The illustration below shows the graphs of fourteen functions.
Two of them have equations
y = (z+6)³-2
y=-(z-9)³ +3
Due to length restrictions, we kindly invite to check the explanation of this question to understand the derivation of the polynomic expressions.
How to determine a family of cubic functions
Cubic functions are polynomials of grade 3. In this case, we have pairs of cubic functions of the following form:
y = (x - h)³ + k (1)
y = - (x - h)³ + k (2)
a) Where (h, k) are the coordinates of the vertex of each cubic function. There is a translation of (x, y) = (3, 1) between each two consecutive pairs of cubic functions. Hence, we have the following fourteen cubic functions:
y = (x + 9)³ - 3y = - (x + 9)³ - 3y = (x + 6)³ - 2y = - (x + 6)³ - 2y = (x + 3)³ - 1y = - (x + 3)³ - 1y = x³ y = - x³y = (x - 3)³ + 1y = - (x - 3)³ + 1y = (x - 6)³ + 2y = - (x - 6)³ + 2y = (x - 9)³ + 3y = - (x - 9)³ + 3b) Another family of functions with a similar pattern is shown below:
y = (x + 9)² - 3y = - (x + 9)² - 3y = (x + 6)² - 2y = - (x + 6)² - 2y = (x + 3)² - 1y = - (x + 3)² - 1y = x² y = - x²y = (x - 3)² + 1y = - (x - 3)² + 1y = (x - 6)² + 2y = - (x - 6)² + 2y = (x - 9)² + 3y = - (x - 9)² + 3To learn more on cubic functions: https://brainly.com/question/25732149
#SPJ1
What is the answer (6√2)(-3√5)
Solution:
[tex] - 18 \sqrt{10} [/tex]
Step-by-step explanation:1. Apply rule : a(-b) = -ab
[tex] = - 6 \sqrt{2} \: \: • \: \: 3 \sqrt{5} [/tex]
2. Apply radical rule : [tex] \sqrt{a} \sqrt{b} = \sqrt{ab} [/tex] , [tex]a \geqslant 0[/tex], [tex]b[/tex]
[tex] = 6 \sqrt{2 \: • \: 5} \: • \: 3[/tex]
3.Multiply the numbers : 2 • 5 = 10=[tex]6 \sqrt{10} •3[/tex]
4.Multiply the numbers : - 6 • 3= - 18[tex] = - 18 \sqrt{10} [/tex]
What is another name for the Sierpinski triangle?
Sierpinski Pyramid
Sierpinski Gasket
Sierpinski Fractal
Fractal Triangle
Answer:
The Sierpinski triangle is also called the Sierpinski gasket.
Step-by-step explanation:
The Sierpinski triangle is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński who described it in 1915.
Find the values of X and Y in the parallelogram.
Answer: x=-5, y=20
Step-by-step explanation:
Opposite sides of a parallelogram are congruent, so AB=CD.
[tex]x^{2}-15=-2x\\x^{2}+2x-15=0\\(x+5)(x-3)=0\\x=-5, 3[/tex]
But as distance must be positive, as CD=-2x, x must be negative, so x=-5.
Opposite angles of a parallelogram are congruent, so [tex]m\angle D=m\angle B[/tex].
[tex]4y+26=106\\4y=80\\y=20[/tex]
can anyone answer this pls!!!!!!!!!!
u₁₂ represents the amount of loan remaining after 12 years
How to interpret u₁₂?The function is given as:
u₀ = 8000
[tex]u_n = u_{n-1}(1 + 0.054) - 500[/tex]
Given that the subscript n in [tex]u_n[/tex] represents number of years and [tex]u_n[/tex] represents the amount left to be paid after n years.
We can conclude that:
u₁₂ represents the amount of loan remaining after 12 years
Read more about loan at
https://brainly.com/question/26011426
#SPJ1
You used $3000 of your budget for training your employees. each hour of training costs $40 per employee plus a one-time $200 fee. a. how many hours of training can your purchase? b. how many hours of training will each of your employees receive? remember how many employees do you have?
A. The number of hours of training that you can purchase with a $3,000 training budget at $40 per employee per hour and a one-time $200 fee is 70-employee-training-hours.
B. Each employee will get 7 hours of training, assuming your organization has 10 employees.
What is the cost of training employees?The training cost of employees varies from one organization to another.
The training cost also depends on the training provider and the number of hours of training being offered.
Data and Calculations:Training budget = $3,000
One-time fee = $200
Remainder after the one-time fee = $2,800 ($3,000 - $200)
Training costs per employer per hour = $40
Hours of training to purchase = 70 ($2,800/$40)
Thus, an organization with 10 employees can obtain 70 hours of training with the training budget.
Learn more about training needs and costs at https://brainly.com/question/26821802
#SPJ1
Kian borrowed £1900 at a simple interest rate of 8% per year.
After a certain number of years, he owes a total of £2812 on this loan.
How many years have passed since he took out the loan?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2812\\ P=\textit{original amount deposited}\dotfill & \$1900\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 2812=1900[1+(0.08)(t)]\implies \cfrac{2812}{1900}=1+0.08t\implies \cfrac{37}{25}=1+0.08t \\\\\\ \cfrac{37}{25}-1=0.08t\implies \cfrac{12}{25}=0.08t\implies \cfrac{ ~~ \frac{12}{25} ~~ }{0.08}=t\implies 6=t[/tex]
What is the answer of 32% of 125
Answer:
40
Step-by-step explanation:
32÷100= 0.32
0.32×125= 40
convert your percentage into a number first, so that you are working with normal numbers only, and then multiply that by your total.
Please help!!
The two-way frequency table below shows data on playing a sport and playing a musical instrument for in a class.
Answer: Check out the screenshot below for the answers
==========================================================
Explanation:
For each column, we divide the values by the sum of each column.
The sum of the first column is 6+8 = 14, and the sum of the second column is 7+3 = 10.
Column 1:
6/14 = 0.438/14 = 0.57Those values are approximate to two decimal places.
Column 2:
7/10 = 0.703/10 = 0.30Those values are exact.
The values in bold are then filled in the table as you see below.
A result like 0.43 means that 43% of those who play a sport also play an instrument. The other values are interpreted in a similar fashion.
A local public library decides to track the number of hours that a certain computer is being used. The table represents the number of hours, y, which is dependent on the number of days, x.
x
y
3
21
5
37
7
53
What is the linear equation that represents this situation?
y = 8 x + 45
y = 8 x minus 3
y = 2 x + 16
y = 2 x minus 32
That statistic is based on a pinterest quote, the actual statistic is closer to 8-10%
In her free time, isabelle likes to read. she kept track of the number of pages in each book she read last summer. this box plot shows the results. what fraction of the books has 200 or fewer pages?
200 is the median (50%) of the data represented in the box plot. The fraction of the books has 200 or fewer pages is: 1/2.
What is the Median of a Data in a Box Plot?In a box plot, the median is indicated as the value marked by the vertical line that divides the rectangular box of the box plot.
The median is the middle of the data and represents the 50th percentile. That is 1/2 the data.
In the box plot given, 200 pages is the median. Therefore, the fraction of the books that have 200 or fewer pages is: 1/2.
Learn more about box plot on:
https://brainly.com/question/14277132
#SPJ1
find the value of x in (2^2x)^3 = 64
Answer: x=12
Step-by-step explanation:
Answer:
x=1
Step-by-step explanation:
The equation can be simplified and solved using the rules of exponents and the usual inverse operations.
__
Interpreted according to the Order of Operations, your equation is ...
((2^2)x)^3 = 64
(4x)^3 = 64x^3 = 64 . . . . . . use (ab)^c = (a^c)(b^c)
x^3 = 1 . . . . . . . . . . . . . . divide by 64
x = ∛1 = 1
__
Perhaps you want x in the exponent:
(2^(2x))^3 = 64
2^(6x) = 2^6 . . . . . . . . . use (a^b)^c = a^(bc)
6x = 6 . . . . . . . . match exponents
x = 1 . . . . . . divide by 6
_____
Additional comment
Folks are often not careful about identifying exponents. It is helpful if you write the exponent in a way that leaves no ambiguity.
What is the length of the missing leg? If necessary, round to the nearest tenth.
Answer:
is that the ixl
website ????????????????????????????????
*Please Help*
F(x) = (x+2)(-x+3)(x-2)^2
Please put F(x) in standard form. Show how you figured it out.
Answer:
F(x) = (x+2)(-x+3)(x-2)^2. I think answer should be like this
PLEASE HELP!
Which of the following statements is/are true? (5 points)
I. If f '(c) = 0, then f has a local maximum or minimum at x = c.
II. If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].
III. The Mean Value Theorem can be applied to f(x) = 1/x2 on the interval [-1, 1].
I only
II only
I and III only
I and II only
I especially need help with the first statement... I think it's true in some situations, but there are some counter-examples. I don't know if this means it's true or false!!!
Both the first and second statements are true and therefore Option D is the correct answer .
What is a Function ?A function can be defined as the equation that identifies relation between a dependent variable and an independent variable.
A function always has a defined range and domain.
In the following statements
I. If f '(c) = 0, then f has a local maximum or minimum at x = c.
f'(c) = 0
It means that the slope of f(x) = 0 at x = c
If f has a local maximum or minimum at x = c It is a True statement
II. If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].
If f'(x) = 0 on (a, b),
then f is neither increasing nor decreasing
and therefore is constant on [a, b]
So it is a True statement.
III. The Mean Value Theorem can be applied to f(x) = 1/x² on the interval [−1, 1].
No the theorem cannot be applied as, f is neither continuous nor differentiable at x = 0
It is a False Statement.
Therefore Option D is the correct answer.
To know more about Function
https://brainly.com/question/12431044
#SPJ1
Are the equations 4-5x=24 and 5x=20 equivalent?
Answer:
not equivalent
Step-by-step explanation:
solve for x
4-5x=24
-5x=20
x = - 4
5x=20
x = 4
no they are not equivalent
the first container of milk has twice as many gallons as the second if john uses 2 gallons from the second and 3 gallons from the first if the first one has 4.5 times more than the second how much did they each have originally
Answer:
SORRY I DONOT KNOW THE ANSWER
Step-by-step explanation:
i am sorry i do not know the amswer
Determine, to the nearest tenth of a year, how long it would taken an investment to double at a 3 3/4% interest rate, compounded continuously
Based on the interest rate and continuous compounding, the investment would double in value after 18.5 years.
We have given that,
investment to double at a 3 3/4% interest rate,
When will the investment double in value?The future value using continuous compounding is:
= Amount x e ^ (rate x time)
Interest is
= 3.75%
What is the formula of an exponential function?2 = e ^ (0.0375 x time)
In2 = 0.0375 x time
t = In2 / 0.0375
t= 18.5 years
To learn more about the compounded continuously visit:
brainly.com/question/16731646.
#SPJ1
Given that ABCD is a rhombus, what is the value of x?
Answer:
E. 18.6
Step-by-step explanation:
The diagonals of a rhombus bisect each other at right angles. The means all of the triangles shown are right triangles, and the two marked angles are complementary.
__
solve for xComplementary angles total 90°.
(x°) +(4x -3)° = 90° . . . . . the marked angles are complementary
5x = 93 . . . . . . . . . . . . divide by °, add 3
x = 93/5 = 18.6 . . . . . divide by the coefficient of x
The value of x is 18.6.
The points (4,2) and (-1, y) are √√74 units apart. What is the
value of y?
Please help!!!
Answer:
y = - 5 or y = 9
Step-by-step explanation:
using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (4, 2 ) and (x₂, y₂ ) = (- 1, y )
d = [tex]\sqrt{(-1-4)^2+(y-2)^2}[/tex]
= [tex]\sqrt{(-5)^2+(y-2)^2}[/tex]
= [tex]\sqrt{25+(y-2)^2}[/tex]
equating to [tex]\sqrt{74}[/tex] , that is
[tex]\sqrt{25+(y-2)^2}[/tex] = [tex]\sqrt{74}[/tex] ( square both sides )
25 + (y - 2)² = 74 ( subtract 25 from both sides )
(y - 2)² = 49 ( take square root of both sides )
y - 2 = ± [tex]\sqrt{49}[/tex] = ± 7 ( add 2 to both sides )
y = 2 ± 7
Then
y = 2 + 7 = 9 or y = 2 - 7 = - 5
A table of values shown below represents a linear function which of these points could also be an ordered pair in the table and why?
Answer:
(18,27) , because the rate of change of the function is 4/3
Step-by-step explanation:
if you do 12 minutes of a 45 minute workout how many calories is it? (the 45 minutes is 1000 calories in total)
help!
Answer:
266[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
if a 45 minute workout is 1000 calories, at the same rate, a 12 minute workout would be 266 calories and 2 thirds. [tex]\frac{12}{45}[/tex] x 1000 = 266[tex]\frac{2}{3}[/tex]
-34 + 2x divided by -8
Answer:
-34+x/4
Step-by-step explanation:
Answer:
x=17
Step-by-step explanation:
Since you did not specify, we will assume that your equation is equal to 0.
1. (-34+2x)/(-8) = 0 (multiply both sides by -8)
2. (-34+2x) = 0 (add 34 to both sides)
3. 2x = 34 (divide both sides by 2)
4. x = 17
A hypothesis regarding the weight of newborn infants at a community hospital is that the mean is 22.1 pounds. a sample of seven infants is randomly selected and their weights at birth are recorded as 21.1, 25.1, 26.1, 27.1, 24.1, 31.1, and 31.1 pounds. if α = 0.010, what is the critical value? the population standard deviation is unknown.
The critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074
How to determine the critical value?The dataset is given as:
21.1, 25.1, 26.1, 27.1, 24.1, 31.1, and 31.1
The sample mean is:
[tex]\bar x = 22.1[/tex]
The significance level is
α = 0.010
Start by calculating the degrees of freedom using:
df = n - 1
Where n represents the sample size (n = 7)
So, we have:
df = 7 - 1
df = 6
Using the table for t critical values for a two-tailed test, we have:
Critical value = ±3.7074
Hence, the critical value at the 0.010 significance level with 6 degrees of freedom are ±3.7074
Read more about critical value at:
https://brainly.com/question/16551840
#SPJ1
Read the statement.
Doubling the dimensions of a rectangle increases the area by a factor of 4.
If p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4, which are
true? Select two options.
Op q represents the original conditional statement.
~p~q represents the inverse of the original conditional statement.
q- p represents the original conditional statement.
-q- ~p represents the converse of the original conditional statement.
Op q represents the contrapositive of the original conditional statement.
-
Mark this and return
Submit
Next
The options that are true as a result of doubling the rectangle dimensions are;
p → q represents the original conditional statement.
p → ~q represents the contrapositive of the original conditional statement.
What are conditional statements?We are told that;
Doubling the dimensions of a rectangle increases the area by a factor of 4.
Now, p represents doubling the dimensions of a rectangle and q represents the area increasing by a factor of 4.
Thus, using conditional statements notation, we can say that;
p → q represents the original conditional statement.
p → ~q represents the contrapositive of the original conditional statement.
Read more about conditional statements at; https://brainly.com/question/11073037
#SPJ1
In a cave, a stalactite gets 44 millimeters longer each year. this year it is 72 centimeters long. how many years until it is 1 meter long?
Answer:
6.36 years (the .36 repeats), so rounded is 6.4.
Step-by-step explanation:
First, I'm going to convert all measurements to meters.
Since 1000 mm = 1 m, divide 44 by 1000.
44/1000 = 0.044 m
Since 100 cm = 1 m, divide 72 by 100.
72/100 = 0.72 m
Next, I'm going to setup an equation using y = mx + b.
b is the beginning amount which is 0.72.
m in the equation represents the rate which is 0.044.
y represents the total which is 1.
