The transformed function is given as,
[tex]f(x)=-2(x-3)^4+1[/tex]The function is a transformation of the parent function,
[tex]g(x)=x^4[/tex]Consider that the horizontal translation by right by 'c' units is given by,
[tex]g(x)\rightarrow g(x-c)[/tex]Applying the definition, it seems that the first transformation is a translation of the function right by 3 units.
After this first transformation, the function will become,
[tex]g(x)=(x-3)^4[/tex]Now, consider the next transformation, that is, vertical stretch (|a|>0),
[tex]g(x)\rightarrow a\cdot g(x)[/tex]Applying the definition to the function,
[tex](x-3)^4\rightarrow2(x-3)^4[/tex]Thus, the second transformation will be the vertical stretch.
Now, consider the reflection of the function about the x-axis, is characterized by,
[tex]g(x)\rightarrow-g(x)[/tex]Applying the definition to the definition,
[tex]2(x-3)^4\rightarrow-2(x-3)^4[/tex]Thus, the third transformation will be a reflection about the x-axis.
Now, consider that the transformation of vertical translation up by 'd' units, is characterized as,
[tex]g(x)\rightarrow g(x)+d[/tex]Applying the definition,
[tex]-2(x-3)^4\rightarrow-2(x-3)^4+1[/tex]This represents the vertical translation of the function by 1 unit.
Thus, the fourth transformation will be the vertical translation by 1 unit.
And finally, the transformed function is obtained.
Thus, it can be concluded that the parent function undergoes the following transformation sequence to be the given function,
1. Translation right by 3 units.
2. Vertical stretch by a factor of 2.
3. Reflection about the x-axis.
4. Vertical translation by 1 unit.
The coordinate plane shown below shows the locations of the library and park in the town where Rasheed lives. 5 Library 4 2 1 -4 -3 -1 2 4 3 5 -1 -2 Park 5 Which expression represents the distance from the library to the park as modeled on the coordinate grid?
Notice that both the Library and the Park lie on the same vertical line.
Then, to find the distance, count how many units apart are they, or substract their y-coordinates.
The y-coordinate of the Library is 5 while the y-coordinate of the Park is -3. Then, the difference is:
[tex]5-(-3)=5+3=8[/tex]Therefore, the distance between the Library and the Park is:
[tex]8[/tex]find the volume of the figure shown here. round your answer to the nearest tenth
The volume of a cylinder is given by the product of the area of its base times its height. If the base of the cylinder has a radius r and the height of the cylinder is h, then its volume V is given by the formula:
[tex]V=\pi r^2h[/tex]Substitute r=5cm, h=8cm and use π=3.14 to find the volume of the cylinder:
[tex]\begin{gathered} V=3.14(5cm)^2(8cm) \\ =3.14\cdot25cm^2\cdot8cm \\ =3.14\cdot200cm^3 \\ =628cm^3 \end{gathered}[/tex]Therefore, the volume of the cylinder is:
[tex]628cm^3[/tex]Let f(x) = x + 3 and g(x) = . The graph of (fog)(x) is shown below.83-6 +5+432->4--2-2343*What is the range of (fºg)(x)?
we can notice the range from the graph, then we see the possible values of y
the graph can take all values of y except y=3 because the graph has an asymptote, never touch 3
the green line is the asymptote
then the range is
[tex](-\infty,3)U(3,\infty)[/tex]or Real numbers except 3
Determine whether the given ordered pair is a solution to the system of equations. 6x−2y =30 −3x+3y =15 and (10,15)
Explanation
We have the simultaneous equation
[tex]\begin{gathered} 6x-2y=30---equation\text{ 1} \\ -3x+3y=15---equation\text{ 2} \end{gathered}[/tex]To check if (10,15) is a solution, we will have to substitute
x=10 and y=15
into both equations and check if it is true
So for equation 1
[tex]\begin{gathered} 6(10)-2(15)=30 \\ True \end{gathered}[/tex]Next, for the second equation
[tex]\begin{gathered} -3(10)+3(15)=15 \\ True \end{gathered}[/tex]Thus,
We can conclude that (10,15) is a solution
Range of 49,49,51,47,49
The range of a set of numbers is the difference between the highest and lowest value.
