Answers
Answer:
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
Step-by-step explanation:
The graph of function f(x) is the parent function.
(Parent functions are the simplest form of a given family of functions).
The graph of g(x) is related to the graph of f(x) by a series of transformations. To determine the series of transformations, work out the steps of how to go from f(x) to g(x).
Transformations
For a > 0
[tex]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of }\:a \\& \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\& \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a \end{aligned}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
Parent function:
[tex]f(x)=x^3[/tex]
Step 1
Multiply the parent function by 6:
[tex]\implies 6f(x)=6x^3[/tex]
Therefore, this is a vertical stretch by a factor of 6.
Step 2
Now make the function negative:
[tex]\implies -6f(x)=-6x^3[/tex]
Therefore, this is a reflection in the x-axis.
Step 3
Finally, add 2 to the function:
[tex]\implies -6f(x)+2=-6x^3+2[/tex]
Therefore, the function has been translated 2 units up.
Conclusion
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
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Related Questions
find arc length
x=t^(3)-2t
y=t^(2)-3
-2>t<2
Answers
Answer:
72
Step-by-step explanation:
I got it right .......
Given the first degree function f(x) = 2x +3, what is the value of f(10)?
a) 23
b) 25
c) 30
d) 50
Answers
Answer:
a
Step-by-step explanation:
substitute x = 10 into f(x) , that is
f(10) = 2(10) + 3 = 20 + 3 = 23
hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა
⊱┈────────────────────────┈⊰
[tex]\large \bold {ANSWER}[/tex]
[tex]\boxed{\underline{\huge{\tt{\orange{\: \: a)23 \: \: }}}}}[/tex][tex]\large \bold {SOLUTION}[/tex]
Given the first-degree function:
[tex]\Large\begin{array}{c}\rm f(x)=2x+3\end{array}[/tex]
We were asked to determine the value of f(10), so, to find its value, just replace the 10 where there is x in the function, see:
[tex]\begin{gathered}\Large\begin{array}{c}\rm f(x)=2x+3\\\\ \rm f(10)=2\cdot 10+3\end{array}\end{gathered}[/tex]
You see, we put that dot there, which indicates multiplication, because when a number is next to a letter it indicates that it is multiplying, thus:
[tex]\begin{gathered}\Large\begin{array}{c}\rm f(10)=2\cdot 10+3\\\\ \rm f(10)=20+3\\\\ \red{\boxed{\rm f(10)=23}}\checkmark\end{array}\end{gathered}[/tex]
Hence, the value of f(10) in this function is equal to 23.
Move the slider on the graph on the right to graph each function:
For the function: y = StartRoot x minus 7 EndRoot + 1
The domain is : x ≥
The range is: y ≥
Answers
Answer:
domain: x ≥ 7 . . . [7, ∞) in interval notationrange: y ≥ 1 . . . [1, ∞) in interval notationStep-by-step explanation:
You want the domain and range of the function y = √(x -7) +1.
DomainThe domain is the horizontal extent of the graph. The graph of the given function extends to the right from x=7, which is included in the solution set.
The domain is x ≥ 7.
RangeThe range is the vertical extent of the graph. The graph of the given function extends upward from y=1, which is included in the solution set.
The range is y ≥ 1.
Answer: domain: 7
range: 1
Step-by-step explanation:
54-90.27-90.22-90.87-90
Answers
Answer: -307.36 I think
Step-by-step explanation:
Over what interval is the function in this graph increasing? A. –5 ≤ x ≤ 5 B. –3 ≤ x ≤ 2 C. –4 ≤ x ≤ –2 D. –2 ≤ x ≤ 3
Answers
The function in this graph is increasing in the interval –2 ≤ x ≤ 3 , Option D is the right answer.
What is a function ?A function is a mathematical statement used to relate a dependent and an independent variable.
From the graph it can be seen that the graph is increasing in the interval
–2 ≤ x ≤ 3
The graph is said to be increasing when the value of y is getting more and more positive
As –2 ≤ x ≤ 3 , y varies from -3 to +3
Therefore Option D is the right answer.
