Answers
The second choice is the correct one
Explanation:
(2x+3)^2 + 8(2x+3) + 11 = 0
To use the u substitution, we will assume that:
2x + 3 = u
Substitute with this in the given expression, we will get:
u^2 + 8u + 11 = 0
The general form of the second degree equation is:
ax^2 + bx + c = 0
Comparing the expression we reached with the general one, we will find that:
a = 1
b = 8
c = 11
The roots can be found using the rule found in the attached picture.
This means that, for the given expression:
u = -4 ± √5
Now, we have:
u = 2x+3
This means that:
at u = -4 + √5
2x + 3 = -4 + √5
2x = -7 + √5
x = (-7 + √5) / 2
at u = -4 - √5
2x + 3 = -4 - √5
2x = -7 - √5
x = (-7 - √5) / 2
This means that, for the given expression:
x = (-7 ± √5 ) / 2
Hope this helps :)
Using substitution we have:
u = 2x + 3
We rewrite:
(u) ^ 2 + 8 (u) + 11 = 0
We use resolvent:
u = (- b +/- root (b ^ 2 - 4ac)) / (2a)
We replace:
u = (- (8) +/- root ((8) ^ 2 - 4 (1) (11))) / (2 (1))
u = (- (8) +/- root (64 - 44)) / (2)
u = (- (8) +/- root (20)) / (2)
u = (- (4) +/- root (5))
We return the change:
u = (- (4) +/- root (5)) = 2x + 3
We clear x:
x = (- (7) +/- root (5)) / 2
Answer:
x = (- (7) +/- root (5)) / 2
(option2)
Related Questions
The sales of homes in a new development have been increasing. In January, 8 homes were sold, in February, 12 homes were sold. In March, 16 homes were sold. This pattern continued for the remainder of the year.
What is the explicit rule that can be used to find the number of homes sold in the nth month of the year?
an=4n−4
an=−4n−4
an=4n+4
an=−4n+4
Answers
a1 = 8
For the second month we have:
a2 = 12
For the third month we have:
a3 = 16
Let's assume that n is the number of months.
The rule that meets the number of homes sold is:
an = 4n + 4
We observe for example that for the third month: (n = 3)
a3 = 4 (3) +4
a3 = 12 + 4
a3 = 16 (result that we already knew according to the statement).
Answer:
an = 4n + 4
Answer:
Answer:
an = 4n + 4
Step-by-step explanation:
Jennifer had $30 to spend on herself. She spent 1\5 of the money on a sandwich, 1\6 for a ticket to a musuem, and 1\2 of it on a book. How much money does she have left over?
Answers
Ticket- 5
Book- 15
6+5+15 = 26
30-26 = 4
Answer = $4
What is the sum of the series?
2+4+8+16+...+512
542
766
1022
1084
Answers
Answer:
The correct answer is 1,022. Hope this helps.
Source: Just took quiz and got 100%
Help me please!!!!!!!!!!!!
Answers
The 2nd selection is appropriate.
You sell bracelets for $2 each and necklaces for $3 each at a local flea market. You collect. $95, selling a total of 37 jewelry items. How many of each type of jewelry did you sell?
Answers
For an instance, b stands for the number of bracelets, n stands for the number of necklaces.
⇒ Total collected money is $95, $2 per bracelet, $3 per necklace
2b + 3n = 95 (first equation)
⇒ 37 jewelry items have been sold
b + n = 37
Find the number of necklaces (n) by eliminating the number of bracelets (b) from the equation system
2b + 3n = 95
b + n = 37 (multiply by 2)
----------------------------------------
2b + 3n = 95
2b + 2n = 74
---------------- - (substract)
n = 21
Find the number of bracelets by substituting the value of n to either of the equations
b + n = 37
b + 21 = 37
b = 37 - 21
b = 16
Type of jewelry have been sold: 16 bracelets, 21 necklaces
The Mid-Atlantic Ridge is a spreading crack between crack between continental plates and it moves apart at 2.5 cm per year. New York is 5567 km from London. In 1,000,000 years, how many far apart will New York be from London.
Answers
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 4 to 3 . If there were 2817 no votes, what was the total number of votes?
