The roots of the equation x³ + 2x² + 36x + 72 = 0 are ( -2 , -6i , +6i )
What is Factorizing?
Brackets should be expanded in the following ways:
For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket
For an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.
Given data ,
Let the equation be x³ + 2x² + 36x = -72
Adding 72 on both sides , we get
x³ + 2x² + 36x + 72 = 0
Now , on simplifying we get
Take the common factor x² in first two terms and 36 in last two terms
So ,
x² ( x + 2 ) + 36 ( x + 2 ) = 0
Now , taking ( x + 2 ) as common factor , we get
( x² + 36 ) ( x + 2 ) = 0
So , for the equation to be 0 , either ( x + 2 ) = 0 or ( x² + 36 ) =0
And , we can find the solutions to the equation as
x + 2 = 0
Subtracting 2 on both sides , we get
x = -2
So , one solution is -2
Now ,
( x² + 36 ) =0
Subtracting 36 on both sides , we get
x² = -36
x = √ ( -36 )
x = ± 6i
So , we got two more solutions as -6i and +6i
Hence , the roots of the equation are -2 , -6i and +6i
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Two boats leave the same dock in Cairo at the same time. One heads north on the Mississippi River while the other heads south. The northbound boat travels four miles per hour. The southbound boat goes eight miles per hour. How many hours will it take them to be 66 miles apart?
It will take the boat going north 16.5hrs and the boat going south will take it 8.25hrs
Step-by-step explanation:
divide 66/4 for the north boat and 66/8 for the south boat
Write the prime factorization for each of the following numbers using exponents if possible.
Which graph represents the equation y=-4/3-2
The graph that represents the equation y [tex]=[/tex] (-4/3)x - 2 is drawn below .
In the question ,
it is given that,
the equation of the line is [tex]y=-\frac{4}{3}x-2[/tex] ,
we need to plot the graph of the given line ,
To sketch the graph we need minimum two points .
when we put x [tex]=[/tex] 3 in the equation , we get
y [tex]=[/tex] (-4/3)(3) - 2
y = -4 - 2
y = -6
the first point is (3,-6) .
For second point put x [tex]=[/tex] 6 ,
we get
y = (-4/3)(6) - 2
y = -4*2 - 2
y = -8 - 2
y = -10
the second point is (6,-10) .
After plotting and joining the point (3,-6) and (6,-10) ,
the graph is shown below .
Therefore , The graph that represents the equation y [tex]=[/tex] (-4/3)x - 2 is drawn below .
The given question is incomplete , the complete question is
Draw the graph which represents the equation y [tex]=[/tex] (-4/3)x - 2 ?
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Consider the following polynomial function.
f(x) = (x+3)(x+1)²(x-1)
Answer the questions regarding the graph of f.
Then, use this information to graph the function.
(a) Choose the end behavior of the graph of f.
Choose One
(b) List each real zero of faccording to the behavior of the graph at the X-axis near that
zero. If there is more than one answer, separate them with commas. If there is no
answer, click on "None".
Zero(s) where the graph crosses the X-axis:
Zero(s) where the graph touches, but
does not cross the X-axis:
(c) Find the y-intercept of the graph of f:
(d) Graph f(x) = (x+3)(x+1)²(x-1) by doing the following.
Plot all points where the graph of f intersects the x-axis or y-axis.
For each point on the X-axis, select the correct behavior.
Click on the graph icon.
The end points behavior of the function:
(a) If x goes to positive infinity then the function goes to positive infinity. If x goes to negative infinity then the function goes to negative infinity.
(b) The zeros of the function f(x) are -3, -1, -1, and 1.
(c) The y-intercept is at (0,-3).
What is the endpoint behaviors of a polynomial?
A polynomial function's final behaviour is how its graph behaves as x gets closer to positive or negative infinity. The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
What are zeros of a polynomial?
The locations where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero (-1). The highest power of the variable x is referred to as a polynomial's degree. A linear polynomial is a polynomial with degree 1.
Given function is f(x) = (x+3)(x+1)^2(x-1).
If x = ∞, then f(x) = ∞. The one endpoint of the function will go positive infinity.
If x =- ∞, then f(x) = -∞. The one endpoint of the function will go negative infinity.
To find the zeros of the polynomial, equate f(x) with zero.
(x+3)(x+1)^2(x-1) = 0
Either, x + 3 =0 → x = -3
or, (x+1)^2 =0 → x = -1
or, x-1 = 0 → x = 1
The zeros of the function are -3, -1, and 1.
To find y-intercept, put x=0 in the given function:
f(0) = (0+3)(0+1)^2(0-1)
→ f(0) = -3
The y-intercept is at (0,-3).
The x-intercepts of the function are zeros of the function.
