The number of roots of the given equation x³ -3x² + 4 = 0 is equal to 3 which are -1, 2, 2.
As given in the question,
Given equation is written as:
x³ -3x² + 4 = 0
Number of roots of the given equation are as follow ;
Let f(x) = x³ -3x² + 4
For x = 1
f(1) = 1³ - 3(1)² + 4
= 2 ≠ 0
x = 1 is not the roots.
Now, x = -1 ,
f(-1) = (-1)³ - 3(-1)² + 4
= -1 -3 + 4
= 0
x = -1 is the roots of the given equation x³ -3x² + 4 = 0
x³ -3x² + 4 = 0
⇒x³ + x² -4x² -4x + 4x + 4 =0
⇒x² ( x + 1) - 4x( x + 1) + 4(x+1) =0
⇒(x+1) ( x² -4x +4 ) = 0
⇒(x+1)( x - 2 )² = 0
⇒ x = -1, 2, 2
Therefore, the number of roots of the given equation x³ -3x² + 4 = 0 are 3 and given by x = -1 , 2, 2.
The above question is incomplete , the complete question is :
How many roots does the equation x³ -3x² + 4 = 0 have ?
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PLEASE HELP WILL GIVE BRAINLIST Identify the transversal connecting each pair of angles.
Then classify the relationship between each pair of angles as alternate
interior, alternate exterior, corresponding, or consecutive interior angles.
Answer:
27and 28
for your question ⁉️
Lori is running in a marathon, which is 35.6 miles long. So far, she has run one-tenth (1/10) of the marathon. How far did Lori run?
31. Find the solution(s) to (x + 3)2 = 49
Answer: x=43/2
Step-by-step explanation: Hope this help
Please help I can’t figure it out NO LINKS
LINKS= REPORT
Mrs. Buchanan gave her two daughters $5 to share equally at the carnival. How much money will each daughter have to spend?
Answer: $2 and 5 cents each
Step-by-step explanation:
Each daughter will equally split up the 5 dollars, so 5 divided by 2, you will get 2.5
Which expression is equivalent to
The product of a number and 32.
Answer:
32y
Step-by-step explanation:
Let the number be y.
The product of a number and 32,
y x 32
= 32y
The number is 32y.
Find the slope of the line through each pair of points.
I give brainliest,thankyou's,and star ratings cuz im like that
Algebra - Answers only - 2021 year - Fast and correct - Free Friends no charge
Answer:
1) ---> -1/26
2) ---> -4/1
3) ---> 11/2
4) ---> -8/11
Answer:
rsdjsdn
Step-by-step explanation:
Angle Measures and segment lengths. Find x.
I hope this helps you
8^2=4.(4+x)
64=4.(4+x)
16=4+x
x=12
The Tober family built a square deck with an area of 75 m'. The length of one
side is between which two whole numbers
Answer:
Between 8 and 9
Step-by-step explanation:
The square root of 75 is about 8.6
Therefore the answer is between the number 8 and 9.
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Answer:
12cm
Step-by-step explanation:
pythagoras theorem
Find the unknown length
a
of right triangle.
Formula :
a
=
√
c
2
−
b
2
Solution :
a
=
√
13
2
−
5
2
=
√
169
−
25
=
√
144
a
=
12
CAN SOMEONE HELP PELASE!!!
Answer:
C
Step-by-step explanation:
RATATATATATATATATATATATATTATATATATATAAT
A cone has a diameter of 4 cm and a height of 11 cm. What is the volume 1 point
of the cone to the nearest tenth? Use 3.14 for pi
PLEASE HELP ME I NEED IT FAST WILL GIVE B IF CORRECT!!!!!
Answer: 46.05
Step-by-step explanation:
1/3 * 3.14 * 4 * 11 = 46.05 (rounded to the tenth)
Area & Surface Area:Question 3
Mr. Beck is making a box pattern using 4 rectangular pieces of wood that are the
same size and 2 square pieces of wood of equal size as shown.
10 cm
10 cm
10 cm
25 cm
What is the surface area of the box that will be formed?
Help please!!!!
Answer:
1200
Step-by-step explanation:
You find the are of one of the rectangles which is 25×10=250
There are 4 of the same size so we are at 1000
Then we do the squares on the side 10×10=100
There are 2 of the squares so we add 200
The answer is 1200
Jameson and Quincy each deposit $7,000 into accounts that earn 6% interest, but Jameson earns annual simple interest while Quincy earns annual compound interest. Assuming neither one of them makes any deposits or withdrawals for 5 years, which of the following is a true statement?
Jameson will have about $9,367.58 less in his account than Quincy.
Jameson will have about $267.58 less in his account than Quincy.
Jameson will have about $2,367.58 more in his account than Quincy.
Jameson will have about $2,100 more in his account than Quincy.
Answer:
$267.58
Step-by-step explanation:
Jameson: simple interest
6% =.06 .06 x 5 = .3 .3 x 7000 = 2,100 = interest
6% =.06 .06 x 5 = .3 .3 x 7000 = 2100 2100 + 7000 = 9,100 = total
Quincy: compound interest
6% =.06 .06 x 5 x 1 = .3 x 7000 = 2100
6% =.06 .06 x 5 x 1 = .3 x 7000 = 2100 + 7000 = 9100
.06 x 5 x 1 x 9100 = 2730 + 9100=11830
repeat five times u would get a interest of 2,367.58
and a total of 9,367.58
the total amounts 9,367.58 - 9,100 = 267.58
the interests 2,367.58 - 2,100. = 267.58
Peter sold an article for $3600 gaining one sixth of its selling price. Find the cost price and the gain percent.
Answer:
See the answers below
Step-by-step explanation:
Given data
Cost of artilce= $3600
Gain= 1/6 of 3600
Hence the Gain is
=1/6*3600
=0.166*3600
=$600
The Gain Percent is
=600/3600*100
=0.1666*100
=16.66%
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Find the slope of the yellow cab. Use the point (4,7), and coordinate for the y-intercept, to find the slope.
An experiment in a wind tunnel generates cyclic waves. When the experiment starts (at time the wind is moving 13 feet per second (the slowest speed recorded). The speed maxes out at 71 feet per second and returns to 13 feet per second after 44 seconds. Let V represent the wind speed (velocity) in feet per second and let t represent the time in seconds. Write a sine equation that describes the wave.
Answer:
The sine equation for the wave is;
y = 29·sin[(π/22)·(x - 11)] + 42
Step-by-step explanation:
The given wind parameters in the wind tunnel are;
The slowest speed of the wind in the wind tunnel, v₁ = 13 feet per second
The maximum speed of the wind, v₂ = 71 feet per second
The time it takes the wind to complete one cycle = 44 seconds
Therefore, we have;
The general form of the sine equation is given as follows;
[tex]y = A \cdot sin \left [B(x - C)\right ] + D[/tex]
The period, T = 44 seconds = 2·π/B
∴ B = 2·π/44 = π/22
Given that the wave starts at the slowest speed, the horizontal shift
The amplitude, A = (v₂ - v₁)/2
∴ A = (71 ft./s - 13 ft./s)/2 = 29 ft./s
The vertical shift, D = v₁ + a = 13 ft./s + 29 ft./s = 42 ft./s
D = 42 ft./s
When x = 0, sin(B·C) = -1
∴ -B × C = -π/2
∴ C = π/2 ÷ B = π/2 ÷ (π/22) = π/2 × 22/π = 11
Therefore, the sine equation for the wave is;
the sine equation for the wave is;
y = 29·sin[(π/22)·(x - 11)] + 42
Complete the pattern. 1/9, 1/3, 1, ?
Answer:
The answer is 3
Komisyon (9-6) 12) Bir araba satıcısı, bir haftalık araba satışlarının% 2,5'ini ve saatine 30 dolar veriyor, haftalık satışları 100.000 S $ idi ve 40 saat çalıştı. Hafta boyunca toplamda ne kadar kazandı?
Cevap:
3700 ABD doları
Adım adım açıklama:
Haftalık satış = 100.000 $
Haftalık satışlarda kazanılan yüzde =% 2,5 = (0,025 * 100.000 ABD Doları) = 2500 ABD Doları
Saatlik kazanç = 30 $
Çalışılan saat sayısı = 40 saat
Çalışılan saat için kazanç = 40 * 30 $ = 1200 $
Toplam kazanç:
Haftalık satış yüzdesi + çalışılan saat için kazanç
(1200 ABD doları + 2500 ABD doları) = 3700 ABD doları
What is the approximate volume of the cone? Use 22/7 for π. Enter your answer in the box.
volume of a cone is 132 cubic centimeter.