To find the range:
1) Find the highest and lowest number.
Highest = 51
Lowest = 47
2) Substract the lowest from the highest value.
Range = 51 - 47
Range = 4
Answer: Range = 4.
Which of the following identities are true? Select all that apply. 3 answers
Solution
Step 1
Trigonometric inverse theorem
[tex]csc\theta\text{ = }\frac{1}{sin\theta}\text{ TRUE}[/tex]Step 2
[tex]\begin{gathered} Trigonometric\text{ ratio} \\ cot\theta\text{ = }\frac{cos\theta}{sin\theta} \\ Option\text{ B is FALSE} \end{gathered}[/tex]Step 3
[tex]\begin{gathered} 1\text{ + cot}^2\theta \\ =\text{ 1 + }\frac{cos^2\theta}{sin^2\theta} \\ =\text{ }\frac{sin^2\theta+cos^2\theta}{sin^2\theta} \\ \text{= }\frac{1}{sin^2\theta} \\ \text{= csc}^2\theta \\ 1\text{ + cot}^2\theta\text{ = csc}^2\theta\text{ TRUE} \end{gathered}[/tex]Step 4
[tex]\begin{gathered} sin(-\pi) \\ =\text{ sin\lparen0-}\pi) \\ =\text{ sin0cos}\pi\text{ - sin}\pi cos0 \\ =\text{ -sin}\pi \\ sin(-\pi)\text{ = -sin}\pi \\ Option\text{ D is FALSE} \end{gathered}[/tex]Step 5
[tex]\begin{gathered} cos(-\pi) \\ =\text{ cos\lparen0-}\pi) \\ =\text{ cos0cos}\pi\text{ + sin0sin}\pi \\ =\text{ cos}\pi \\ cos(-\pi)\text{ = cos}\pi\text{ TRUE} \end{gathered}[/tex]M R 3 5 N 6 10. B S 6 L 7 ALMN А E 6 D B 8 20 20
8) To see if the triangles are similar que hace to calculate the ratio beetwen the side so:
[tex]\begin{gathered} \frac{5}{6}=\frac{6}{7}=\frac{3}{4} \\ 0.83=0.88=0.75 \end{gathered}[/tex]So the ratios are nor constant so the triangles are not similar
Which of the following shows the simplified function of sec x sin?
we have the expression
[tex]secxsin(\frac{\pi}{2}-x)[/tex]Remember that
[tex]sin(A-B)=sinAcosB-cosAsinB[/tex]therefore
[tex]\begin{gathered} sin(\frac{\pi}{2}-x)=sin\frac{\pi}{2}cosx-cos\frac{\pi}{2}sinx \\ \\ sin(\frac{\pi}{2}-x)=cosx \end{gathered}[/tex]substitute in the given expression
[tex]\begin{gathered} secx(cosx) \\ (\frac{1}{cosx})cosx \\ 1 \end{gathered}[/tex]The answer is 1Profit, P(x), is the difference between revenue, R(2), and cost, C(2), so P(x) = R(x) - C(x) whichexpression represents P(x), if R(x) = 2x4 - 3x + 2x – 1 and C(x) = x4 – x2 + 2x + 3?
Given:
[tex]\begin{gathered} P(x)=R(x)-C(x) \\ R(x)=2x^4-3x+2x-1 \\ C(x)=x^4-x^2+2x+3 \end{gathered}[/tex]Substitute the expression of R(x) and C(x) in the expression of P(x).
[tex]\begin{gathered} P(x)=2x^4-3x+2x-1-(x^4-x^2+2x+3) \\ P(x)=2x^4-3x+2x-1-x^4+x^2-2x-3 \\ P(x)=(2x^4-x^4)+(-3x+2x-2x)+(x^2)-3-1 \\ P(x)=x^4(2-1)+x(-3+2-2)+x^2-4 \\ P(x)=x^4\times1+x\times-3+x^2-4 \\ P(x)=x^4-3x+x^2-4 \\ P(x)=x^4+x^2-3x-4 \end{gathered}[/tex]Thus, the above expression of P(x) represents the simplest expression of P(x).