Answers
so if there is 2817 votes in the no
==> (2817*4)/3 = 3756 votes for yes
3756/2817 will be 4/3
I need the answer to the blank questions
Answers
n 12 part a)
actual distance-------------> 124 miles
map distance----------------> 4 cms
scale factor of the map =124 miles/4 cms=31 miles/cm
n 12 part b)
map distance=21 cms
actual distance?
[actual distance]=[map distance]*factor scale-----------> 21*(31)=651 miles
n 13)
we know that
(13.5/9)=(x/8)--------------> x=(13.5/9)*8-----------> x=12 units
n14)
we have that
x/26=(32-x)/18-----------> 18x=832-26x--------> x=18.91 units
Fractions must have a common denominator in order to subtract them. TrueFalse
Answers
The numerator of a fraction is the number that is written in the upper part of it and the denominator is the number that is written in the lower part.
To substract fractions, they must have a common denominator. There is two cases:
1. When the fractions have the same denominator, you just have to rewrite the denominator and substract the numerators. For example:
8/3-1/3=(8-1)/3=7/3
2. When the fractions have different denominators, you must calculate the Least commom multiple (LCM):
5/2-3/4
L.C.M.=2²=4
(10-3)/4=7/4
Answer:
true
A numerator of a fraction is the number that is written in the upper part of it and the denominator is the number that is written in the lower part.
Robin's scores: 99, 108, 102, 107, 119 mean = 107; mad = 5.2 evelyn's scores: 125, 137, 138, 145, 145 mean = 138; mad = 5.6 explain what the mean absolute deviation is in general. explain what the mad means in the context of robin and evelyn's data.
Answers
Answer:
The MAD describes the average distance from a data point to the mean. It measures variability. For this data, it shows that Evelyn’s scores varied slightly more than Robin’s.
Step-by-step explanation:
Answer:
Sample response: The MAD describes the average distance from a data point to the mean. It measures variability. For this data, it shows that Evelyn’s scores varied slightly more than Robin’s.
Or
The MAD measures the average distance between a data point and the mean. It measures variation. According to this information, Evelyn's scores varied a little more than Robin's.
Step-by-step explanation:
Took the test on edge! Hope this helps! have a great day!
3.6m by 1.8 m wall How many 6 cm by 6 cm pictures could fit on the wall?
Answers
(1.8*100)/6=30
60*30=1800
there are 1800 pictures could fit on the wall.
Answer:
1800 pictures could fit on the wall.
Step-by-step explanation:
If the area of a space is given as A and this space is to be filled by pictures of area A' then number of pictures will be = [tex]\frac{A}{A'}[/tex]
Now we know area of wall is A and area of picture is A'.
Length and width of wall = 3.6×1.8 m
So area of the wall A = 3.6×1.8 = 6.48 m²
Dimensions of one picture = 6×6 cm Or 0.06×0.06 m
So are of one picture A' = 0.0036 m²
Therefore, Number of pictures on the wall = [tex]\frac{A}{A'}[/tex] = [tex]\frac{6.48}{0.0036}=1800[/tex]
Number of pictures required to cover the wall = 1800
1.
Kara, a 25-year-old female, bought a $50,000, 10-year life insurance policy through her employer. Kara is paid semimonthly. How much is deducted from each of her paychecks for life insurance? Use the table.
A. $4.81
B. $5.21
C. $6.25
D. $6.77
2.
Dawson, a 42-year-old male, bought a $180,000, 20-year life insurance policy. What is Dawson's annual premium? Use the table.
A.$819.00
B.$1040.40
C.$1859.40
D.$2462.40
Answers
Answer:
The answer for number one is $5.21. NOT $6.25
Step-by-step explanation:
The amount deducted from the paychecks are: 6.25 dollars
The annual premium of Dawson is D.$2462.40
How to solve for the annual premiumTo get Karas annual premium
$1000 of coverage.
$50,000 at 2.50 dollars cost
since she is paid semi monthly
2.50 / 2 = 1.25
annual premium = 1.25 / 100 * 50
= 6.25 dollars
2. Under 20 year coverage for a 40 - 44 year old mail we have $13.68 as the amount
180000 / 1000
= 180
180 x 13.68
= D.$2462.40
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Vicente wants to plant 3 different types of onions in 1/4 of his garden. He will use an equal amount of space to pkant each ytpe of onion. what fraction of the total garden space will contain each type of onion
Answers
= 1/4 ÷ 3
when dividing fractions, multiply by reciprocal/inverse
= 1/4 ÷ 3/1
= 1/4 * 1/3
= (1*1)/(4*3)
= 1/12
He has 1/12 of his garden for each type of onion.
