Answers
Step-by-step explanation:
g(x) has clearly in its core the same function curve.
but it is
1. upside-down
2. moved up from the x-axis by 1 unit
3. moved to the right of the y-axis by 3 units
so, how do we express these 3 attributes in the functional definition ?
1. easily : by flipping the sign. g(x) = -x² is the same function type just upside-down (mirrored into the negative y space).
g(x) = -x²
2. also very easy : a function is moved up or down on the coordinate grid by adding (or subtracting) a constant.
we need to move our function up by 1 unit : we add 1.
that makes currently g(x) = -x² + 1
3. this is the trickiest part. to move a function left or right we need to make the function "think" that the input value x is not x, but it is (x ± constant).
let's ignore 1. and 2. for the moment and just focus moving the original function 3 units to the right.
that tells us that the functional result value of x in the shifted function must be the same as the functional result value in the original function for an input value that is 3 units "earlier" on the x-axis.
that would mean g(0) = f(-3), g(1) = f(-2), g(2) = f(-1), g(3) = f(0), ...
so, we see, g(x) = f(x-3) = (x-3)²
now, we combine again 1., 2. and 3., and we get
g(x) = -f(x-3) + 1 = -(x-3)² + 1
Related Questions
1) La suma de dos números es 58. Si uno de los números es 12 más que el otro
número,
cuáles son los números?
Answers
Answer:
Los números son 23 y 35.
Step-by-step explanation:
Q: The sum of two numbers is 58. If one of the numbers is 12 more than the other number, what are the numbers?
Set the numbers as x and y. Using the given information, we have two equations:
x+y=58
x=y+12
Solving using substitution, we have:
y+y+12=58 -> y=23
Substituting, x=23+12=35
The numbers are 23 and 35.
I am a parallelogram. Two of my sides are parallel to the bottom of the paper. The endpoints of the bottom side are at (2, 5) and (9, 5). The slope of the line segments that form my two sides is 0.75, and the length of each side is 5 units. What are my other two vertices?
Answers
According to the information, the vertex at the top left of the parallelogram is (4, 8.25). Thus, the other two vertices of the parallelogram are (2, 5), (9, 5), (7, 8), and (4, 8.25).
How to find the vertices of the parallelogram?To find the vertex of the parallelogram we can use the point-slope form of a line: y - y1 = m(x - x1), where,
m = slope(x1, y1) = point on the lineFor the side sloping up from left to right, we can use the point (2, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:
y - 5 = 0.75(x - 2)Simplifying, we get:
y = 0.75x + 3.5To find the point where this line intersects the top side of the parallelogram, we can use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (2, 5) is 5 units away from the intersection point in the x-direction, so we can add 5 to the x-coordinate to find the intersection point. Plugging in x = 7 into the equation above, we get:
y = 0.75(7) + 3.5 = 8Therefore, the vertex at the top right of the parallelogram is (7, 8).
For the side sloping down from left to right, we can use the point (9, 5), since it is on the bottom side of the parallelogram. Plugging in the values, we get:
y - 5 = -0.75(x - 9)Simplifying, we get:
y = -0.75x + 11.25To find the point where this line intersects the top side of the parallelogram, we can again use the fact that the length of the sloping side is 5 units. We know that the endpoint of the bottom side at (9, 5) is 5 units away from the intersection point in the x-direction, so we can subtract 5 from the x-coordinate to find the intersection point. Plugging in x = 4 into the equation above, we get:
y = -0.75(4) + 11.25 = 8.25Learn more about parallelograms in: https://brainly.com/question/29147156
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Solve For X.
1
8
12
27
if right i will give brainlist
Answers
Julia ran 1000 meters in 9 minutes. How many meters per minute did she run?
Answers
To be able to solve the rate of Julia's running per minute, we can divide 1000 meters by 9 mins.
\(\begin{gathered} \text{rate}=\frac{distance}{\text{time}} \\ \text{rate}=\frac{1000\text{meters}}{9\text{minutes}} \\ \text{rate}=111.11\text{ meters/minute} \end{gathered}\)Therefore, Julia runs approximately 111.11 meters per minute.
San is currently three times Harry's age. Sam's age is also 10 more than twice Harry's age. the following systems of equation models this scenario. x=3y, x=10+2y
Answers
Step-by-step explanation:
so, what do we need to do ?
just solve these equations and find Sam's age (and Harry's) ?
x = 3y
x = 10 + 2y
so, we simply use the first equation in the second :
3y = 10 + 2y
y = 10
x = 3y = 3×10 = 30
Sam is currently 30 years old, Harry is 10.
Angle FGH is a straight angle. The measure of angle JGH is 65°. The measure of angle FGH is x°. What is the value of x?