23. S is the sum of the first 100 consecutive positive even integers, and T' is the sum of the first 100 consecutive positive integers. S is what percent greater than 7?A. 100%B. 50%C.10%D.2%
S is the sum of the first 100 consecutive positive even integers, and T' is the sum of the first 100 consecutive positive integers. S is what percent greater than T?
A. 100%
B. 50%
C.10%
D.2%
we have that
t=1/2 * n(n+1) = sum all numbers from 1 to n
For n=100
t=1/2 * 100(100+1)=5,050
s=n(n+1) = sum 1st n even numbers
s=100(100+1)=10,100
so
s/t=10,100/5,050
s/t=2
therefore
the answer is 100%option AQuestion 20 - 5 PointsJon 14, 10:17:14 PM?In APRQ shown below, point S is on QR, and point T is on PR so thatZPQR = ZSTR. If PQ = 104, ST = 40, and RP = 130, find the length ofRS. Figures are not necessarily drawn to scale.TQSRoo
Since we are told that angles PQR and STR are congruent, we can draw each triangle apart from each other, as follows
Since they have one congruent angle, we can see that one triangle is a drawn as scale from the other. Having the congruent angle in the same position (left most corner of each triangle) allows us to relate the sides of each triangle regarding their positions with respect to the congruent angle. In the picture we have draw colored lines for each pair of related sides. Since they are similar triangles, we can establish the following equation
[tex]\frac{ST}{PQ}=\frac{SR}{PR}[/tex]We have PQ=104, ST =40 and PR = 130. Thus
[tex]\frac{SR}{130}=\frac{40}{104}[/tex]So, by multiplying both sides by 130 we get
[tex]SR=\frac{130\cdot40}{104}=\frac{5200}{104}=50[/tex]find the sum of the angle measures of each polygon 50 - gon
To be able to find the sum of all angles in a 50 - gon, we will be using the following formula:
[tex]\text{ (n - 2) x 180}[/tex]Where,
n = number of sides = 50
We get,
[tex]\text{ (n - 2) x 180}[/tex][tex]\text{ = (50 - 2) x 180}[/tex][tex]\text{ = 48 x 180}[/tex][tex]\text{ = 8,640}^{\circ}[/tex]Therefore, the sum of all angles inside a polygon is 8,640
Answer:
8640°
Step-by-step explanation:
Formula: 180(n-2) = 180(50-2) = 8640
Louise Tammy Dolores and Cheryl score 78 points in the tennis matches they play. A score consecutive number of points from smallest to greatest in respect to the order of the name is mentioned. How many points does Lewis score? Options:A. 19 pB. 20 pC. 21 pD. 18 p
Given that:
• Louise Tammy Dolores and Cheryl score 78 points in the tennis matches they play.
• A score consecutive number of points from smallest to greatest in respect to the order of the names: Louise Tammy Dolores and Cheryl.
Let be:
- The number of points that Louise scored in the tennis matches:
[tex]n[/tex]- The number of points that Tammy scored in the tennis matches:
[tex]n+1[/tex]-The number of points that Dolores scored in the tennis matches:
[tex]n+2[/tex]- The number of points that Cheryl scored in the tennis matches:
[tex]n+3[/tex]You can set up the following equation to represent the total number of points they scored in the tennis matches:
[tex]n+(n+1)+(n+2)+(n+3)=78[/tex]Now you can solve for "n":
[tex]n+n+1+n+2+n+3=78[/tex][tex]4n+6=78[/tex][tex]4n=78-6[/tex][tex]\begin{gathered} n=\frac{72}{4} \\ \\ n=18 \end{gathered}[/tex]Hence, the answer is: Option D.
Would the top be 1 and the bottom be 6
2÷ 0
We cannot divide by 0
Take a piece of paper and cut it into zero pieces.
We cannot do that. We will still have pieces of paper.
We cannot divide by 0
2 ÷ 0 = undefined
0 ÷ 6
If you start with 0 and divide by something, you will still have 0
You cannot divide nothing into something
0 ÷ 6 = 0
I need help with the steps to solve the attach problem in the photo.
• We are told that there were 3/8 in the begining , where 3 is the number of advaced maths and 8 is the number of regular maths .