Hope this helps! :)
Find the probability that the student is male or a nursing major.
Answers
The table below shows the number of male and female students enrolled in nursing at a particular university for a recent semester. (a) y Find the probability that a randomly selected student is male or a nursing major.
see the attached table
a) the probability that a randomly selected student is male, or a nursing major
total students=[1151+2409]=3560
total male=[98+1053]=1151
P (selected student is male)=1151/3560=0.3233
total nursing mayor=[98+741]=839
P (selected student is nursing major)=839/3560=0.2357
P(selected student is male, or a nursing major)=0.3233+0.2357=0.5590
the answer is 0.5590 (55.90%)
The probability that a student is male or a nursing major is expressed by the formula P(M OR N) = P(M) + P(N) - P(M AND N), which requires actual data to calculate.
Explanation:To find the probability that a student is male or a nursing major, we can use the principle of addition in probabilities. Let's denote P(M) as the probability that a student is male, P(N) as the probability that a student is a nursing major, and P(M AND N) as the probability that a student is both male and a nursing major. The formula for the probability of either event occurring is given by P(M OR N) = P(M) + P(N) - P(M AND N). We need actual data to calculate these probabilities.
Since we don't have the actual probabilities, we can only provide the symbolic representation of the required probability as P(M OR N). However, if the events of being male and majoring in nursing are mutually exclusive (which in reality, they are not), the probability would simplify to just the sum of the two individual probabilities, P(M) + P(N).
Five times what number plus 10 equals 20?
A) -6
B) 2
C) 4
D) 6
Answers
Answer:
2
Step-by-step explanation:
Five times 2 plus 10 will be equal to 20. Hence, option B is correct.
What is an arithmetic operation?Addition, subtraction, multiplication, and division of two or even more integers are the four basic mathematical operations. Included among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per the data provided in the question,
The equation according to the statement will be,
Let the number be x.
5x + 10 = 20
5x = 20 - 10
x = 10/5
x = 2
Therefore, the number is 2.
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A scientist wants to find the radius, in feet, of this hemispherical dome. He found that the surface area of the entire sphere containing the dome is 294 square feet. Which equation could he use to find the dome's radius?
A. r2=294 square feet ÷ 4π
B. r2=294 square feet ÷ 2π
C. r2=294 square feet ÷ π
D.r2=588 square feet ÷ 4π
Answers
A = 4 * π * r ^ 2
Where,
r: radius of the sphere.
Substituting the values we have:
294 = 4 * π * r ^ 2
We cleared the radio:
r ^ 2 = (294) / (4 * π)
Answer:
An equation that I could use to find the dome's radius is:
A. r2 = 294 square feet ÷ 4π
Answer:
A. r2 = 294 square feet ÷ 4π
The sides of a square are 5^2/5. What is the area of the square?
A. 5^4/5 square inches
B. 5^4/25 square inches
C. 25^4/5 square inches
D. 25^4/25 square inches
Answers
A=(s)(s)
A=s²
"A" is the area of the square.
"s" is the lenght of the side of the square.
2. So, the lenght of the side given in the problem is 5^2/5 inches (s=5^2/5 inches). Therefore, you only have to substitute this value into the formula A=s².
3. Then, you obtain:
A=s²
A=(5^2/5 inches)²
A=5^4/5 inches²
What is the area of the square?
The answer is: A. 5^4/5 square inches.
a/b ∙ b/2a
or a≠0, b≠0
So a/b is a fraction. Then multiply by b/2a.
The a's and the b's aren't equal to zero
Answers
a/b*b/2a= ab/2ab or 1/a
1/a*b/2a=b/3a
Which ordered pair is the best estimate for the solution of the system of equations?
y=−12x+4
y=12x−3
(7.5, 0.5)
(7, 0.5)
(7, 1)
(7, 0)
Answers
The 2nd selection is appropriate.
