The required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 + i√3, -2 - i√3
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .
Now the given equation is,
4x^3 + 16x^2 + 28x = 0
Taking x common we get,
x(4x^2 + 16x + 28) = 0
So, we get
x = 0
And 4x^2 + 16x + 28 = 0
or, x^2 + 4x + 7 = 0
Thus from the above equation is of the form
ax^2 + bx + c = 0
where, a = 1, b = 4 and c = 7
Therefore solution of the above equation is given as,
x = [-b ± √(b^2 - 4ac)] / 2a
Putting the values we get,
x = [-4 ± √(4^2 - 4*1*7)] / 2*1
so, x = [-4 ± √(16 - 28)] / 2
x = [-4 ± √(- 12)] / 2
x = [-4 ± 2√(- 3)] / 2
or, x = [-2 ± √(- 3)]
Since √-1 = i
∴ √(- 3) = i√3
Thus,
x = -2 ± i√3
So, the required values of x are 0, -2 + i√3, -2 - i√3.
Thus, the required solution to the equation 4x^3 + 16x^2 + 28x = 0 is 0, -2 + i√3, -2 - i√3.
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d•r=r•d
O Commutative Property of Multiplication
O Identity Property of Multiplication.
O Zero Property of Multiplication
O Commutative Property of Addition
Answer:
Commutative property of multiplication
A side of the triangle below has been extended to form an exterior angle of 125. Find the value of x
Answer:
55°
Step-by-step explanation:
The angle that is represented with x and the exterior angle with a measure 125° are supplementary angles.
As known the sum of supplementary angles is 180 so the value of x:
180 - 125 = 55 and
x = 55 is the answer to the question.
100 POINTS + BRAINLYIEST
given f(x)=3(4-x) what's the value of f(-4)
Answer:x= −12/15
Step-by-step explanation:
Answer:
f(-4) = 24
Step-by-step explanation:
In order to find f(-4), set the value of x as -4 in the equation.
Given equation:
f(x) = 3(4 - x)
Substitute x = -4:
f(-4) = 3(4 - (-4))
f(-4) = 3(4 + 4)
f(-4) = 3(8)
f(-4) = 24
At a price of $180 there is demand for 2520 items and a supply of 1440 items. At a price of $330 there is demand for 1470 items and a supply of 2640 items. Assuming supply and demand are linear, find the equilibrium price and quantity.
Assuming supply and demand are linear, the equilibrium price is equal to $252 and the equilibrium quantity is equal to 2,016 items.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
First of all, we would determine a linear function for both supply and demand by finding the slope using this formula as follows:
[tex]Slope,\;m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope,\;m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Note: price (p) in dollars would be the output and quantity (q) would be the input.
For supply, the points include the following:
Points (p, q) = (1,440, 180).Points (p, q) = (2640, 330).Slope, m = (330 - 180)/(2640 - 1440)
Slope, m = 150/1200
Slope, m = 1/8.
Next, we would find the y-intercept at (1,440, 180):
p = qm + c
180 = 1/8(1440) + c
180 = 180 + c
c = 0.
Therefore, the supply equation is p = q/8.
For demand, the points include the following:
Points (p, q) = (2,520, 180).Points (p, q) = (1,470, 330).Slope, m = (330 - 180)/(1,470 - 2,520)
Slope, m = 150/-1,050
Slope, m = -1/7.
Next, we would find the y-intercept at (2,520, 180):
p = qm + c
180 = -1/7(2,520) + c
180 = -360 + c
c = 180 + 360.
y-intercept, c = 540.
Therefore, the demand equation is p = -q/7 + 540.
In order to find the equilibrium price and quantity, we would set the supply equal to the demand:
q/8 = -q/7 + 540
Multiplying all through by 56, we have:
7q = -8q + 30,240
15q = 30,240
q = 30,240/15
Equilibrium quantity, q = 2,016 items.
For the equilibrium price, we have:
p = q/8
p = 2,016/8
Equilibrium price, p = $252.
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work
Question 2, 2.3.5
Part 1 of 2
Select the correct choice below and, if necessary, fill in the answer box within your choice
OA. The slope is (Simplify your answer.)
OB. The slope is undefined.
