Answer:
[tex]x=+/-i\sqrt{13}[/tex]
Step-by-step explanation:
To find the roots, factor and set equal to 0 or use the quadratic formula. This quadratic equation does not factor and must be solved using the quadratic formula.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]
where a = 2, b=0, and c=26
[tex]x=\frac{0+/-\sqrt{0^2-4(2)(26)} }{2(2)} \\x=\frac{+/-\sqrt{-208)} }{4} \\x=\frac{+/-i\sqrt{16*13)} }{4}\\x=\frac{+/4i\sqrt{13} }{4}\\x=+/-i\sqrt{13}[/tex]
Answer:
Step-by-step explanation:
X=-i√13,x=i√13
Twice x,plus 3,is the same as -6
write the equation out as given:
2x+3=-6
subtract 3 from each side
2x = -9
x=-9/2
x = -4.5
Write the standard form of the line that passes through the given points.
4, 7) and (0, 7)
The equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).
What is the slope of the line?The slope of a line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Given that line passes through points (4, 7) and (0, 7)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = 4, y₁ = 7
x₂ = 0, y₂ = 7
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 7 = (7 - 7)/(0- 4)[x -4]
⇒ y - 7 = (0)/(-10 )[x -4]
⇒ y - 7 = 0(x -4)
⇒ y - 7 = 0
⇒ y = 7
Therefore, the equation of the line would be y = 7 which passes through the points (4, 7) and (0, 7).
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Standard form to 15409
You are driving 70 miles per hour, starting at mile marker 255. How many hours will it take you to reach mile marker 115?
255-115 = 140 miles
140/70 = 2 hours
The number 4 is the smallest positive integer that has exactly three factors: 1, 2, and 4. If k is the next-highest integer that also has exactly three factors, what is the sum of the three factors of k
To solve this problem, we must do a method of trial and error to find for the next highest integer with exactly three factors. We know that the value of k must be greater than 4, therefore by using trial and error to find for the correct answer:
Factors of 5:1, 5
Factors of 6:1, 2, 3, 6
Factors of 7:1, 7
Factors of 8:1, 2, 4, 8
Factors of 9:1, 3, 9
Therefore we stop at 9 since this is already our answer. It has exactly three factors.
The sum of the factors is:
sum of factors = 1 + 3 + 9
sum of factors = 13
A taxi company charges passengers $1.75 for a ride, no matter how long the ride is, and an additional $0.40 for each mile traveled. The rule mc014-1.jpg describes the relationship between the number of miles m and the total cost of the ride c. What is the charge for a 2.7-mile ride?
Which of the following statements is true?
A
6.75 < 6.759 < 6.751 < 6.85
B
5.55 < 5.559 < 5.65 < 5.69
C
4.11 < 4.12 < 4.17 < 4.15
D
7.42 < 7.41 < 7.40 < 7.39
Zach bought two new jet skis for 15,490. He will make 36 equal payments . How much will each payment be?
The mayor of a small city has proposed that a gambling casino be built in the downtown area, arguing that the construction project, resulting jobs, and tax revenue will boost the local economy. A total of 183 residents attend a public hearing on the proposal and a show of hands finds only 31 in favor of the casino. What does this vote tell the city council about public support for the project?
A roulette wheel contains the integers 1 through 36, 0, and 00. suppose that you spin the wheel 6 times and that each time you bet on a single number. what is the probability (rounded to the nearest hundredth) that you win on at least one bet?
Answer:
18/38
Step-by-step explanation:
edmentum/plato
On may 31, the cash account of bottle's r us had a normal balance of $5,000. during may, the account was debited for a total of $12,200 and credited for a total of $11,500. what was the balance in the cash account at the beginning of may?
The balance in the cash account at the beginning of May was -$6,500.
Explanation:The balance in the cash account at the beginning of May can be calculated by adding up the debits and credits for the month and subtracting them from the normal balance at the end of May.
In this case, the total debits for May were $12,200 and the total credits were $11,500.
To find the beginning balance, subtract the total credits from the normal balance:
Beginning balance = Normal balance - Total credits
Beginning balance = $5,000 - $11,500 = $-6,500
Therefore, the balance in the cash account at the beginning of May was -$6,500.
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a House sits on a 5/8 acre lot and 1/2 of the lot is lawn. 2/3 of lawn was mowed. how much was mowed?
5/8 x 1/2 = 5/16 acre is lawn
5/16 x 2/3 = 10/48 reduces to 5/24 of the lawn was mowed
How much would $300 invested at 7% interest compounded continuously be worth after 4 years
Answer:
$396.93
Step-by-step explanation:
It asks to round to the nearest cent not dollar.
A solid has all of the following charateristics, except for which? A. has a closed space B. is three-dimensional C. has an open space D. is measured in volume
On two investments totaling $11,500, Peter lost 3% on one and earned 4% on the other. If his net annual receipts were $201, how much was each investment?