,• 4 /7 were the final results . meaning 4 advanced and 7 regular maths
,• 4/7 : 92/x ( where x is final advanced, and x is the regular maths )
so, 3+8 = 11 and 4+7 = 11
if 92 students are equal to 4 in the final ratio;
92 / 4 = 23 in the ratio of 1
therefore :
if 4 : 92
then 7 : 23
7 x 23 = 161 students in regular maths
161 + 92 = 253 students in total
(extra notes :if you want to find the original class numbers
253 /11 = 23
23 X 3 = 69
23 X8 = 184
this means that there were 69 advanced and 184 regular students)
The table shows the height, in centimeters, of the water in a swimming pool at different times since the pool started to be filled.Does the height of the water increase by the same amount each minute? Explain how you know.Does the height of the water increase by the same factor each minute? Explain how you know.
The table shows us the next information:
0 mins - 150 height
1 min - 150.5, the height increase 0.5 because 150+0.5 = 150.5
2 mins - 151, the height increase 0.5 because 150.5 +0.5 = 151
3 min - 151, the height increase 0.5 becuase 151.5
Question 1
Therefore, we can deduce that we have a linear equation because we have a common difference. Hence, the height of water increase by the same amount each time.
Question 2
Now, the table doesnt increase by the same factor because the tables doesnt represents an exponential equation.The factors are close but not the same.
The box plot below represents some data set. What percentage of the data values aregreater than 78?
To determine the percentage of the data that is greater than 78, the first step is to identify the value on the number line and the corresponding part on the box plot.
Each division on the number line represents 2 units.
The left side of the box is determined by the first quartile (Q1), if you look at the picture above, the first quartile is equal to 66.
The line in the middle of the box represents the second quartile (Q2) or median of the data set, in this case, the second quartile is 72.
The right side of the box is determined by the third quartile (Q3) of the data set, looking at the number line, the value of the third quartile corresponds to 78.
The third quartile is the value of any data set that divides the bottom 75% of the values from the top 25% of the values.
This means that the percentage of values less than 78 is 75%, and the percentage of values greater than 78 is 25%
What is the equation of the circle shown?785432.А1-B-8-5-4-3-2-1 02.4-1-2-3-4-5(x2 + (y)2 =IIWord Bank:10 -2 5 + 2 - 1+ 1 25Blank 1:Blank 2:Blank 3:
Consider that the equation of a circle with center (h,k) and radius 'r' units, is given by,
[tex](x-h)^2-(y-k)^2=r^2[/tex]Observe the given diagram carefully.
The center of the circle lies at (-2,1),
[tex](h,k)=(-2,1)[/tex]The radius of the circle is the distance of any point on the circle from the center. Since the point (3,0) lies on the circle, the radius is calculated as,
[tex]r=3-(-2)=3+2=5[/tex]Substitute the values in the standard equation of circle,
[tex]\begin{gathered} (x-(-2))^2-(y-1)^2=5^2 \\ (x+2)^2-(y-1)^2=25 \end{gathered}[/tex]Thus, the equation of the given circle is,
[tex](x+2)^2-(y-1)^2=25[/tex]determine the domain of each functions y=3/2
The equation is given
[tex]y=\frac{3}{2}[/tex]The domain of each functions y=3/2 is
[tex]D=(-\infty,\infty)[/tex]
A vertical tower is 20 m high from the horizontal ground. The angle of depression of aball from the top of the tower is 42°. Calculate the distance, in m, of the ball from thebase of the tower
ANSWER
22.2 m
EXPLANATION
Let us make a sketch of the problem.
From the diagram:
T = top of the tower
B = Ball
O = Base of the tower
Now, we have to find x, which is the distance from the ball to the base of the tower.
Since the angle of depression is 42°, it means that angle
To find x, we can apply Pythagoras Rule:
[tex]\begin{gathered} \tan (<\text{OTB) = }\frac{x}{20} \\ \Rightarrow\text{ x = 20 }\cdot\text{ tan(48)} \\ x\text{ = 20 }\cdot\text{ 1.11} \\ x\text{ = 22.2 m} \end{gathered}[/tex]The distance of the ball from the base of the tower is 22.2 m
find three points that solve the equation X - 3y = -6
Given the linear equation:
[tex]x-3y=-6[/tex]The single linear equation above contains two variables. Hence, there is no unique solution but infinitely many pairs of solutions. For every value of x, there is a value for y.
