[tex]~~~~x^4+4x^3 +4x^2 +4x +3=0\\\\\implies x^4 +x^3 +3x^3 + 3x^2 +x^2+x+3x+3=0\\\\\implies x^3(x+1) +3x^2(x+1) + x(x+1) +3(x+1)=0\\\\\implies (x+1) (x^3+3x^2 +x +3)=0\\\\\implies (x+1) \textbf{[} x^2(x+3)+(x+3)\textbf{]}=0\\\\\implies (x+1)(x+3)(x^2+1)=0\\\\\implies x = -1 ,~~ x = -3,~~ x = \pm i[/tex]
Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant value, how many
number solutions does the equation have?
real
Discriminant = b2-4ac
O 0
O 1
O 2
O 12
Number of solution for the given quadratic equation as Discriminant=0 is equals to 1.
What is quadratic equation?" Quadratic equation is defined as the polynomial containing variables with highest exponent equals to 2."
Formula used
For quadratic equation
[tex]ax^{2} +bx+c=0[/tex]
Discriminant = b²-4ac
According to the question,
Given quadratic equation
[tex]-3 = x^{2} +4x+1[/tex]
⇒[tex]x^{2} +4x+1 +3 =0[/tex]
⇒[tex]x^{2} +4x+4 =0[/tex]
Here, a=1 , b= 4 , c =4
Substitute the value in the formula we get,
Discriminant = [tex]4^{2} - 4(1)(4)[/tex]
= [tex]16 -16[/tex]
= 0
Number of solution discriminant =0 is 1.
[tex]x^{2} +4x+4 =0[/tex]
⇒[tex](x+2)^{2} =0[/tex]
⇒[tex]x= -2[/tex] has unique solution.
Hence, number of solution for the given quadratic equation as Discriminant=0 is equals to 1.
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Mr.Smith has p pounds of cookie dough. He is going to split it equally among his three children. Each child will get 0.42 pounds of cookie dough. Write and solve an equation that can be used to determine the weight of the cookie dough Mr. Smith has.
Answer:
p = 1.26
Step-by-step explanation:
We know that the total weight (p) is going to be split equally (divided) by 3.
We also know that divided weight will be equal to 0.42 pounds.
p / 3 = 0.42
To solve:
multiply both sides by 3 to cancel the division by 3
p = 1.26
To test this you could divide 1.26 by 3 again to get 0.42
Tracy has 40 feet of material to make the perimeter of a rectangular sandbox for her little brother.
What rectangle with whole-number side lengths would give the sandbox with the greatest area?
Answer:
11 and 9
Step-by-step explanation:
With a width of 11 and a length of 9 the area of the rectangle would be
11 * 9 = 99
By adding 11 and 9, then mulitplying it by 2 we get the perimeter
11 + 9 = 20
20 * 2 = 40
If the discriminant of a quadratic equation is equal to Negative 8, which statement describes the roots?
Answer:
There are two complex roots
Step-by-step explanation:
Answer:
A. There are two complex roots
Step-by-step explanation:
got it right on edg.2022 <3
Justify the first step that David took in verifying that x = 5 is a solution for the equation
8x – 13 = 2x + 17.
8x – 13 = 2x + 17
8(5) – 13 = 2(5) + 17
A.
David multiplied 8 by 5.
B.
David subtracted 13 from both sides.
C.
David replaced x with 5.
D.
David added 17 to both sides.
Answer:
Step by step I don't see the correct first step.
Step-by-step explanation:
Solve for x:
8 x - 13 = 2 x + 17
Hint: | Move terms with x to the left hand side.
Subtract 2 x from both sides:
(8 x - 2 x) - 13 = (2 x - 2 x) + 17
Hint: | Combine like terms in 8 x - 2 x.
8 x - 2 x = 6 x:
6 x - 13 = (2 x - 2 x) + 17
Hint: | Look for the difference of two identical terms.
2 x - 2 x = 0:
6 x - 13 = 17
Hint: | Isolate terms with x to the left hand side.
Add 13 to both sides:
6 x + (13 - 13) = 13 + 17
Hint: | Look for the difference of two identical terms.
13 - 13 = 0:
6 x = 17 + 13
Hint: | Evaluate 17 + 13.
17 + 13 = 30:
6 x = 30
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 6 x = 30 by 6:
(6 x)/6 = 30/6
Hint: | Any nonzero number divided by itself is one.
