Parent Function Description: A cubic (cubing) function that is reflected over thex axis, has a vertical stretch of 3 units, is shifted right 2 units, and is shifted down4 units.
Answers
Parent function:
f(x) = x³
that is reflected over the x axis
f(x) = -x³
has a vertical stretch of 3 units:
f(x) = -3x³
is shifted right 2 units:
f(x) = -3(x - 2)³
and is shifted down 4 units:
f(x) = -3(x - 2)³ - 4
Related Questions
Simplify the absolute value 8|cos | if = sin−1 8/x for some real number x. (Give your answer in terms of .)
Answers
The absolute value of 8|Cosθ| is 8√(x² - 8²)/|x|.
The value of the angle θ is Sin−1 (8/x). We need to find the absolute value of 8|Cosθ|.
θ = Sin−1 (8/x)
Sinθ = 8/x
We know the trigonometric identity that Sin²θ + Cos²θ = 1.
Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.
(8/x)² + Cos²θ = 1.
Cos²θ = 1 - (8/x)²
Cos²θ = (x² - 8²)/x²
Cosθ = √[(x² - 8²)/x²]
Cosθ = √(x² - 8²)/x
Multiply both the sides with 8.
8Cosθ = 8√(x² - 8²)/x
Apply modulus on both the sides.
A modulus function is one that returns the absolute value of a number or variable.
8|Cosθ| = 8√(x² - 8²)/|x|
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Shen runs each lap in 4 minutes. He will run at least 48 minutes today. What are the possible numbers of laps he will run today?Use n for the number of laps he will run today.Write your answer as an inequality solved for n.
Answers
From the statement, we know that:
0. Shen runs each lap in 4 minutes,
,1. he will run ,at least, 48 minutes today ⇒ t ≥ 48 min.
(1) From point 1, we know that Shen's speed is:
[tex]s=\frac{1\text{ lap}}{4\text{ min}}=\frac{1}{4}\cdot\frac{\text{lap}}{\text{min}}.[/tex](2) The speed (s) times the time (t), we get the # of laps (n):
[tex]n=s\cdot t\ge\frac{1}{4}\cdot\frac{\text{laps}}{\text{min}}\cdot48\text{ min}=\frac{48}{4}\text{ laps}=12\text{ laps}\Rightarrow n\ge12\text{ laps.}[/tex]Answern ≥ 12
Pls help fast !!!!!!!
Answers
The required solution of the function f(x) = -3x + 5 at x = -2 is 11.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given function,
f(x) = -3x + 5
Substitute x with -2 to find f(-2).
f(-2) = -3(-2) + 5
f(-2) = +6 + 5
f(-2) = 11
Thus, the required solution of the function at x = -2 is 11.
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The residents of a city voted on whether to raise property taxes. The ratio of yes to no votes was 5 to 3. If there were 4440 total votes, how many yes votes were there?
Answers
Total votes of the residents of the city = 4,440
Ratio of yes to no = 5:3
Yes votes = 4,440 * 3/5 = 2,664
No votes = 4,440 - 2,664 = 1,776
The profit, in dollars, made by selling x bottles of 100% All-Natural Certified Free-Trade Organic Sasquatch Tonic is given by P ( x ) = − x 2 + 85 x − 620 for 0 ≤ x ≤ 95 . How many bottles of tonic must be sold to make at least $ 130 in profit? Write answer in interval notation.
