Third-degree, with zeros of -4, -2, and 1, and a y-intercept of -11.
Answers
\(\begin{cases} x = -4\implies &x+4=0\\ x=-2\implies &x+2=0\\ x=1\implies &x-1=0 \end{cases}\qquad \implies (x+4)(x+2)(x-1)=\stackrel{y}{0}\)
now, that's the equation or polynomial in factored form, hmmm we also know that it has a y-intercept of -11, namely, when x = 0 y = -11, well let's plug in a factor to it, that will reflect those values, namely say hmmm factor "a", so
\((x+4)(x+2)(x-1)=y\qquad \stackrel{\textit{adding "a" factor for vertical shift}}{a(x+4)(x+2)(x-1)}=y \\\\\\ \stackrel{\textit{we know that when x = 0, y = -11}}{a(0+4)(0+2)(0-1)=-11}\implies -8a=-11\implies a=\cfrac{-11}{-8}\implies a = \cfrac{11}{8} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\mathbb{FOIL}}{\cfrac{11}{8}(x^2+6x+8)}(x-1)=y\implies \cfrac{11}{8}(x^3+6x^2+8x-x^2-6x-8)=y \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \cfrac{11}{8}(x^3+5x^2+2x-8)=y~\hfill\)
Related Questions
employees at an arcade are paid according to the number of hours worked as shown in the graph
Answers
Answer:
B, C, G
Step-by-step explanation:
If we look at the graph, it shows that if an employee works for 5 hours, then they will earn $36.25.
We can take 36.25 and divide that by 5 to get the hourly wage.
36.25 ÷ 5 = 7.25
We now know that employees get $7.25 every hour.
Using this we can look back to the graph.
'A' says that if an employee does not work, they will earn $7.25.
We know that this is wrong because if you do not work, then you do not earn money.
Let's look at 'B'.
If employees work for one hour, they will earn $7.25
We know this is correct because we now know the hourly wage.
Let's look at 'C'
If employees work for 4 hours, then they will get a revenue of $29.
We can figure this out by using this equation.
number of hours × hourly wage = total payment
4 × 7.25 = 29
Then this means that this is correct.
Let's look at 'D'
It says that if employees work for 10 hours, they will earn $73
Let's use that same equation again.
10 × 7.25 = 72.5
Employees earn $72.5 for working 10 hours, not $73.
So, this is obviously incorrect.
Let's look at 'E'
It says that if employees work for 3.5 hours, they will get a revenue of $21.75.
3.5 × 7.25 = 25.375
Therefore, this is incorrect.
Now let's take a look at 'F'.
It says that if employees work for 7.25 hours, then they earn $1.
This is incorrect.
And lastly, 'G'.
We know that if you do not work, then you do not earn money.
Therefore, A, B and G are the correct answers.
answer fast plz.........................
Answers
Answer:
180 customers
Step-by-step explanation:
72/100 × x/250
cross multiply
72 × 250 = 100 × x
18000 = 100x
divide both sides by 100
180 = x
Answer:
180
Step-by-step explanation:
72% of 250 is 180 :)
Yang owed two credit cards with balances of $7,500 and $3,500. The card with the $3,500 balance charged 1.4% more than the other. At the end of one year, he paid is $797. What was the simple interest of each card?
Answers
The simple interest on the balance of $3,500 is 8.88%
The simple interest on the balance of $7,500 is 7.48%
What is simple interest?
The simple interest on a credit card is the annual interest multiplied by the credit card balance, in other words, the total interest paid on both credit cards in the year under review summed up to $797.
Let us assume that simple interest on the credit card with a balance of $7500 is X
interest=$7500*X
The interest on the other credit card would be X+1.4%
interest in dollars=$3500*(X+1.4%)
total interest cost in dollars on both cards can be determined as the sum of the interest costs
total interest=$7500*X+$3500*(X+1.4%)
total interest=7500X+3500X+49
total interest=797
797=7500X+3500X+49
797=10000X+49
797-49=10000X
748=10000X
X=748/10000
X=7.48%
The simple interest on the credit balance of $7500 is 7.48%
The simple interest on the credit balance of $3,500=7.48%+1.4%
The simple interest on the credit balance of $3,500=8.88%
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PLEASE HELP ASAP!! WILL GIVE BRAINLIEST
A regular polygon has 12 sides. If one of its angles measures (8h − 30)°, what is the value of h?
h = 10.75
h = 18.75
h = 20.25
h = 22.5
Answers
Answer: h = 22.5
Step-by-step explanation:
Total angle area of a 12 sided polygon is 1800
1. One angle would be 1800/12= 150
8h - 30 = 1502. Add 30 one each side to cancel out and only leave 8h.