Answer:
hope this helps :)
If the area of the trapezoid is 2.52 cm 2, what is the height? A 0.45 cm B 0.9 cm
C 2.1 cm D 2.2 cm
Answers
Answer:
0.9cm
Step-by-step explanation:
That was the answer on my assignment.
"there are 362 first-grade students in park elementary school. if there are 34 more girls than boys, how many girls are there"
Answers
you subtract 34 from 362 which is 328
you then divide 328 by 2 which is 164
next you add 34 to 164 which gives you 198 which is the number of girls
A certain human red blood cell has a diameter of 0.000007 meters. Write an expression that represents this diameter, in meters in scientific notation.
Answers
Given is the diameter of a human red blood cell equal to 0.000007 meters. It says to convert and rewrite this measurement in meters in scientific notation.
A scientific notation is written as product of a significant number and exponent of 10's. To find significant number from given 0.000007, we must move decimal point in either right or left direction such that it becomes integral value and in addition we would multiply some exponent of 10's to make its value equivalent to given 0.000007 meters.
Re-writing in scientific notation :-
0.000007 meters
= [tex] \frac{7}{1000000} \;meters [/tex]
= [tex] \frac{7}{10^{6}} \;meters [/tex]
[tex] =7*10^{-6} \;meters [/tex]
So, final answer is 7 x 10⁻⁶ meters.
which best describes a number that cannot be irrational
Answers
Answer:
All numbers that can be made by dividing two integers cannot be irrational.Step-by-step explanation:
Irrational numbers are real number that cannot be expressed as the quotient between two integers, remember that integers are whole numbers, that is, they don't have a fractional part.
So, all numbers that can be made by dividing two integers cannot be irrational.
For example, number 3/2 is not an irrational number, because it can be expressed as the divison of two integers.
In which of the following cases would you most likely buy a point when closing on a home loan?
Answers
Final answer:
Buying a point during a home loan closing is most likely to make sense if interest rates have fallen, you plan to stay in the home long term, and you have ample cash for upfront costs, as this could result in significant savings over the life of the loan.
Explanation:
When considering the question of whether you would most likely buy a point when closing on a home loan, the main factors to consider are the interest rates and the duration for which you plan to hold the loan. Buying a point refers to paying an upfront fee to lower your mortgage interest rate, which is attractive if you plan to stay in the home for a long period, as the savings on interest payments could outweigh the initial cost. You would be more inclined to buy a point if:
Interest rates in the economy have fallen, and you want to lock in a lower rate for the duration of your loan.
The available cash for upfront costs is sufficient to cover the cost of buying points without detrimentally impacting other financial commitments.
The assessment is that staying in the property for a long duration will allow for greater cumulated savings due to the reduced interest payments over time.
These scenarios are more likely to justify the transaction costs of purchasing a home with an upfront payment to buy points, thus securing a lower interest rate for the mortgage.
Find all the zeros of x^3-5x^2-x+5
Answers
The zeros are x = -1, +1, +5.
___
A graphing calculator confirms this.
Bacteria triples every hour. How much bacteria will there be after two days if they started with 13,000 bacteria.
Answers
Now we take the one hours worth 39,000 • 48 (hours in two days) = 1,872,000
Hope this helps!
How many terms are in 8y+7z
Answers
there are 2 terms.
hope it helps
blake is signing a lease for a studio apartment that rents for $425/month. how much will blake pay to move in if he must pay the first and last months rent and a security deposit equal to 50% of his monthly rent?
Answers
Total amount he needs to pay is $1,062.5
Sum of money based problem:Given that;
Rent of apartment = $425 / month
Security deposit = 50% monthly rent
Find:
Total amount he needs to pay
Computation:
Total amount of rent he needs to pay = 425 + 425 + 50%[425]
Total amount he needs to pay = 425 + 425 + 212.5
Total amount he needs to pay = $1,062.5
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Write an equation in point-slope form of the line having the given slope that contains the given point. m=56m=56m (30,12)
Answers
We have a point (30, 12) and a slope of 56.
So we write [tex]y-12=56(x-30)[/tex]. And we're done.
Alice had 4 1/4 pounds of walnuts at the beginning of the week. At the end of the week, she had 2 3/4 pounds. How much has she used
Answers
11/4 (2 3/4 as an improper fraction)
17/4-11/4=6/4=1 1/2
she used 1 1/2 pounds