Three points that solve the equation would be:
Solution 1
Put x = -6 into the equation
[tex]\begin{gathered} -6-3y=-6 \\ -3y=-6+6 \\ \frac{-3y}{-3}=\frac{0}{-3} \\ y=0 \end{gathered}[/tex]Solution 2
Put x = 0 into the equation
[tex]\begin{gathered} 0-3y=-6 \\ -3y=-6 \\ \frac{-3y}{-3}=\frac{-6}{-3} \\ y=2 \end{gathered}[/tex]Solution 3
Put x = 12 into the equation
[tex]\begin{gathered} 12-3y=-6 \\ -3y=-6-12 \\ -3y=-18 \\ \frac{-3y}{-3}=\frac{-18}{-3} \\ y=6 \end{gathered}[/tex]Therefore, three points that solve the linear equation as shown above are:
[tex]\begin{gathered} (x,y)=(-6,0) \\ (x,y)=(0,2) \\ (x,y)=(12,6) \end{gathered}[/tex]
Can you help me please i will give you a branlist and i did part a i want part b please
Given:
D (2, 6)
E (4, 2)
F (6, 4)
and scale factor of 3/2. To find D'E'F' you have to multiply each coordinate by the scale factor, as follows:
D' (2*3/2, 6*3/2) = D' (3, 9)
E' (4*3/2, 2*3/2) = E' (6, 3)
F' (6*3/2, 4*3/2) = F' (9, 6)
Hey! Can anyone help me with my practice worksheet question?
Since the inequality has a greater or equal sign, the boundary line of inequality must be a solid line.
So, options on the left side are out.
Now, it says that y ≥ 1-3x, so the shaded area must be above the y-axis.
Test a point to see if it satisfies the inequality:
x=0 and y =0 ; y ≥ 1-3x
0 ≥ 1-3(0)
0 ≥ 1
Since the point doesn't satisfy the inequality, point (0,0) doesn't belong to the shaded region.
Correct option is the top right one.
For each linear system of equations, identify the
solution; if there is no solution, put an asterisk (*) in
the boxes for the coordinate values.
System A has a solution at
System B has a solution at(
System C has a solution at
A. y=x+5
V = 3x -3
B.
-2V
-1+7
8V = 4x + 10
C. y=
-3x
x+ y = 16
EXPLANATION
First equation:
y = x + 5
y = 3x - 3
[tex]\mathrm{Substitute\:}y=3x-3[/tex][tex]\begin{bmatrix}3x-3=x+5\end{bmatrix}[/tex][tex]\mathrm{Add\:}3\mathrm{\:to\:both\:sides}[/tex][tex]x-3+3=x+5+3[/tex]Simplify:
[tex]3x=x+8[/tex][tex]\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}[/tex][tex]3x-x=x+8-x[/tex]Simplify:
[tex]2x=8[/tex][tex]\mathrm{Divide\:both\:sides\:by\:}2[/tex][tex]\frac{2x}{2}=\frac{8}{2}[/tex]Simplify:
[tex]x=4[/tex][tex]\mathrm{For\:}y=3x-3[/tex][tex]\mathrm{Substitute\:}x=4[/tex][tex]y=3\cdot \:4-3[/tex][tex]\mathrm{Simplify}[/tex][tex]y=9[/tex]Therefore, System A has a solution at (4,9)
Second equation:
[tex]\begin{bmatrix}-2y=-x+7 \\ 8y=4x+10\end{bmatrix}[/tex][tex]\mathrm{Divide\:both\:sides\:by\:}-2[/tex][tex]\frac{-2y}{-2}=-\frac{x}{-2}+\frac{7}{-2}[/tex]Simplifying:
[tex]y=-\frac{-x+7}{2}[/tex][tex]\mathrm{Substitute\:}y=-\frac{-x+7}{2}[/tex][tex]\begin{bmatrix}8\left(-\frac{-x+7}{2}\right)=4x+10\end{bmatrix}[/tex]Removing the parentheses:
[tex]=-8\cdot \frac{-x+7}{2}[/tex]Multiplying fractions:
[tex]=-\frac{\left(-x+7\right)\cdot \:8}{2}[/tex][tex]\mathrm{Divide\:the\:numbers:}\:\frac{8}{2}=4[/tex][tex]-4\left(-x+7\right)=4x+10[/tex][tex]\mathrm{Refine\:}-4\left(-x+7\right)=4x+10[/tex][tex]-38=0[/tex][tex]-38=0\:\mathrm{\:is\:false,\:therefore\:the\:system\:of\:equations\:has\:no\:solution}[/tex]System B has a solution at (*,*)
Third equation:
[tex]\begin{bmatrix}y=-3x\\ x+y=16\end{bmatrix}[/tex][tex]\mathrm{Substitute\:}y=-3x[/tex][tex]\begin{bmatrix}x-3x=16\end{bmatrix}[/tex][tex]\begin{bmatrix}-2x=16\end{bmatrix}[/tex][tex]\mathrm{Divide\:both\:sides\:by\:}-2[/tex][tex]\frac{-2x}{-2}=\frac{16}{-2}[/tex]Simplify the expression:
