The graph of the inverse function is attached and the points are
(-1, 1)
(-4, 10)
(-5, 5)
(-9, 5)
(-10, 10)
How to write the inverse of the equation of parabolaQuadratic equation in standard vertex form,
x = a(y - k)² + h
The vertex
v (h, k) = (1,-7)
substitution of the values into the equation gives
x = a(y + 7)² + 1
using point (0, -6)
0 = a(-6 + 7)² + 1
-1 = a(1)²
a = -1
hence x = -(y + 7)² + 1
The inverse
x = -(y + 7)² + 1
x - 1 = -(y + 7)²
-7 ± √(-x - 1) = y
interchanging the parameters
-7 ± √(-y - 1) = x
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sadadjskjdlfhsadidshoichuedhhefhksjdhfihdpihdifhjehj;fhsuhfehkjfjkshxjhf
Answer:
\(x<5\)
Step-by-step explanation:
Lol, y did you post this question twice?
\(4-x<9\)
Subtract 4 to both sides
\(x<5\)
Answer:
x > -5
Step-by-step explanation:
Lets start by bringing the 4 to the right as -4. We are now at -x < 5. We now divide the total by -1, which flips the sign so now x > -5
Y=-3x-1 find the solution
The equation Y=-3x-1 represents a linear relationship between x and y, and can be used to model real-world situations such as distance vs. time or cost vs. quantity.
The equation Y=-3x-1 represents a straight line on a coordinate plane. The "slope-intercept" form of the equation is y=mx+b, where m is the slope and b is the y-intercept.
In this case, the slope is -3 and the y-intercept is -1. This means that the line goes downwards at a rate of 3 units for every 1 unit to the right, and intersects the y-axis at -1.
To find the solution to this equation, you would need to have a specific value for either x or y.
If you were given a value for x, you could plug it into the equation to find the corresponding value for y. If you were given a value for y, you could solve for x by rearranging the equation.
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1) There are 8 college basketball teams in a certain
Sub-Division
How many ways are there to choose 6 teams for the playoffs?
There are 28 ways to choose 6 teams for the playoffs if there are 8 college basketball teams in a certain sub-division.
To determine the number of ways to choose 6 teams for the playoffs out of the 8 college basketball teams in a certain Sub-Division, we can use the combination formula. The formula for combinations is given by
nCr = n! / (r! * (n-r)!),
where n represents the total number of teams and r represents the number of teams to be chosen.
In this case, n = 8 and r = 6.
Plugging in these values, we have
8C6 = 8! / (6! * (8-6)!) = 8! / (6! * 2!) = (8 * 7) / (2 * 1) = 28.
Therefore, there are total 28 ways to choose 6 teams.
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is a parallelogram. is the midpoint of . and trisect .
Let ⃗⃗⃗⃗⃗ = ⃗ and ⃗⃗⃗⃗⃗ = . Show your work on the diagram as well.
Answer:
option 6b):) is correct
Given the function f(x)= (x+3)^2 determine the value of f^-1 (49) include a complete solution
Answer:
Step-by-step explanation:
taking the inverse is essentially saying
x = (f(x) + 3)^2
root(x) - 3 = f(x) and -root(x) -3 = f(x)
(you have to take both the positive and negative roots)
plug in 49 for x and get 4 and -10.
The value of the inverse function, to the function f(x) = (x + 3)², at f(x) = 49, is; f⁻¹(49) = 4
What does the inverse notation f⁻¹(x) represents?The notation f⁻¹(x) represents the inverse of the function f(x). The inverse function, f⁻¹(x) undoes the the effect of the function f(x), meaning, that if y = f(x), then x = f⁻¹(y)
The value of f⁻¹(49) for the function, f(x) = (x + 3)² is the x-value, such that f(x) = 49, which can be obtained by solving the equation f(x) = (x + 3)², for x as follows;
Taking the square root of both sides of the equation, we get;
√(f(x)) = √((x + 3)²)
√(f(x)) = (x + 3)
Subtracting 3 from both sides, we get;
√(f(x)) - 3 = x + 3 - 3 = x
√(f(x)) - 3 = x
The above function is the inverse function, f⁻¹(x) that takes an output value, f(x), to produce the corresponding input value, x of the original function;
The inverse function, f⁻¹(x) = √(f(x)) - 3, takes the original output, f(x) to produce the original input x
When the output value is f(x) = 49 we get;
f⁻¹(49) = √(49) - 3 = ±7 - 3
Restricting the domain of the original function, f(x) to (x + 3) ≥ 0, or x ≥ -3, so that its inverse is also a function and produces only one value, we get;
f⁻¹(49) = 7 - 3 = 4
f⁻¹(49) = 4
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Which equation should you solve to find x?
Answer:
C
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos24° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{x}{10}\) → C
Note
sin24° = \(\frac{opposite}{hypotenuse}\) = \(\frac{4}{10}\) ( which does not include x )
tan24° = \(\frac{opposite}{adjacent}\) = \(\frac{4}{x}\) ≠ \(\frac{x}{4}\)
In the expression 4 + 3x + 5y, what is the coefficient of x?
Answer:
The coefficient of x is 3.
Step-by-step explanation:
In the given expression, 4 + 3x + 5y, the term "3x" represents the product of the coefficient and the variable x.
A coefficient is a numerical factor that is multiplied by a variable. It indicates the amount or quantity associated with the variable. In this case, the coefficient of x is 3 because it is the number that is multiplied by the variable x.
So, in the expression 4 + 3x + 5y, the coefficient of x is 3.
5/8 times by 1/12
What is the answer in its simplest form?
Answer: 5/96
Step-by-step explanation:
convert each fraction to a decimal then a percent 4/25 3/11
Answer:
4/25=0.16=16%
3/11=0.27=27%
Step-by-step explanation:
follow the guided instructions below to rotate the figure 180° counter-clockwise about the origin
we know that
When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y)
so
the rule is
(x,y) -----------> (-x,-y)
Applying the rule of the rotation to the given figure
we have the following coordinates
A(1,5) -----------> A'(-1,-5)
B(4,8) ---------> B'(-4,-8)
C(7,7) --------> C'(-7,-7)
D(7,5) ------> D'(-7,-5)
E(5,3) ------> E'(-5,-3)
using a graphing tool
Draw the image of the rotated figure
see the attached figure
please wait a minute
How can you write the value of 6 hundred thousandths?
We can write the value of 6 hundred thousandths by using multiplication and the required value is 6,00,000.
This problem can be done by using multiplication. Like 6 hundred can be multiplied with the thousand then the value gets. We can write the value of 6 hundred thousandths by using multiplication and the required value is 6lakhs.
In mathematics, the number has ones place, tens place and hundreds place, thousands place. So, by that we can conclude the required value.
The value can be get by multiplying the given terms
Given 600 and multiplied by thousandths
600 * 1000 = 6,00,000
So, the required value is 6 lakhs or 6,00,000.
Therefore, this problem can be done by using multiplication. Like 6 hundred can be multiplied with the thousand then the value gets. We can write the value of 6 hundred thousandths by using multiplication and the required value is 6lakhs.
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The time t (in minutes) needed to read an article appearing on a foreign-language placement test is given by the probability density function f(t) = 0.012t2 − 0.0012t3, 0 ≤ t ≤ 10. For a test taker chosen at random, find the probability that this person takes 9 minutes or more to read the article. (Round your answer to four decimal places.)
The probability that a test taker chosen at random takes 9 minutes or more to read the article is 0.38. Rounded to four decimal places, this is 0.3800.
To find the probability that a test taker chosen at random takes 9 minutes or more to read the article, we need to calculate the integral of the probability density function f(t) from 9 to 10 (since t is between 0 and 10).
∫(9 to 10) 0.012t^2 − 0.0012t^3 dt
Using the power rule of integration, we get:
[0.004t^3 - 0.0003t^4] from 9 to 10
Substituting the limits, we get:
[0.004(10)^3 - 0.0003(10)^4] - [0.004(9)^3 - 0.0003(9)^4]
Simplifying, we get:
0.38
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3 + (2 + 8)2 ÷ 4 × 1 over 2 to the power of 4
Answer:
\(\frac{13}{32}\)
Step-by-step explanation:
How many questions were on Victoria test
Directions: Rewrite the following expressions in factored form by determining the GCF4) 16p^4 + 4p^3Factored Form:
16p^4 + 4p^3 = 4p^3(p + 1)
The greatest common factor is 4p^3
then the factored form is:
4p^3(p + 1)
Answer:
4p^3(p + 1)
\(undefined\)
Several friends (Calvin, Dean, Kelli, and Lee) went to Cal's Late Night Diner for a bite to eat. Match each person to their drink (Iced tea, Lemonade, Root Beer, and Water) and determine how much each paid ($4.99, $5.99, $6.99, and $7.99) for their meal.
Clues:
1. The Diner who paid $4.99 was either Calvin or the one who got the Root Beer.
2. Kelli paid $6.99
3. The one who got the water paid 1 dollar less than Dean.
4. Calvin paid more than Lee.
5. The one who got the Root beer paid 1 dollar less than the one who got the Iced Tea.
Based on the given clues, we can determine the person, drink, and price paid for each individual:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
How to determine how much each friends paidFrom clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.
From clue 2, Kelli paid $6.99.
From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.
From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.
Therefore, the final assignments are:
Calvin: Root Beer, $4.99
Dean: Lemonade, $7.99
Kelli: Water, $6.99
Lee: Iced Tea, $5.99
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Write an equation of a line through the point (6, 2) with slope 2/3.
Answer:
y=2/3x-2
Step-by-step explanation:
HEY CAN ANYONE PLS ANSWER DIS MATH PROBLEM I RLY NEED IT!!!
Answer:
Step-by-step explanation:
What is the change of rate for y=4x-3?
Answer:
the rate of change is 4/1
The points X, Y, and Z are on the same directed line segment XYZ. The ratio of XY:XZ is 2:3. If point X is located at (6,10) and point Y is located at (-1,8), what are the coordinates of point Z?
The coordinates of Z are (-11.5, 5)
What is section formula?When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula. Let us say, we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:
P(x, y) = (m\(x_2\) + n \(x_1\) / m+ n, m \(y_2\) +n\(y_1\) /m+ n)
Given coordinates:
XY:XZ is 2:3
X is located at (6,10) and Y is located at (-1,8).
let the coordinates of Z(x, y)
using section formula
-1 = (2x + 18)/ 5
-5 = 2x +18
2x = -23
x= -11.5
and, 8 = 2y + 30 /5
40 = 2y + 30
2y= 10
y=5
Hence, the coordinates of Z are (-11.5, 5)
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IXL graph a line using slope (don't judge how bad I am at it)
Answer:
Place the point at (5,-1) and then go up 9, and right 5. Continue doing this until you feel you can draw a line. Usually once or twice works.
Step-by-step explanation:
I would draw it for you but I can't on this
A 12 pack of soda cost $3.25 What is the unit price
Answer:
About $0.2708 per unit ' each can '.
Answer:
$.27
Step-by-step explanation:
$3.25 / 12 = 27
Amada wants to add 6,732
Amanda adds to numbers 6,732 and 4,975 by the use of mental math, she gets a total of 11,707.
How to add the number ?Amanda wants to add 6,732 and 4, 975 by using mental math.
To add the number we can use them, first of all, we need to split the number and then add the number.
split the number into two parts.
6,732 can be written as = 6,732 = 6,700 + 32
4,975 can be written as = 4,975 = 4,900 + 75
First, add the numbers 6,700 and 4,900
Therefore we get,
6,700 + 4,900 = 11,600
Now add the remaining number 32 +75 = 107
Finally add both the numbers = 11,600 + 107
We get the final result = 11, 707
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Complete question:
Amanda wants to add 6,732 and 4,975 by the use of mental math.
a sphere of radius $10$ inches is inscribed in a cone with a base of radius $15$ inches. in cubic inches, what is the volume of the cone?
The volume of the cone is approximately 2941.6 cubic inches.
To begin with, let's recall the formula for the volume of a cone. The volume of a cone is given by the formula V = (1/3)πr²h, where V is the volume, r is the radius of the base, and h is the height of the cone.
We can see that the radius of the base of the cone is 15 inches. However, we do not know the height of the cone yet. To find the height, we can use the fact that the sphere is inscribed in the cone.
We have a right triangle with the height of the cone, the radius of the base of the cone (which is one leg of the triangle), and the diameter of the sphere (which is the hypotenuse of the triangle). Using the Pythagorean theorem, we get:
h² + 15² = 20²
Simplifying this equation, we get:
h² + 225 = 400
h² = 175
h ≈ 13.23
Now that we know the height of the cone, we can plug in the values of the radius and the height in the formula for the volume of the cone. We get:
V = (1/3)π(15²)(13.23) ≈ 2941.6 cubic inches
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The graph of the function f(x) =x^2 is shown on the grid below. Graph the function g(x) =(x-2)^2 -4 in the interactive graph.
Answer:
shift it down by 4 units
Step-by-step explanation:
by the placement of the -4 it can be determined that you would shift it according to the y axis
The formula a(x-h)^2 + k = y
h represents change in x, k represents change in y
-k means shift down
HELP ASAP PLEASE. Points will be given I just need help understanding!
Answer:
19
Step-by-step explanation:
your welcome
May 23, 8:49:32 PM
Watch help video
In physics lab, Austin attaches a wireless sensor to one of the spokes of a bicycle
wheel spinning freely on its axle. The sensor's height above the ground, in
centimeters, is given by the function h(t) = 7.46 cos(2(t-0.25)) + 38.86,
where t is time measured in seconds.
What is the minimum and what does it represent in this
context?
The minimum is 29 cm and it represents the sensor's minimum height above the ground.
How to interpret the graph of a cosine function?In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):
y = Acos(Bx - C) + D
Where:
A represents the amplitude.B = 2π/P.P represents the period.C represents the phase shift.D represents the center line (midline).By critically observing the graph which models the sensor's height above the ground (in centimeters) shown in the image attached below, we can reasonably infer and logically deduce that it has a minimum height of 29 centimeters.
In conclusion, the sensor's minimum height above the ground cannot exceed 29 centimeters.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Circle C is inscribed with 5 lines. Point C is at the center of the circle. 3 lines come out of point C and make points D, A, and B on the edge of the circle. Another line comes out of point C and goes past the edge to point E. Another line connects points D and A. Which geometric figures are drawn on the diagram? Check all that apply. Line segment C A Ray A C ∠ABC Circle C Ray B E ∠BCE Line segment A E
Answer:
A, B, D, F is the correct answer
The answers is shown below:
What is line segment?In geometry, a line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects two points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints.
For ∠ABCThe geometric figure is not drawn.
For ∠BCEThe geometric figure is drawn.
For line segment CAThe geometric figure is drawn.
For Ray CAThe geometric figure is drawn.
For Circle CThe geometric figure is drawn.
For Ray BEThe geometric figure is not drawn.
For Line segment AEThe geometric figure is not drawn.
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2.83 in expanded form
Answer:
2+0.8+0.03
Step-by-step explanation:
Find an equation of the line perpendicular to the line 3x+6y=5 and passing through the point (1,3). Write the equation in the standard form.
The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)
To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:
1. Obtain the slope of the provided line.
To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):
6y = -3x + 5
y =\(-\frac{1}{2}x + \frac{5}{6}\)
The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).
2. Determine the slope of the line perpendicular to the provided line.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.
So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.
3. Use the slope and the provided point to obtain the equation of the perpendicular line.
We can use the point-slope form of a line to determine the equation:
y - y1 = m(x - x1)
where x1, y1 is the provided point and m is the slope.
Substituting the provided point (1, 3) and the slope 2 into the equation, we have:
y - 3 = 2(x - 1)
4. Convert the equation to standard form.
To convert the equation to standard form, we expand the expression:
y - 3 = 2x - 2
2x - y = -1
Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:
2x - y = -1
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