Answers
Answer:
f(x) = 1/4(x + 4)(x - 2)²Step-by-step explanation:
Let's analyze the graph.
We observe that:
It is an increasing function, so leading coefficient is positive,It has one x-intercept (- 4, 0), It has one touching point at x-axis (2, 0), so it has at least multiplicity of 2,It has a y-intercept (0, 4), It has a local maximum (- 2, 8).Based on our observations, the least degree polynomial function will have the form of:
f(x) = a(x + 4)(x - 2)²To find the value of a we'll use the y-intercept:
4 = a(0 + 4)(0 - 2)²4 = a*16a = 4/16a = 1/4Let's prove it with local maximum:
8 = 1/4(- 2 + 4)(-2 - 2)²8 = 1/4*2*168 = 8So the function is:
f(x) = 1/4(x + 4)(x - 2)²Related Questions
On the 1:1000 scale plan, the length and width of the house are drawn as 2 cm and 1.5 cm.
a. Find the actual size.
6. Find the ratio of the area of the foundation of the house to the area on the floor plan.
Answers
Answer:
a. Actual size: 20 m x 15m
b. 1,000,000 : 1
Step-by-step explanation:
(a) Since scale is 1:1000, multiply both length and width on the floor pan to get actual length and width of house
a. Actual size
= 2 x 1000 cm x 1.5 x 1000 cm
= 2000 cm x 1500 cm
= 20m x 15m (since 1 m = 100 cm
(b) Area on plan = 2 x 1.5 = 3 cm²
Actual area = 2000 x 1500 = 3,000,000 cm²
Ratio of actual area to floor plan area
= 3,000,000 / 3 = 1,000,000 : 1
Calculate rates (backwards)
If you pay $60 for bulk rice, at $4.00 / kg, how many kilograms can you buy?
Answers
Answer:
15kg
Step-by-step explanation:
$60 divide by $4 kg
60/4=15
graph a linear function is shown.
Which word describes the slope of the line?
O positive
O negative
O zero
O undefined
Answers
Word (C) zero describes the slope of the line of the given graph of the linear function.
What is a graph of a linear function?Function in Linear A straight line on the graph has the expression or formula y = f(x) = px + q. One independent and one dependent variable are present. X and Y are the independent and dependent variables, respectively. P is the y-intercept or constant term, and it also represents the value of the dependent variable.So, we can infer from the provided graph that its equation is:
y = -3Which is also readable as:
y = 0 × x - 5Putting it into comparison with the slope-intercept form:
y = mx + bWe will obtain a slope of 0.
Therefore, word (C) zero describes the slope of the line of the given graph of the linear function.
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The correct question is given below;
graph a linear function is shown.
Which word describes the slope of the line?
A. positive
B. negative
C. zero
D. undefined
Find the inverse of f(x) = 12x - 3
Answers
ANSWER
[tex]f^{-1}(x)\text{ = }\frac{y}{12}+\frac{1}{4}[/tex]EXPLANATION
We want to find the inverse of the function given:
f(x) = 12x - 3
First, replace f(x) with y:
y = 12x - 3
Now, make x the subject of the function:
y + 3 = 12x
[tex]\begin{gathered} \Rightarrow\text{ x = }\frac{y}{12}\text{ + }\frac{3}{12} \\ x\text{ = }\frac{y}{12}\text{ + }\frac{1}{4} \end{gathered}[/tex]Now, replace x with f-1(x) and y with x:
[tex]f^{-1}(x)\text{ = }\frac{y}{12}+\frac{1}{4}[/tex]That is the inverse function.
Devon records 4 hours of reality shows on her dvr. she records comedy shows for 3/8 of that amount of time. devon watches all the reality and comedy shows in half hour sittings.
Answers
If Devon records 4 hours of reality shows on her dvr and she records comedy shows for 3/8 of that amount of time, then the number of hours taken to record the comedy show is 1.5 hours
Number of hours the Devon record the reality shows = 4 hours
she records comedy shows for 3/8 of that amount of time
The number of hours taken to record the comedy show = (3/8)×Number of hours the Devon record the reality shows
Substitute the values in the equation
= (3/8)×4
= 12/8
= 1.5 hours
Hence, if Devon records 4 hours of reality shows on her dvr and she records comedy shows for 3/8 of that amount of time, then the number of hours taken to record the comedy show is 1.5 hours
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Estimate the difference by rounding each number
to the nearest hundredth: 0.076 -0.011
A 0.08
B 0.06
C 0.05
D 0.07
Answers
Answer:
answer is D= 0.07
Step-by-step explanation:
The equation:
0.076 - 0.011
By rounding to the nearest hundredth
0.076 = 0.08
0.011 = 0.01
=0.08-0.01
=0.07
"Complete the table" can i get some help with this pls and thank you
Answers
2. 2 yards
3. 18 feets
4. 21 feets
Is this right?
Look at this graph.
What is the equation of the line in slope-intercept form?
Answers
Answer:
I think the answer is (3,10) sorry if I got this wrong!
Step-by-step explanation:
Using coordinates (0,3) for y intercept
Using coordinates to solve (1,6)
y - y1 = m (x - x)
y - 6 = 3 (x - 1)
y - 6 = 3x -3
y = 3x + 3
(5 points) use coordinate vectors to test the linear independence of the sets of polynomials. do they form a basis for the space of polynomials of third degree? why or why not? explain your work.
Answers
The linear independence of vector sets forms the basis of the space of polynomials of third degree.
In vector space theory, a collection of matrices is said to be heavily dependent if there is a nontrivial concatenation of the vectors that equal the zero vector. If no such linear combination exists, the vectors are said to be linearly independent. These concepts are crucial to the concept of dimension.
The maximum number of nonzero vectors determines whether the dimensions of a vector space are finite or infinite. The capacity to recognize whether a subset of columns in a vector space is dependent, as well as the concept of linear dependence, are crucial for determining a vector space's dimensionality.
If the same vector appears twice in a vector sequence, it must be dependent. The linear dependency of a vector series is independent of the order of the terms. A restricted collection of vectors can have linear independence if the sequence obtained by sorting a finite number of lines is linearly independent. In other words, the following outcome is frequently useful.
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Let the graph of g be a translation 2 units left and 1 unit down, followed by a reflection in the y -axis of the graph of f(x)=(2x+1)^2-4 . Write a rule for g .
Answers
The rule for the function g(x) is (2x + 5)² - 5.
We are given a function f(x). The function f(x) is defined as given below :
f(x) = (2x + 1)² - 4
A function connects an input with an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input.
We first need to do a translation with 2 units left.
The translation is given by f(x + 2).
f(x + 2) = (2x + 5)² - 4
We now need to do a translation with 1 unit downwards.
The translation is given by f(x + 2) - 1.
f(x + 2) - 1 = (2x + 5)² - 4 - 1
f(x + 2) - 1 = (2x + 5)² - 5
The definition of the function is given below :
g(x) = (2x + 5)² - 5
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Give the domain and range of each relation below. (help please)
Answers
Answer:
Domain is (-infinity, infinity), range is (-infinity, 0]
Step-by-step explanation:
The x values are infinite on both sides, but the y values are not. Let me know if you want me to explain more :)
the length of a small garden is 12.64 feet. the width of the garden is 14 feet. samuel wants to fence the garden in on all sides. he has 50 feet of fencing. calculate the perimeter of the garden to determine if samuel has enough fencing.
Answers
Answer:
He does not have enough for fencing the garden
Step-by-step explanation:
The garden is in the shape of a rectangle
The perimeter of a rectangle of length L and width W is given by
P = 2 (L + W)
Since we are given L = 12.64 ft and W = 14 ft, the perimeter of the garden is
2 ( 12.64 + 14) = 2 (26.64) = 53.28 feet
Since Samuel only has 50 feet of fencing, there is not enough to fence. He is short by 3.28 feet
Suki has placed $800 in an account that pays 4 percent interest compounded quarterly. at the end of two years (eight quarters), the balance in the account will be $ 0.08 . that means suki will have earned $ in interest during that time. (round your answers to the nearest cent.) what will be the balance in the account at the end of two years (eight quarters)? how much interest will suki have earned during that time? (round your answers to the nearest cent.)
Answers
The balance in the account at the end of two years is $864.
The interest earned by Suki during that time is $64.
The initial principal amount "P" is $800.
The interest rate "R" is 4%.
The interest is compounded quarterly.
This means the value of "n" is 4.
The time period for which the interest is earned is 2 years.
The formula for compound interest is :
A = P*[1 + (R/n)]^(n*t)
A = 800*[1 + (0.04/4)]^(4*2)
A = 800*[1 + 0.01]^(4*2)
A = 800*[1.01]^(8)
A = 800*1.08
A = 864
The total interest earned is the final amount minus the principal amount.
The total interest earned is $864 - $800.
The total interest earned is $64.
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The area of a circle is 25 pi ft 2.
Answers
how much will Yoona charge to walk 8 dogs
Answers
Yoona will charge $20.75 to walk 8 dogs based on the trend of Yoona charges to walk dogs.
How to find the amount to be charged?First, find the pattern in the amount that Yoona charges to walk each additional dog.
Additional cost to walk 2 dogs:
= 40 - 37.25
= $2.75
Additional cost to walk 3 dogs:
= 37.25 - 34.50
= $2.75
Additional cost to walk 4 dogs:
= 34.50 - 31.75
= $2.75
Every extra dog therefore leads to a fall in price by $2.75. For eight dogs, Yoona would charge:
= 40 - (7 x 2.75)
= 40 - 19.25
= $20.75
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Juan Fuentes is a computer programmer. His annual salary is
$32,190.00. Benefits he receives consist of $1,881.73 in vacation time,
holidays worth $1,287.60, health insurance premiums of
$2,300.00 paid by the employer, Social Security of $1,995.78,
Medicare of $466.76, and unemployment insurance of $541.06.
a. What are the total benefits?
b. What is the rate of benefits?
Answers
In linear equation,$7185.33 is the total benefits.
What are a definition and an example of a linear equation?
An equation with only one variable is referred to as a linear equation in one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value. One such linear equation in one variable is 9x + 78 = 18.the total benefits of Juan Fuentes = $1,881.73 + $2,300.00 + $1,995.78 +
$466.76 + $541.06
= $7185.33
the rate of benefits of Juan Fuentes = $1,287.60
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How do I find simple interest? I am currently working on a CYU that requires this information. Thank you!
Answers
think of all the things s you like
The correlation coefficient (r) between the number of volunteers x and the number of bags of trash collected y is 0.964.
What percent of the variation in the number of bags of trash collected can be explained by differences in the number of volunteers?
Answers
The correlation coefficient between the number of volunteers x and the number of bags of trash collected y, so the percentage of variation in the number of bags of trash collected is 92.92 %.
What is the Correlation coefficient?You may gauge how closely two variables are related by looking at their correlation coefficients. Pearson's correlation coefficient is the most often used of the several correlation coefficient types. Often employed in linear regression, Pearson's correlation (also known as Pearson's R) is a correlation coefficient. It's likely that you'll learn about Pearson's R first if you're just getting started in statistics. Actually, Pearson's is typically mentioned when someone mentions the correlation coefficient.
According to the question,
The correlation coefficient i.e., r between x and y is 0.964.
r = 0.964
Squaring on both sides :
r² = 0.964²
r² = 0.9292
Now, convert this into percentage form by multiplying it will 100.
⇒0.9292 × 100
= 92.92 %.
Hence, the percentage of the variation will be 92.92 %.
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2/3 + 9/10 adding fractions
My teacher is making us show work :(
Answers
Answer: 47/30
Step-by-step explanation:
1) Find the common denominator
2/3 + 9/10
10/10 * 2/3 + 9/10 * 3/3
2) Add the numerator
20/30 + 27/30
47/30
f(x)=√x+11. Find the inverse of f(x).
O A. f¹(x) = x³ – 11
O B. f¹(x) = (x - 11)³
O c. f¹(x) = x³ + 11
O D. f¹(x) = (x +11)³
Answers
Answer: Your answer would be C: f¹(x) = x³ + 11
Point-slope form: y minus y 1 = m (x minus x 1).
Use the point-slope form of a line to write the equation of a line that has a slope of 2 and passes through the point (–4, 3). Write the equation in slope-intercept form.
Choose the equation of the line.
y = 2x – 7
y = 2x + 11
y = –4x + 14
y = 3x +14
Help me please!!
Answers
Ryan deposits $775 in an account that pays 4.24% simple interest for four years. Brian deposits $775 in an account that pays 4.24% simple interest for one year.
Answers
The interest earned by Ryan is $131.44 and the interest earned by Brian is $32.86 .
In the question,
it is given that
amount deposited by Ryan = $775
time for which the amount is deposited = 4 years
rate at which the amount is deposited = 4.24%
So the simple interest = (p*r*t)/100
= (775 * 4.24*4 ) /100
= 13144/100
= 131.44
amount deposited by Brian = $775
time for which the amount is deposited = 1 years
rate at which the amount is deposited = 4.24%
So the simple interest = (p*r*t)/100
= (775 * 4.24 * 1 ) /100
= 3286/100
= 32.86
Therefore , the interest earned by Ryan is $131.44 and the interest earned by Brian is $32.86 .