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Answer:
–2 ≤ x ≤ 3
Step-by-step explanation:
Barbara buys a box of pens for $4. For every additional box she buys, she gets a $1 discount. Which expression represents the total cost of the -
pens, c, as a function of the number of boxes, b?
Answers
Answer:
Step-by-step explanation:
If a heart beats 36 times in 30 seconds, how many times will it beat in 60 seconds
Answers
Given sinθ=1/2 determine the value of sec θ. 0°<θ<90°
Given Choices
2/√3
√3/2
2
1
Answers
Answer:
[tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]
Step-by-step explanation:
Given [tex]sin(\theta)=\frac{1}{2}[/tex] , to find [tex]sec(\theta)[/tex], it will be helpful to visualize a right triangle (triangle with a 90 degree angle) associated with that particular θ. There are a few ways to go about this:
A general solution methodAll of the basic trigonometric functions, applied to an angle) are a ratio of two specific sides of any right triangle that holds that angle.
Remember that the Sine of an angle is defined specifically, the ratio of the opposite side (the side across from the angle in the Sine function), and the hypotenuse (the side across from the right angle). You might remember this through SohCahToa
[tex]sin(\theta)=\frac{opp}{hyp}[/tex]
In our case, since [tex]sin(\theta)=\frac{1}{2}[/tex] , so [tex]\frac{opp}{hyp}=\frac{1}{2}[/tex] . While there are an infinite number of triangles that have that ratio of those sides, they are all "similar" triangles (corresponding angles congruent, and corresponding sides are proportional, yielding common ratios of sides), and for ease, we can consider simply the triangle where the value of the numerator is the length of the opposite side, and the value of the denominator is equal to the hypotenuse. So, [tex]opp=1[/tex], and [tex]hyp=2[/tex].
While we haven't actually talked about θ yet, we can still set up the triangle that has these sides so that we can visualize what the triangle looks like. (see image)
This triangle represents the triangle for the unknown θ in the original sine function. We're tasked with finding the secant of that particular unknown θ.
Working toward Secant
Here, it will be helpful to remember either the reciprocal identities for[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex], or the definition of the secant function [tex]sec(\theta)=\frac{hyp}{adj}[/tex].
I find that most people remember the reciprocal identities more easily than keeping track of the definitions, so, since secant is related to cosine, it will be important to remember that [tex]cos(\theta)=\frac{adj}{hyp}[/tex]. From there, take the reciprocal of the cosine-value to get the secant-value (which matches the definition of the secant function).
Either way, it comes down to knowing the lengths of the side adjacent to theta, and the hypotenuse. We already know the length of the hypotenuse, so we just need the length of the adjacent side.
Applying the Pythagorean Theorem
Fortunately, because it is a right triangle, the Pythagorean Theorem applies: [tex]a^{2} +b^{2} =c^{2}[/tex] (where c is the length of the hypotenuse, and a & b are the lengths of the legs)
Substituting the known values for the sides we do know...[tex](adj)^{2} +(1)^{2} =(2)^{2}\\(adj)^{2} +1 =4[/tex]
...isolating "adj" by subtraction...
[tex](adj)^2=4-1\\(adj)^2=3[/tex]
...applying the square root property...
[tex]adj=\sqrt{3}[/tex] or [tex]adj=-\sqrt{3}[/tex]
Identifying which Quadrant the triangle is in
Since we were given that [tex]0^o < \theta < 90^o[/tex], our triangle is an acute triangle (as drawn in the diagram), and is in quadrant I (indicating that both legs will be measured with a positive value.
Thus, we discard the negative solution and conclude that [tex]adj=\sqrt{3}[/tex].
Finding the final solution
From there, [tex]cos(\theta)=\frac{adj}{hyp}[/tex] implies [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex], and through the reciprocal relationship (or simply the definition of secant, whichever is easier for you to remember), [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex]
Note: This method did not require knowing what the angle θ was.
