If a, b, and c are real numbers where a > 0 and b^2 - 4ac > 0, then the quadratic equation ax^2 + bx + c = 0 will have two distinct real roots.
In this case, if we are looking for solutions to the inequality ax^2 + bx + c < 0, then we can conclude that the graph of the quadratic function will open downward and the solutions will be the values of x that lie between the two roots. Specifically, if the two roots are x1 and x2 (where x1 < x2), then the solution to the inequality will be:
x1 < x < x2
In other words, the values of x that make the quadratic expression negative will be the values of x that lie between the two roots.
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Does this represent a function? Yes or no and explain why. (Please fast! im being timed(
Answer:
Hello
No function.There are two 7's on the x-axis. There can be 2 or more same numbers on the y-axis.
Step-by-step explanation:
Answer is No.
Type the correct answer in the box use numerals instead of words
Answer:
Subtracting \(3x^2+4x-5\) from \(7x^2+x+9\) results in a polynomial. After subtracting \(4x^2-3x\) from this polynomial the difference is 14
Step-by-step explanation:
The question given is:
Subtracting \(3x^2+4x-5\) from \(7x^2+x+9\) results in a polynomial. After subtracting \(4x^2-3x\) from this polynomial the difference is?
First we will Subtracting \(3x^2+4x-5\) from \(7x^2+x+9\)
\(7x^2+x+9-(3x^2+4x-5)\\=7x^2+x+9-3x^2-4x+5\\Combining\:like\:terms\\=7x^2-3x^2+x-4x+9+5\\=4x^2-3x+14\)
So, the polynomial we get is: \(4x^2-3x+14\)
Now, subtracting \(4x^2-3x\: from\: 4x^2-3x+14\)
\(4x^2-3x+14-(4x^2-3x) \\=4x^2-3x+14-4x^2+3x\\Combining\:like\:terms\\=4x^2-4x^2-3x+3x+14\\=14\)
The difference is 14
So, Subtracting \(3x^2+4x-5\) from \(7x^2+x+9\) results in a polynomial. After subtracting \(4x^2-3x\) from this polynomial the difference is 14
What is the completely factored form of this polynomial?
– 8x²+
+ 16
Answer:
-8(x²-2)
Step-by-step explanation:
Factor -8 out of -8x²
-8(x²)+16
Factor -8 out of 16.
-8(x²)-8(-2)
Factor -8 out of -8(x²)-8(-2).
2 years 7 years 5 years 6 years After 25 years, neither John nor Tommy will have enough money to retire, but how much more will Tommy's account be worth at this time? $162,869 $107,938 $186,514 $215,877 $130,073 John is jealous of Tommy because Tommy is scheduled to retire before him, so John decides to make whatever end-of-year contribution is necessary to reach the $1,500,000 goal at the same time as Tommy. If John continues to eam 7.6% annual interest, what annual contributions must he make in arder to retire at the same time as Tommy? $8,789 $11,695 58,226 $13,361 $16,452 John has decided to retire once he has $1,500,000 in his retirement account, At the end of each year, he will contribute 55,500 to the account, which is expected to provide an anauat return of 7,60%. How many years will it take until he can retire? 32 years 41 years 37 years 42 years 36 years Suppose 3ahn's friend, