y = x^2 - 10x + 25 - 25
y = (x-5)^2 - 25
y+25 = (x-5)^2
x-5 = +/-sqrt(y+25)
And you get TWO inverses:
x = 5 + sqrt(y+25), for x>=5
x = 5 - sqrt(y+25), for x<=5
Answer:
[tex]y=5\pm \sqrt{(25+x)}[/tex]
Step-by-step explanation:
We are asked to find the inverse for the function [tex]y=x^2-10x[/tex].
We know that to find inverse, we interchange x and y values and then solve for y.
After interchanging x and y values, we will get:
[tex]x=y^2-10y[/tex]
Switch sides:
[tex]y^2-10y=x[/tex]
[tex]y^2-10y-x=x-x[/tex]
[tex]y^2-10y-x=0[/tex]
Now, we will use quadratic formula to solve for y.
[tex]y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]y=\frac{-(-10)\pm \sqrt{(-10)^2-4(1)(-x)}}{2(1)}[/tex]
[tex]y=\frac{10\pm \sqrt{100+4x}}{2}[/tex]
[tex]y=\frac{10\pm \sqrt{4*25+4x}}{2}[/tex]
[tex]y=\frac{10\pm \sqrt{4(25+x)}}{2}[/tex]
[tex]y=\frac{10\pm 2\sqrt{(25+x)}}{2}[/tex]
[tex]y=5\pm \sqrt{(25+x)}[/tex]
Therefore, the inverse function for our given function would be [tex]y=5\pm \sqrt{(25+x)}[/tex].
Which rule describes the translation?
PLEASE ANSWER
(x, y) → (x – 8, y – 3)
(x, y) → (x – 3, y + 8)
(x, y) → (x + 8, y – 3)
(x, y) → (x + 3, y + 8)
Answer:
its C
Step-by-step explanation:
(x, y) → (x + 8, y – 3)
A nut mixture of walnuts and cashew nuts at a small fair is $1.00 per pound of walnuts and $3.10 per pound of cashew nuts. Over the entire day, 134 pounds of the nut mixture were sold for $241.10. If p is the number walnuts and n is the number of cashew nuts, then the system of equations that models this scenario is: p+n=134p+3.10n=241.10 Determine the correct description and amount of pounds for walnuts and cashew nuts that were sold.
Answer: 83 pounds of walnuts and 51 pounds of cashew nuts.
Step-by-step explanation:
Let p be the amount of pounds for walnuts and n be the amount of pounds for cashew nuts that were sold.
Given : A nut mixture of walnuts and cashew nuts at a small fair is $1.00 per pound of walnuts and $3.10 per pound of cashew nuts.
Over the entire day, 134 pounds of the nut mixture were sold for $241.10.
Then, system of equation represents the given situation will be :-
[tex]p+n=134----------(1)\\\\p+3.10n=241.10----------(2)[/tex]
Eliminate (1) from (2), we get
[tex]2.10n=107.1[/tex]
Divide 2.10 from both sides , we get
[tex]n=51[/tex]
Put value of n in (1), we get
[tex]p+51=134\\\\\Rightarrow\ p=134-51=83[/tex]
Hence, the correct description will be : 83 pounds of walnuts and 51 pounds of cashew nuts.
Classify the polynomial 3x^5 by degree
A: cubic
B:quadratic
C:quintic
D:quartic
The degree of the given polynomial [tex]3x^5[/tex] is quintic that is 5 and this can be determined by comparing the given polynomial with the generalized quintic equation.
Given :
Polynomial -- [tex]3x^5[/tex]
The following points should be remembered in order to determine the degree of any polynomial:
The generalized quadratic equation is represented by: [tex]ax^2 + bx + c =0[/tex]The generalized cubic equation is represented by: [tex]ax^3 + bx^2 + cx + d =0[/tex]The generalized quartic equation is represented by: [tex]ax^4 + bx^3 + cx^2 + dx+e =0[/tex]The generalized quintic equation is represented by: [tex]ax^5 + bx^4 + cx^3 + dx^2+ex + f =0[/tex]So, from the above points, it can be concluded that the degree of the given polynomial [tex]3x^5[/tex] is quintic that is 5. Therefore, the correct option is C).
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can anyone help me with this
△XYZ∼△DEF , YZ is 10 meters, XZ is 15 meters, and EF is 8 meters.
What is DF ?
____ m
Answer:
The measure of KL is 12 meters.
Step-by-step explanation:
It is given that △XYZ∼△DEF.
The corresponding sides of two similar triangles are proportional.
[tex]\frac{YZ}{EF}=\frac{XZ}{DF}[/tex]
[tex]\frac{10}{8}=\frac{15}{DF}[/tex]
[tex]10\times DF=15\times 8[/tex]
Divide both sides by 10.
[tex]DF=\frac{120}{10}[/tex]
[tex]DF=12[/tex]
Therefore we can say that if △XYZ∼△DEF, then the measure of DF is 12 meters.
At summer camp, 150 kids had the opportunity to choose their activities. of those kids selected archery for their morning activity. Of that group, also chose to study drama in the afternoons. How many kids chose both archery in the morning and drama in the afternoons?
The correct answer is [tex]D = 23[/tex]
To solve this problem , let's define the given information:
Let [tex]T[/tex] be the total number of kids at the summer camp:
[tex]T = 150[/tex]
Let [tex]A[/tex] be the number of kids who chose archery for their morning activity:
[tex]\frac{A}{T} = \frac{3}{5}[/tex]
Let [tex]D[/tex] be the number of kids from the archery group who also chose drama in the afternoons:
[tex]\frac{D}{A} = \frac{1}{4}[/tex]
We want to find the value of [tex]D[/tex], which represents the number of kids who chose both archery in the morning and drama in the afternoons.
We can set up the following equations:
[tex]\frac{A}{T} &= \frac{3}{5}[/tex]
[tex]A &= \frac{3}{5}T[/tex]
[tex]A &= \frac{3}{5}(150)[/tex]
[tex]A &= 90[/tex]
[tex]\frac{D}{A} &= \frac{1}{4}[/tex]
[tex]D &= \frac{1}{4}A[/tex]
[tex]D &= \frac{1}{4}(90)[/tex]
[tex]D &= 22.5[/tex]
Therefore, the number of kids who chose both archery in the morning and drama in the afternoons is [tex]22.5 or 23[/tex] (since we cannot have a fractional number of kids).
[tex]D = 23[/tex]
Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. if you choose the upside-down cone to have the largest possible volume, what fraction of the volume of the larger cone does it occupy?
When a smaller, upside-down cone is placed inside a larger cone, both cones being similar and the vertex of the smaller one being at the center of the base of the larger one, the smaller cone would occupy 1/8 or 12.5% of the volume of the larger cone.
Explanation:The relationship between the volume of the larger cone and the smaller, upside-down cone placed inside it is represented through the formula for the volume of a cone, which is 1/3 * π * r² * h, where 'r' is the radius of the base and 'h' is the height. If you manage to place the smaller cone such that it has the largest possible volume (which will happen when the smaller cone is similar to the larger cone), the smaller cone will have a height and radius proportionately smaller than the larger one.
Thus, the volumes are proportional to the cube of their corresponding proportions, so the smaller cone will occupy 1/n³ of the volume of the larger cone, where 'n' is the proportion between their linear dimensions. In this particular set-up, the 'n' will equal 2 because when the vertex of the smaller cone is at the center of the base of the larger cone, the smaller cone's height is half that of the larger cone. Hence, the smaller cone will occupy 1/2³ = 1/8 or 12.5% of the volume of the larger cone.
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look at the pictures below // please help // 50 points
QRS~TUV. What is the measure of V?
What’s the answer?
∠V is calculated to be 70°.
When two triangles are similar (QRS ~ TUV), their corresponding angles are equal. This means:
∠Q corresponds to ∠T∠R corresponds to ∠U∠S corresponds to ∠VGiven ∠R = 47° and ∠Q = 63°, we know that ∠T = 63° and ∠U = 47°.
Since the sum of the angles in any triangle is 180°:
∠Q + ∠R + ∠S = 180°
Substituting the known values:
63° + 47° + ∠S = 180°
Solving for ∠S:
∠S = 180° - 63° - 47° = 70°
Therefore, ∠V = 70° because ∠S corresponds to ∠V in the similar triangles.
Complete question: Triangle QRS is similar to triangle TUV. ∠R=47°, ∠Q=63°. What is the measure of angle V?
If F(x)=x-5 and G(x)=x^2, what is F(F(x))?
How much interest would an account earn if 3,000 is invested at an interest rate of 4.8% compounded semiannually for 2 years
Please help, picture included!
State the domain of the relation.
A) {-4, -3, -2, -1, 0, 2, 5, 8}
B) {-4, -3, -2, -1, 0}
C) {-4, -3, -2, -1}
D) {-4, -1, 2, 5, 8}
Kaylie had $1250 in her savings account. She withdrew $82 each month for 8 months in order to pay for a summer vacation. How much did Kaylie have in her account at the end of the 8 months?
Find the area of the shaded region of the trapezoid.
Find the product. (7 q - 5)(7 q + 5)
49q^2 - 10q - 25
49q^2 + 10q - 25
49q^2 - 25
[tex]Use\ (a-b)(a+b)=a^2-b^2.\\\\(7q-5)(7q+5)=(7q)^2-5^2=\boxed{49q^2-25}[/tex]
Final answer:
The product of the binomials (7q - 5) and (7q + 5) is found using the difference of squares formula, resulting in 49q² - 25.
Explanation:
To find the product of the given expressions (7q - 5)(7q + 5), we can use the difference of squares formula, which states that (a - b)(a + b) = a² - b².
Here, a is 7q and b is 5.
Applying the formula, we get:
(7q)² - (5)²49q² - 25This is because the mixed term +7q(-5) and the term -7q(+5) cancel each other out, leaving us with just the square terms.
What is the volume of a cube with length 7 cm? V = lwh
Answer:
it is i also took da test
Step-by-step explanation:
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x= 15
here is the work:
101 +37 = 138
138/2 = 69
5x-6 = 69
add 6 to each side
5x = 75
divide:
x = 75/5
x = 15
Which description compares the vertical asymptote(s) of Function A and Function B correctly?
Function A: f(x)= 1/ x+4
Function B
Both functions have a vertical asymptote at x=−4 .
Function A has a vertical asymptote at x = 1.
Function B has a vertical asymptote at x = 3.
Function A has a vertical asymptote at x = 4.
Function B has a vertical asymptote at x = 2.
Function A has a vertical asymptote at x=−4x=−4 .
Function B has a vertical asymptote at x = 2.
Function A has a vertical asymptote at x = -4.
The graph B has vertical asymptote is 2.
We have given function
A : f(x)=1/(x+4)
Since the rational function has the vertical asymptote at x=-4 then the denominator of function f(x) contains the term (x+4)
Function B :
What is the vertical asymptote?
A vertical asymptote is is a vertical line that guides the graph of function but is not part of it.
So from the graph we can see that the graph does not pass from the point at x=2
Therefore, the vertical asymptote is 2.
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A) –72
B) 72
C) –36
D) 36
if 2 inches equals 25 miles. how many miles would 0.25in (1/4 inch) equal?
A new board game uses special dice. Each die has eight sides. The game uses three of these special dice. How many outcomes are possible?
Final answer:
To find the number of possible outcomes when rolling three eight-sided dice, you multiply the number of outcomes of each die together, resulting in 512 total outcomes.
Explanation:
To determine how many outcomes are possible when rolling three eight-sided dice, we need to calculate the total number of combinations that can occur. Since each die has eight possible outcomes and the dice are rolled simultaneously, the number of outcomes for each die can be multiplied together to find the total number of outcomes for all three dice.
So, the calculation for the total number of outcomes is as follows:
8 (outcomes for die 1) × 8 (outcomes for die 2) × 8 (outcomes for die 3) = 512 total outcomes.
Therefore, there are 512 different possible outcomes when rolling three eight-sided dice.
There are 40 total students in the class and 12 of them are girls. what percentage of the class is boys?
(8)
7/x 11/x cross multiply x^2 = 77, square root of both sides x = sqroot of 77
My answer: D
Which equation can be rewritten as x + 4 = x2? Assume mc006-1.jpg
Answer:
The answer is C
Step-by-step explanation:
Got it right on edge 2020
Solve using substitution
Which of the following is an advantage of an observational study over a sample survey? A)Observational studies are not dependent on people’s responses, which may not be truthful.
B)Observational studies involve the random selection of subjects.
C)Observational studies do not manipulate variables.
D)Observational studies do not involve treatments.
Observational studies involve the random selection of subjects.
What is an observational study?An observational study is used in subjects like epidemiology, social sciences, psychology, and statistics to draw inferences from a sample to a population where the independent variable is not under the researcher's control due to ethical concerns or logistical restrictions.
Observational studies are ones in which a researcher makes observations about his thoughts and views. He observes the risk and other effects before the actual test takes place.
This is usually the initial phase of research where observations are made for the suitability of certain things that are to be researched. There is an initial feasibility test conducted to identify whether the further research process is beneficial or not.
Therefore Observational studies involve the random selection of subjects.
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Will graphs for these equations show parallel lines? Explain.
y=6x+1
y=6x-5
The area of a rectangle is 16, and its diagonal is 68−−√. find its dimensions and perimeter.
Use Distributive Property to write 4m + 4p
Factor out the common numbers/variables from the terms given
4 is a common number
4m + 4p
4(m + p) is your answer
hope this helps
Given the functions m(x) = 4x − 11 and n(x) = x − 10, solve m[n(x)] and select the correct answer below. (2 points)
Select one:
a. m[n(x)] = 4x − 51
b. m[n(x)] = 4x − 29
c. m[n(x)] = 4x^2 − 51
d. m[n(x)] = 4x^2 − 29
Answer:
got it right and was option A thx
Step-by-step explanation: