The quadratic equation whose roots are -3 and -1, and whose leading coefficient is 1 is x^2 + 4x + 3 = 0.
We know that the standard form of a quadratic equation is given by;
y = f(x) = ax² + bx + c = 0
We are given:
The roots of the quadratic equation are -3 and -1.
The leading coefficient of the quadratic equation is 1.
We need to find the quadratic equation.
The roots of the quadratic equation are -3 and -1.
So, (x + 3) and (x + 1) will be the factors.
Since the leading coefficient of the quadratic equation is 1.
So, the quadratic equation is given by;
1 * (x + 3) * (x + 1) = 0
x (x + 1) + 3 (x + 1) = 0
x^2 + x + 3x + 3 = 0
x^2 + 4x + 3 = 0
So, the required quadratic equation is x^2 + 4x + 3 = 0.
Thus, the quadratic equation whose roots are -3 and -1, and whose leading coefficient is 1 is x^2 + 4x + 3 = 0.
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Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Third-degree, with zeros of −3, −1, and 4, and a y-intercept of −13.
The third degree polynomial function with zeros of −3, −1, and 4, and a y-intercept of −13 is y = -13/12 (x³ - 13x + 12)
Polynomial function:
polynomial function refers a functions of single independent variables, in which variables can occur more than once, raised to an integer power.
Given,
Third-degree, with zeros of −3, −1, and 4, and a y-intercept of −13.
Here we need to construct a polynomial function with the stated properties and reduce all fractions to lowest terms.
The standard form for the third degree polynomial function is written as,
y = K (x + zero1) (x + zero2) (x + zero3)
Here we know the values of zeros as -3, -1 and -4.
Apply it on the general form,
y = K (x -3) (x - 1) (x + 4) ----------------------(1)
And the value of y intercept is -13 then the value of x is 0.
So, it can be written as,
-13 = K(0 - 3) (0 - 1) (0 + 4)
-13 = K (-3)(-1)(4)
-13 = K (12)
K = -13/12
Now, we have to apply these value on the equation (1), then we get,
y = -13/12 (x -3) (x - 1) (x + 4)
When we expand these, then we get the polynomial function as,
y = -13/12 (x³ - 13x + 12)
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I need help with this. I attached a photo. Thanks - Rylee
The quadratic function that produces the area, f(x) = A = x², can be used to complete the table which is presented as follows;
Side length[tex]{}[/tex] 1 2 3 4 5 6
Area[tex]{}[/tex] 1 4 9 16 25 36
What is a quadratic function?A quadratic function is a function which is of the general form;
f(x) = a·x² + b·x + c, where;
a, b, c, are numbers and the value of 'a' is not zero
The side lengths of a square are the same
The area of a square = Length of Side × Length of side
Therefore;
Area of a square = (Side length)²
The quadratic equation that gives the area, A, from a side length, x, is therefore;
A = x²The table in the question can completed using the following calculations
When the side length = 1, The area = 1² = 1
Area = (Side length)²Therefore;
Side length = √(Area)When the area = 4, the side length = √4 = 2
When the area = 9, the side length = √9 = 3
When the side length = 4, the area = 4² = 16
When the area = 25, the side length = √(25) = 5
When the side length = 6, the area = 6² = 36
The completed table is therefore;
Side length[tex]{}[/tex] 1 2 3 4 5 6
Area[tex]{}[/tex] 1 4 9 16 25 36
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Select the correct answer.
Solve the following inequality for x.
-26 + 13z + 2 > 2 132
O A. X<2
X2-1
OB.
O C.
X>1
OD. x < -2
z >1 for the given inequality for x.
To solve the following inequality for x.
-26 + 13z + 2 > 2 132
Since there is no x in this I'm assuming we are looking for z
Step 1: Simplify both sides
15r - 26 > -13z + 2
Step 2: Add 13z to both sides
15r - 26 + 13z > -13z + 2 + 13z
28 - 26 > 2
Step 3: Add 26 on both sides
28 - 26 + 26 > 2 + 26
28z > 28
Step 4: Divide both sides by 28z / 28 > 28 / 28
z > 1
Hence the answer is z >1 for the given inequality for x.
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If M is the centroid of triangle ABC, AM = 44, CE = 54, and DM = 23 Find each missing measure
FM=
A F=
CM=
ME=
MB=
DB=
Applying the centroid theorem, the missing measures are:
FM = 22
A.F = 66
CM = 36
ME = 18
MB = 46
DB = 69
What is the Centroid Theorem?The centroid theorem states that the distance from the centroid of the triangle to the opposite vertex is equal to one-third of the length of the segment that connects the midpoint of a side of a triangle to the opposite vertex.
Given:
AM = 44, CE = 54, and DM = 23, where M is the centroid of the triangle, thus:
FM = 1/3(FA) = 1/3(AM + FM)
Substitute
FM = 1/3(44 + FM)
3FM = 44 + FM
3FM - FM = 44
2FM = 44
FM = 44/2
FM = 22
A.F = AM + FM = 44 + 22
A.F = 66
CM = 2/3(CE)
CM = 2/3(54)
CM = 36
ME = CE - CM = 54 - 36
ME = 18
MB = 2/3(DB) = 2/3(DM + MB)
MB = 2/3(23 + MB)
3MB = 2(23 + MB)
3MB = 46 + 2MB
3MB - 2MB = 46
MB = 46
DB = DM + MB = 23 + 46
DB = 69
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Find the missing length indicated.
Answer:
5+5=10
Step-by-step explanation:
Ren sets aside $1,000 into an online savings account with an annual interest rate of 2. 3%, compounded annually. How long will it take for the money in his account to double? round to the nearest year.
Ren will have to wait for approximately 31 years for the money compounded annually and a rate of 2.3% to double it's original investment.
Compound InterestCompound interest is the interest imposed on a loan or deposit amount. It is the most commonly used concept in our daily existence. The compound interest for an amount depends on both Principal and interest gained over periods. This is the main difference between compound and simple interest.
The formula of compound interest is given as
A = P(1 + r/n)^nt
A = compounded interest = $2000 (Since the investment doubled)r = rate = 2.3%n = number of times compounded = 12t = time = ?Substituting the values into the equation;
It will take approximately 31 years to double the investment.
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Find the sale price of each item. Round to two decimal places when necessary.
Original price: $45.00; Markdown: 22%
Answer:
$35.10
Step-by-step explanation:
45 x 0.22= 9.9
45-9.90= 35.10
Ann's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Ann $5.60 per pound, and type B coffee costs $4.20 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $637.00. How many pounds of type A coffee were used?
Using system of equations to solve the problem, the coffee shop made use of a total of 91 pounds of blend A coffee for that month.
System Of EquationA system of equations is a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.
The equations in the system can be linear or non-linear.
In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables.
Let;
x = Blend Ay = Blend B5.60x + 4.20y = 637... eq(i)
x = 3y ... eq(ii)
Solving equation (i) and (ii)
x = 91, y = 91/3
The Coffee shop used 91 pounds of blend A
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Choose the graph of y=|x|+3 by translating the parent function
The graph that indicates the transformation translating of the parent function to get, y = |x| + 3, created with MS Excel is attached
What is the transformation of a function?A function ix transformed when the graph of the function is translated, resized or reflected.
The formula for the transformation of a function, f(x) is y = a·f(b·(x + c)) + d
Where;
a indicates the graph of the function is dilated vertically
b indicates a dilation horizontally
c indicates a translation horizontally
d indicates a vertical translation
The transformation applied to the parent function is the f(x) is an addition of a term, d = 3, which is a vertical translation
In a vertical translation of the form f(x) ± d
When d > 0, the graph of f(x) is moved up d units to get the graph of f(x) + d
When d < 0, the graph of f(x) is moved down d units to get f(x) - d
The graph of y = |x| + 3, obtained from the parent function, y = |x|, by a transformation of d = +3, therefore, the graph of y = |x| is moved up 3 units to get the graph of y = |x| + 3
Please find attached the graph that indicates the translating of the parent function, created with MS Excel.
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Given f(x) = (x − 1)(x + 2)(x − 3), what are the zeros and end behavior of the function? −1, 2, −3; continues downward to the left and upward to the right −1, 2, −3; continues upward to the left and downward to the right 1, −2, 3; continues downward to the left and upward to the right 1, −2, 3; continues upward to the left and downward to the right.
A function assigns the value of each element of one set to the other specific element of another set. The zeroes of the functions are -2, 1, and 3.
Function : -
A function assigns the value of each element of one set to the other specific element of another set.
Zeroes of a function: -The zeros of a function are defined as the values of the variable of the function such that the function equals 0. Graphically, the zeros of a function are the points on the x-axis where the graph cuts the x-axis. In other words, we can say that the zeros of a function are the x-intercepts of its graph.
Now, According t the question:
Given that, f(x) = (x - 1)(x + 2)(x − 3)
Therefore, the zeroes of the functions are -2, 1, and 3. The end behavior of the function is that if x approaches ∞ then f(x) approaches ∞, while if x approaches -∞ then f(x) approaches -∞, as can be observed from the given graph.
Hence, the zeroes of the functions are -2, 1, and 3.
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help please and thankyou 2
The length of the right triangle, y is 8.94 units.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees.
The sides of a right angle triangle can be found using trigonometric ratios or Pythagoras's theorem.
c² = a² + b²
where
c = hypotenuse sidea and b are the other legs.Therefore,
12² - 8² = y²
144 - 64 = y²
y = √80
y = 8.94427191
y = 8.94 units
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Ichiro and Ivo are playing a game called Factor Subtractor. In the game, they each select a number from 11 to 15. For the number that is selected, they write down all of the whole numbers between 1 and their selected number. They then cross out all of the factors of the number they selected. Finally, they add all of the numbers that remain. The person who has the highest total is the winner. Complete parts a to c. Question content area bottom Part 1 a. Ichiro chooses the number 15. What is his score?
Answer:
96
Step-by-Step Explanation:
1, 3, 5 and 15 are the factors of 15.
On a piece of paper, graph y = -2x - 3. Then determine which answer
matches the graph you drew.
The graph is in the image uploaded.
Given function:
y = -2x - 3
Table:
x y
-2 0
0 -2
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In AEFG, f= 1.5 inches, 10th of an inch.
A meenger earn #2,640 per year and pay tax at the rate of 10k on a naira. How much tax doe he pay in a year
264 naira tax doe he pays in a year.
Amount earned per year = 2460
Rate of interest paid: 10k per naira earned
Tax paid by messenger per year :
100k = 1 naira
10k = (100/10) = 0.1 naira
Hence 0.1 naira is paid as tax on every naira earned
The total amount paid off is 2640 Naira :
Amount paid per naira * total amount earned
(0.1 * 2640) = 264 nairas.
A tax is a compulsory monetary charge or a few other sorts of levy imposed on a taxpayer (a man or woman or criminal entity) by using a governmental agency if you want to fund authorities' spending and numerous public expenses (regional, neighborhood, or countrywide), and tax compliance refers to coverage movements and character behavior geared toward making sure that taxpayers are paying the right amount of tax on the proper time and securing the right tax allowances and tax reliefs. the first known taxation passed off in historical Egypt around 3000–2800 BC. A failure to pay in a well-timed way (non-compliance), together with evasion of or resistance to taxation, is punishable by means of regulation. Taxes consist of direct or oblique taxes and may be paid in cash or as its labor equivalent.
Maximum nations have a tax system in the region, so as to pay for public, common societal, or agreed-on country-wide needs and for the capabilities of the presidency. a few levies a flat percentage rate of taxation on private annual profits, however, maximum scale taxes are modern and based on brackets of annual earnings amounts. most nations charge a tax on a character's profits as well as on corporate earnings. nations or subunits regularly additionally impose wealth taxes, inheritance taxes, estate taxes, gift taxes, property taxes, sales taxes, use taxes, payroll taxes, duties, and/or tariffs.
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wait times for customers once they enter the bank. wait time is defined as the time between when a customer enters the bank until they reach a teller. a random sample of customers are recorded and their wait times in minutes are as follows: (4.21, 5.55, 3.02, 5.13, 4.77, 2.34, 3.54, 3.20, 4.50, 6.10, 0.38, 5.12, 6.46, 6.19, 3.79). determine the t test statistic for the bank's claim that wait times are not longer than five minutes.
The t test statistic for the bank's claim that wait times are not longer than five minutes is 4.29.
T - test statistic
T test statistic refer an inferential statistic used to determine if there is a significant difference between the means of two groups and how they are related.
Given,
Wait times for customers once they enter the bank. wait time is defined as the time between when a customer enters the bank until they reach a teller. a random sample of customers are recorded and their wait times in minutes are as follows: (4.21, 5.55, 3.02, 5.13, 4.77, 2.34, 3.54, 3.20, 4.50, 6.10, 0.38, 5.12, 6.46, 6.19, 3.79).
Here we need to determine the t test statistic for the bank's claim that wait times are not longer than five minutes.
In order to find the t test statistic, we have to calculated the average for the given waiting time,
Here the given wait times are:
(4.21, 5.55, 3.02, 5.13, 4.77, 2.34, 3.54, 3.20, 4.50, 6.10, 0.38, 5.12, 6.46, 6.19, 3.79).
In this list there are 15 members timings are presented.
Therefore, the average is calculated as,
=> (4.21 + 5.55 + 3.02 + 5.13 + 4.77 + 2.34 + 3.54 + 3.20 + 4.50 + 6.10 + 0.38 + 5.12 + 6.46 + 6.1 + 3.79) /15
=> 64.3/15
=> 4.29.
Therefore, the t test statistic for the bank's claim that wait times are not longer than five minutes is 4.29.
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PLEASE HELP ME WITH THESE PROBLEMS!
Answer:
1. Congruent, SAS
2. Congruent, SSS
3. Not congruent
4. Congruent, SAS
5. Congruent, SSS
6. Not congruent
7. Congruent, SAS
8. Not congruent
Alice, Ben and Charlie share $213
The ratio to Alice's share to Ben's share is 4:3
The ratio to Ben's share to Charlies share is 8:5
How much does Ben get?
After finding the ratio for each person, Ben will get $72
What is a Ratio?
A ratio shows the relative sizes of two or more values. Ratios can be shown in different ways:
using the ":" to separate example valuesusing the "/" to separate one value from the totalas a decimal, after dividing one value by the totalas a percentage, after dividing one value by the totalIt was given that Alice, Ben and Charlie are to share $213.
Ratio of Alice's share to Ben = 4 : 3
Ratio of Ben's share to Charlie = 8 : 5
Combining these ratios, their shared item (Ben's share) must be the same in each ratio.
Taking Alice's share to Ben, 4 : 3 and multiplying both parts by 8 to get an equivalent ratio, we have:
Alice : Ben = 4(8) : 3(8) = 32 : 24
Likewise, taking Ben's share to Charlie, 8 : 5 and multiplying both parts by 3, we have:
Ben : Charlie = 8(3) : 5(3) = 24 : 15
Combining these ratios, we have:
Alice : Ben : Charlie = 32 : 24 : 15
Adding the ratios together, we have: 32 + 24 + 15 = 71
If the money to be shared is $213, Ben's share will be:
[tex]\frac{24}{71}[/tex] × [tex]$213[/tex] = 72
Therefore, Ben will get $72 from the total amount of $213
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Write the following fractions in ascending order
3/4
1/2
5/8
Answer:
5/8, 3/4, 1/2
Step-by-step explanation:
divide each and find out which one is the smallest to biggest :)
a fair die with its faces numbered from 1 to 6 will be rolled. which of the following is the best interpretation of the probability that the number landing face up will be less than 3 ?
When a fair die with faces numbered 1 to 6, the probability that the number landing face up is less than 3 is 1/3.
The probability measures how likely an event to occur. The probability of an event A is defined as:
P(A) = number of ways that event A can occur / all possible outcomes
In the given problem, let x be any number of die's face, then
number of ways x will show up = 1
all possible outcomes = 6
Hence,
P(x) = 1/6
Numbers that are less than 3 is 1 and 3. Therefore,
P (x<3) = P(1) + P(2)
P (x<3) = 1/6 + 1/6 = 2/6 = 1/3
Therefore, we can conclude that the probability that the number landing face up is less than 3 is 1/3
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find five consecutive of integers if the um of the first three integers is 3 more than the sum of the last two.
Answer: 4,5,6,7,8
Step-by-step explanation:
Let the first integer be A; then the five consecutive integers are A, A+1, A+2, A+3, and A+4.
If the sum of the first three equals the sum of the last two, then A + (A+1) + (A+2) = (A+3) + (A+4)
Combining, 3A + 3 = 2A + 7 … A =4
The five Integers are thus 4, 5, 6, 7, and 8
What is the equation for the line of reflection?
Answer:
The line of reflection is usually given in the form y = m x + b y = mx + b y=mx+by, equals, m, x, plus, b
What are the two solutions of this equation + workings out. Please help!!!!
Answer:
God is good, satanist are L
Answer:
0 and -6
Step-by-step explanation:
Either x=0
Or, x+6=0 i.e, x= -6
2(v + 13) = 14
How do you solve this two step equation?
Answer:
solving for v or your variable
v= -6
Step-by-step explanation:
distribute the 2 outside the parentheses to get: 2v + 26 = 14Then you would solve for your variable in this case, v by subtracting 26 to get 2v = -12then you divide by 2 to get v by itselfgetting:
v = -6
Now, reverse the relationship of jersey number and player height. What if player height is the input and jersey number is the output? The diagram below helps you see that when the input is 68, the output may be either 10 or 18. this relationship is not a function. why is the relationship between the height (input) in the jersey number (output) not a function.
A.in a function, one input can only have one output
B.in a function, one outputcan have one input
C.in a function, one input can have two or more outputs
D. in a function two or more outputs can have one input
Answer:
A
Step-by-step explanation:
you want to select a sample of 100 employees of company x. you assign a number to every employee in the company database from 1 to 1000, and use a random number generator to select 100 numbers. is this a simple random sampling?
Yes this an example of simple random sampling.
What is simple random sampling?
Every person in the population has an equal probability of getting chosen in a simple random sampling. The entire population should be included in your sampling frame.
You might utilize instruments like random number generators or other methods that just rely on chance to carry out this kind of sampling.
Main Body:
It is uncommonly attainable to collect knowledge from each member of a gaggle of people once conducting analysis on them. In its place, you choose a sample. The population that may really participate within the study is that the sample.
As in this case we select 100 random people out of 1000 , so it is an example of simple random sampling.
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Hello guys I need help
Answer:
B
Step-by-step explanation:
I jus did this in class becaueyeah dhdjajajakaksksnsnammamanajajajjanKa
What is the product of 18.5 • 0.31?
0.5735
5.730
5.735
57.35
Answer:
The answer is C 5.735
Step-by-step explanation:
I hope this helps!
Twice the sum of a number and 4 is 18
Answer: 7
Explain: 2x + 4 = 18 which is required an equation, so the sum of thrice a number and 7 is 25. So 3x + 7 = 25
Answer:
7
Step-by-step explanation:
A lab technician is dividing a cell that has a diameter of 4. 32×10−4 millimeters. Each of the new cells has a diameter measuring exactly one half of the diameter of the original cell. Which is the diameter of a new cell?.
Answer:
38
Step-by-step explanation:
32 + 10 = 42 subtract 42-4 = 38