←
Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical
(7.1) and (2.1)
The slope of the line passing through the pair of points is
Given points are:
A (7,1) = (x₁ , y₁)
B (2,1) = (x₂ , y₂)
slope of a line is : y₂ ₋ y₁/x₂ ₋ x₁
Slope equals a height change /Change in width. You may also say that a slope is a climb or a run. This formula changes if the graph's horizontal axis is represented by x and the vertical axis by y.
Assume that the line's slope is'm'.
m = y₂ ₋ y₁/x₂ ₋ x₁
m= 1 ₋ 1/2 ₋ 7
m = 0/₋5
m = 0
hence, when the slope is 0 then the line is horizontal .
Therefore, the slope is 0 which indicates that the line is horizontal.
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Tripling the radius of a cylinder find the dimensions, surface area, before change and after change. Help ASAP please !
The dimensions before tripling the radius of the cylinder are:
radius = 2 and height = 7 yd
and surface area = 113.1
The dimensions after tripling the radius of the cylinder are:
radius = 6 and height = 7 yd
surface area = 490.08
Given, we know that the dimensions are:
radius = 2 and height = 7 yd
therefore, surface area = 2πrh + 2πr²
= 2π2×7 + 2π(2)²
= 2×22/7×14 + 2π×4
= 88 + 25.12
= 113.1
After tripling the radius, we get:
radius = 6 and height = 7 yd
therefore, surface area = 2πrh + 2πr²
= 2π6×7 + 2π(6)²
= 2×22/7×42 + 2π×36
= 264 + 226.08
= 490.08
Hence we get the before and after dimensions of the cylinder.
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The table below summarizes results from a study of people who refused to answer survey questions. A pharmaceutical
company is interested in opinions of the elderly. What is the probability that the selected subject is someone 60 and over
who responded?
Responded
Refused
18-21
76
15
22-29
258
24
30-39
248
37
Age
40-49
139
30
50-59
141
39
60 and over
205
61
Answer:
okay. We need to find the probability that I've met a person is of age 45 to 64 given that they do not smoke. Okay, well, says we're interested in the second Age Group. Would Look, we need to look at this. The second row here of the table. Okay, Um, now, since they don't so so we can't quite look at just these products directly says we're given that they don't smoke instead of the fact that they do smoke. So instead of looking at instead of just using this product that I've circled in red, I need to I need to take this green circled number and subtracted. So? So when I mean, it's gree this green circle numbers subtracted. Red circle number. Okay. And what would that give us? That's work. That out on the calculator. So points reform minus 0.7 for eight. That's 0.2652 My brave Onda, who, instead of looking at the total of these products, you need to subtract one from it or two. Oh, Uh, 31 Asher B 0.7 se 7969 Okay, so then this Just 0.2652 over it. 0.79 69 Okay, so let's do that. We have. Let's work that out on a calculator. We get around 0.33 three. Thank you for watching.
A ladder leaning against a wall forms a triangle and exterior angles with the wall and the ground. What is the measure of exterior angle formed on the ground? 5 degrees 90 degrees 125 degrees 180 degrees
In linear equation 125 degrees is the measure of exterior angle formed on the ground.
What in mathematics is a linear equation?
There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that together make a linear equation true and plot those values on a coordinate grid.we know that the sum of all the angles of a triangle is 180
therefore
11x+7x+90=180
18x=90
x=5
exterior angle formed on the ground=180-11x
=180-55
=125
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A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 140 gallons of a mixture that contains 65% pure antifreeze. How many gallons of each brand of antifreeze must be used?
If a chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze, and the second brand is 95% pure antifreeze. The number of gallons each brand of antifreeze must be used is: 56 gallons of 20% antifreeze and 84 gallons of 95% antifreeze.
Number of gallons for each brand of antifreezeLet call x = The amount of 20% pure antifreeze needed
Let 140 - x = amount of 95% antifreeze needed
Hence,
x gallons of 20% antifreeze + (140-x) gallons of 95% = 140 gallons of 65%
Thus,
.20x + .95(140-x) = .65(140)
.20x + 133 - .95x = 91
Collect like terms
42= .75x
Divide both side by .75x
x=42/.75
x=56
Hence,
56 gallons of 20% antifreeze
84 gallons of 95% antifreeze
Therefore the number of gallons each brand of antifreeze must be used is: 56 gallons of 20% antifreeze and 84 gallons of 95% antifreeze.
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HELP ME OUT PLEASE I NEED BETTER GRADES
Answer:
person above me is right pls give them brainliest!!!
Step-by-step explanation:
In order for a computer to work properly it needs a memory disk of at least
4 GB. Memory disks can fluctuate 0.2 GB. What is the smallest amount of
storage a memory disk has?
4.2 GB
2.3 GB
3.8 GB
4 GB
The smallest amount of storage a memory disk is 3.8 GB. The correct option is C.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given that for a computer to work properly it needs a memory disk of at least 4 GB. Memory disks can fluctuate 0.2 GB. Therefore, the smallest amount of storage a memory disk has is,
Smallest amount of storage a memory disk have = 4 GB - 0.2 GB
= 3.8 GB
Hence, the smallest amount of storage a memory disk is 3.8 GB.
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2) Jerry and Gwen were running a relay race. The race was 12.06 kilometers total. If Jerry ran
6.76 kilometers how far did Gwen run?
3.
4.
Answer:
5.3 kilometers
Step-by-step explanation:
12.06 - 6.76 = 5.3
If the product of a number and -7 is subtracted from the number the result is 6 more than a number , what is the equation writte
The number is -6/7 and the equation is x-7*x=x+6.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given:
Let the number be x.
We have to find the number.
According to given question we have
If the product of a number and -7 is subtracted from the number the result is 6 more than a number
product of a number and -7 =-7*x
subtracted from the number=x-7*x
6 more than a number=x+6
i.e
x-7*x=x+6
compare the like terms we have,
x-7*x=x+6
Subtract x from both sides we get ,
-7x=6
x=-6/7
Therefore, the number is -6/7 and the equation is x-7*x=x+6.
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Which of the following properties is demonstrated by the equation below?
9(x+3)=9x+27
distributive property
inverse property of addition
associative property of addition
communitive property of addition
Answer: Distributive Property
Step-by-step explanation:
This is an example of the distributive property because the 9 is being distributed into each term, yielding the 9x and the 27.
A manager recorded the performance review scores for each employee and placed the results in the bar chart below. All employees received a rating on each of the Evaluation Categories. If Person 6 obtained the highest score possible, what score did Person 2 receive? Use the graph and tables below.
The score of person 2 is 30.
What is a bar chart?A bar chart is a graph that shows the numerical values of variables represented by the height rectangles of equal width. In a bar graph, the rectangles must be of equal width and the space between each bars must be equal.
Total score of person 6 with the highest score possible : highest score x number of options
5 x 9 = 45
This means that on the bar chart, the value of person 6's rectangle is 45. This means that each the value of the graph increases by 5. This means that each line increases by the value of 5.
Score of person 2 = number of lines to the height of the bar x 5
6 x 5 = 30
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Read this excerpt from “The All American Slurp”
In china we never ate celery raw or any other kind of vegetable raw. We always had to disinfect the vegetables in boiling water first. When we were presented with our first relish tray, the raw celery caught us unprepared
What story element does the author develop in this excerpt?
Conflict between family members.
Character traits of the Lin family.
Plot details about the Gleason party.
Setting details about the Lins hometown.
From the excerpt that we have here the story element that the Character traits of the Lin family.
What does the character trait mean?This is the term that is used to refer to the words that are used in order to offer the characterization of a person. These are the terms that would help to show the personalities and the qualities that a person has. It tells us who these persons are and the way they would be described if we are to talk about them to other people.
Based on the description that I have given here, the way that we would be able to talk about this family would be that they are known to prepare their food in a different way that the Americans made theirs.
From what they said, they would always have to put their vegetables first in boiling water. This would make it less raw. But from what they were offered in America, they had to eat the vegetables that had been left raw.
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Which of the following sets is NOT closed under addition.
A) Natural Numbers
B) Whole numbers
C) Integers
D) Odd numbers
The odd numbers do not follow the closure property of addition.
What is a closure property of addition?
The closure property of addition states that when any two numbers from the set of reals are added, the result will always be a real number. For example 2 + 3 = 5
Explanation
When we add any two natural numbers, the result is always a natural number, i.e. 2 + 1 = 3. Thus, it follows the closure property of addition.
When we add any two whole numbers, the result is always a whole number, i.e. 3 + 0 = 3. Thus, it follows the closure property of addition.
When we add any two integers, the result is always an integer, i.e. 2 + (-5) = -3. Thus, it follows the closure property of addition.
When we add any two odd numbers, the result is not an odd number, i.e. 3 + 1 = 4. Thus, it does not follow the closure property of addition.
Hence, the odd numbers do not follow the closure property of addition.
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Solve the following quadratic equation for all values of x in simplest form.
11- x² = -3
Answer:
x = √14
Step-by-step explanation:
11- x² = -3
x² = 14
x = √14
A transportation company charges a fee of $125 plus $50 per hour to rent a limousine. If John paid $425 for a limousine, for how many hours did he rent the limousine?
A. 7
B. 6
C. 5
D. 4
John rented the limousine for 6 hours.
The minimum fee charged by the transportation company to rent a limousine is $125.The hourly fee charged by the transportation company to rent a limousine is $50.The amount of money paid by John to rent a limousine is $425.Let the number of hours for which John paid for the rent of the limousine be "x".A formula that represents the equality of two expressions by linking them with the equals sign is known as an equation.The above-given data helps us to form the linear equation given below :425 = 125 + 50x300 = 50xx = 6Thus, John rented the limousine for 6 hours.To learn more about equations, visit :
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74 oz at $4.64
42 oz at $2.91
Answer: 4.64+2.92 = 7.55oz
Step-by-step explanation:
the difference of twice
a number and seven is nine
Answer:
16!
Step-by-step explanation:
A bathtub is partially filled with g gallons of water.
Alice adds 10 more gallons of water to the tub,
making it 50% full. If Marco then adds 40 more
gallons of water, the tub will be 100% full. What is
the value of g?
A. 20
B. 24
C. 30
D. 40
Answer: C.) 30
Step-by-step explanation: 40 gallons = 50% full Alice added 10 more gallons to make it 50% full there was already 30 gallons in.
Can someone do 4,6,8 for me pls show work I give l Brainly and extra point
Answer:
4.) T = M - N
T(-M) = M - N (-M)
(/-1) T - M = -N (/-1)
-T + M = N
6.) Ax + By = C
(-Ax) Ax + By = C (-Ax)
By = C - Ax
By (/B) = (C - Ax)/(B)
y= (C - Ax)/B
8.) C = pi(d)
(/pi) C = d
C/pi = d
f(x) = cube root 2x
g(x) = 2x + 1
Find (f/g) (X) Include any restrictions on the domain
Divide 6/13 by 6/12 .
A. 12/13
B. 9/16
C. 1/12
D. 13/12
The set of real numbers is composed of rational and irrational numbers.
A. true
B.false
Answer:
true..... ............
Stanley can purchas a 15.4-ounce bottle of
olive oil for $5.39 or a 23.6-ounce bottle of olive oil for $7.08.
Which bottle is the better buy? Explain.
Answer: They are the same deal
Step-by-step explanation:
15.4/5.39=3.33333...
23.6/7.08=3.333333...
GUYS HELP Albert buys a tv that has a regular price of $2,399. The tv is on sales for "21% off". If
the sales tax rate is 8.25%, what is his final cost of the tv?
The final cost of the TV is $1966.9
How to determine the final cost of the TV?The given parameters are:
Regular price = $2300
Discount = 21%
Sales tax = 8.25%
The final cost of the TV is calculated as
Final cost = Regular price * (1 - Discount) * (1 + Sales tax)
So, we have:
Final cost = $2300 * (1 - 21%) * (1 + 8.25%)
Evaluate
Final cost = $1966.9
Hence, the final cost of the TV is $1966.9
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Just 17 and 18 please!
[16] f(-3) = -5
#17 is asking us to find what the function equals when x is equal to -3. We will find x = -3 on the graph, then find what y equals.
[17] f(4) = 0
#17 is quite similar, it is asking us to find what the function equals when x is equal to 4. We will find x = 4 on the graph, then find what y equals.
You asked in the comments for #16 and #17, I hope this helps.
Simplify the expression (X1/6)3
X2
X3
X1/3
X1/2