The transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)If f(x) = x³ and g(x) = -2x³, then the transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.
Hence, the transformation that is applied to f(x) to get g(x) is that the function f(x) is vertically stretched by a factor of -2.
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MATH: GRAPHS AND FUNCTIONS 3. HELP! 12 PTS (HARD)
Answer:
Step-by-step explanation:
Suppose that f(n)=f(n/5)+3n when n is a positive integer divisible by 5, and f(1)=4.
By means of recurrence formulas and a given initial value, we find the following three results: f(5) = 19, f(125) = 469, f(3125) = 11719.
How to find the value the elements of a sequence by recurrence formula
Sequences are sets of values defined by at least one condition. In this case, we have three conditions to generate the required values:
f(n) = f(n/5) + 3 · n
f(1) = 4
[tex]n \in \mathbb{N}[/tex]
Now we proceed to find the elements by recurrence:
f(5) = f(1) + 3 · 5
f(5) = 4 + 15
f(5) = 19
f(25) = f(5) + 3 · 25
f(25) = 19 + 75
f(25) = 94
f(125) = f(25) + 3 · 125
f(125) = 94 + 375
f(125) = 469
f(625) = f(125) + 3 · 625
f(625) = 469 + 3 · 625
f(625) = 469 + 1875
f(625) = 2344
f(3125) = f(625) + 3 · 3125
f(3125) = 2344 + 9375
f(3125) = 11719
By means of recurrence formulas and a given initial value, we find the following three results: f(5) = 19, f(125) = 469, f(3125) = 11719.
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rewrite y= 16x-32 -3 to make it easy to graph using a translation describe the graph
We can rewrite the given expression to:
[tex]4*\sqrt{x - 2} - 3[/tex]
So the correct option is the third one.
How to rewrite the expression?
Here we have the expression:
[tex]\sqrt{16x - 32} - 3[/tex]
Taking the 16 as a common factor inside the square root:
[tex]\sqrt{16*(x - 2)} - 3[/tex]
and 16 = 4², then:
[tex]\sqrt{16*(x - 2)} - 3 = \sqrt{4^2*(x - 2)} - 3\\\\4* \sqrt{(x - 2)} - 3[/tex]
Now, if the parent function is:
[tex]y = 4*\sqrt{x}[/tex]
Our function is the parent function translated 2 units to the right and 3 units down. The correct option is the third one
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What is the value of the function when x = 1 in the
piecewise function
g(x) =
{
3x
-2x
when x>1
when x≤1
Answer:
-2
Step-by-step explanation:
3x isnt used because it stated when x>1.
so -2(1) is -2, because x =< 1 is true
Use the function below to find F(3).
Answer:
D
Step-by-step explanation:
Answer:
D. 1/125
Step-by-step explanation:
[tex]f(3)=(\frac{1}{5} )^{3} =\frac{1^{3} }{5^{3} } =\frac{1}{125}[/tex]
Hope this helps
How can the following expression be written so that no negative exponents appear?
(a5)³a-6
Q-2
Answer:
a^11
Step-by-step explanation:
1) Simplify the numerator. Use the laws: (x^a)^y = x^ay, x^a × x^b = x^a+b.
= a¹⁵ × a^-6 / a^-2
= a⁹ / a^-2
2) Divide them. Use the law: x^a / x^b = x^a - b.
= a^9 - (-2) / 1
= a^9 + 2 / 1
= a^11
Assume that the halting language [tex]H_T_M[/tex] is reducible to
some language B ([tex]H_T_M[/tex] [tex]$\leq$[/tex] [tex]_m[/tex] B). Is it possible that is decidable? Answer true/false and explain. Please help me this answer?
H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.
How to Interpret Machine Language?A language is referred to as Decidable or Recursive if there is a Turing machine that accepts and halts on every input string w. This tells us that every decidable language is Turing-Acceptable.
Now, we are told that the halting language is reducible to some language B. This means that it is an undecidability via reduction.
Now, Using the idea that “ If A is undecidable and reducible to B, then B is undecidable.” Suppose R decides HALT_TM, we will construct S to decide ATM .
S = “On input (M, B)
This means that H_TM is reduced to HALT_TM and as such, HALT_TM is undecidable.
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don’t understand the question would be a pleasure if someone were to explain and answer the questions! thank you
Set up an algebraic equation and then solve.
One integer is 4 times another. If the product of the two integers is 256, then find t
integers.
One possible set of answers is:
Another possible set of answers is :
The first set of integers are: 8 and 32
The second set of integers are: -8 and -32
What is an Integer?An integer is a whole number.
It is also the ratio of any real number and 1.