Answers
The number of bottles of tonic that must be sold to make at least $130 in profit is [10, 75]
How to determine the number of bottles?The profit function is given as
P(x) = -x^2 + 85x - 620
The earnings are given as
Earnings = at least $130
This means that
P(x) ≥ 130
So, we have
-x^2 + 85x - 620 ≥ 130
Subtract 130 from both sides of the inequality
So, we have
-x^2 + 85x - 750 ≥ 0
Divide through by -1
So, we have
x^2 - 85x + 750 ≤ 0
Expand the expression
x^2 - 75x - 10x + 750 ≤ 0
Factorize
x(x - 75) - 10(x - 75) ≤ 0
Factor out x - 75
(x - 75)(x - 10) ≤ 0
Split
x - 10 ≤ 0 and x - 75 ≤ 0
Solve for x
x ≤ 10 and x ≤ 75
Combine the inequality
10 ≤ x ≤ 75
Express as interval
10 ≤ x ≤ 75 = [10, 75]
Hence, the number of bottles is [10, 75]
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N N Which of the following is an equation of line k in the xy-plane above? (A) y=-x-4 (B) y = x+2 (C) 2y - 3x = -8 (D) 2y - 3x = -4
Answers
Answer:
[tex]2y-3x=-8[/tex]Explanation:
Given the graph in the attached image;
The intercept of the line on the y-axis is at;
[tex]\begin{gathered} y=-4 \\ At\text{ point;} \\ (0,-4) \\ \text{ intercept b is;} \\ b=-4 \end{gathered}[/tex]At the x=2, the value of y is;
[tex]\begin{gathered} y=-1 \\ at\text{ point;} \\ (2,-1) \\ \end{gathered}[/tex]The slope of the line can be calculated using the two points on the graph;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-1-(-4)}{2-0}=\frac{-1+4}{2} \\ m=\frac{3}{2} \end{gathered}[/tex]The slope intercept equation of a straight line is of the form;
[tex]y=mx+b[/tex]substituting the slope m and intercept b we have;
[tex]y=\frac{3}{2}x-4[/tex]As this is not among the given options, let us solve further;
multiply through by 2 and move the x term to the left side;
[tex]\begin{gathered} y(2)=\frac{3}{2}x(2)-4(2) \\ 2y=3x-8 \\ 2y-3x=-8 \end{gathered}[/tex]Therefore, from the given options the correct equation for the line is C;
[tex]2y-3x=-8[/tex]'g & & eggs 1 10 15 2015-2016 time {uash. bpeed (m/sec) The graph represents the elapsed time for running with connected speed schedules for two different racers. As the speed increases what happens to the elapsed time for racer B? * 6 Points) Enter your answer
Answers
The relationship between the speed and the elapsed time is a negative relationship. That means as the speed increases, the time elapsed decreases. Thats why the line goes downward from left to right.
For racer B, as the speed increases, the time elapsed decreases at a rate lesser than that of racer A.
what is the absolute value of 1 -32 1?what is the opposite of 6 on the number line?
Answers
Given data:
The given number is | -32| .
The value of given modulus function is,
[tex]|-32|=32[/tex]The opposite of 6 on number line is -6.
Thus, the value of first number is 32, and second is -6.
Find the value of x. Round lengths of segments to the nearest tenth andangle measures to the nearest degree.
Answers
Answer:
7.8
Explanation:
The length x, the side with length 6, and the angle of 40 degrees are related by the trigonometric function cosine, so
[tex]\cos 40=\frac{6}{x}[/tex]Because x is the hypotenuse and 6 is the adjacent side.
Solving for x, we get
[tex]\begin{gathered} x\cos 40=x\cdot\frac{6}{x} \\ x\cos 40=6 \\ \frac{xcos40}{\cos40}=\frac{6}{\cos 40} \\ x=\frac{6}{\cos 40}=\frac{6}{0.766}=7.8 \end{gathered}[/tex]Therefore, the value of x is 7.8
Sort the sequences into categories. Determine which sequences are arithmetic and which are geometric. Drag each label to the correct location on the table. Each label can be used more than once. Arithmetic Sequence Geometric Sequence (90, 87, 84, 81, 78, ...) (4, 12, 36, 108, 324, ...) (8,1,1/8,1/64,1/512,...) (3, 10, 17, 24, 31,...) (1,1.4,1.8, 2.2, 2.6, ...) (3,1.5, 0.75, 0.375,...)
Answers
Given the sequences we are asked to identify whether they are geometric or arithmeti. This can be seen below.
Explanation
For an arithmetic sequence
[tex]T_2-T_1=T_3-T_2^[/tex]For a geometric sequence
[tex]\frac{T_2}{T_1}=\frac{T_3}{T_2}[/tex]Therefore;
Answer:
[tex]\begin{gathered} Arithmetic\text{ sequence}\Rightarrow90,87,84,81,78,.. \\ Geometric\text{ sequence}\Rightarrow4,12,36,108,324,... \\ Geometric\text{ sequence}\Rightarrow8,1,1/8,1/64,1/512,... \\ Arithmetic\text{ sequence}\Rightarrow3,10,17,24,31..... \\ Arithmetic\text{ sequence}\Rightarrow1,1.4,1.8,2.2,2.6.... \\ Geometric\text{ sequence}\Rightarrow3,1.5,0.75,0.375,... \end{gathered}[/tex]Определите количество сторон правильного многоуголь
ника, если угол, смежный с углом многоугольника, составляет 2/3 угла многоугольника
Answers
Answer:
n=6
Step-by-step explanation:
Угол многоугольника 2х, смежного угла х.
2х+х=180.
3х=180.
х=60° .
Углы многоугольника 120°.
Формула углов правильного многоугольника.
аₙ=(n-2)/n * 180.
120=(n-2)/n *180. после преобразования
3(n-2)=2n.
n=6.
Answer: n=6.
Step-by-step explanation:
Factor f(x) = 4x² - 576 = 0
Answers
4x^2 - 576 = (2x - 24)(2x + 24)
Because of conjugated binomials
(a + b)(a - b) = a^2 - b^2
2x is the square root of 4x^2
24 is the square root of 576
answer:
(2x - 24)(2x + 24)
Find the value of x in the triangle shown below.227ASCAssChoose 1 answer:MY= 45Col= 9MY= 5ProProD2 = 53Tea
Answers
The given triangle is a right triangle as shown by the square symbol inside. With this, we can solve the length "x" of this triangle using the Pythagorean Theorem.
[tex]c^2=a^2+b^2[/tex]where c = length of the hypotenuse and "a" and "b" are any of the remaining sides.
In our triangle, we have 7 as our hypotenuse and 2 as the length of the one side. Let's apply these values in the formula above.
[tex]\begin{gathered} 7^2=2^2+b^2 \\ 49=4+b^2 \\ 49-4=4+b^2-4 \\ 45=b^2 \\ \sqrt[]{45}=\sqrt[]{b^2} \\ \sqrt[]{45}=b \\ 3\sqrt[]{5}=b \end{gathered}[/tex]Therefore, the value of x is √45.
6g7g7v7c6clvyc5cubibigl
Answers
he needs to walk the dog 6 times more}
The distance from Earth to the sun is about 9.3 × 107 miles. The distance from Jupiter to the sun is about 4.84 × 108 miles. How much closer is the Earth to the sun than Jupiter to the sun?
Answers
The earth is 3.91×10^8 miles closer to the sun than jupiter
What is distance?Distance is the space or gap between two points or bodies. It is a scalar quantity and measured in cm, m, km, miles e.t.c
The distance between the earth and the is 9.3×10^7 miles and the distance of Jupiter from the sun is 4.84×10^8 . This shows that the earth is closer to sun than Jupiter.
The dimension of how closer the earth is to the sun than Jupiter is therefore
( 4.84×10^8)-(9.3×10^7)= 3.91×10^8 miles
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pleaseeee help!! !!!!!
Answers
Answer: it’s c
Step-by-step explanation: dude that’s ez
How much money should you invest at 5.3% annual simple interest rate to have $7200 in 9 months?
Answers
Answer:
181 132$
Step-by-step explanation:
Co - initial capital
I - interest
r - 5.3% annual simple interest
t - time
I = Co * r * t
7200 = Co * 0.053 * 9/12
Co = 181 132$
Mona borrowed $6,000 for college expenses. After 2 1/2 years she will have paid $750 in interest. What is the interest rate?