The given question is incomplete , the complete question is
Ryan deposits $775 in an account that pays 4.24% simple interest for four years. Brian deposits $775 in an account that pays 4.24% simple interest for one year. Find the interest earned by both Ryan and Brian ?
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what is the answer to -9+7x < 47
Answers
The solution of the inequality - 9 + 7x < 47 will be;
⇒ x < 8
What is mean by Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is;
⇒ - 9 + 7x < 47
Now, Solve the expression as;
The inequality is;
⇒ - 9 + 7x < 47
Solve as;
⇒ - 9 + 7x < 47
Add 9 both side;
⇒ - 9 + 7x + 9 < 47 + 9
⇒ 7x < 56
Divide by 7, we get;
⇒ 7x/7 < 56/7
⇒ x < 8
Therefore, The solution of the inequality - 9 + 7x < 47 will be;
⇒ x < 8
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This shape is made up of one half-circle attached to a square with side lengths 11 inches. You can use 3.14 as an approximation for π. help i don't know it
Answers
The approximate perimeter of the entire shape is 50.27 inches.
How to find the perimeter of a figure?The perimeter of a figure is the sum of the whole sides of the figure.
Therefore, the perimeter of the entire shape can be calculated as follows:
The shape is made of three sides of a square and half a circle.
Therefore,
circumference of the semi circle = πr
r = 11 / 2 = 5.5 inches
circumference of the semi circle = 5.5π
Hence,
perimeter of the shape = 11 + 11 + 11 + 5.5π
perimeter of the shape = 33 + 5.5(3.14)
perimeter of the shape = 33 + 17.27
Therefore,
perimeter of the shape = 50.27 inches
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Seven cards are chosen from a well-shuffled deck of 52 playing cards. In how many selections do at least 3 jacks occur?.
Answers
In 193 selections at least 3 jacks occur.
Combination or permutation?To decide whether to use combination or permutation, we need to look at whether the order matters, as follows:
Order matters: permutation is used.Order does not matter: combination is used.In the context of this problem, the order in which the cards are chosen is not important, hence a combination is used.
The number of combinations of x elements from a set of n elements is given according to the formula presented below.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
There are two cases in which at least 3 jacks occur, as follows, considering that a standard deck has 4 jacks:
3 Jacks selected from a set of 4, and one non Jack card selected from a set of 48.4 Jacks cards from a set of 4.Hence the number of ways to choose the cards is calculated as follows:
[tex]C_{4,3}C_{48,1} + C_{4,4} = 4(48) + 1 = 193[/tex]
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A tissue factory produces 3,876 tissues a day. How many tissues does it produce after 7 days?
Answers
Answer:
27,132 tissues
Step-by-step explanation:
if it produces 3,876 tissues a day, and a week has 7 days, then the answer would be 3,876 x 7=27,132 tissues
Answer:
27132 tissues
Step-by-step explanation:
everyday 3876 tussues are made
so the equation would be 3876×7 to get how many tissues are made in 7 days
Find the missing number so that the equation has no solutions.
2 x + 4 = – 3 x – 18 + blank x
Answers
The value of x in the equation given is x = -4.4
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe a scenario.
In this case, the value will be expressed by subtracting the variables that are given in order to get the other term. This will be:
2x + 4 = -3x - 18
Collect like terms
2x + 3x = -18 - 4.
5x = -22
Divide
x = -22 / 5
x = -4.4
This illustrates the concept of equations.
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f(x)=5x+10 solve when f(x)=20
Answers
When f(x) = 20
Then
5x + 10 = 20
Therefore
5x=20-10=10
x = 10 / 5 = 2
x= 2
What are the terms of each expression?
4x + 3z
Answers
Answer:
4x and 3z are the only 2 terms in this esxpression.
Question 8
Given the equations y=-4x-4 and y=4(x+1), is (-1,0) a solution of the system of
equations?
True
False
Question 9
The solution to the system of linear equation
1 pts
1 pts
Answers
Yes is (-1,0) a solution of the system of equations.
A linear equation is defined.A linear equation is one that has a maximum degree of 1. No variable in a linear equation has an exponent greater than 1, thus. A linear equation's graph is always a straight line.
Since each term in a linear equation has an exponent of 1, graphing an algebraic equation always yields a straight line. It is called a "linear equation" because of this.
Given
y=-4x-4...(i)
y=4(x+1)
=> y =4x + 4....(ii)
Adding (i) and (ii) we get
y= 0
Now putting y = 0 in Equation (i)
we get x = -1
Therefore (-1,0) is the solution of the two given equations.
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