It does not have a decimal part or the decimal part of the integer is zero.
Analysis:
Let the two inters be x and 4x
product of integers = 4x(x) = 256
4[tex]x^{2}[/tex] = 256
[tex]x^{2}[/tex] = 256/4
[tex]x^{2}[/tex] = 64
x = ±[tex]\sqrt{64}[/tex]
x = -8 0r 8
The other integer = 4 x -8 = -32 or 32
In conclusion the two integers are -8 and -32 or 8 and 32
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A cookware consultant sells two types of pizza stones. The circular(e) stone sells for $26 and the rectangular (r) one sells for $34. In one month she sold 37 stones. If she made a total of $1138 from the sale of the pizza stones, how many of each size did she sell?
Answer:
Step-by-step explanation:
Conditions
Let the circular stones = x
Let the rectangular stones = y
Equations
x + y = 37 Subtract x from both sides of this equation.
y = 37 - x Notice that x is on the right side of the equation
Solution
26x + 34y = 1138 Substitute for y
26x + 34(37 - x) = 1138 Remove the brackets
26x + 1258 -34x= 1138 Combine
-8x + 1258 = 1138 Subtract 1258 from both sides
-8x +1258-1258 = 1138-1258 Combine.
-8x = -120 Divide both sides by -8
-8x/-8 = -120/-8
x = 15 Two minuses make a plus (last step)
x+ y = 37
15 + y = 37 Subtract 15 from both sides
15-15 +y = 37-15 Combine
y = 22
Answer
x = 15 Circular pizza dishes
y = 22 square pizza dishes
The consultant sold 15 circular pizza stones and 22 rectangular pizza stones.
How to determine how many of each size did she sell?Let's assume the number of circular pizza stones sold is "c" and the number of rectangular pizza stones sold is "r."
We are given two pieces of information:
1. The total number of stones sold: c + r = 37
2. The total amount earned from the sale of the stones: 26c + 34r = 1138
Now, we can use these two equations to solve for the values of "c" and "r."
First, let's use the first equation to express "c" in terms of "r":
c = 37 - r
Now, substitute this value of "c" into the second equation:
26c + 34r = 1138
26(37 - r) + 34r = 1138
962 - 26r + 34r = 1138
Combine the "r" terms:
8r = 1138 - 962
8r = 176
Now, divide by 8 to find the value of "r":
r = 176 / 8
r = 22
Now that we have the value of "r," we can find the value of "c" using the first equation:
c = 37 - r
c = 37 - 22
c = 15
So, the consultant sold 15 circular pizza stones and 22 rectangular pizza stones.
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Which expression correctly represents “twice the sum of four and a number”?
Answer:
2 (4+x)
Step-by-step explanation:
4 + x is the sum of four and a number 'x' now multiply by 2
2 ( 4+ x)
G.SRT.1 In the coordinate plane, quadrilateral ABCD has vertices A (1, 1), * 1 point B (5,1), C (5,9), and D (1, 9). Quadrilateral FGHJ is shown in the coordinate plane below. What are the scale factor and the center of dilation that map quadrilateral BCD onto quadrilateral FGHJ?
Based on the vertices of quadrilateral ABCD and Quadrilateral FGHJ, A. The scale factor is 1/2, and the center of dilation is point A.
What is the scale factor?First, note the vertices of Quadrilateral FGHJ:
F(1,1) G(3 ,1) J (1 , 5) H(3 , 5)
Find the lengths of the sides of both quadrilaterals:
FG = (3, 1) - (1, 1) AB = (5,1) - (1, 1)
= (2,0) = (4, 0)
FH = (3, 5) - (1, 1) AC = (5,9) - (1, 1)
= (2,4) = (4, 8)
AB is twice the size of FG.
AC is twice the size of FH
This shows that quadrilateral FGHJ is 1/2 the size of quadrilateral ABCD.
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Determine the composition of transformations that would map figure ABCD to figure A''B'C''D'
The composition of transformations that would map figure ABCD to figure A''B'C''D' is 180° degree rotation about point C.
What is transformation?It should be noted that transformation simply means the manipulation of a shape or geometric figure.
In this case, the composition of transformations that would map figure ABCD to figure A''B'C''D' is 180° degree rotation about point C.
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What is the quotient of
6/7 and 3/14 ?
Answer:
4/1 or 4
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
[tex]\frac{\frac{6}{7} }{\frac{3}{14} } =\frac{(6)(14)}{(7)(3)} =\frac{84}{21} =4[/tex]
Hope this helps
Find the diffrence between 6/7 and 2/3 In lowest terms
Answer:
4/7
Step-by-step explanation: Multiply 2/3 x 6/7 Put your answer in lowest terms a. 4/7
Answer:
Difference: 4/21
Step-by-step explanation:
the difference between two quantities is the result of a subtraction
[tex]\frac{6}{7} -\frac{2}{3} =\frac{(6)(3)-(7)(2)}{(7)(3)} =\frac{18-14}{21} =\frac{4}{21}[/tex]
The fraction can no longer be reduced
Hope this helps
please help I will report if wrong... Brainlyest for the first right answer
Answer:
first three expressions are polynomials and last three are not.
Step-by-step explanation:
last three expression has negative powers of X and some powers of Xs are not integers.
The principal represents an amount of money deposited in a savings account subject to
compound interest at the given rate.
A. Find how much money there will be in the account after the given number of years.
B. Find the interest earned.
Click the icon to view some finance formulas.
A. The amount of money in the account after 5 years is $
(Round to the nearest hundredth as needed.)
Principal
$11,000
Rate
5%
Compounded
annually
Time
5 years
Step-by-step explanation:
So the general formula for compound interest is [tex]A = P(1+\frac{r}{n})^{nt}[/tex] where t is typically time in years, and n is how many times it's compounded per year. But in this case it's only compounded 1 time per year so the equation is just [tex]A = P(1+r)^t[/tex]. in this case P is the principal amount, r is the interest, and A is the final amount. So the 5% interest rate becomes 0.05 by dividing by 100 to convert it into decimal form and the principle amount of 11,000. This gives you the formula [tex]A = 11000(1.05)^t[/tex]. This is the answer to the first question where t is the time in years. When it says "Find interest earned" I'm a bit confused, is it giving you x amount of years where you have to calculate the interest earned or does it want a general equation? Because the general equation would be the final amount - the principle amount which calculates the difference. So the equation for interest earned would be [tex]11000(1.05)^t-11000[/tex]. To calculate the amount of money after 5 years you simply plug in 5 as t. this gives you the equation [tex]11000(1.05)^5 \approx 11000(1.276) \approx 14,039.10[/tex]
graph g(x) = 5|x-6| + 2
Answer + Step-by-step explanation:
[tex]f(x) = 5|x-6|+2 = \begin{cases}5\left( x-6\right) +2&if\ x\geq 6\\ 5\left( 6-x\right) +2 &if\ x\leq 6\end{cases}[/tex]
[tex]\Longrightarrow f(x) = \begin{cases}5x-30+2&if\ x\geq 6\\ 30-5x +2 &if\ x\leq 6\end{cases}[/tex]
[tex]\Longrightarrow f(x) = \begin{cases}5x-28&if\ x\geq 6\\ -5x +32 &if\ x\leq 6\end{cases}[/tex]
case 1: x ≥ 6 → f(x) = 5x - 28
5(6) - 28 = 30 - 28 = 2
Then
the point A(6 ,2) lie on the graph (line) of f
5(7) - 28 = 35 - 28 = 7
Then
the point B(7 ,7) lie on the graph (line) of f
Graphing :
When x ≥ 6 ,the graph of f is the ray [AB) (just connect the points A and B)
case 2: x ≤ 6 → f(x) = -5x + 32
-5(6) +32 = -30 + 32 = 2
Then
the point A(6 ,2) lie on the graph (line) of f
-5(5) +32 = -25 + 32 = 7
Then
the point C(5 ,7) lie on the graph (line) of f
Graphing :
When x ≤ 6 ,the graph of f is the ray [AC) (just connect the points A and C)
b) A different sequence has this expression for the nth term: 1 (n + 1)² Work out the first four terms in the sequence. b ) A different sequence has this expression for the nth term : 1 ( n + 1 ) ² Work out the first four terms in the sequence.
The first four terms in the sequence are 4, 9, 16 and 25.
Given that, the nth term of the sequence is 1 (n + 1)².
We need to find the first four terms in the sequence.
What is the sequence?In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
To find the first four terms of the sequence, replace n=1, 2, 3 and 4.
Now, when n=1
1(1+1)²=1×4=4
When n=2
1(1+2)²=1×9=9
When n=3
1(1+3)²=1×16=16
When n=4
1(1+4)²=1×25=25
Therefore, the first four terms in the sequence are 4, 9, 16 and 25.
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Hi, need help please to get my HS diploma...did not graduate :(
Write the point-slope form of an equation of the line through the points (-2, -3) and (-7, 4).