Answers
Simple interest is represented by the expression:
[tex]\begin{gathered} I=p\cdot r\cdot t \\ I=\text{interest earned after t years} \\ p=\text{ money borrowed} \\ r=\text{annual rate of interest} \\ t=\text{ the length of time you borrow} \end{gathered}[/tex]Understanding this expression, we can substitute our values:
[tex]750=6,000\cdot r\cdot2.5[/tex]Isolating our variable of interest (r):
[tex]\begin{gathered} r=\frac{750}{6,000\cdot2.5} \\ r=0.05 \end{gathered}[/tex]The interest rate is 0.05 or 5%
(2x^3+13x^2+16x+5)÷(x^2+9x+5)
Answers
The answer will be (x-1). (2x-1). The polynomial equation P(x) = 0 has roots, or solutions, that may be found by setting each factor to 0 and figuring out what x is. Factor the polynomial equation to find the solution. Set each variable to 0. x - 6 = 0 or x + 1 = 0 or 2x4 = 0
Finding polynomial roots (zeroes) is the focus of this solution.
What is quadratic equations?Due to the fact that the variable is squared, the word "quadratic," which means "square," was coined (like x2).
Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a). See examples of how to solve different equations using the formula.
f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.
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Instructions: Identify the type of sequence and write the explicit rule.
Answers
SOLUTION:
Case: Sequences
Method:
3, 12, 48, 192,...
Step1:
The sequence is increasing exponentially
Type: Geometric/Exponential Sequence
Step 2:
The Explicit rule is gotten from the formula:
[tex]a_n=ar^{n-1}[/tex]a= 3,
r= (12/3)
r= 4.
The rule, therefore:
[tex]a_n=3(4)^{n-1}[/tex]Final answer:
Type: Geometric sequence
Explicit rule
[tex]a_n=3(4)^{n-1}[/tex]find the area of the shaded region. Note that the total radius from the center out to the edge of the shaded region is 8+3 = 11.
Answers
Given
The figure.
To find the area of the shaded region.
Explanation:
It is given that,
The radius of the whole circle is 11cm.
And, the radius of the small circle is 3cm.
Then,
The area of the shaded region is,
[tex]\begin{gathered} Area\text{ of the shaded region}=Area\text{ of the whole circle-area of smaller circle} \\ =\pi(11^2)-\pi(3^2) \\ =121\pi-9\pi \\ =112\pi \\ =112\times\frac{22}{7} \\ =351.85cm^2 \end{gathered}[/tex]Hence, the area of the shaded region is 351.85cm^2.
There are 12 girls and 24 boys in a class. What is the ratio of boys to total number of students in the class?
Answers
Answer: 1:2
24 is half of 48
12 + 24 = 36
There are 36 total students.
We can rewrite this ratio with boys to total students:
24 (boys): 36 (total)
The ratio of boys to total students is 24:36; however, we can divide these numbers by 12 to find that the simplified ratio is 2:3.
The ratio of boys to total number of students in the class is 2:3.
Point O is the midpoint of DG. The coordinates of points D and O are (-4, 0) and (-1,-5) respectively
What are the coordinates of point G
Answers
Coordinates of Point G is (1,-10)
To find Coordinates :
O is midpoint of DGCoordinates of O (-1,-5)Coordinates of D (-4,0)Let the coordinates of G are (x,y)
To find coordinates of G
[tex]\frac{x + (-4)}{2} = -1[/tex] [tex]\frac{y + 0}2} = -5[/tex]
= x + (-2) = -1 y+0 = -5 * 2
x = -1 + 2 y = -5 * 2
x = 1 y = -10
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The temperature of a mixture changes by -5.2 Fahrenheit between 8am and 11am. At 6pm the temperature is 14.5 Fahrenheit, which is half of what it was at 11am. What was the temperature at 8am of the mixture. I have this equation , but not sure is correct. 1/2(x-6.8)= -3.1
Answers
Explanation
Let us have a sketch of the question
If the temperature at 6 pm is 14.5 F
And the temperature at 11am is twice that of 6pm
Then the temperature at 11am will be
[tex]2\times14.5F=29F[/tex]Since the temperature of a mixture changes by -5.2 Fahrenheit between 8 am and 11 am.