Plugin the numbers and solve for x.
1 = 0.044x + 0.72
1 - 0.72 = 0.044x + 0.72 - 0.72
0.28 = 0.044x
0.28/0.044 = 0.044x/0.044
6.36 = x
Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list. Enter your answers in terms of degrees. Round your answers to two decimal places.) (−6,-9), (2,7),(7,2)
Answer:
23.20°, 71.57°, 85.24°
Step-by-step explanation:
The angle between two vectors can be found by making use of the definition of the dot product. The computed angle is the angle between the vectors when they are placed tail-to-tail.
__
setupvector definition
The second attachment shows the given points plotted as A, B, C in the order given. In the diagram, the vectors a, b, c are defined as BA, CB, AC, respectively. That is, the vector a is ...
a = A -B = (-6, -9) -(2, 7) = (-6-2, -9-7) = (-8, -16)
The vectors are defined in counterclockwise order around the triangle, though that makes no difference to the calculation.
dot product definition
The definition of the dot product of vectors A and B is ...
A·B = |A|×|B|×cos(θ) . . . . . where θ is the angle between the vectors
Solving for the angle, we find it to be ...
[tex]\theta=\arccos\left(\dfrac{\vec{A}\cdot\vec{B}}{|\vec{A}|\,|\vec{B}|}\right)[/tex]
__
computationBecause of the way the vectors in this solution are defined, the angle between any given pair of vectors will be an exterior angle of the triangle. In order to find the measure of the interior angle, we must reverse one of the vectors. That is, the dot product used in our computation will be the opposite of the dot product of the vectors we have found.
The spreadsheet shown in the first attachment does the necessary computations.
Each vector is the difference of successive points. (x1 -x2, y1 -y2)Each dot product shown is the opposite of the dot product of successive vectors. -(x1x2 +y1y2)The magnitude is computed in the usual way: the root of the sum of the squares of the components of the vector. √(x²+y²)The cosine is the dot product of successive vectors, divided by each of the vector magnitudes.The spreadsheet shows the angle in degrees, having converted it from the radian value produced by the ACOS function.As a check, the spreadsheet shows the sum of the angle values. (The rounded values add up to 180.01°.)
The interior angles of the triangle are 23.20°, 71.57°, 85.24°.
_____
Additional comment
Another way to find the interior angles from coordinates is to consider the slope of each side of the triangle as being the tangent of the angle it makes with the x-axis. The difference of these angles can be used to find the interior angles of the triangle. Less work is involved because there is no dot-product or magnitude computation.
Which equation is equivalent to StartRoot x squared + 81 EndRoot = x + 10?
The given equation is equivalent to Option D .
The mission option is
A. x+10= x+10
B. x+9 =x² + 20x + 100
C. x² +81 = x² + 100
D. x² + 81 = x² +20x + 100
What is an Equation ?An equation is a mathematical statement formed when two algebraic expression is equated by an equal sign .
An equation is given in the question
[tex]\rm \sqrt{x^2 + 81} = x +10[/tex]
[tex]\rm {x^2 + 9^2} = (x +10)^2[/tex]
[tex]\rm {x^2 + 81} = x^2 +20x + 100[/tex]
Therefore the given equation is equivalent to Option D .
To know more about Equation
https://brainly.com/question/10413253
#SPJ1
You and your family are going on a
family cruise this summer! WOO HOO!
Your parents had to put down a $250
deposit. Then, the cruise costs $500
per person on top of that. There are 5
people in your family. How much will
the entire cruise cost? Okay
triangle png What is the angle measure of angle B?
Answer:
[tex]m\angle B = 28^{\circ}[/tex]
Step-by-step explanation:
All angles in a triangle must add up to [tex]180^{\circ}[/tex]
We can solve for [tex]\angle B[/tex] using this knowledge
[tex]\angle B + 40 + 112 = 180\\\angle B + 152 = 180\\\boxed{\angle B = 28}[/tex]
That is the answer
- Kan Academy Advance