Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
Answers
Answer:
A) -2 - i√3 , -2 + i√3
Step-by-step explanation:
Solve using quadratic formula
x² + 4x + 7 = 0
The Almighty Formula
= -b ± √b² - 4ac/2a
Where ax + bx² + c = 0
From the above question
a = 1, b = 4, c= 7
Hence,
-4 ± √4² - 4 × 1 × 7/2 × 1
-4 ± √16 - 28/2
=( -4 ± √-12)/2
Since
b² - 4ac < 0
We have two complex roots
Simplifying
( -4 ± √-12)/2
= -4/2 ± √-12/2
= -2 ± 2√3i/2
= -2 ± √3i
Therefore,
-2 - √3i , -2 + √3i
or
-2 - i√3 , -2 + i√3
Option A , is the correct answer
Related Questions
if the perimeter of the rectangle was known to be 90 in what would the value of x be in order for this to be true
Answers
Answer:
x = 30 in
Step-by-step explanation:
length of rectangle is (2/3)x + 10; width is (1/3)x + 5;
perimeter is 90 in; find x:
P = 90 in = 2(2/3)x + 2(10) + 2(1/3)x + 2(5), or
90 in = (6/3)x + 30 in
Solving for x, we get (2)x = 60 in, or x = 30 in
please help thxssssssssssssssssssssssssssss
Answers
Answer:
The visiting team took more shots than the home team.
Step-by-step explanation:
A certain map shows two roads. Road A is 1 1/5 miles long but is 1 4/5 inches on the map. What is the unit rate for inches per mile on the map. If road B is 2 miles long, how long is road B on the map ?
Answers
The length of the map would be 3 inches.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: length of the road as 6/5 miles and on the map 9/5 inches and thus 1 mile = 1.5 inches and therefore the length of the 2 mile road on the map is 2×1.5=3 inches
Hence, The length of the map would be 3 inches.
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Davis earns a 4% commission for all furniture he sells. If David receives $7509 in commission this year , what is the dollar amount of his sales?
Answers
Answer:
187,725
Step-by-step explanation:
7,509/.04=187,725
While Mike was visiting his sister in Arlington, he bought an aquarium that was marked down 60% from an original price of $100. If the sales tax in Arlington is 5%, what was the total cost of the aquarium?
Answers
Answer:
$42
Step-by-step explanation:
100 - 60% * 100 = $40
Since tax is 5%, therefore:
40 + 5% of 40 = $42
Thenks and mark me brainliest :))
Answer:
The answer is $42 but give the other guy brainliest.
Step-by-step explanation:
Kias mom is having triplets. Each baby could either be male or female. Which outcome would be included in the compound event "more than one female"
Answers
Answer:
The outcomes that have more than 1 female are -
MFF, FMF, FFM, FFF
Step-by-step explanation:
Given - Kias mom is having triplets. Each baby could either be male or female.
To find - Which outcome would be included in the compound event "more than one female"
Solution -
The sample space outcomes are -
{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF}
Now,
The outcomes that have more than 1 female are -
MFF, FMF, FFM, FFF
Find the area of the shaded region.
Answers
Answer:
i think 132. but I could be wrong.
Step-by-step explanation:
3.5 x 4 + 11 x 2.2 = 38.2 i used a calculator already but i need to show i how got the answer i dont know if i can give the brain thing
Answers
Step-by-step explanation: To solve this equation, you'll need to use the order of operations to determine the correct sequence of steps to follow. The order of operations is a set of rules that specifies the order in which calculations should be performed in a math problem. It helps to prevent ambiguity and ensures that all calculations are performed consistently.Here is the order of operations:Perform any calculations inside parentheses or brackets first.Perform all multiplications and divisions, working from left to right.Perform all additions and subtractions, working from left to right.Using this order, we can solve the equation as follows:3.5 x 4 + 11 x 2.2 = 14 + 11 x 2.2
3.5 x 4 + 11 x 2.2 = 14 + 24.2
3.5 x 4 + 11 x 2.2 = 38.2Therefore, the solution to the equation is 38.2.
Using BODMAS,
B-Bracket
O-Of
D-Division
M-Multiplication
A-Addition
S-Subtraction
Multiplication comes first before addition, so
3.5×4=17
+
11×2.2=24.2
17+24.2=41.2
A cylinder has a height of 14 millimeters. Its volume is 17,584 cubic millimeters. What is the radius of the cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
help me
Answers
Answer:
V = πr2h (Volume of a cylinder is the area of a circle times its height). V = 8167.14. π = 3.14. h = 9.
Step-by-step explanation:
Please Help ASAP!!!!
Will mark branliest if correct.
Answers
Q1: 5
Med:15.5
Q3: 18
Max:19
Kendra and Haley are each saving money. Kendra starts with $100 in his savings
account and adds $5 per week. Haley starts with $10 in her savings account and adds
$20 each week. After how many weeks will Haley have at least the same amount of
money as Kendra?
OX26
Ox>6
O x 216
Ox< 16
Answers
That means after 6 weeks will Haley have at least the same amount of
money as Kendra
Kendra and Haley are each saving money. Kendra starts with $100 in his savings account and adds $5 per week. Haley starts with $10 in her savings account and adds $20 each week. After how many weeks will Haley have at least the same amount of money as Kendra?
Kendra and Haley are each saving money.
Kendra starts with $100 in his savings
account and adds $5 per week.
After 6 week 6* 5 = 30
Total amount in After 6 week in Kendra savings
account = $100 + $30
= $130
Haley starts with $10 in her savings account and
adds $20 each week.
After 6 week 6* 20 =120
Total amount in After 6 week in Haley savings
account = $10 + $120
= $130
That means after 6 weeks will Haley have at least the same amount of
money as Kendra
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Need help with my final it’s my final grade
Answers
How much of a radioactive kind of barium will be left after 39 days if you start with 52,256 grams and the half-life is 13 days?
Answers
Answer:
Step-by-step explanation:
Answer:
6,532
Step-by-step explanation:
ixl
Edwin got 95% of the questions right on a quiz. If there were 20 questions on the quiz, how many questions did he miss??
Answers
Answer:
He got a 19 out of 20, great job Edwin ;)
Step-by-step explanation:
Hope this helps :)
Edwin missed 1 question on the quiz.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
If Edwin got 95% of the questions right on a quiz and there were 20 questions in total, we can calculate the number of questions he missed by finding 5% of the total number of questions.
First, let's find 5% of 20:
= 5% of 20
= (5/100) x 20
= 1 x 20 / 100
= 20 / 100
= 0.2
Since we can't have a fraction of a question, we round the decimal up to the nearest whole number.
In this case, 0.2 rounds up to 1.
Therefore, Edwin missed 1 question on the quiz.
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Explain how the Quotient of Powers property was used to simplify this expression. 2 to the fifth power, over 8 = 22
Answers
The Quotient of Powers was used to simplify this expression is By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents
We have given that,
2 to the fifth power, over 8 = 22
What is the simplified form of expression?The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form or to rewriting the same algebraic expression with no like terms and in a compact manner.
By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents.
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How do you simplify 3 Way ratios?
Answers
To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.
To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.
The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.
For example reduce the ratio 225: 125: 25
The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.
If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.
Now divide each number by 5 and see what we get.
225/5: 125/5: 25/5
45: 25: 5
When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.
Now divide each number by 5 again and get a final ratio of 9: 5: 5.
45/5: 25/5: 5/5
9: 5: 1
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Leo's bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively. The balances form a geometric sequence.
What will Leo's balance be after 8 months?
Leo's bank balance will be $
after 8 months.
Answers
Leo's balance after 8 months is $1725.
What is a geometric sequence?A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
Example:
2, 4, 8, 16 is a geometric sequence.
We have,
1500, 1530, and 1560 is a geometric sequence.
First term.
a = 1500
Common ratio.
r = 1.02
The nth term of a geometric sequence is a[tex]r^{n-1}[/tex].
Now,
For n = 8,
8th term.
= 1500 x [tex]1.02^7[/tex]
= 1500 x 1.15
= 1725
Thus,
The balance after 8 months is $1725.
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You are hired to work for a company at age 25 and the company has a retirement plan
where you can put up to 6% of your salary into the plan each month and they will match
that amount. Your starting monthly salary is $6,100, assume for simplicity sake you
never get a raise, and the retirement plan guarantees a 6.28% interest rate over the life of
the plan.
Scenario 1: You decide to start the retirement plan right away and you can afford
to put the full amount (6% of your salary) into the plan each month.
a) What is 6% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
Scenario 2: You decide to start the retirement plan right away, but you can only
afford to put 3% of your salary into the plan each month.
a) What is 3% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
What is the difference in the amount of money you will have at age 62 between scenarios
1 and 2? ________________
What is the difference in the amounts of money you put into retirement between
scenarios 1 and 2? _______________
How much more money did you get from your employer in scenario 1 than 2?
Answers
In scenerio 1, the money in the retirement account at 62 years old is $1,267,250.76
In scenerio 2, the money in the retirement account at 62 years old is $ 633,625.38.
How do we calculate future value of an ordinary annuity?Scenerio 1:
a) 6% of salary = Salary * 6% = $6,100 * 6% = $366
b) Total amount the company paid monthly = 6% of salary = Salary * 6% = $6,100 * 6% = $366
c) The money in the retirement account at 62 years old can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity given as follows:
FV = M * (((1 + r)^n - 1) / r) ................................. (1)
Where:
FV = Future value = Money in the retirement account at 62 years old = ?
M = Monthly payment = Contribution you + Contribution by the employer = $366 + $366 = $732
r = Monthly interest rate = Annual interest rate / 12 = 6.28% / 12 = 0.0628 / 12 = 0.0052
n = number of months = Number years * Number of months in a year = (Retirement age – Age when hired) * 12 = (62 - 25) * 12 = 37 * 12 = 444
Substituting all the values into equation (1), we have:
FV = $732 * (((1 + 0.0052)^444 - 1) / 0.0052)
FV = Money in the retirement account at 62 years old = $1,267,250.76
d) Amount of money you put into the account = 6% of salary * number of months = $366 * 444 = $162,504
e) Amount of money your employer put into your account = Amount of money you put into the account = $162,504
f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $1,267,250.76 – ($162,504 + $162,504) = $942,242.76
Scenario 2:
a) 3% of salary = Salary * 3% = $6,100 * 3% = $183
b) Total amount the company paid monthly = 3% of salary = Salary * 3% = $6,100 * 3% = $183
c) Using equation (1), we have:
M = Monthly payment = Contribution you + Contribution by the employer = $183 + $183 = $366
Substituting all the values into equation (1), we have:
FV = $366 * (((1 + 0.0052)^444 - 1) / 0.0052)
FV = Money in the retirement account at 62 years old = $633,625.38
d) Amount of money you put into the account = 3% of salary * number of months = $183 * 444 = $81,252.00
e) Amount of money your employer put into your account = Amount of money you put into the account = $81,252
f) Amount your account gained in interest over the years = FV – (Amount of money you put into the account + Amount of money your employer put into your account) = $633,625.38 – ($81,252 + $81,252) = $471,121.38
The difference in the amount of money at age 62 between scenarios 1 and 2 = Money in the retirement account at 62 years old in scenarios 1 + Money in the retirement account at 62 years old in scenarios 2 = $1,267,250.76 - $633,625.38 = $633,625.38
Difference in the amounts of money you put into retirement between scenarios 1 and 2 = $366 - $183 = $183
Amount got from your employer in scenario 1 than 2 = $366 - $183 = $183
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2. Gravetter/Wallnau/Forzano, Essentials - Chapter 4 - End-of-chapter question 2
What is the range for the following set of scores? (You may have more than one answer. )
6, 12, 9, 17, 11, 4, 14
Answers
The range for the following set of scores: 6, 12, 9, 17, 11, 4, and 14 is 13.
In statistics, the range is a measure of dispersion that describes the difference between the largest and smallest values in a dataset. The range is used to describe the spread of a dataset and can be a simple way to identify outliers or unusually large or small values. It is a simple measure of statistical dispersion and is most useful for interval and ratio data.
It is calculated by subtracting the minimum value from the maximum value among the data set.
range = maximum value - minimum value
Plug in the necessary values and solve for the range.
range = 17 - 4
range = 13
Therefore, the range for the following set of scores is 13.
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The price of a video game was orginally $60. There was a $15 discount. By what percentage was the price of the video game reduced?
Answers
Answer$84:
Step-by-step explanation:
Answer: 25%
Step-by-step explanation:
The temperature is -3 degrees celcius and 6:00 and rises 12 degress celcius by midday what is the temperature at midday
Answers
Answer:
9°C
Step-by-step explanation:
Given that :
Temperature at 6:00 = - 3°C
The change in temperature by midday = temperature rise of 12°C
The temperature at midday is :
Temperature at 6:00 + change in temperature
-3°C + 12°C
= 9°C
11. - a? - 2bc - Icl
if a = -2, b = 3,
and c = -3
problem in the photo
algebra
Answers
The value of expression - a² - 2bc - |c| if a = -2, b = 3, and c = -3, is 11.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
- a² - 2bc - |c|, a = -2, b = 3, and c = -3,
Plug the values of a, b, and c as shown below,
- a² - 2bc - |c| = -(-2)² - 2 × (3) × (-3) - |-3|
- a² - 2bc - |c| = - 4 - 6 × (-3) - 3
- a² - 2bc - |c| = -4 + 18 - 3
- a² - 2bc - |c| = 18 - 7
- a² - 2bc - |c| = 11
Thus, the value of the expression is 11.
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Task #2: Jack makes $32 when he sells 4 pumpkins. How many pumpkins will he have to sell to make $48? If Jack finds that he has $120 at the end of the day, how many pumpkins did he sell?
Answers
Answer:
1. 6
2. 15
Step-by-step explanation:
4 pumpkins: $32
=> 1 pumpkin = 32 : 4 = $8
- He will have to sell 48 : 8 = 6 pumpkins to make $48
- He sold: 120 : 8 = 15 pumpkins that day
What does the expression 5n represents The quotient of 5n and a number The product of 5and a number The sum of 5 and a number The difference of 5 and a number
Answers
Answer: The product of 5 and a number
Step-by-step explanation:
The expression 5n represents the product of 5 and a number. For example, let the number be 8. Therefore, the value of the expression will be:
= 5n
= 5 × 8
= 40
The sum of 5 and a number will be:
= 5 + n
The difference of 5 and a number will be:
= 5 - n
if a:b is 2:5 and b:c is 3:4, find a:b:c
Answers
Answer:
just keep in mind am not sure if the answer 6:15:20
Step-by-step explanation:
now we have ab= 2 : 5
and bc= 3 : 4
so b is the common one between them so multiply both of the b together which will give u 15 so now we have b = 15
to get a multiply 2 by 3 to get 6 so a = 6
to get c multiply 4 by 5 to get 20 so c = 20
now I hope that its correct and that u understood
find the area of the figure below:
Answers
Answer:
104 ft^2
Step-by-step explanation:
Answer:
104 ft²
Step-by-step explanation:
you can solve this multiple ways, one way is: find the area of the big rectangle and subtract from it the area of the small rectangle
big rectangle
A big = 8 * (5+6+5)= 8 * 16 = 128 ft²
small rectangle
Asmall = 4*6 = 24 ft²
area of the shape
Abig -Asmall = 128-24 = 104 ft²
A statistics content developer at Aplia wanted to know whether study skills are related to memory quality. She invited student volunteers to perform an online memory task. The students saw a list of 60 words and were then asked to recognize a list of five brand new words that are related to words that were on the original list. Students were also asked to provide their GPAs. Consider the following data set, which was collected from student volunteers in 2009. The table gives the frequency for the number of incorrectly identified related words. Use the dropdown menus to complete the table by filling in the missing values for the proportions and percentages
Answers
The proportion and percentage is as follows;
[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & 0.34 & 34 \% \\ 5-6 & 50 & 0.32 & 32 \% \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]
What is the difference between proportions and percentages?A percentage represents a ratio or fraction with a denominator that is always 100 as opposed to a proportion, which asserts the equivalent of two ratios or fractions.
Given
[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & & \\ 5-6 & 50 & & \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]
To estimate the total frequency:
Total = sum f
Total = 29 + 53 + 50 + 22 + 1
Total = 155
The proportion (p) exists calculated by:
[tex]$p = \frac{f}{\text { Total }}[/tex]
The percentage (P) exists calculated by:
P = p × 100 %
For interval 7 - 8, we have:
p = 53 / 155 = 0.34
P = 0.34 × 100 % = 34 %
For interval 5 - 6, we have:
p = 50 / 155 = 0.32
P = 0.32 × 100 % = 32 %
So, the complete table is:
[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & 0.34 & 34 \% \\ 5-6 & 50 & 0.32 & 32 \% \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]
The complete question is:
A statistics content developer at Aplia wanted to know whether study skills are related to memory quality. She invited student volunteers to perform an online memory task. The students saw a list of 60 words and were then asked to recognize a list of five brand new words that are related to words that were on the original list. Students were also asked to provide their GPAs.
Consider the following data set, which was collected from student volunteers in 2009. The table gives the frequency for the number of incorrectly identified related words. Use the dropdown menus to complete the table by filling in the missing values for the proportions and percentages.
Score Interval f Proportion Percentage
9â10 29 0.19 19%
7â8 53
5â6 50
3â4 22 0.14 14%
1â2 1 0.01 1%
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Solve this system of equation by elimination. 2x-5y=8 3x+5y=-13
Answers
Answer:
x=-1, y=-2. (-1, -2).
Step-by-step explanation:
2x-5y=8
3x+5y=-13
----------------
5x=-5
x=-5/5
x=-1
2(-1)-5y=8
-2-5y=8
5y=-2-8
5y=-10
y=-10/5
y=-2
Draw a tape diagram to represent the following
equation:
3x + 15 = 90
Answers
Answer:
25
Step-by-step explanation:
Subtract 15 from both sides then divide by 3.
Answer:
3x + 15 = 90
3x = 90 - 15
3x = 75
x = 25
What are my financial goals? What major purchases should I save for?
Answers
It depends on your personal financial situation and goals. Generally, it is important to save for major purchases such as a house, car, and vacations, as well as setting aside money for retirement. Additionally, you may want to consider investing in stocks, bonds, or mutual funds to achieve your long-term financial goals.