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30x43x54545454545455454x82409284x098908098x8908089808x56678909876543-32131273138x1000 =
Answer:
7,036,363,636,363,635,660,000
Step-by-step explanation:
this one hert my head
How do I figure the total of a 4:3 ratio?
Step-by-step explanation:
If you take the 4:3 aspect ratio and divide 4 by 3, the result is 1.33. Therefore, you could alternately describe the 4:3 aspect ratio as 1.33:1, meaning that for every 1.33 units in width, there is 1 unit in height. Again, the same applies for the 16:9.
Learn at brainlyDaisy has one cucumber that is 3 inches long and another that is 5inches long. She cuts the cucumber into 3/8 inch thick slices and adds them to a salad. How many 3/8 inch thick slices does Daisy have? How much of a slice will be left over?
If She cuts the cucumber into 3/8 inch thick slices and adds them to a salad. The number of 3/8 inch thick slices that Daisy have 21 1/3.
How to find the thickness ?Given data:
Cucumber length = 3 inches
Second cucumber length = 5 inches
Cucumber slices = 3/8
Now let find the the number of thickness that daisy have
Thickness = (3+5) ÷ 3/8
Thickness = 8× 3/8
Thickness = 64/3
Thickness = 21 1/3
Therefore the thickness is 21 1/3.
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A swimming pool is in the shape of the following figure. The homeowner wishes to build a fence around the perimeter of the pool. How many feet of fencing are required?
Round your answer to the nearest hundredth, if necessary.
71.849 feet of fencing are required.
Given:
In a rectangle two sides are 13 feet and 12 feet.
In right angled triangle sides are 15 feet and 13 feet.
Let x be the hypotenuse of the triangle.
From rectangle opposite sides are equal so the other two sides are equal to 12 feet and 13 feet.
According to pythagorean theorem:
[tex]15^{2} +13^{2} =x^{2}[/tex]
x = [tex]\sqrt{225+169}[/tex]
x = 19.849
The perimeter of the pool = 15 + 12 + 13 + 12 + 19.849
= 27 + 13 + 12 + 19.849
= 52+19.849
= 71.849 feet.
Therefore 71.849 feet of fencing are required.
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e. Explain why time is not a function of height in the bouncing ball experiment.
The value of velocity is [tex]v = 7.67\frac{m}{s}[/tex].
The coefficient of restitution is the ratio of the final to initial speed between two bodies after the collision. While a value of 1 indicates a perfectly elastic collision, a value of 0 indicates a perfectly inelastic collision.
The first option is
We can find the displacement by using the area under the graph, which is equal to the displacement. The area of the triangle can be found using the formula below.
[tex]Area = \frac{1}{2} . base . length[/tex]
[tex]Area = 0.5m.50m.50. = 1250 m^{3}[/tex]
The other option is
We use the conservation of energy. So, we equate the potential energy and the kinetic energy.
[tex]E_{pot} = E_{kin}\\ \\ m.g.h = \frac{1}{2}.m.v^{2}[/tex]
The mass is cancelled out in the above equation, and we re-arrange with respect to velocity.
[tex]v^{2} = 2.g.h\\ \\v = \sqrt{2.9.81\frac{m}{s^{2} }.3m } = 7.67\frac{m}{s}[/tex]
Hence the answer is the value of velocity is [tex]v = 7.67\frac{m}{s}[/tex].
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Terry needs 40 gal of a 40% acid solution. The only available acid solutions are 25% and 80% acid. How much of each should she mix together (to the nearest gallon)?
Terry should mix 29 gallons of the 25% acid solution and 11 gallons of the 80% acid solution
How to determine the amount of each acid to be mixed together?Given: 40% acid and 80% acid solutions
Terry needs 40 gal of a 40% acid solution
Let x represent the amount of the 25% acid solution required in gal
Thus, the amount of the 80% acid solution required will be (40-x) gal
The amount of acid in these solutions is 0.25x + 0.8(40-x)
Since Terry wants exactly 40% or 0.4 of 40 gallons i.e. 0.4×40 gallons
The amount of acid in these solutions will be:
0.25x + 0.8(40-x) = 0.4×40 Solve for x
0.25x + 32-0.8x = 16
0.8x-0.25x = 32-16
0.55x = 16
x = 16/0.55 = 29 gallons
40-x = 40 -29 = 11 gallons
Therefore, the amount of the 25% acid solution required is 29 gallons
and the amount of the 80% acid solution required is 11 gallons. So she should mix 29 gallons and 11 gallons respectively
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See question in screenshot below:
The point only can be on the unit circle and on the second quadrant if:
x = -√55/8
How to get the value of the x-coordinate?
