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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.
Answers
To graph y = a*f (x)
if a> 1, the graph of y = f (x) is expanded vertically by a factor a.
We have then:
f (x) = 2/5 x ^ 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 (2/5 x ^ 2-2)
g (x) = 4/5 x ^ 2-4
Answer:
The equation of g (x) is:
g (x) = 4/5 x ^ 2-4
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.
What is the length of BB' ?
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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!
The cylinders are similar. The volume of the larger cylinder is 9648 cubic inches. What is the volume of the smaller cylinder?
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The volume formula of a cylinder is:
V = [tex] \pi [/tex]r²h
The volume of the larger volume is given to be 9648³ and the height is 18 in
We need to find the radius first
9648 = [tex] \pi [/tex]r²(18)
[tex] \frac{9648}{18} [/tex] = [tex] \pi [/tex]r²
536 = [tex] \pi [/tex]r²
[tex] \frac{536}{ \pi} [/tex] = r²
[tex] \sqrt{ \frac{536}{ \pi } } [/tex] = r
r ≈ 13.06
The ratio of the big cylinder to small cylinder is:
18 : 9 (given height)
So the big cylinder is 2 times bigger than the small cylinder
Therefore the radius of the big cylinder is as well 2 times bigger
[tex] \frac{13.06}{2} = r [/tex]
r ≈ 6.53 ( the radius of the small radius )
V (of small cylinder) = [tex] \pi [/tex](6.53)²(9)
= 1206 in³
3x+11y=8 SOLVE FOR Y
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-3x -3x
11y = 8 - 3x
/11 /11
y = 0.72 - 3x/11
To solve 3x + 11y = 8 for y, first subtract 3x on both sides to isolate 11y.
3x + 11y = 8
-3x -3x
----------------------
11y = -3x + 8
divide both sides by 11.
11y = -3x + 8
y = -3/11 +8/11
Hope this helped! :)
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.,
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We have then:
y = A * (b) ^ t
Where,
A: Initial population
b: Population growth as time passes
t: time
y: population after t hours.
Part A:
The equation for this case is:
y = 150 * (2) ^ t
Part B
See attached image.
Part C:
For this case we should evaluate the function for t = 12
We have then:
y = 150 * (2) ^ (12)
y = 614400
y = 150 * (2) ^ t
t= 12
y = 150 * (2) ^ (12)
y = 614400
The answer to your questions is y is equals to 614400.
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
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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.
X^2-7x+10=0
It says to “solve each equation by factoring and using the Zero Product Rule
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.. 10 = -1*-10 = -2*-5
The latter two factors add to -7, so we can use them to write the factored form.
.. (x -2)(x -5) = 0
The Zero Product Rule says that if a product is zero, at least one of the factors must be zero.
.. x -2 = 0 . . . . . first factor is zero
.. x = 2
.. x -5 = 0 . . . . . second factor is zero
.. x = 5
The two solutions are x=2 or x=5.
Please help ASAP!!! 15 points!
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Use the Law of Sines to find the missing side of the triangle. Find b.
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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.
Preform the indicated operation. Then choose the best answer. 27.7 x 1.9
5.363
52.63
53.62
5.263
Choose the best estimate. 64.1 ÷ 97
641
6.41
0.641
6410
The estimation to determine whether the result is reasonable or not. 108.93 x 355.112
Reasonable
Not reasonable
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64.1/97=0.66 best answer is 0.641
108.93*355.112= 38,682.35 reasonable to do mental math and think like 100*360 will give you an aprox answer
MATHHHHHHHHHHHHHHHHHHHHHHHHA
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|b| > 2
Solve for the absolute value
We know either b > 2 or b < -2
b > 2
b < -2
Thus,
The correct answer is option A
b < -2 or b > 2
in the formula for a sphere what is decimal that represents the fraction 4.3
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the volume of a sphere is V = 4/3 πr³
the fraction (4/3) is equal to 1.33
the answer is 1.33
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.)
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Chan = 2.5 miles
5 ÷ 2.5 = 2
Dale ran twice as fast as Chan
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.
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.
Answers
https://brainly.com/question/9030327
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?
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:)
Hope this helps
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.
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.