8h = 1803. To get rid of the 8 we divide the the other side by 8.
h = 22.5The answer is 22.5
Answer: D 22.5 i got it right on the exam
Step-by-step explanation:
Supergym is a national chain of gyms. Its employees sold 318,860 gym memberships last year. This year, they sold 80% more memberships than that. How many memberships did they sell this year?
Answers
Answer: 573,948 memberships
Step-by-step explanation:
1. Multiply the number of memberships the year prior by 80%
318,860 * 0.8 = 255088
If they sold 80% more memberships this year, that means you would add 80% of the previous year's memberships (255088) to the number of memberships sold last year (318860).
2. Add 80% of the previous year's memberships to the number of memberships sold last year
255088 + 318860 = 573948
for a normal distribution with mean 47 and standard deviation 6, find the upper value and lower value of the range of outcomes associated with the middle 25%.
Answers
Using statistics, the upper value and lower value of the range of outcomes associated with the middle 25% = (41, 53)
What are statistics?Understanding the data and focusing on various applications are the two main goals of statistics. The study of data gathering, analysis, and mathematical synthesis is known as statistics. As part of their state science studies, statisticians used to collect and evaluate data about a country's economy, population, and other aspects. Mathematical statistics is the application of mathematical ideas such as linear algebra, differential equations, mathematical analysis, and probability theories.
Given, the mean of the normal distribution = 47.
μ =47
The standard deviation is 6.
σ = 6
The formula for range = (μ-σ, μ+σ)
Putting the values of μ and σ,
Range= (47-6, 47+6)
Range= (41, 53)
Hence, the range of outcomes associated with the middle 25%'s upper and lower values are equal to (41, 53)
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Find the value of the expression
28.6 - 35 + 12.7 - (-5.2)=
Answers
Answer:
Step-by-step explanation:
28.6 - 35 + 12.7 - (-5.2) = ?
28.6 - 35 + 12.7 + 5.2 = 11.5
The value of the expression 28.6 - 35 + 12.7 - (-5.2) is 11.5.
To find the value of the expression, simply follow the order of operations (PEMDAS):
28.6 - 35 + 12.7 - (-5.2)
Step 1: First, deal with the parentheses:
28.6 - 35 + 12.7 + 5.2
Step 2: Then, perform addition and subtraction from left to right:
(28.6 - 35) + 12.7 + 5.2
-6.4 + 12.7 + 5.2
Step 3: Continue with the addition and subtraction:
6.3 + 5.2
Step 4: Finally, calculate the sum:
11.5
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What is the solution to the following system of equations?
x-3y=6
2x + 2y = 4
(-1,3)
(3,-1)
(1, -3)
(-3,1)
Answers
Answer:
(b) (3,-1)
Step-by-step explanation:
One can determine the correct answer by checking to see if it satisfies the equations.
CheckingThe first equation can be rewritten to ...
x = 6 +3y . . . . . . . add 3y to both sides
This makes it easier to check answer choices:
a) -1 = 6 +3(3) . . . . no
b) 3 = 6 +3(-1) . . . . yes . . . . . (3, -1) is the solution
c) 1 = 6 +3(-3) . . . . no
d) -3 = 6 +3(1) . . . . no
__
Additional comment
We can further convince ourselves this is the correct choice by seeing if it satisfies the second equation:
2x +2y = 4 . . . for (x, y) = (3, -1)
2(3) +2(-1) = 4 . . . . yes
what is the probability of pulling a red marble and then a green marble if you do not replace the marbles
Answers
Answer:
i think you have a picture of the jar which have the marble but i am unable to watch that and then i got the full question from somewhere
Step-by-step explanation:
total no. of marbles = 20
red marbles = 7
green marbles = 10
probability of red marbles = 7/20
probability of green = 10/20
Suppose we are minimizing the objective function value of a linear program. The feasible region is defined by 5 corner points. The objective function values at the five corner points are 4, 11, 7, 4, and 10. What type of solution do we have for this problem?.
Answers
The linear program shows that there are different attainable arrangements that accomplish the same ideal objective function value..
How to determine the solution to the objective function value of a linear programBased on the given data, since the objective function values at the five corner points are diverse, able to conclude that there's no one-of-a-kind ideal arrangement for this linear program.