We know that we have a point of the form:
P = (x, y)
And the value of y is:
y = 3/8
Then our point is:
P = (x, 3/8)
And it is on the unit circle, then the values of x and y are solutions of:
x^2 + y^2 = 1
x^2 + (3/8)^2 = 1
x^2 = 1 - (3/8)^2 = 1 - 9/64 =
x^2 = 64/64 - 9/64
x^2 = 55/64
x = ±√(55/64) = ±√55/8
And P is on the second quadrant, then we take the negative option:
x = -√55/8
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1.) REVIEW: Evaluate: 3 +5² - 50 ÷ 10
Answer:
23
Step-by-step explanation:
5^2=25
50/10 = 5
3+25-5
5. Minnie had 9 coins in her
purse. If they were nickels
and dimes and totaled
$0.65, how many of each
coin did she have?
Answer:
5 nickels and 4 dimes
Step-by-step explanation:
5 nickels = 25 (5 x 5)
4 dimes = 40 (4 x 10)
A ABC has a right angle at C, BC = 9.2 centimeters, and mA = 63°.
What is CA?
In the right-angled triangle ABC, CA is 4.2cm.
What is a right-angled triangle? How to identify it?
Any angle that is a right angle or has one of its interior angles equal to 90 degrees is considered to be in a right-angled triangle. This triangle is also known as the right triangle or the 90-degree triangle for this reason. Trigonometry heavily utilizes the right triangle. In this article, let's learn more about this triangle.
By applying Pythagoras' theorem, one can determine whether a triangle has a right angle. If the squares of the triangle's two shorter sides equal the square of the hypotenuse, a right angle is present.
Solution explained:
A/Q, we have
BC = 9.2cm and m∠A = 63°
Using the tangent ratio formula (ratio of a side that is not the hypotenuse to a side that is near to an angle), we get
[tex]tanA = \frac{BC}{CA}[/tex]
tan 63° = [tex]\frac{9.2}{CA}[/tex]
CA = [tex]\frac{9.2}{1.96}[/tex] (tan 63° = 1.96)
CA = 4.687 ≅ 4.7cm
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Which of the following mixed numbers is equal to the improper fraction 29/4
A: 7 1/4
B: 7 1/2
C: 7 3/4
D: 7
Answer: A
Step-by-step explanation:
Wayne rents a car from a company that charges $35 per day plus $0.10 per mile he drives. What is a linear equation for the monthly charge, C, dollars, in terms of the number of miles driven, n?
The linear equation for the monthly charge C dollars , in terms of the number of miles driven(n) is C(n) = 35 + 0.10×n .
In the question ,
it is given that ,
the fixed rent for a car is = $35 .
the per mile charge for the car is = $0.10 miles
let the number of miles driven is = n miles
the function C that represents the linear equation for the monthly charge C dollars , in terms of the number of miles driven(n) is given by
C(n) = fixed charge + (per mile charge)×(number of miles)
Substituting the values , we get
C(n) = 35 + 0.10×n
Therefore , The linear equation for the monthly charge C dollars , in terms of the number of miles driven(n) is C(n) = 35 + 0.10×n .
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Answer:
id say, C=0.10=35
Step-by-step explanation:
not really sure, but I tried!
The length of a rectangle is six times its width. If the perimeter of the rectangle is 112 ft, find its length and width.
A rectangular wall is √240 ft by
√50 ft. You need to paint the wall twice to
cover the area with two coats of paint. If
each can of paint can cover 60 square feet,
how many cans of paint will you need?
Answer:
Step-by-step explanation: √240 = 15.49…. √50 = 7.07…
15.5 x 7.07 = 109.58 rounded to 110. Therefore the area is 110 feet so at least 2 can is needed to fill up the wall. But if the problem is being precise it’s 1 can and 5/6 of a can.
2 cans of paint will be needed to cover 110 square feet area.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given,
A rectangular wall is √240 ft by √50 ft.
Need to paint the wall twice to cover the area with two coats of paint.
Area of wall=Length×Width
=√240×√50
=√12000
=109.5=110
Given that each can of paint can cover 60 square feet,
110/60=1.83
=2
Hence, 2 cans of paint will be needed to cover 110 square feet area.
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Question 6(Multiple Choice Worth 2 points)
(Pythagorean Theorem LC)
Can a triangle be formed with side lengths 13, 7, and 5? Explain.
O Yes, because 13 +7 > 5
O Yes, because 13+5<7
O No, because 5+7 < 13
O No, because 5+7 > 13
Answer:
the first one
Step-by-step explanation:
one because 13+7= 20 and 20 is a bigger than 5 so there for it i one
Determine whether the equation 2+y=x+4 represents a linear or nonlinear function.
Answer:
linear
Step-by-step explanation:
Because if you graph it. It creates a line which makes it a linear
Given that -5 is a zero of the polynomial P(x) = x³ + 3x²-12x-10, find the other zeros.
Answer:
Below
Step-by-step explanation:
If -5 is one of the roots then that means (x+5) is one of the factors
divide (x+5) into x^3 + 3x^2 -12x -10
to get x^2-2x-2 which you can easily (using Quadratic Formula) find the roots 1 + sqrt 3 and 1 -sqrt 3
('roots' and 'zeroes' are the same thing)
The side of a square field is 125 m. There are two paths running inside it along the sides, crossing each other at the centre. The width of the lengthwise path is 3 m and the width of the breadthwise path is 5 m. Find the area of the two pathways.
The area of lengthwise pathway is 610 m²
The area of breadthwise pathway is 360 m²
The total area of the two pathways is 985 m²
Given,
The side of square field = 125 m
The width of the lengthwise path = 3 m
The width of the breadthwise path = 5 m
We have to find the area of the two pathways.
Here,
Area of path on length wise = (125 - 3) × 5 = 610 m².
Area of path on breadth wise = (125 - 5 ) × 3 = 360 m²
Area of rectangle at intersection of paths = 5 × 3 = 15 m².
Thus the Total area of two pathways = 610 + 360+15 = 985 m²
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Ratchet Manufacturing anticipates total sales for August, September, and October of $110,000, $120,000, and $130,500 respectively. Cash sales are normally 20% of total sales and the remaining sales are on credit. All credit sales are collected in the first month after the sale. Compute the amount of accounts receivable to be reported on the company's budgeted balance sheet at the end of August.
The amount of accounts receivable to be reported on the company's budgeted balance sheet at the end of August is $22000.
What is the percentage?The percentage is a ratio that can be expressed as a fraction of 100.
Given that, the sales of the company for August, September, and October are $110000, $120000, and $130500.
The company collects 20% of total sales in cash, therefore, the cash received by the company for the august month is,
110000×20%
= 110000×20/100
= 22000
Hence, the amount of accounts receivable to be reported on the company's budgeted balance sheet at the end of August is $22000.
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If y=-2x^3+4x+9, what is y when x=3?
Answer:
39
Step-by-step explanation:
2*3^3+4*3+9
= 39
Mark me as brainliest
5+4+7+5+3-4=?
helpppppppp
Answer: 20
Step-by-step explanation:
What are m and b in the linear equation y = 18x + 25?
Answer: m=18 and b=25
Step-by-step explanation:
y = mx + b ==> standard slope intercept equation
y = 18x + 25
Notice any similarities?
y = 18x + 25
m=18 and b=25
Let the vector v have an initial point at (4, 8) and a terminal point at
(-2, 3). Plot the vector v and afterwards follow the guided steps to analyze
the vector.
The vector having a magnitude √61 and direction 140.2° has been shown in the figure.
Given,
Let the vector v have an initial point at (4, 8) and a terminal point at
(-2, 3).
we are asked to Plot the vector v .
Given that the initial point of the vector is (4,8) and the termination point of the vector is (-2,3).
So, the tail of the vector is at point (4,8) and the head of the vector is at (-2,3).
The vector , v, has been shown.
I v I = √(4-(-2))²+(8-3)²
= √(4+2)²+(8-3)²
= √(6)²+(5)²
= √36+25
= √61
The direction of a vector is the angle made by a vector with the positive direction of the x-axis.
θ = 180° tan⁻¹ I 3-8/-2-4I
θ = 180° tan⁻¹ (5/6)
θ = 180° - tan⁻¹(5/6)
θ = 180° - 39.80°
θ = 140.2°
Hence, the required vector having a magnitude √61 and direction 140.2° has been shown in the figure.
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4. Look at the following inequality.
x(5+2) > 22
Which value will make this inequality true?
A. 1
B.2
C.3
D.4
Answer:
D.4
Step-by-step explanation:
You can try replacing x value with the answer one by one.
A. 1(7) > 22 = 7 > 22, false, 7 smaller than 22
B. 2(7) > 22 = 14 > 22, false, 14 smaller than 22
C. 3(7) > 22 = 21 > 22, false, 21 smaller than 22
D. 4(7) > 22 = 28 > 22, true, 28 is larger than 22
write an equation in slop intercept form to represent the relationship in a table
The equation of the table is y=2x+8 when the slope and intercept are 2 and 8.
Given that,
In the picture we can see the table.
We have to find the equation of the table.
We know the equation is in the form
y=mx+b
Here,
m is rise/run
Which is slope
b is intercept.
Take the point as (0,8) and (1,10)
Slope is m =(10-8)/(1-0)
m= 2/1
m=2
Then b is
8=2(0)+b
b=8
The equation will be y=2x+8
Therefore, The equation of the table is y=2x+8 when the slope and intercept are 2 and 8.
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A box of 12 tacos cost $10.20. At this rate, how much does one taco cost?
Step-by-step explanation:
One taco =$10.20/12=$0.85
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