Answer:
The answer is A Find the point-slope form.
y+3= −7/5 ⋅ (x+2)
Step-by-step explanation:
The next number in the series 7, 9, 13, 29, is:
Answer:
67
Step-by-step explanation:
7 + 2 =9
9 + 4 = 13
13 + 16 = 29
29 + 38 = 67
QUESTION IS DOWN BELOW WORTH 30 POINTS
Answer:
40 yds^3
Step-by-step explanation:
Answer two questions about Equations A and B:
A. 2x - 1 = 5x
B. - 1 = 3x
1) How can we get Equation B from Equation A?
Choose 1 answer:
A. Add/Subtract the same quantity to/from both sides
B. Add/Subtract a quantity to/from only one side
C. Rewrite one side (or both) by combining like terms
D. Rewrite one side (or both) using the distributive property
2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
A. Yes
B. No
1. Rewrite one side (or both) by combining like terms. Option C
2. Yes, the equations are equivalent. Option A
Reasons for the answers
1.
Equation A ; 2x -1 = 5x
Equation B ; -1 = 3x
To get equation B from equation A
2x - 1 = 5x
Collect like terms
-1 = 5x -2x
Subtract the like terms
-1 = 3x
Thus, rewrite one side (or both) by combining like terms. Option C
2. 2x - 1 = 5x ...... equation A
Solution ;
2x -5x = 1
-3x = 1
x = -1/3
-1 = 3x
Solution;
x = -1/3
Thus, the equations are equivalent. Option A
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3x - 6y = 8 then x - 2y
Equations are written by equating two expressionsThe value of x - 2y is 8/3
Equations are written by equating two expressions. Given the following equation
3x - 6y = 8
Divide through by 3 to have:
3x/3 - 6y/3 = 8/3
x - 2y = 8/3
Hence the value of x - 2y is 8/3
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Which expression is equivalent to √-80
O 4√5
O -4√√51
4√√51
O 4√√5
Answer: [tex]4i\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{-80}\\\\=\sqrt{-1} \sqrt{80}\\\\=\sqrt{-1} \sqrt{16} \sqrt{5}\\\\=4i\sqrt{5}[/tex]
None of the provided options is equivalent to √-80.
We have,
To simplify the expression √-80, we need to determine the square root of -80.
However, since -80 is a negative number, its square root is not a real number.
The square root of a negative number is usually expressed using the imaginary unit "i," where i = √(-1).
In this case, we can rewrite the expression as:
√(-1 * 80) = √(-1) * √(80) = i * √(80).
Therefore,
None of the provided options is equivalent to √-80.
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For the system of inequalities below, which ordered pair is a solution?
3x-y<2
3y<9x-6
The solution to the given pair of inequalities is at any point on the line
System of inequalitiesInequalities are expressions that are not separated by an equal sign. Given the system of inequalities as shown:
3x-y<2
3y<9x-6
The solution of the system of inequality is the point of intersection of the lines. From the graphed line below, you can see that the point of intersection is at any point on the line since the lines are the same
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Solve log 5x = 3
A)
B)
C)
D)
Answer:
200
Step-by-step explanation:
log a is the same thing as: [tex]log_{10}{a}=b[/tex] which can be rewritten as [tex]10^b=a[/tex] and in general logarithms are in the form [tex]log_ba=c[/tex] which can be written as [tex]b^c=a[/tex]
Rewrite into exponential form
[tex]10^3=5x[/tex]
Simplify exponent
[tex]1000=5x[/tex]
Divide by 5
x=200
Answer:
200
Step-by-step explanation:
I don't know if there are answer choices but the answer is 200
Find f^-1(x) and it’s domain.
Answer: A
Step-by-step explanation:
Letting [tex]f(y)=x[/tex],
[tex]x=\sqrt{y}-5\\\\x+5=\sqrt{y}\\\\y=(x+5)^{2}[/tex]
Also, the domain of an inverse is the same as the range of the original function, so the range is [tex]x \geq 0[/tex]
a) The difference between the circumference and the diameter of a circle is 90cmFind the radius of the circle
Answer:
r=21.01 cm
Step-by-step explanation:
2r = diameter
Circumference of a circle = pi 2r
difference = 90
pi2r - 2r =90
2r (pi-1) =90
90/(2(pi-1) = r = 21.01 cm
Select all the correct answers.
For which values is this expression undefined?
x-1/(x^2-2x-3) + 5/(2x^2+2x)
The answer choice which represents values for which the expression is undefined is; x = -1.
What value of x renders the expression undefined?It follows from the task content that the expression in discuss is made up of 2 rational expressions and hence, the value of x which makes the expression undefined is -1 because, upon substitution, we have; (1/0) + (5/0); which yields undefined.
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Answer:
x= 3. x= 0, x= -1
Step-by-step explanation:
Correct on edmentum