The reality that there are numerous distinctive objective function values at the corner points suggests that there are numerous ideal arrangements or that the objective work isn't maximized or minimized at any of the corner points.
In this case, the linear program may have numerous ideal arrangements, showing that there are different attainable arrangements that accomplish the same ideal objective function value.
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a new crew of painters takes two times as long to paint a small apartment as the experienced crew together both crews can paint the apartment in 6 hours how many hours does it take the experienced crew to paint the apartment
Answers
In the equation , it take 2 hours for the experienced crew to paint the apartment.
What is equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here let us take x as time taken by new crew of painters apartment and y as time taken by experienced crew of painters apartment .
Now a new crew of painters takes two times as long to paint a small apartment as the experienced crew then,
x = 2y ----> 1
both crews can paint the apartment in 6 hours then,
=> x+y = 6
Now put equation 1 into x+y=6 then,
=> 2y+y=6
=> 3y = 6
=> y = 6/3 = 2 hours.
Hence it take 2 hours for the experienced crew to paint the apartment.
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In 1980, the median age of the U.S. population was 30.0; in 2000, the median age was 35.3. Consider 1980 as the starting point (time zero) for this problem. Create an explicit exponential formula for the median age of the U.S. population t years after 1980, assuming the median age has exponential growth.
Answers
Answer: \(30e^{0.00813x}\)
Step-by-step explanation:
Given
Median age in 1980 is \(30\)
It is \(35.3\) in year 2000
Suppose the median age follows the function \(ae^{bx}\). Consider 1980 as starting year. Write the equation for year 1980
\(\Rightarrow 30=ae^{b(0)}\\\Rightarrow 30=a\)
For year 2000
\(\Rightarrow 35.3=30e^{20b}\\\\\Rightarrow \dfrac{30e^{20b}}{30}=\dfrac{35.3}{30}\\\\\Rightarrow e^{20b}=1.17666\\\\\Rightarrow b=0.00813\)
After t years of 1980
\(\Rightarrow 30e^{0.00813x}\)
a worker gets utility from consumption and leisure. he has 24 hours a day to allocate either to leisure or to working at a nominal wage of w dollars per hour. one unit of consumption costs p dollars.
Answers
The worker's utility function can be represented as a combination of consumption and leisure. Let x be the number of hours worked per day, and c be the amount of consumption. Then, the worker's utility can be represented as:
U(c, 24-x) = f(c) + g(24-x)
where f(c) represents the utility from consumption, and g(24-x) represents the utility from leisure. The worker faces a budget constraint that states the amount of income they earn from work must equal their spending on consumption:
wx = pc
This constraint can be used to solve for the optimal combination of leisure and consumption that maximizes the worker's utility. By combining the utility function and the budget constraint, the worker's problem can be formulated as a maximization problem:
Maximize U(c, 24-x) subject to wx = pc
This problem can be solved using techniques such as Lagrangian optimization or constraint optimization to find the optimal values of c and x that maximize the worker's utility. The solution will depend on the specific forms of the functions f and g, as well as the values of w and p.
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What is the range of these wages
245,140,525,163,195,174,140
Answers
825 use each digit once. make the smallest 3digit number
Answers
Step-by-step explanation:
Given: To make smallest 3-digit number of 825.
To find: The smallest 3-digit number of 825.
Solution: We can make the smallest 3-digit number of 825 by separating the numbers and arranging it to ascending order. The given number is 825. ...
Final answer: The smallest 3-digit number of 825 is 258.
hope it helps
Answer:
258
Step-by-step explanation:
We are given 3 numbers:
8 2 5
And we are asked to find the smallest 3 digit number using those 3 digits above.
To make the smallest number, place the numbers in value from least to greatest:
2 5 8
This is your 3 digit number: 258.
Hope this helps! :)
Find the perimeter of a rectangular garden that has a width of 4x−6 and a length of 2x+4.
Answers
Answer:
perimwter = 2(4x-6 + 2x+4) = 2 (6x-2) = 12x-4
1.Write an inequality comparing the rational numbers -3/4 and -2 .
2. Using complete sentences, explain what your inequality means about the position of the two numbers on the number line.
Answers
Answer:
\(-2<x<-\dfrac{3}{4}\) Or \(x\in (-2,-\dfrac{3}{4})\)
Step-by-step explanation:
The numbers are \(-\dfrac{3}{4}\) and \(-2\).
We need an inequality that gives us the numbers between the above numbers.
The inequality will be
\(-2<x<-\dfrac{3}{4}\)
Or
\(x\in (-2,-\dfrac{3}{4})\)
This means that \(x\) is a number that is in between the rational numbers \(-\dfrac{3}{4}\) and \(-2\). Also, \(x\) is greater than \(-2\) and less than \(-\dfrac{3}{4}\)
The positions in the number line are shown in the figure where the numbers are marked by arrow.
The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion differs from 30%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.5. Find the P-value for a two-tailed test of hypothesis.
Answers
The probability of observing such an extreme result by chance alone is 0.0124.
To find the P-value for a two-tailed test of hypothesis, we need to first determine the significance level (alpha) of the test. Let's assume a significance level of 0.05, which is a common choice.
Since this is a two-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme than 2.5 in either direction. We can find this probability using a standard normal distribution table or a calculator.
Using a standard normal distribution table, we can find that the probability of observing a z-score of 2.5 or greater is 0.0062. The probability of observing a z-score of -2.5 or smaller is also 0.0062. Therefore, the P-value for the two-tailed test of hypothesis is:
P-value = 2 * 0.0062
P-value = 0.0124
This means that if the true proportion of business students who have personal computers at home differs from 30%, with a significance level of 0.05, and we obtain a test statistic of 2.5, then the probability of observing such an extreme result by chance alone is 0.0124.
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Which value is a solution to the inequality x 4
Answers
Answer:
0
Step-by-step explanation:
x < 4 means all numbers less than 4, excluding 4 itself.
4.5 > 4.
5 > 4.
so 0 is the solution
Answer:
4
Step-by-step explanation:
interval notation ( negative infinity, 4)
what is the property of 3x(5x7)=(3x5)7
Answers
The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.
In the equation you provided: 3x(5x7) = (3x5)7
The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.
What is the end behavior of the graph of the polynomial function f(x) = 3x6 + 30x5 + 75x4?
As x→-co, Y→- and as x→∞o, y →→∞
As x→-co Y→- and as x→∞ Y→∞
As x→-co, Y→∞ and as x→∞o, y →-co
As x→-co, y →∞and as x→∞o, y →∞
Answers
The end behavior of the graph of the polynomial function (x)=3x⁶+ 30x⁵ + 75x⁴ is x→±∞, y→∞.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given polynomial function is f(x)=3x⁶+ 30x⁵ + 75x⁴
y=f(x)=3x⁴(x+5)²≥0
The zeros are 0, 0, 0,0,-5 and -5.
x-intercept ( y = 0 ): x = -5.
Local mini/max turning points ( y' = 0 ): 0 0, 0, -10/3 and -5.-,
As x→±∞, y→∞.
Hence, the end behavior of the graph of the polynomial function (x)=3x⁶+ 30x⁵ + 75x⁴ is x→±∞, y→∞.
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Answer:
the 4th option
Step-by-step explanation:
ed2023
Pls help I need this answer now As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and hair color among students. The table below contains the results of the survey.
Answers
Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63. Option D
To find the relative frequency of students with red hair among the sample population of students with gray eyes, we need to divide the number of students with gray eyes and red hair by the total number of students with gray eyes.
From the given table, we can see that there are 22 students with gray eyes and red hair.
The total number of students with gray eyes is the marginal total for gray eyes, which is 35.
To find the relative frequency, we divide the number of students with gray eyes and red hair by the total number of students with gray eyes:
Relative frequency = Number of students with gray eyes and red hair / Total number of students with gray eyes
Relative frequency = 22 / 35
Simplifying the fraction, we have:
Relative frequency = 0.6286
Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63.
Therefore, the correct answer is option OD) 0.63.
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whats the distance between (4,6) and (-7,6)
Answers
Answer:
\(d = 11\)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra II
Distance Formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)Step-by-step explanation:
Step 1: Define
Point (4, 6)
Point (-7, 6)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute [DF]: \(d = \sqrt{(-7-4)^2+(6-6)^2}\)Subtract: \(d = \sqrt{(-11)^2+(0)^2}\)Exponents: \(d = \sqrt{121}\)Evaluate: \(d = 11\)1. Copy and complete: To multiply two powers with the same base, ? their exponents.
2. Give an example of an expression you could simplify using the quotient of powers property.
Find the product or quotient. Write your answer using exponents.
3. 4².4⁹ 4. 5³.5⁸ 5. 6₇.6 6. 7³.7⁴.7²
Answers
(1) To multiply two powers with the same base, add their exponents.
(2) An example of an expression you could simplify using the quotient of powers property is xᵃ / xᵇ
(3) The answer of following exponents are 4¹¹ , 5¹¹ , 6⁸ and 7⁹
A number's exponent indicates how many times the number has been multiplied by itself.
In general, xⁿ denotes that x has been multiplied by itself n times.
According to the question,
(1) Assuming two exponent having same base be xᵃ and xᵇ
Multiplying both the number => xᵃ . xᵇ
To Multiplying two exponent having same base , we add the power
=> x⁽ᵃ ⁺ᵇ⁾
Hence , To multiply two powers with the same base, add their exponents
(2) Simplifying using the quotient of powers property
Let xᵃ / xᵇ
Dividing exponent with same base , we subtract the powers
=> xᵃ⁻ᵇ
Simplifying the followings
3. 4².4⁹
=> 4⁽²⁺⁹⁾
=> 4¹¹
4. 5³.5⁸
=> 5 ⁽³⁺⁸⁾
=> 5¹¹
5. 6⁷.6
=> 6⁸
6. 7³.7⁴.7²
=> 7⁽³⁺⁴⁺²⁾
=> 7⁹
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Sasha spent $7.00 of the $20.00 in her wallet. Which decimal represents the fraction of the $20.00 Sasha spent?
Answers
Answer:
0.7
Step-by-step explanation:
Answer:
0.35
Step-by-step explanation:
A mathematical phrase represented by numbers, variables, and operations is a(n)
pls help:)
Answers
Answer:
Expression
Step-by-step explanation:
Answer: Expression
Got this right!!!
Hope this helps!!!
4
MP.1 Make Sense and Persevere Alicia
measured 1/4 yard of the Blue Diamonds fabric and5/6
yard of the Yellow Bonnets fabric to make a quilt.
Rename each length of fabric. Use the number of
inches in a yard as a common denominator.
HINT: 1 yard = 3 feet; 1 foot = 12 inches
Answers
Alicia made a quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.
Describe the length.The end-to-end measurement or size is called the length. In other words, the larger of the two or three dimensions of a geometric shape or object. For example, the length and width of a rectangle define its dimensions. In the international size system, length is also a dimensional distance quantity.
Blue Diamond fabric is 1/4" x 36" or 9" quarter yards.
5/6 yards of yellow bonnet fabric equals 5/6 x 36 inches or 30 inches.
Alicia made the quilt using 9 inches of Blue Diamonds fabric and 30 inches of Yellow Bonnets fabric.
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Let T(n) denote the nth term of a sequence t. if T(1) = 3, and T(n+1) = T(n) +5 for n>1, what are the first four terms of the sequence
Answers
Based on the given analysis where T(1) = 3, and T(n+1) = T(n) +5 for n>1, the first four terms of the sequence are 3, 7, 8, 9
What is the first four terms of the sequence?First term, T(1) = 3
nth term, T(n+1) = T(n) +5 for n>1
Second term, T2 = T(n) +5
= 2 + 5
= 7
Third term, T3 = T(n) +5
= 3 + 5
= 8
Fourth term, T3 = T(n) +5
= 4 + 5
= 9
Therefore, the first four terms of the sequence are 3, 7, 8, 9
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Help me learn how to solve this please
Answers
The percentage that can be filled with $3 in 1990 is: 29.41%
How to solve percentage increase problems?To calculate percentage growth rate:
Beginning:
Calculate the difference (increase) between the two numbers you are comparing. after that:
Divide the increment by the original number and multiply the result by 100. Growth rate = increment / original number * 100.
We are told that it cost $3 to fill a gas tank as at 1970.
Now, there was a percentage price increase of (78.8 - 23.1)% = 55.2% from 1970 to 1990. Thus:
Cost of a gallon in 1970 = $0.36
Thus, number of gallons bought with $3 = 3/0.36 = 8.33 gallons at full tank
Now, in 1990, the cost is $1.23 and as such:
Quantity that can be bought = 3/1.23 = 2.45 gallons
Percentage of tank filled = 2.45/8.33 * 100% = 29.41%
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The table shows the outcomes and probabilities for a spinner game.
Which statement is true?
A. On average, players lose $0.50 per game.
B. Every player loses $0.50 per game.
C. On average, players lose $2.40 per game.
Answers
Answer: on average, players lose $.50 per game
Step-by-step explanation: i just took the test and got a 100!!!
Answer:
On average, players lose $0.50 per game.
Step-by-step explanation:
Got it right on the test.