[tex]x=-8[/tex][tex]\mathrm{For\:}y=-3x[/tex][tex]\mathrm{Substitute\:}x=-8[/tex][tex]y=-3\left(-8\right)[/tex][tex]\mathrm{Simplify}[/tex][tex]y=24[/tex][tex]\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}[/tex][tex]y=24,\:x=-8[/tex]Therefore, System C has a solution at (-8,24)
What is 12 = 4 + 7 x 8
Answer:
Step-by-step explanation:
PEMDAS
I need help with this question
Let:
[tex]\begin{gathered} B=(3,2) \\ B^{\prime}=(-2,-2) \\ \end{gathered}[/tex]After a translation 5 units left
[tex]B\to(3-5,2)\to(-2,2)[/tex]and after a reflection across the x-axis:
[tex]B\to(x,-y)\to(-2,-2)[/tex]Identify the type of observational study. A researcher plans to obtain data by examining the financial transactions of victims who perished in a tornado.Choose the correct type of observational study below.A. retrospectiveB. cross-sectionalC. prospective
Take into account that a retrospective study looks backwards and examines different types of situations based on previous results.
Based in the previous definition, you can conclude that for the given case, the type of observational study is
A. retrospective
because the information is about situations in the past
1. Choose the correct verbal expression for thealgebraic expression 2(y2-9) + 4.*
All algebraix expression follow rules of ( PEMDAS ) where,
[tex]\begin{gathered} P\colon\text{ Paranthesis} \\ E\colon\text{Exponents} \\ M\colon\text{ Multiplication} \\ D\colon\text{ Division} \\ A\colon\text{ Addition} \\ S\colon\text{ Subtraction} \end{gathered}[/tex]The acronyms for algebraic manipulation rule ( PEMDAS ) is given above. The same rule is also applied when you are verbally describing any algebraic expressions or equations.
The priority of algebraic manipulation decreases down the list given above.
We are given an algebraic expression as follows:
A 12 -ounce can of fizzy cola has a mean volume of 12oz with a standard deviation of 0.25oz harry opens a can and measures and fines he has less than 11.5 oz of cola. What’s the probability of this occurring?
Given:
[tex]\begin{gathered} Mean=12 \\ Standarddeviation=0.25 \end{gathered}[/tex]To Determine: The probability of a measures that has less than 11.5
Solution
The formula for finding the z for a one sample of a random distribution is given as
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]See attached I wasn’t able to write all the characters:Suppose r and p are true, and the statements s and t are false. Indicate the truth value of each statement. Do not construct a truth table
r and p = true
s and t = false
The logical expression is given by
[tex](p\wedge t)\leftrightarrow(p\rightarrow s)[/tex]Let us solve the above expression.
(p ∧ t) means p and t
(p ∧ t) is true if p and t both are true.
But we know that both p and t are not true since t is false.
So, (p ∧ t) is false.
(p -> s) means p implies s
(p -> s) is true if p is false or s is true.
But we know that p is true and s is false.
This means that (p -> s) is false.
Finally,
↔ means equivalent
(p ∧ t) ↔ (p -> s) is true if both are true or both are false.
We know that (p ∧ t) is false and (p -> s) is false
So, (p ∧ t) ↔ (p -> s) is true since both of them are false.