What is volume of cone?The volume of a cone is defined as the amount of space or capacity a cone occupies. The volume of a cone formula is given as one-third the product of the area of the circular base and the height of the cone.
Volume of cone V = [tex]\frac{1}{3} \pi r^{2} h[/tex]
Given
Radius of cone r = 3 cm
Height of cone h = 14 cm
[tex]\pi[/tex] = [tex]\frac{22}{7}[/tex]
Volume of cone V = [tex]\frac{1}{3} \pi r^{2} h[/tex]
V = [tex]\frac{1}{3}[/tex] × [tex]\frac{22}{7}[/tex] × [tex]3^{2}[/tex] × [tex]14[/tex]
V = 22 × 3 × 2
V = 132 cubic centimeter
Hence, volume of a cone is 132 cubic centimeter.
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Josh gets paid at a rate of $10.73 per hour. He also gets paid time and a half for overtime (over 40 hours). If he worked 47 hours this week, what is his pay before taxes?
Answer:
$541.90
Step-by-step explanation:
We'll start with his regular pay, 40 hours times $10.73
10.73 x 40 = 429.20
His overtime pay is 10.73 + 1/2(10.73) = 10.73 + 5.365 = 16.095, rounded to 16.10
He worked 7 hours at the rate of $16.10/hour
16.10 x 7 = 112.70
Add the two totals together for his total pay before taxes:
429.20 + 112.70 = 541.90
Please lmk if you have questions.
Misaki’s fish tank is half full of water because she is cleaning it. The tank is a right rectangular prism with a length of 8 inches, a width of 6 inches, and a height of 6 inches.
A prism has a length of 8 inches, width of 6 inches, and height of 6 inches.
What is the volume of water in the tank while Misaki is cleaning it?
10 Inches cubed
36 Inches cubed
144 Inches cubed
288 Inches cubed
Answer:
The correct answer would be 144(c)
Step-by-step explanation:
You are very much welcome
Miss Garry played the Game of Life during Spring Break and kept track of the results from all the times she spun the wheel. During the game, she spun the wheel 80 times and the spinner landed on the number three 25 times. What is the experimental probability of spinning a three?
Answer:
it would be a 10% chance because think about it you have ten numbers so with each number there is a 10% chance of landing on it.
What is the image of point (2,4) under
the
translation T-6,1?
there are 15 questions in this quiz. Im sorry if im putting too much pressure on yall
Answer:
86
Step-by-step explanation:
i dont really kbow why but i think it 86
Answer:
It is 89
Step-by-step explanation: it is really 88.57 but it ask whats it closest to and that would be 89
Write the word sentence as an inequality.
A number a is more than 6.
Please explain in simple language how to complete the square.
Answer:
Step 1 Divide all terms by a (the coefficient of x2).
Step 2 Move the number term (c/a) to the right side of the equation.
Step 3 Complete the square on the left side of the equation and balance this by adding the same value to the right side of the equation.
Step-by-step explanation:
hope i helped
Find the volume of a cone that has a radius of 4 centimeters and a height of 19
centimeters.
(Use 3.14 for pi and round the answer to the nearest hundredth.)
Answer:
Volume of the cone = 318.19 cubic cm
Step-by-step explanation:
Volume of a cone = 1/3πr²h
r is the radius = 4cm
h is the height = 19cm
Substitute into the formula
Volume of a cone = 1/3π(4)²(19)
Volume of a cone = 1/3* 3.14 * 16 * 19
Volume of a cone = 954.56/3
Volume of a cone = 318.19 cubic cm
Find the measure of angle YUV
Answer: 77 degrees
Step-by-step explanation:
When looking at an arc, you use the inscribed angle theorem, which states that the measure of an inscribed angle is half of the measure of its interpreted arc. So since the measure of the arc is 154 degrees, you divide that by 2 and that will give you the measure of the angle, which is 77 degrees.