Then the temperature at 8 am will be
[tex]\begin{gathered} \theta_{11am}-\theta_{8am}=-5.2 \\ 29F-\theta_{8am}=-5.2F \\ \theta_{8am}=29F+5.2F \\ \theta_{8am}=34.2F \end{gathered}[/tex]Therefore, the temperature at 8 am will be 34.2 F
Identify the values of a, b, and c that could be used with the quadratic formula to solve the equation. Enter a as a positive integer value. x^2=4(x-9)
Answers
Given the following equation:
[tex]x^2=4(x-9)[/tex]First of all, we note that the quadratic equation is written in the general form shown below;
[tex]ax^2+bx+c=0[/tex]We shall now attempt to re-write the equation given in the form shown above. This is shown as follows;
[tex]\begin{gathered} x^2=4(x-9)_{} \\ We\text{ shall now expand the parenthesis;} \\ x^2=4x-36 \\ We\text{ shall now collect all like terms;} \\ \text{Subtract 4x and add 36 to both sides to both sides} \end{gathered}[/tex][tex]\begin{gathered} x^2-4x+36=4x-4x-36+36 \\ x^2-4x+36=0 \end{gathered}[/tex]We now have our quadratic equation as shown above.
Comparing this with the general form of a quadratic equation, we can now identify a, b and c as follows;
[tex]\begin{gathered} a=1 \\ b=-4 \\ c=36 \end{gathered}[/tex]ANSWER:
a = 1
b = -4 and
c = 36
18) Find the greatest common factor (GCF) for list of terms: 10x3y5, -15x4y8, 20x5y6
Answers
10x3y5,
-15x4y8,
20x5y6
[tex]undefined[/tex]greatest common factor of 10, 15, and 20 is 5
greatest common factor of x^3, x^4 and x^5 is x^3
greatest common factor of y^5, y^8 and y^6 is y^5
Therefore the greatest common factor of all is:
5x^3y^5
[tex]5x^3y^5^{}[/tex]Question is attached, im confused on the steps to follow.
Answers
A year has 52 weeks.
Since Officer Milton has 3 weeks of vacation, then he works for 49 weeks a year.
Since he visits 3 groups per week, the total number of groups that he visists in a year is:
[tex]49\times3=147[/tex]Therefore, the correct choice is option C) 147.
Use synthetic division to find the function value. Then, check your work using a graphing calculator.
Answers
we have the function
f(x)=x^4-x^3-7x^2+45x-39
Find out f(-5)
so
Use synthetic division
x^4-x^3-7x^2+45x-39 : (x+5)
x^3-6x^2+23x-70
-x^4-5x^3
-------------------------------
-6x^3-7x^2+45x-39
6x^3+30x^2
----------------------------
23x^2+45x-39
-23x^2-115x
------------------------
-70x-39
70x+350
------------------
311 ----------------> remainder
therefore
f(-5)=311
Verify
using a graphing tool
For x=-5 ------------> f(x)=311 is ok
Write an equation (-5,-2) and (-4,-3)
Answers
The equation from (-5, -2) and (-4, -3) is y = -1x - 7
What is Equation of line?
A straight line's equation is a mathematical formula that describes the relationship between the coordinate locations along the line. It can be expressed in a variety of ways and provides the line's slope, x-intercept, and y-intercept.
Given:
P1: (-5, -2)
P2: (-4, -3)
Find:
The equation for the line that passes thru P1 & P2
Solution:
y = mx + b
Will be the equation to arrive to at the very end, but we need m & b, the slope and the y-intercept
m = ( y2 - y1 ) / ( x2 - x1 )
= ( -3 + 2 ) / ( -4 + 5 ) )
= -1 / 1
∴ m = -1
Using either P1 or P2, plug in one of their respective x- and y-values into:
y = -1 x + b
For (-5, -2)
-2 = -1 ( -5 ) + b
-2 = 5 + b
-7 = b
∴ b = -7
∴ y = -1x - 7 is the equation of the line that passes thru both points (-5, -2) and (-4, -3)
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Determine which integer will make the inequality 20 > 4x + 16 true.
Answers
Answer:
-1
Step-by-step explanation:
That's my best shot.