Final answer:
Peter invested $3,700 at a 3% loss and $7,800 at a 4% gain. By setting up a system of equations and solving them, we determined the amount invested in each.
Explanation:
To solve the problem of how much was invested by Peter in each investment, we need to set up a system of equations. Let's call the amount invested at 3% loss x, and the amount invested at 4% gain y. The total amount invested is $11,500, so we have x + y = $11,500.
Peter's net annual receipts were $201, which comes from a loss of 3% on investment x and a gain of 4% on investment y. The equation for this would be -0.03x + 0.04y = $201.
Now we have a system of two equations:
-0.03x + 0.04y = $201
Adding (1) and (2) gives us:
0.03y + 0.04y = $546
Combining like terms, we get:
0.07y = $546
Dividing both sides by 0.07, we find that:
y = $7,800
Substituting y back into the first equation, we get:
x = $11,500 - $7,800 = $3,700
So, Peter invested $3,700 in the investment with a 3% loss and $7,800 in the investment with a 4% gain.
If 3x^2=4y=12 what is the value ofx^2y
Determine whether it is reasonably possible that the proportion of adults from country a and the proportion of adults from country b are equal and explain your reasoning. choose the correct answer below.
Five times the sum of a number and 27 ig greater than or equal to six times the sum of that number and 26 . What is the solution set of this problem
Given
5(x + 27) ≥ 6(x + 26)
Find
The solution set of x
Solution
Eliminate parenthses.
... 5x + 135 ≥ 6x + 156
Subtract 5x+156
... -21 ≥ x
The solution set is all real numbers less than or equal to -21.
What compound inequality represents the phrase? Graph the solutions.
all real numbers that are greater than –8 and less than 8
How many numbers are equal to the sum of two odd one digit numbers
Which of the followings explains the difference between a regular subquery and a correlated subquery?
A regular subquery is a standalone query that can be executed independently of the outer query and passes its result to the outer query. Conversely, a correlated subquery is linked with the outer query, executes for each row processed by the outer query, and may be slower due to these repeated executions.
The primary difference between a regular subquery and a correlated subquery resides in the way they operate and when they execute the control flow. A regular subquery is a standalone query, which means it can be executed independently of the outer query. Once it executes, it passes its result to the outer query.
On the other hand, a correlated subquery, as its name suggests, is 'correlated' with the outer query. It cannot be executed independently and must be run for each row processed by the outer query.
For example, if you use a correlated subquery to determine whether a record exists in another table, the subquery will run once for each record in the primary query. This can potentially be slower than a regular subquery due to the repeated executions.
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The question probable may be:
What distinguishes a regular subquery from a correlated subquery in terms of execution and operation? How does the control flow differ, and why might a correlated subquery be slower than a regular subquery in certain scenarios?
In what instance would you use the upside down U when doing interval notation
Charlie cannot remember how much he financed to buy his car. He does remember that his monthly payment is $200. His add-on interest rate was 9% and he made a total of 30 payments. Find the amount of his loan to the nearest penny.
The initial amount that Charlie financed to buy his car is approximately $5,364.93. This was calculated using the add-on interest loan formula with the provided monthly payments, interest rates, and number of payments.
Explanation:The question is asking us to find out the initial amount that Charlie financed to buy his car, given that he made monthly payments of $200 at an interest rate of 9% over a total of 30 payments. This is a simple interest loan problem in mathematics, specifically dealing with add-on interest. To determine the original loan amount, we will use the formula for calculating the loan amount in an add-on interest loan. It is calculated by dividing the amount paid in total by the sum of one plus the product of the rate and time: Loan Amount = Total Payment / (1 + (Interest Rate * Time)) .
In this case, the total repayment made by Charlie is $200 * 30 = $6,000. The interest rate is 9% per year, but since he is making monthly payments we need to divide this by 12 to get the monthly interest rate, which is 0.0075. The time is 30 months. Substituting these values into our formula gives: Loan Amount = 6,000 / (1 + (0.0075 * 30)).
Hence, after calculations, the initial amount that Charlie financed to buy his car is approximately $5,364.93.
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Consider H0: μ = 45 versus H1: μ < 45. A random sample of 25 observations produced a sample mean of 41.8. Using α = .025 and the population is known to be normally distributed with σ = 6.
which number is the standard equation for a circle centered at the origin should one increase to make the circle larger
How many perfect cube whole numbers are between 6000 and 8500?
Simplifying the following Expressions by combining adding together what is alike like term 8n+5-n+13
A tree has a shadow of 30ft how tall is the tree? And a triangle has a right angle with a line of 2ft tall and the base of 5ft what do they have in common.
Rose plans to go for vacation to europe in 6 years from now. she estimates that she will need $24,388 for the trip. how much does she need to place in a saving account today that earns 5.13% per year (compounded annually) to accumulate this amount? all the work has to be shown! round the answer to two decimal places.
Determine the domain of the function. f as a function of x is equal to the square root of two minus x.