6/6 = 1:
x = 30/6
Hint: | Reduce 30/6 to lowest terms. Start by finding the GCD of 30 and 6.
The gcd of 30 and 6 is 6, so 30/6 = (6×5)/(6×1) = 6/6×5 = 5:
Answer: x = 5
In the equation 3s +135= 4.5 (s +10) what is s
Find the area
Please!
(Give explanation)
Answer:
58.8 ft^2
Step-by-step explanation:
The formula for the area of a parallelogram is simply base times height.
the base is 9.8, and the height is 6.
9.8 * 6 = 58.8.
If you found this helpful, I would appreciate if you gave me brainliest :D
The doubling time of a population of flies is 8 hours. By what factor does the population increase in 34 hours? By what factor does the population increase in 1 week ?
Answer:
19.017 in 34 hours2,097,152 in 1 weekStep-by-step explanation:
An exponent is used to signify repeated multiplication. When the population doubles, it is multiplied by 2. The number of times the population has doubled will be an exponent of 2.
a)In 34 hours, the population will have doubled 34/8 = 4.25 times. The multiplier is 2 with an exponent of 4.25:
factor = 2^4.25 ≈ 19.027
__
b)The population will double 24/8 = 3 times each day. After 7 days, the population will have doubled 7×3 = 21 times. The multiplication factor is ...
factor = 2^21 = 2,097,152
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.3 inches, and standard deviation of 1 inches. What is the probability that the height of a randomly chosen child is between 53.3 and 55.3 inches
Answer:
a) We need to find p(x<68.15)
Standardize x to z, we have, z = (68.15-μ)/σ
=(68.15-57)/8.1
=1.38
Reading from standard normal tables,
p(z<1.38) =0.9162.
b) We need to find p(x>54.4)
Standardize x to z, we have, z = (54.4-μ)/σ
=(54.4-57)/8.1
=-0.32
Reading from standard normal tables,
p(z>-0.32) = 0.6255
If limx-b f(x)=2 and limx-b f(x)=10, then limx-b [3f(x)-4g(x)]=-34
true or false?
Answer:
True
Step-by-step explanation:
limx→b [3f(x)-4g(x)]
limx→b [3f(x)-4g(x)]= limx→b [3f(x)] - limx→b [4g(x)]
= 3[limx→b f(x)] - 4[limx→b g(x)]
Since limx→b f(x) = 2 and limx→b g(x) = 10,
= 3(2)-4(10)
= -34
joshua drinks 8 cups of water a day. The recommended daily amout is given in fluid ounces.How many fluid ounces of water does he drink each day?
Question:
Joshua drinks 8 cups of water a day. The recommended daily amout is given in fluid ounces. How many fluid ounces of water does he drink each day?
What were being asked:
How many fluid ounces of water does he drink each day?
Answer:
The answer is
→ 64 fluid ounces
Step-by-step explanation:
1 cup of water = 8 fluids.
8 cups of water x 8 fluids = 64 ounces
Therefore, your answer is 64 fluid ounces.
Hope this helped! :^)
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- ✨7272033Alt✨
Submitted on 4/18/2022 at 4:08 PM
(To avoid plagarism, by users whom decide to copy.)
Drawing a 3 cards that are all 9 from a deck of cards
Answer:
the answer is 3 :))
Step-by-step explanation:
9/3= 3
The recursive formula for an arithmetic sequence is:
{a1 = -6
{an-an-1+2
What is the 3rd term in the sequence?
A. - 2
B. -4
C. -10
D. -18
(WHO WANTS BRAINLIEST! :D)
Sitting in your sailboat looking at the horizon, you see a lighthouse 500 feet away. Looking up at a 20 degrees, you see the light at the top of the lighthouse. How far off the ground is the light in the lighthouse? Round your answer to the nearest tenth.
Answer:
182.0
Step-by-step explanation:
500 tan20
=181.98
=182.0(to nearest tenth)
According to an article, 75% of high school seniors have a driver's license. Suppose we take a random sample of 300 high school seniors and find the proportion who have a driver's license. Find the probability that more than 77% of the sample have a driver's license. Begin by verifying that the conditions for the Central Limit Theorem for Sample Proportions have been met.