Alternative method using the Unit CircleIf you know well the values of special triangles in the unit circle, you may have identified that [tex]sin(\theta)=\frac{1}{2}[/tex] is associated with [tex]\theta=30^o[/tex]. If so, if you also recall that the ordered pair associated with that point on the unit circle is [tex](\frac{\sqrt3}{2} ,\frac{1}{2} )[/tex], and that the [tex]cos(\theta)=x\text{-coordinate on the unit circle}[/tex], then you can quickly identify that [tex]cos(\theta)=\frac{\sqrt3}{2}[/tex].
This method still ends the same: recalling the reciprocal relationship between cosine and secant, giving [tex]sec(\theta)=\frac{2}{\sqrt3}[/tex].
The polynomial f(x) has degree 3. Choose each statement that could describe all zeros of f.
Answers
The true statements are
(a) -one zero with multiplicity 3(d) -one zero with multiplicity 1 and one zero with multiplicity 2(l) -Three zeros with multiplicity 1Missing information in the question-one zero with multiplicity 3
-one zero with multiplicity 4
-one zero with multiplicity 5
-one zero with multiplicity 1 and one zero with multiplicity 2
-one zero with multiplicity 1 and one zero with multiplicity 3
-one zero with multiplicity 2 and two zeros with multiplicity 1
-one zero with multiplicity 2 and three zeros with multiplicity 1
-Two zeros with multiplicity 2
-Two zero with multiplicity 2 and two zeros with multiplicity 1
-Two zero with multiplicity 2 and three zeros with multiplicity 1
-Two zero with multiplicity 1
-Three zeros with multiplicity 1
-Four zeros with multiplicity 1
-Five zeros with multiplicity 1
How to determine the true statements?The function is given as:
f(x)
And it has a degree of 3
This means that
The total multiplicity of the zeros of the function is 3 It cannot have more than three zeros i.e. it can have 1, 2 or 3 zerosUsing the above highlight as a guide, the true statements are (a), (d),and (l)
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(-7x^2+3)-(-4x-3)
(−7x
2
+3)−(−4x−3)
Answers
Answer:
-28x^3-28x^2+16x+15
Step-by-step explanation:-28x^3-28x^2+16x+15
A company has 200 machines. Each machine has 129 probability of not working. If you were to pick 40 machines randomly, the probability that 5 would not be working is and the probability that at least one machine would be working is the probability that all would be working is
Answers
The probability that 5 would not be working is 0.18665, the probability that at least one machine would be working is 0.00602 and the probability that all would be working is 1.
Given a company has 200 machines. Each machine has a 12% probability of not working.
If we working pick 40 machines randomly then we have to find the probability that 5 would not be working, the probability that at least one machine would be working, and the probability that all would be working.
So
1) probability that 5 would not be working
C(40,5)·0.12⁵·0.88³⁵= 40!/(5!(40-5)!)·0.12⁵·0.88³⁵
≈ 0.18665
2) probability that at least one machine would be working
0.88⁴⁰ ≈ 0.00602
3) probability that all would be working
1 - 0.12⁴⁰ ≈ 1.0000
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James has available a 10% alcohol solution and a 60% alcohol solution find how many liters of each solution he shouldn’t mix to make 50 L of a 40% alcohol solution
Answers
Answer:
20 L
Step-by-step explanation:
I am guessing that you meant should instead of shouldn't.
To solve this we can set the amount of 10% solution needed equal to x. This means that the 60% solution will be the remaining amount needed, so 50 L - x.
We can do 10%*x+60%*(50-x)=50*40%. Solving for x we get:
0.1*x+0.6*50-0.6*x=50*0.4
0.1*x+30-0.6*x=20
-0.5*x=-10
x=20
As a summer job, Bart is picking strawberries at his uncle's farm. He can pick 6
gallons of strawberries in 9 minutes, and his uncles pays him $5 for 2 bushels. How
much does Bart make per hour picking strawberries?
