Answer: The required value of f(3) is 81.
Step-by-step explanation: We are given the following function :
[tex]f(x)=\left(\dfrac{1}{9}\right)9^x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the value of f(3).
Substituting x = 3 in equation (i), we get
[tex]f(3)\\\\\\=\left(\dfrac{1}{9}\right)\times9^3\\\\=9^2\\\\=81.[/tex]
Thus, the required value of f(3) is 81.
Answer:
81
Step-by-step explanation:
APEX
Both Dale and Chan went running for an hour. Dale ran 5 miles and Chan ran 2.5 miles. How did Dale’s distance compare to Chan’s? (Use division to compare.)
In the given hour, Dale ran 5 miles and Chan ran 2.5 miles.
Let Dale's running miles be represented by the variable D and let Chan's running miles be represented by the variable C.
In-order to compare Dale's running miles to Chan's by using division we get:
[tex] \frac{D}{C}=\frac{5}{2.5} = \frac{2}{1} [/tex]
[tex] D=2C [/tex]
Thus, Dale ran twice the distance Chan ran in the same amount of time of 1 hour.
Equivalently we can say that Chan ran half the distance Dale ran in the same amount of time of 1 hour.
(Please Help~! 20 Points~!)
Which of the following is the solution to the equation 3/4y = 24?
y = 18
y = 32
y = 64
y = 72
Does this set of ordered pairs represent a function? Why or why not?
{(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)}
A. Yes, because there are two x-values that are the same.
B. No, because two of the y-values are the same.
C. Yes, because every x-value corresponds to exactly one y-value.
D. No, because one x-value corresponds to two different y-values.
Final answer:
The set of ordered pairs represents a function Yes, because every x-value corresponds to exactly one y-value(C).
Explanation:
The set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)} represents a function because every x-value corresponds to exactly one y-value. In a function, each input (x-value) has only one output (y-value). The set does not have two different y-values for the same x-value, so option D is incorrect. Therefore, option C is the correct answer.
(C). Yes, because every x-value corresponds to exactly one y-value.
You can see that each unique x-value corresponds to exactly one y-value, and there are no repeated x-values. Therefore, this set of ordered pairs represents a function.
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Use the Law of Sines to find the missing side of the triangle. Find b.
Answer:
43.82 units.
Step-by-step explanation:
We have been given a triangle. We are asked to find the value of b using Law of Sines.
[tex]\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}[/tex], where, a, b and c are opposite sides of angles A, B and C respectively.
Upon substituting our given values in above formula, we will get:
[tex]\frac{50}{\text{sin}(58^{\circ})}=\frac{b}{\text{sin}(48^{\circ})}[/tex]
Switch sides:
[tex]\frac{b}{\text{sin}(48^{\circ})}=\frac{50}{\text{sin}(58^{\circ})}[/tex]
[tex]\frac{b}{0.743144825477}=\frac{50}{0.848048096156}[/tex]
[tex]\frac{b}{0.743144825477}*0.743144825477=\frac{50}{0.848048096156}*0.743144825477[/tex]
[tex]b=43.81501643866[/tex]
[tex]b\approx 43.82[/tex]
Therefore, the value of b is approximately 43.82 units.
Two angles of a triangle measure 58° and 42°. What is the measure, in degrees, of the third angle?
A.60 degrees
B. 90 degrees
C.75 degrees
D.80 degrees
The correct answer will receive full points and the brainiest
If t(n) 2n+3 what is the 3rd term
A cafe offers senior citizens a 15% discount off its regular price of $8.95 for the dinner buffet. How much of a discount does a senior citizen receive off of the $8.95 price?
Answer:
$1.3425
Step-by-step explanation:
The regular price of the dinner buffet is 8.95. If this has a discount of 15%, we would have to multiply the total price by 0.15 and this would give us how much of the total amount is 15% and therefore it would give us how much of a discount the senior receives off of the 8.95 price
8.95 x 0.15 = 1.3425
Therefore, a senior citizen gets $1.3425 discount.
Let f(x)=x^2−3x−4 .
What is the average rate of change from x = 7 to x = 10?
Enter your answer in the box.
what two numbers have a sum of 24 and have a quotient of 3?
What did the Beat generation writers try to defeat in America?
A) pacifism
B)traditionalism
C)individualism
D)Feminism
Option: B is the correct answer.
B) Traditionalism.
Step-by-step explanation:Beat generation was a literary movement that was started by a group of authors and belongs to the post World War || period.
They started this movement to reject literary formalism and the American culture built on capitalism and materialism.
It has a major impact on both poetry as well as culture in America.
Hence, the Beat generation writers try to defeat in America is:
Traditionalism.
3x+11y=8 SOLVE FOR Y
Ppose you have two coins, one biased, one fair, but you don't know which coin is which. coin 1 is biased. it comes up heads with probability 2/3, while coin 2 comes up heads with probability 1/2. suppose you pick a coin at random and flip it. let ci denote the event that coin i is picked. let h and t denote the possible outcomes of the flip. given that the outcome of the flip is a head, what is p[c1|h], the probability that the biased coin is picked?
Solve the equation using the quadratic formula.x squared minus 4 x plus 3 equals 0 (1 point)x equals 2 semicolon x equals 4x equals 0 semicolon x equals 4x equals 1 semicolon x equals 3x equals negative 1 semicolon x equals 92. Solve the equation using the quadratic formula. x squared plus 10 x equals negative 25 (1 point)x equals 5x equals negative 5x equals 15x equals 253. Using the discriminant, determine the number of real solutions.negative 4 x squared plus 20 x minus 25 equals 0 (1 point)no real solutionsone real solutiontwo real solutions4. Using the discriminant, determine the number of real solutions.2 x squared plus 7 x minus 15 equals 0 (1 point)no real solutionsone real solutiontwo real solutions5. Using the discriminant, determine the number of real solutions.negative 2 x squared plus x minus 28 equals 0 (1 point)no real solutionsone real solutiontwo real solutions6. If the discriminant of a quadratic is zero, determine the number of real solutions. (1 point)no real solutionsone real solutiontwo real solutions7. Solve the equation using the quadratic formula.3 x squared equals 2 left-parenthesis 2 x plus 1 right-parenthesis (1 point)x equals StartFraction 3 plus minus StartRoot of 13 EndRoot over 6 EndFractionx equals StartFraction 2 plus minus StartRoot of 10 EndRoot over 3 EndFraction x equals one-sixth semicolon x equals one-halfx equals 3 semicolon x equals negative 18. Solve the equation using any technique.x squared plus 8 x plus 12 equals 0 (1 point)x equals negative 4 semicolon x equals 4x equals negative 6 semicolon x equals negative 2x equals 3 semicolon x equals 7x equals 6 semicolon x equals 89. Solve the equation using any technique.6 x squared minus 5 x minus 1 equals 0 (1 point)x equals one-fifth semicolon x equals one thirdx equals 2 semicolon x equals 6x equals 3 semicolon x equals negative one-halfx equals negative one-sixth semicolon x equals 110. Solve the equation using any technique.x squared equals 3 x minus 1 (1 point)x equals StartFraction 2 plus minus StartRoot 7 EndRoot over 3 EndFractionx equals StartFraction 1 plus minus StartRoot 3 EndRoot over 2 EndFractionx equals StartFraction 3 plus minus StartRoot 5 EndRoot over 2 EndFractionx equals StartFraction negative 2 plus minus 2 StartRoot 3 EndRoot over 3 EndFraction
This answer details the use of the quadratic formula to solve quadratic equations and the discriminant's role in determining the number of real solutions.
Explanation:The question involves solving quadratic equations and using the discriminant to determine the number of real solutions. The quadratic formula, \(x = \frac{-b \pm \sqrt[tex]{b^2[/tex] - 4ac}}{2a}\), is a powerful tool in finding the roots of any quadratic equation of the form \([tex]ax^2[/tex]+ bx + c = 0\). The discriminant, \(\Delta =[tex]b^2[/tex] - 4ac\), helps in understanding the nature of the roots without actually solving the equation. If \(\Delta > 0\), there are two distinct real solutions; if \(\Delta = 0\), there is exactly one real solution; and if \(\Delta < 0\), there are no real solutions and instead two complex solutions.
Ellen has a $19,750 balance on a credit card with an APR of 18%. If she makes minimum monthly payments of $300, how much will it cost Ellen to repay the total amount on the credit card? $
Solve the triangle.
A = 48, a = 32, b = 27
I am completely blanking on how to do this, so if you could please do a step by step process, that would be greatly appreciated :)
Answer:
The triangle is A = 48°, a = 32, B = 38.83°, b = 27, C = 93.17° and c = 42.99
Step-by-step explanation:
We have sine rule,
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
Here given A = 48°, a = 32, b = 27
Substituting
[tex]\frac{32}{sin48}=\frac{27}{sinB}=\frac{c}{sinC}\\\\sinB=0.627\\\\B=38.83^0[/tex]
We have
A + B + C = 180°
48 + 38.83 + C = 180
C = 93.17°
Using sine rule again
[tex]\frac{32}{sin48}=\frac{c}{sin93.17}\\\\c=42.99[/tex]
So the triangle is A = 48°, a = 32, B = 38.83°, b = 27, C = 93.17° and c = 42.99
An acidophilus culture containing 150 bacteria doubles in population every hour. (a) Write a function representing the bacteria population for every hour that passes. (b) Graph the function. (c) Use the graph to predict the number of bacteria after 12 hours.,
Find the value of a and b
Answer:
The value of a is 14 unit and the value of b is [tex]6\sqrt{2}[/tex] unit
EXPLANATION:
Draw a perpendicular line from vertex B to DC at E.
Labeling the diagram as shown in the attachment:
Now, as you can see from the Figure as shown in the attachment that [tex]ABDE[/tex] represents the rectangle because a rectangle is a quadrilateral with four right angles and their opposite sides would be parallel.
Therefore, we have the sides [tex]AB=DE=8[/tex] unit , and [tex]AD=BE=6[/tex] unit.
Consider the right triangle BEC
BY 45 45 90 triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
therefore, the length of side, [tex]BE=EC=6[/tex] unit
Using trigonometric ratio; to find the value of b:
[tex]\sin \theta =\frac{perpendicular}{Hypotenuse}[/tex]
∴ using trigonometric sine ratio in triangle BEC, we have
[tex]\sin 45^{\circ} =\frac{6}{b}[/tex] or
[tex]\frac{1}{\sqrt{2} }= \frac{6}{b}[/tex]
On Simplify:
[tex]b=6\sqrt{2}[/tex] unit
and the value of a = DC = DE+EC=8+6=14 unit
Therefore, the value of a is 14 unit and b is [tex]6\sqrt{2}[/tex] unit
Please help ASAP!!! 15 points!
The average of 3 numbers is 22, and the smallest of these numbers is 2. what is the value of the other two numbers if they are equal?
A tree standing vertically on level ground casts a 140 foot long shadow. The angle of elevation from the end of the shadow to the top of the tree is 24.7°. Find the height of the tree to the nearest foot.,
X^2-7x+10=0
It says to “solve each equation by factoring and using the Zero Product Rule
MATHHHHHHHHHHHHHHHHHHHHHHHHA
On Chris' birthday in 1992, he was half the age of his brother Joseph. On Chris' birthday in 1998, he was two-thirds the age of Joseph. How old will Chris be on his birthday in 2018?
how do i solve problem a. and problem b? (using the pythagorean theorem). a. the median to the hypotenuse. b. the altitude to the hypotenuse.
in the formula for a sphere what is decimal that represents the fraction 4.3
The cylinders are similar. The volume of the larger cylinder is 9648 cubic inches. What is the volume of the smaller cylinder?
HELP PLS
Let f(x)=2/5 x^2−2 .
The function g(x) is a vertical stretch of f(x) by a factor of 2.
What is the equation of g(x)?
Enter your answer in the box.
Answer:
We have then:
f(x) = 2/5x^2-2 The function g (x) is a vertical stretch of f(x) by a factor of 2:
g(x) = 2f (x)
g(x) = 2 (2/5x^2-2)
g(x) = 4/5 x^2-4 is a required equation.
describe the graph of a quadratic function
The graph of a quadratic function, or a parabola, is U or n-shaped and its direction depends on the sign of the coefficient of the x-squared term. The vertex and line of symmetry can be found using formulas based on this coefficient.
Explanation:The graph of a quadratic function, also known as a parabola, generally takes on a 'U' or 'n' shape. The direction that the 'U' faces depends on the sign of the coefficient, which is the number associated with the x-squared term in the equation. If this coefficient is positive, the graph opens upwards; if it's negative, the graph opens downwards. The vertex (the highest or lowest point on a parabola) can be calculated using the formula -b/2a. The line of symmetry can be found using the equation x = -b/2a.
For example, consider the quadratic function f(x)=x^2. This equation represents a parabola that opens upwards. Its vertex is at the point (0,0) and its line of symmetry is x=0.
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What is the length of BB' ?
Answer:
The answer is sqrt29
Step-by-step explanation:
If you are doing the same program as me, there will be other questions similar to this one. What is the length to AA', BB', and CC'. All of these share the same answer which is also sqrt29. We are almost finished with the semester, hang on!
A volume of ______ is formed by revolving a plane figure through 360 degrees around a line.
Answer:
Correct Answer: Revolution
Step-by-step explanation: