be the correct answer for x?
Answers
correct value of x will 9 if Maggie corrected her mistake.
WHAT IS LINEAR EQUATION ?When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it. The typical form of a linear equation with one variable is Ax + B = 0. The variables x and A in this situation are variables, whereas B is a constant.
CALCULATIONApplying the parallel line theorem
alternate angles are always equal -
therefore ,
4x + 2 = 7x - 25
27 = 3x
x = 9
so , the correct value of x will be 9 if maggie corrected her mistake
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the associative property holds true for multiplication because -3 x4 x-2 = -3 x 4 x-2 does the associative property hold true for divison of integers
Answers
Answer:
Step-by-step explanation:
No it does not hold for division nor subtraction. An example would be 8÷(4÷2)≠(8÷4)÷2. You would get two complete different answers. For the first equation you would get 4 where as for the second equation you would get 1.
The square root of a number is between seven and eight .which could be the number?
Answers
Answer: 51
Step-by-step explanation:
I need help with this assignment
Answers
Answer:
8800000 or 88x 10^5
Step-by-step explanation:
4x2200000=8800000
an elementary school is offering 3 language classes: one in spanish, one in french, and one in german. the classes are open to any of the 100 students in the school. there are 28 students in the spanish class, 26 in the french class, and 16 in the german class. there are 12 students that are in both spanish and french, 4 that are in both spanish and german, and 6 that are in both french and german. in addition, there are 2 students taking all 3 classes.
Answers
Using Venn diagram, if a student is chosen randomly, (a) the probability that he or she is not in any of the language classes is 0.5, (b) the probability that he or she is taking exactly one language class is 0.32, and (c) if 2 students are chosen randomly, the probability that at least 1 is taking a language class is 0.753.
Venn diagram is a diagram used to present the relationship between sets in a logical form. (See attached image)
Let A = students in the Spanish class = 28
B = students in the French class = 26
C = students in the German class = 16
Hence, the probability of each class is:
P(A) = 28/100 = 0.28
P(B) = 26/100 = 0.26
P(C) = 16/100 = 0.16
P(A ∩ B) = 12/100 = 0.12
P(B ∩ C) = 6/100 = 0.06
P(A ∩ C) = 4/100 = 0.04
P(A ∩ B ∩ C) = 2/100 = 0.02
(a) P(not A, B, C) = 1 - P(A ∪ B ∪ C)
P(not A, B, C) = 1 - [P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]
P(not A, B, C) = 1 - (0.28 + 0.26 + 0.16 - 0.12 - 0.06 - 0.04 + 0.02)
P(not A, B, C) = 1 - 0.5
P(not A, B, C) = 0.5
(b) P(A, B, C only) = P(A only) + P(B only) + P(c only)
P(A, B, C only) = [P(A) - P(A ∩ B) - P(A ∩ C) + P(A ∩ B ∩ C)] + [P(B) - P(A ∩ B) - P(B ∩ C) + P(A ∩ B ∩ C)] + [P(C) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]
P(A, B, C only) = (0.28 - 0.12 - 0.04 + 0.02) + (0.26 - 0.12 - 0.06 + 0.02) + (0.16 - 0.06 - 0.04 + 0.02)
P(A, B, C only) = 0.14 + 0.10 + 0.08
P(A, B, C only) = 0.32
(c) P = 1 - (50/100 x 49/99)
P = 1 - (49/198)
P = 149/198
P = 0.753
To complete the problem, here are the questions:
(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?
(b) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?
(c) If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?
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The price of a math textbook can be modeled by the equation:
y = 2x + 76, where x is time in years and y is the price of
the textbook. This equation tells us that the textbook originally
cost $76 and each year the cost went up $2. How many years
will it take for the textbook to cost $100?
Answers
Please answer all questions. I really need help! Thank you
Answers
For the quadratic equation:
x^2 + 7x = 8x + 12
The two solutions are:
x = 4
x = -3
How to find the zeros of the quadratic equation?I'm only solving the first question, as it is how the guidelines say.
Here we have the quadratic equation:
x^2 + 7x = 8x + 12
First, we can rewrite this equation as:
x^2 + 7x - 8x - 12 = 0
x^2 - x - 12 = 0.
Using Quadratic formula we can see that the solutions (or zeros of the quadratic) are:
x = (1 ± √( (-1)^2 - 4*1*-12))/(2*1)
x = (1 ± 7)/2
Then the two solutions are:
x = (1 + 7)/2 = 4
x = (1 - 7)/2 = -3
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find the value of x when y=10 and 2y+y=x
Answers
x = 30
Step-by-step explanation:
Given,
y = 10, x = ?
2y+y = x → Equation no. (1)
Substitute the value of y in Equation no. (1) then,
2(10)+10 = x
20+10 = x
30 = x (OR) x = 30.
Please help. I would appreciate it! Will mark brainlyest if you remind me and if someone replies just remind me!
Answers
In the picture there is a prism with measures. The surface area of prism is 156.
Given that,
In the picture there is a prism with measures.
We have to find the surface area of prism.
The surface area of prism=(2×base area)+(Base perimeter×height)
The base is trapezoid
So, the area of trapezoid is (a+b)/2×h
=(6+12)/2×4
=18/2×4
=9×4
=36
Here base area we got is 36.
Now, we find the perimeter of trapezoid is a+b+c+d
=6+12+5+5
=18+10
=28
Here, base perimeter we got is 28.
Now surface area of prism is
=(2×36)+(28×3)
=72+84
=156
Therefore, the surface area of prism is 156.
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Find all values for x that will make this expression equal to 0.
3x(x+6)
Answers
Answer:
3x(x+6)
=(3x)(x+6)
=(3x)(x)+(3x)(6)
=3x2+18x
Step-by-step explanation:
How do you write 6% as a fraction or mixed number?
Answers
Answer:
As a fraction: 3/50
It cannot be turned into a mixed number
6/10 = 3/5 ( because they are divisible by 2)
Hi, I am taking PSAT and I am working on the math section. I need help with answering this math type of question. Please give the best explanation.
Answers
By using the concept of uniform rectilinear motion, the distance surplus of the average race car is equal to 3 / 4 miles. (Right choice: A)
How many more distance does the average race car travels than the average consumer car?
In accordance with the statement, both the average consumer car and the average race car travel at constant speed (v), in miles per hour. The distance traveled by the vehicle (s), in miles, is equal to the product of the speed and time (t), in hours. The distance surplus (s'), in miles, done by the average race car is determined by the following expression:
s' = (v' - v) · t
Where:
v' - Speed of the average race car, in miles per hour.v - Speed of the average consumer car, in miles per hour.t - Time, in hours.Please notice that a hour equal 3600 seconds. If we know that v' = 210 mi / h, v = 120 mi / h and t = 30 / 3600 h, then the distance surplus of the average race car is:
s' = (210 - 120) · (30 / 3600)
s' = 3 / 4 mi
The distance surplus of the average race car is equal to 3 / 4 miles.
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