Answer:
33%
Step-by-step explanation:
77 + 233= 300 so 33% don't have a license
Which point is located at (-1, 1 1/4)
A
B
C
D
Answer: Point A.
Step-by-step explanation: To find the location of points such as (-1, 1 1/4), you need to know what part of the point is the x-axis and the y-axis. The first part of the point is the x-axis, which is the horizontal line that goes left to right on the coordinate graph. The first part of the point (-1, 1 1/4), is -1. The second part of the point is the y-axis, which is the vertical line that goes up and down on the coordinate graph. The second part of the point (-1, 1 1/4), is 1 1/4. Therefore, we first find the x-axis to the point (-1, 1 1/4), which is -1, and so far, point A is the only option that matches. However, we need to make sure that the point (-1, 1 1/4)'s y-axis matches to point A as well. The y-axis to the point (-1, 1 1/4) is 1 1/4 so we need to go up 1 1/4 times, and the point that matches these actions is point A. Therefore, that's your answer.
Let me know if this is right! :)
a retailer purchased a camera for rs.1560 and sold it at 5% loss find the loss amount
Answer:
Loss is Rs. 78
Step-by-step explanation:
Solution:
Given,
Cost Price (CP)= Rs.1560Loss Percent (L%) = 5%Here,
L%= L/CP ×100%
or,. 5 =L/1560×100
or,. 5×1560/100 =L
or,. L= Rs.78
Therefore, Loss is Rs.78
Find 12 1/2% of #400.00
find 12 1/2 percentage of 400 naira
Answer:
I think its 50 if this is correct can u mark me brainliest?
Find the measure picture below
By the vertical angle theorem, angle K is equal to the angle of measure 28 degrees.
--> so k is 28 degrees
Def. of vertical angle theorem: states that the opposite (vertical) angles of two intersecting lines are congruent
Hope that helps!
What is entrepreneurial finance?
Answer:
The process of making financial decisions for new ventures (i.e. startups). New ventures are inherently different from established ventures, as are entrepreneurs inherently different from conventional business managers.
. Mai skated miles, and Clare skated farther than that. Write an equation to Accelerated 6 Unit 6 Lesson 1 represent the relationship between the distance Mai skated ( ) and the distance Clare skated ( ).
Answer:
X over y or x/y since y is claire and she skated more
Step-by-step explanation:
since y is claire and she skated more
Y=Clarie skated
X= Mai skated
QUESTION 3 I [12] A student must answer a multiple-choice question with five possible answers. He knows the correct answer with probability 0.55. If he does not know the correct answer, he randomly guesses one of the possible answers. a) Draw a tree diagram and clearly define all relevant events.
The probability that the student does not know the answer but he randomly guesses it is 0.146025
How to solve for the probability of having a correct guessThe question has only one right answer out of 5 choices.
Probability he answers incorrectly:
1 - 0.55 * 4/5
= 0.45 * 0.8
= 0.36
Probability he does not know answer but answers the question correctly
[tex]\frac{(1-0.55)\frac{1}{5} }{0.55+(1-0.55)\frac{1}{5} }[/tex]
= 0.09/0.55+0.09
= 0.140625
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help me help me help me
Answer:
For the third one,
3, 8, 15, 24, 35, 48, 63
For the fourth one,
4, 6, 10, 18, 30, 46, 66
Step-by-step explanation:
Identify the GCF of 6x^2y^2 − 8xy^2 + 10xy
Answer:
The GCF for the numerical part is 2
Step-by-step explanation:
6x^2y^2-8xy^2+10xy
It contains both numbers and variables, there are two steps to find the GCF(HCF).
1). Find the GCF for the numerical part 6, -8,10
2). Find the GCF for the variable part x^2,y^2,x^1,y^2,x^1,y^3
3).Multiply the values together.
Find the common factors for the numerical part:
6,-8,10
Factors of 6
6: 1,2,3,6
Factors of -8
-8: -8,-4,-2,-1,1,2,4,8
Factors of 10
10:1,2,5,10
Common factors of 6,-8, 10 are 1,2
The GCF Numerical=2
The GCF Variable= xy^2
Multiply the GCF of the numerical part 2 and the GCF of the variable part xy^2, and you'll get 2xy^2
A club elects a president, vice president and secretary treasurer. How many sets of officers are possible if there are 8 members and any member can be elected to each position? No person can hold more than one office.
Ahhh yes, the time-honored permutations.
The permutation format, to start with, is P(n, r).
The formula is:
[tex]\frac{n!}{(n-r)!}[/tex]In this instance, we have P(8, 3).
8 will go in for n and 3 for r. So now let's solve.
[tex]\frac{8!}{(8 - 3)!}[/tex] → [tex]\frac{8!}{5!}[/tex] → [tex]\frac{8*7*6*5*4*3*2*1}{5*4*3*2*1}[/tex] → [tex]8*7*6[/tex] → [tex]336[/tex]
Therefore 336 is our answer. I hope this answers your question.
-Toremi
The sum of three number is 14. The sum of twice the first number, 4 times the second number, and 5 times the third number is 41. The difference between 7 times the first number and the second number is 51. Find the three
numbers.
Answer:
The numbers are 8 , 5 , 1
Step-by-step explanation:
Let the three numbers be x,y,z
Sum of three numbere is 14
⇒ x +y + z = 14 ---------------(I)
The sum of twice the first number, 4 times the second number, and 5 times the third number is 41.
⇒ 2x + 4y + 5z = 41 -----------(II)
The difference between 7 times the first number and the second number is 51.
⇒ 7x -y = 51 ---------------(III)
Multiply equation (I) by (-5) and then add this wiht equation (II). Thus 'z' will be eliminated.
(I)*(-5) -5x - 5y - 5z = -70
(II 2x + 4y + 5z = 41 {Now add}
-3x - y = - 29 ------------(IV)
Multiply (III by (-1) and then add it with equation (IV)
(III)*(-1) -7x + y = -51
(IV) -3x - y = -29 {Now add}
-10x = -80
x = -80 ÷ (-10)
x = 8
Plugin x = 8 in equation (III) and we obtain the value of y
7*8 - y = 51
56 - y = 51
-y = 51 - 56
-y = -5
y = -5 ÷ (-1)
y = 5
Plugin x =8 and y =5 in equaiton (I)
8 + 5 + z = 14
13 + z = 14
z = 14 - 13
z = 1
[80 POINTS] An engineer is designing a new drill bit as shown in the diagram. To finalize the design, the engineer needs to know the volume of the drill bit.
What is the volume of the drill bit?
Answer:
2,106 pi mm3
Step-by-step explanation:
Volume of the drill bit is equals to [tex]2,106\pi mm^{3}[/tex].
What is volume?" Volume is defined as the total space occupied by a three dimensional object enclosed in it. It is measured in cubic unit."
Formula used
Volume of the cone = [tex]\frac{1}{3} \pi r^{2}h[/tex]
Volume of the cylinder =[tex]\pi r^{2}h[/tex]
r = radius of the cone / cylinder
h = height of the cone / cylinder
According to the question,
Given,
Radius of the cylinder = 9 mm
Radius of the cone = 9 mm
Height of the cone = 24 mm
Height of the cylinder = 18 mm
Substitute the values in the formula to obtained the required volume,
Volume of the cone [tex]= \frac{1}{3} \pi (9^{2})(24)[/tex]
[tex]= \pi (81)(8)\\=648\pi mm^{3}[/tex]
Volume of the cylinder [tex]= \pi (9^{2} )(18)[/tex]
[tex]=1458\pi mm^{3}[/tex]
Required Volume of the drill pit
= Volume of the cone + Volume of the cylinder
[tex]= (648\pi + 1458\pi )mm^{3} \\= 2106\pi mm^{3}[/tex]
Hence, Option(B) is the correct answer.
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Simplify the expression. (–8.6)0
A)–1
B)–8.6
C)1
D)0
Answer: D
Explanation: Anything times 0 is 0.
Mae has 36 orange slices. She will fill each of
7 bags with the same number of orange slices.
How many slices will be in each bag? How many
slices will be left over?
Answer:
5 orange slices will be in each bag with 1 left over
Step-by-step explanation:
36 ÷ 7 = 5 with a remainder of 1
Find the area
A. 300 units
B. 520
C. 500 units
Answer:
b.520 units
Step-by-step explanation:
find the area of the bigger triangle the base is 20 which is 10×2 while the height is 28. 1/2×20×28=280units find the area of the smaller triangle. the base is also 20 while the height is 24. 1/2×20×24=240. sum the areas of the two triangles. 280+240=520units