Answers
Answer:
115 degrees
Step-by-step explanation:
The addition of 2 straight angles = 180 degrees
180-65 = 115
Find the area of the shape shown below.
3.5
2
2
Answers
Answer:
26.75 units²
Step-by-step explanation:
Cube Area: A = l²
Triangle Area: A = 1/2bh
Step 1: Find area of biggest triangle
A = 1/2(3.5)(2 + 2 + 5)
A = 1.75(9)
A = 15.75
Step 2: Find area of 2nd biggest triangle
A = 1/2(5)(2)
A = 1/2(10)
A = 5
Step 3: Find area of smallest triangle
A = 1/2(2)(2)
A = 1/2(4)
A = 2
Step 4: Find area of cube
A = 2²
A = 4
Step 5: Add all the values together
A = 15.75 + 5 + 2 + 4
A = 20.75 + 2 + 4
A = 22.75 + 4
A = 26.75
Find the mean of the data in the bar chart below. money in each persons piggy bank
Answers
Answer:
The chart is showing how much many is in each persons piggy bank.
Step-by-step explanation:
Just a heads up , The title at the top of the graph gives off all the answers as to what the graph is showing.
Answer: 10.5
Step-by-step explanation:
C a l c u l a t o r
also I tried it myself so thats even more proof :D
how to explain distributive property to show equivalent expression for 54 and 42
Answers
I may be correct or not
54(x+42)
How much is 10% of 10 litters of milk
Answers
Explanation: if 10 litters is 100% then each litter is 10 because 10 x 10
Is 100
Answer:
1 litter of milk
Step-by-step explanation:
I Hope That This Helps! :)
A proposed design for a habitable Mars colony is a hemispherical
biodome used to maintain a breathable atmosphere for the colonists.
Estimate the radius of the biodome if it is required to contain 5.5
billion cubic feet of air.
Answers
Answer:
r = 1.37 billion feet
Step-by-step explanation:
It is given that,
A proposed design for a habitable Mars colony is a hemispherical biodome used to maintain a breathable atmosphere for the colonists.
The volume of biodome is 5.5 billion cubic feet of air.
It is in the shape of a hemisphere. The volume of a hemisphere is given by :
\(V=\dfrac{2}{3}\pi r^3\), r = radius
V = 5.5 billion cubic feet
\(r^3=\dfrac{3V}{2\pi}\\\\r^3=\dfrac{3\times 5.5}{2\times 3.14}\\\\r=(\dfrac{3\times 5.5}{2\times 3.14})^{1/3}\\\\r=1.37\ \text{billion feet}\)
So, the radius of the biodome is 1.37 billion feet.
The radius of the biodome if it is required to contain 5.5 billion cubic feet of air is 1.38 billion feet and this can be determined by using the formula of the volume of the hemisphere.
Given :
A proposed design for a habitable Mars colony is a hemispherical biodome used to maintain a breathable atmosphere for the colonists.Volume of the biodome is 5.5 billion cubic feet.The following steps can be used in order to determine the radius of the biodome:
Step 1 - The formula of the volume of the hemisphere can be used in order to determine the radius of the biodome.
Step 2 - Formula of the volume of the hemisphere is given by:
\(\rm V =\dfrac{2}{3}\pi r^3\)
where r is the radius of the hemisphere.
Step 3 - Now, substitute the value of V in the above formula in order to determine the value of 'r'.
\(\rm 5.5=\dfrac{2}{3}\pi r^3\)
Step 4 - Simplify the above expression.
\(r^3=\dfrac{5.5\times 3}{2\pi}\)
\(r = \sqrt[3]{\dfrac{16.5}{2\pi}}\)
r = 1.38 billion feet
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A0 12BExplanationD3 4 5 6 7 8 9 10 11Use the figure and the table to answer the parts below.(a) Find the probability that a real number between 0 and 4 is picked.0(b) Find the probability that a real number between 2 and 7 is picked.0CheckRegionABCDXArea0.100.300.450.15 I need help with this math problem please.
Answers
(a) The probability that a real number between 0 and 4 is picked is 0.68.
(b) The probability that a real number between 2 and 7 is picked is 0.72.
The graph and table are attached below.
Probability is an area of mathematics that deals with numerical representations of how likely an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
The probability that a real number between 0 and 4 is picked is the sum of regions B and C.
P1 = 0.2 + 0.48
P1 = 0.68
The probability that a real number between 2 and 7 is picked is the sum of regions C and D.
P2 = 0.48 + 0.24
P2 = 0.72
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YMC
15
A А
14
B
9
12
11
X
4 5 6
2 3
3
5
The image of AABC is AA'B'C. What transformations would result in this image?
Triangle ABC is reflected over the y-axis then rotated 90 degrees around the origin
Triangle ABC is translated T: (x,y) -> (X - 6,y), then rotated 90 degrees around the
origin
Triangle ABC is rotated 90 degrees around the origin, then T: (x,y) -> (x,y - 6)
Triangle ABC is rotated 90 degrees around the origin, then is reflected over the line y =
1
lo
Answers
Answer:
1.2.3.4.5.6.7.8.9.0.2.3.4.5.6.7.8.9.0
Step-by-step explanation:
Find the length of the third side.
Answers
I'm not sure if I did this right.
Answer:
2
Step-by-step explanation:
\(1^2+x^2=\sqrt{5}^2\)
\(x^2+1=5\)
\(x=\frac{+}{-} \sqrt{4}\)
2 or -2
You visit the tallest building in a city and drop a penny off the edge of the observation deck. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and then it will continue falling at the same rate. How many feet will the penny fall during the 8th second?
384 feet
272 feet
256 feet
240 feet
Answers
The distance that an object falls due to gravity is given by the equation:
d = 1/2 * g * t^2
where d is the distance fallen, g is the acceleration due to gravity, and t is the time elapsed.
In this case, we are given that the penny falls 16 feet during the first second, 48 feet during the second second, and 80 feet during the third second. From this, we can see that the penny is falling with a constant acceleration of 32 feet per second per second (since the distance is increasing by 32 feet each second).
To find the distance that the penny falls during the eighth second, we can use the same equation as before, but with a value of t equal to 8 seconds:
d = 1/2 * g * t^2
d = 1/2 * 32 * 8^2
d = 1/2 * 32 * 64
d = 1024 feet
Therefore, the penny will fall 1024 feet during the eighth second.
Algebra 1 : How to find the nth term of an arithmetic sequence
Answers
An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
The formula known as the nth term allows us to locate any term in a series. The letter "n" stands for "number." By changing the term number's value, we can create a series that uses the nth term (n). Following the sequence's formula, we would substitute 10 for 'n' to discover the tenth term, and 50 for 'n' to find the fiftieth term.
If, for instance, the nth word equals 2n + 1
We change the nth term's value from n = n to n = 1 to get the first term.
Initial term: 2(1) + 1 is equals to 3.
We change n = 2 into the nth term to get the second term.
Second term: 2(2) + 1 = 5.
We change n = 3 into the nth term to get the third term.
Third term: 2(3) + 1 = 7.
We change the nth term's value to n = 10 to find the tenth term.
tenth term = 2(10) + 1 = twenty-one (21)
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Sally can paint a room in 6 hours while it takes Steve 8 hours to paint the same room. how long would it take them to paint the room if they work together
Answers
Answer:
It will take them 3.5 hours to paint the room.
Step-by-step explanation:
Step 1: Add the number of hours it takes them together
A. 6 + 8
Step 2: Divide the total number of hours by two (since two people are working together)
B. 12 / 2 = 7 hours
Step 3: Divide by two again since you now have twice the speed
C. 7 / 2 = 3.5 hours
Which linear function has the same y-intercept as the one that is represented by the graph?
On a coordinate plane, a line goes through points (3, 4) and (5, 0).
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 3, negative 1, 1, 3. Column 2 is labeled y with entries negative 4, 2, 8, 14.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, negative 2, 2, 4. Column 2 is labeled y with entries negative 26, negative 18, negative 2, 6.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 5, negative 3, 3, 5. Column 2 is labeled y with entries negative 15, negative 11, 1, 5.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative 4, 4, 6. Column 2 is lab
eled y with entries negative 26, negative 14, 34, 46.
Answers
The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).
First, let's find the slope of the line using the formula:
slope (m) = (change in y) / (change in x)
m = (0 - 4) / (5 - 3)
m = -4 / 2
m = -2
Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Using the point (3, 4) as our reference point, we have:
y - 4 = -2(x - 3)
Expanding the equation:
y - 4 = -2x + 6
Simplifying:
y = -2x + 10
Now, let's check the given options to find the linear function with the same y-intercept:
Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)
The y-intercept is not the same as the given line. So, this option is not correct.
Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)
The y-intercept is the same as the given line (10). So, this option is correct.
Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)
The y-intercept is not the same as the given line. So, this option is not correct.
Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.
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if the system of equations y=b/6x-3 and y=2/3x-3 has infinitely many solutions, what is the value of b?
Answers
Answer:
b = 4
Step-by-step explanation:
4/6 is equivalent to 2/3, so with the slopes and y-intercepts being the same, there will be infinitely many solutions
If f(x) = 2^x + 4 and g(x) = x^2 – 4 what is the value of f(5) +g(-3)
Answers
f(5)=2^5+4
f(5)=32+4=36
g(-3)=(-3)^2-4
=9-4
=5
f(5)+g(-3)=36+5
=41
What is the volume of this rectangular prism 2, 7/3, 2
Answers
Answer:
The volume V of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively.