Given: 8 gallons = 1 bushel & 60 minutes = 1 hour
Answers
Answer:
125
Step-by-step explanation:
All the work is in picture attat
Given the exponential growth function f ( x ) = 75 ( 1.02 ) x f ( x ) = 75 ( 1.02 ) x What is the initial value of the function? What is the growth factor, or growth rate of the function (as a percent)? %
Answers
Answer:
Step-by-step explanation:
The initial vale is when x = 0
- That is 75,
The growth factor is 2%.
Please help me find the area of this trapeziod.
Answers
Answer:
37.5 m
Step-by-step explanation:
Since the trapezoid area formula is ((base 1+base 2)/2)*height, we can plug in the values.
((8+7)/2)*5
(15/2)*5
7.5*5=37.5
Now we add the unit, "m" to get 37.5 m!
what is the probability that a family with three children will have all girls?
A) 1/2
B) 1/8
C) 25%
D) .10
Answers
Answer:
B) 1/8
Step-by-step explanation:
each child born has 50/50 to be a boy or a girl, so, we determine a Bernoulli process where p=0.5, and we need 3 out of 3 successes.
the probability will then be:
(0.5)³=0.125=1/8
Explain how to graph a scatterplot and its regression line using a regression calculator
Answers
Press the Linear Regression button to generate the regression line.
We have given that, regression line using a regression calculator
We have to determine how to graph a scatterplot and its regression line using a regression calculator.
Before entering data into the regression calculator, it is important to determine which variable should be associated with the x-axis and which with the y-axis.
What is the regression line?
Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more independent variables.
Enter the data pairs.
Press the Linear Regression button to generate the regression line.
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4x^2 +16x -20 = 0
What is x
Answers
Answer:
x = 1, -5
Step-by-step explanation:
4(x^2 + 4x - 5) = 0
4(x - 1)(x + 5) = 0
x = 1, -5
If f(x) = 3x + 2 what is f(5)?
Answers
Answer:
f(1)= 3×1 + 2 = 5
....
.....
....
f(5)= 3×5 + 2 = 17
Answer:
f(5) = 17
Step-by-step explanation:
Given: f(x) = 3x + 2
We are asked to find the value of the function when the value of x is 5
Substitute 5 as the value of x in the function:
⇒ f(x) = 3x + 2
⇒ f(5) = 3(5) + 2 [multiply]
⇒ f(5) = 15 + 2 [add]
⇒ f(5) = 17
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Sarah and her friends split a bag of candy evenly. They each ate 13 pieces of candy and there are 2 pieces leftover. How many pieces of candy were originally in the bag?
Answers
Answer:
54
Step-by-step explanation:
⇒ 1 + 3 = 4
⇒ 4 * 13 = 52
⇒ 52 + 2 = 54 (Basic Operation)
convert 0.390 as a fraction
Answers
Answer:
390/1000
This is the answer and hope it helps
Which measure of center is shown in a box plot?
mean
median
mode
range
Answers
5,1
3,1
4,1 is the correct answer
Answer:
(b) median
Step-by-step explanation:
A box-plot is a graphical representation of the 5-number summary of a data set. It includes the minimum, maximum, median, and 1st and 3rd quartiles.
__
The measure of center shown in a box plot is the median.
Find the reciprocal of 8 2/5
Answers
[tex]\huge\underline\red{Answer -}[/tex]
[tex]\bold{8 \frac{2}{5} }\: \\\\ \implies \: \frac{5 × 8 + 2}{5} \: \\ \\ \implies \: \frac{ 40 + 2}{5} \\\\ \implies \frac{42}{5} \\\\ \rightarrow \:\boxed {reciprocal \: = \frac{5}{42} } \\ \\[/tex]
hope helpful ~
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{8 \dfrac{2}{5}}\\\\\mathsf{= \dfrac{8\times5+2}{5}}\\\\\mathsf{= \dfrac{40 + 2}{5}}\\\\\mathsf{= \dfrac{42}{5}}\\\\\mathsf{=\dfrac{5}{42}}\\\\\huge\text{Therefore, the answer should be: \boxed{\mathsf{\dfrac{5}{42}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Complete the following table using the equation: Y = negative 2 x Squared x -2 -1 0 1 2 y Plot the points on a graph and determine which graph best represents the equation. Graph A On a coordinate plane, a parabola opens up. It goes through (negative 1, 2), has a vertex at (0, 0), and goes through (1, 2). Graph B On a coordinate plane, a parabola opens down. It goes through (negative 1, negative 1), has a vertex at (0, 0), and goes through (1, negative 1). a. 8, 2, 0, 2, 8; Graph A b. -8, -2, 0, -2, -8; Graph A c. 8, 2, 0, 2, 8; Graph B d. -8, -2, 0, -2, -8; Graph B Please select the best answer from the choices provided A B C D
Answers
The Graph B best represents a parabola , Option D has the correct data points and so is the right answer.