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from mathopenref: median: "A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side."
if we draw a median to the hypotenuse, then we have to draw from the right angle to the hypotenuse.
we use a theorem: "In a right triangle, the median drawn to the hypotenuse has the measure half the hypotenuse. "
the length of the median to the hypotenuse is half the hypotenuse: 5
for altitude:
we draw line on hypotenuse that is perpendicular to hypotenuse to a vertex of the angle opposite to it.
look at my diagram: h is the altitude length
x and y are segments of the original hypotenuse
we have ΔABD with legs of x and h and hypotenuse of 6
ΔABD: x² + h² = 6²
we have ΔBCD with legs of 10-x and h and hypotenuse of 8
ΔBCD: (10-x)² + h² = 8²
this is a system of equations
x² + h² = 6²
(10-x)² + h² = 8²
isolate h² in x² + h² = 6² so that we can substitute:
h² = 6² - x²
h² = 36 - x²
substituting into (10-x)² + h² = 8² we have
(10-x)² + h² = 8²
(10-x)² + (36 - x²) = 8² ...............substitution done
(10-x)² expands to 100 - 20x + x²
100 - 20x + x² + (36 - x²) = 64
+x² and -x² cancel
100 - 20x + 36 = 64
136 - 20x = 64
-20x = -72
x = 3.6
Since h² = 36 - x², then h = √(36 - x²) and
h = √(36 - 3.6²) =4.8
the altitude is 4.8
What did the Beat generation writers try to defeat in America?
A) pacifism
B)traditionalism
C)individualism
D)Feminism
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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.
A volume of ______ is formed by revolving a plane figure through 360 degrees around a line.
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volume of a revolution
hope it helps
Answer:
Correct Answer: Revolution
Step-by-step explanation:
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?
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Step 1: Form an equation.
We know that in 1992, Chris was HALF the age of Joseph. So Chris was x years old, while his brother was twice his age, or 2x. 6 years later, he was two-thirds the age of his brother. So, he was (x+6) while his brother was (2x+6).
So, we can form this:
(X+6)=(2/3)(2x+6)
Step 2: Simplify the equation. Distribute, Subtract, multiply
(X+6)=(2/3)(2x+6)
Distribute: X+6=(2/3)(2x)+(2/3)(6)
X+6=4/3x+4
Subtract:
X+6-4/3x=4/3x+4-4/3x
-1/3x+6=4
Subtract:
-1/3x+6-6=4-6
1/3x=-2
Multiply:
(3/-1) * (-1/3x)=(3/-1)*(-2)
X=6
This means in 1992, Chris was indeed 6 years old, while his brother was 12. 6 years later, Chris was 12 years old, while his brother was 18. (6/12=1/2; 12/18=2/3)
So, from 1992-2018=26 years.
In 1992 Chris was already 6.
26+6=32
In 2018, Chris is 32 years old, his brother is 6 years older, 38.
Chris is 32 years old.
~Hope this helps!
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.,
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(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
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Brainliest please?
I am trying to move up my rank to Ace!
[tex] \dfrac{3}{4}y = 24[/tex]
Rewrite into single fractions
[tex] \dfrac{3y}{4} = \dfrac{24}{1} [/tex]
Cross multiply
[tex]3y = 24 \times 4[/tex]
Evaluate the right side
[tex]3y = 96[/tex]
Divide by 3 on both sides
[tex]y = 32[/tex]
-------------------------------
Answer: y = 32
-------------------------------
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 :)
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sin B = (27/32)*sin 48 = 0.6270 or
B = 39°; C=180-48-39 = 93°
c^2 = a^2 +b^2 -2abcos C = 32^2 +27^2 -{2*32*27*cos 93}=1843 or
c =43
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
what two numbers have a sum of 24 and have a quotient of 3?
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then the other will be 3x
3x+x=24
4x=24
x=6-first number
2nd is 3*6=18
Define x and y :
--------------------------------------------
Let one number be x.
Let the other number be y.
--------------------------------------------
Construct equation :
--------------------------------------------
x + y = 24
x ÷ y = 3
--------------------------------------------
Solve for x and y :
--------------------------------------------
x + y = 24 ------------------- (1)
x ÷ y = 3 --------------------- (2)
--------------------------------------------
From equation 1 :
--------------------------------------------
x + y = 24
x = 24 - y
--------------------------------------------
Sub x = 24 - y into 2 :
--------------------------------------------
x ÷ y = 3 // Equation 2
(24 - y) ÷ y = 3 // Sub x = 24
24 - y = 3y // Multiply by y on both sides
24 = 4y // Add y to both sides
4y = 24 // Switch side, make y the subject
y = 6 // Divide by 4 on both sides
--------------------------------------------
Sub y = 6 into equation 1 :
--------------------------------------------
x + y = 24 // Equation 1
x + 6 = 24 // sub y = 6
x = 18 // Take away 6 from both sides
--------------------------------------------
Find the two numbers :
--------------------------------------------
One number = x = 18
The one number = y = 6
------------------------------------------------------------------
Answer: The two numbers are 18 and 6.
------------------------------------------------------------------
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?
Answers
2 + x + x = 66
2x = 64
x = 32
The numbers are:
2 32 and 32
(2 + 32 + 32) / 3 = 22
66 / 3 = 22
Correct!!
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? $
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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?
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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
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If t(n) 2n+3 what is the 3rd term
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t(3)=2(3)+3
6+3 = 9
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.
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C. Yes, because every x-value corresponds to exactly one y-value.
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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describe the graph of a quadratic function
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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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