In this case, we have l = 2, w = 7/3, and h = 2. Therefore, the volume is:
V = (2)(7/3)(2)
V = 28/3
V = 9.33 (rounded to two decimal places)
So the volume of the rectangular prism is approximately 9.33 cubic units.
If you roll a die 100 times, what is the approximate probability that you will roll between 9 and 16 ones, inclusive? (Round your answer to two decimal places.) HINT [See Example 4.]
Answers
Answer: 0.47
Step-by-step explanation:
Given that
n = 100, probability of rolling 1 = 1/6
binomial approximation
np = 100 ( 1/6) = 16.667
standard deviation = √ 100 × 1/6 ×5/6 = 3.7627
P ( 9 ≤ X ≤ 16 )
= P ( 8.5 < X < 16.5 )
so,
= P ((8.5 - 16.6667) / 3.7627 < Z < (16.5 - 16.6667) / 3.7627
= P ( -2.17 < Z < -0.04 )
= 0.484 - 0.015
= 0.47
Therefore the approximate probability that you will roll between 9 and 16 ones is 0.47
1) Rewrite the expression as the difference of two squares.
(X+y)(x-y)-6x+9
A) (x + 3)2 + y2
B) (x + 3)2 - y2
c)(x – 3)2 + y2
D) (x – 3)2 - y2
Answers
Answer:
c
Step-by-step explanation:
Is the answer
Caleb started with 50 bacteria for his science experiment, and the number of bacteria doubled in one day.
Answers
Answer:
100+50²=2600
Step-by-step explanation:
because 50x2=100 and 50² is 2500. Add those and you get 2600.
it would be 50 to the power of 2
so your answer is
2500
Find theta in radians
Answers
Answer:
0.4636 radians
Step-by-step explanation:
To find theta in radians, we need to use the inverse tangent function, also known as arctangent. From the right triangle in the image, we have:
tangent(theta) = opposite/adjacent = 10/20 = 1/2
Taking the inverse tangent of both sides, we get:
theta = arctan(1/2)
Using a calculator or a trigonometric table, we find:
theta ≈ 0.4636 radians
Therefore, theta is approximately 0.4636 radians
How many ways are there to choose a soccer team consisting of 3 forwards, 4 midfield players, and 3 defensive players, if the players are chosen from 9 forwards, 7 midfield players, and 7 defensive players?
Answers
Using the combination formula, it is found that there are 37,044 ways to form the soccer team.
What is the combination formula?\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
In this problem:
3 forwards are taken from a set of 9.4 midfielders are taken from a set of 7.3 defenders are taken from a set of 7.Since they are independent of each other, the total number of combinations is given by:
\(T = C_{9,3} \times C_{7,4} \times C_{7,3} = \frac{9!}{3!6!} \times \frac{7!}{3!4!} \times \frac{7!}{3!4!} = 37,044\)
There are 37,044 ways to form the soccer team.
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if you are asked to find the value of the 100th term of a sequence, would you use the explicit formula for that sequence or the recursive formula?
Answers
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
We know that,
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
a_n = a_1 + (n-1)d
where d is the difference and a₁ is the first term of the sequence.
The major distinction between recursive and explicit formulas is that a recursive formula returns the value of a particular term depending on the preceding term, whereas an explicit formula returns the value of a given term based on its location.
When the value of the first term and the common difference is known then an explicit formula is used, while the recursive formula will be used when the value of the previous value is known and the value of the common difference is known.
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complete question:
what is the difference between the explicit formula and recursive formula for sequences when would you use one over the other
if the vertex of a parabola is negative for 6 and the other point of the curve is (-3,14) what is the coefficient of the squared expression in Parabola equation?
A. 6
B. 4
C. 8
D. 2
Answers
Answer:
coefficient of the square is a.6
Some more
f. Rr. E. e.
P. o. ii. N. T. s
Answers
Answer:
uwu
Step-by-step explanation:
florine,rhenium, ?, ?, polonium, oxygen, iodine, iodine, nitrogen, ?, ?
Solve
2(4x + 3) = 10x - 2
Answers
Answer:
x = 4
Step-by-step explanation:
2(4x + 3) = 10x - 2
2 × 4x + 2 × 3 = 10x - 2
8x + 6 = 10x - 2
8x - 10x = - 6 - 2
- 2x = - 8
2x = 8
x = 8/2
x = 4
-TheUnknownScientist
Answer:
x= 4
Step-by-step explanation:
we open brackets first
2(4x + 3) = 10x - 2
8x+6=10x-2
transpose
6+2= 10x-8x
8= 2x
x= 8/2
x= 4