What is a function ?A function is a mathematical way of representing relation between two variables.
The function given is
y = 2x²
For x = - 2, y = -2(- 2)² = -8
For x = - 1, y = -2(- 1)² = -2
For x = 0, y = -2(0)² = 0
For x = 1, y = -2(1)² = -2
For x = 2, y = -2(2)² = -8
the table of x-y will be:
x - 2 - 1 0 1 2
y -8 -2 0 -2 -8
The graph is attached with the answer.
The parabola opens downward and has the data points as mentioned above .
Therefore Option D is the correct answer.
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Answer:
Step-by-step explanation:
Complete the following table using the equation: y = 2 x squared
x
-2
-1
0
1
2
y
Plot the points on a graph and determine which graph best represents the equation.
Graph A
On a coordinate plane, a parabola opens up and goes through (1, 3), has a vertex at (0, 0), and goes through (1, 3).
Graph B
On a coordinate plane, a parabola opens down and goes through (negative 1, negative 2), has a vertex at (0, 0), and goes through (1, negative 2).
a.
8, 2, 0, 2, 8; Graph A
b.
-8, -2, 0, -2, -8; Graph A
c.
8, 2, 0, 2, 8; Graph B
d.
-8, -2, 0, -2, -8; Graph B
Please select the best answer from the choices provided
A
B
C
D
answer is '' a ' got it right
2x-3<1 or 3x-1<17
Solve compound inequality
Answers
The union consists of all of the elements that are contained in each interval.
Inequality Form:
x<6
Interval Notation:
(−∞,6)
The image of a point K(1,2) after translation is K¹ (-1,2). what is the coordinate of the point R whose image is R¹ (-3,3) after undergoing the same translation.
Answers
simplify: (-291) × 134
Answers
Answer:
-38,994
Step-by-step explanation:
-291*134
=-38,994
Answer:
-38,994
Step-by-step explanation:
(-291) × 134
Apply PEMDAS.
Remember,
- × - = +- × 1 = -Solution:
Evaluating,we obtain
(-291) × 134-38,994if the figure forms the base of a right solid 110 centimeters high, find the surphase area.
Answers
the answer should be 5 inches I guess
A linear function contains the following points: 0,-3 and 6,15.
WHat is the slope and y-intercept
Answers
The slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
A linear function contains the following points: (0,-3) and (6,15)
The slope:
[tex]\rm m =\dfrac{15-(-3)}{6-0}[/tex]
m = 18/6
m = 3
The equation of a line:
y = mx + c
Plug x = 0, y = -3
-3 = c
Thus, the slope of the linear function is 3 and the y-intercept is -3 if the linear function contains the following points: (0,-3) and (6,15)
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Covert 3/7into a percent
Answers
Answer:
42.86%
Step-by-step explanation:
Our percent fraction is 42.857142857143/100, which means that 37 as a percentage is 42.86%
Here we are going to show you step by step how to convert the fraction 3/7 to a percentage.
In the fraction 3/7, 3 is the numerator and 7 is the denominator.
First, we are going to divide the numerator by the denominator. Therefore, we are going to divide 3 by 7.
3 ÷ 7 = 0.428571A percentage shows a number as a proportion of one hundred.
Now we are going to multiply 0.72 by 100 to get the percentage.
0.428571 x 100 = 42.86Therefore, the answer to 3/7 percent is
42.86%Note: If necessary, we round to the nearest hundred.
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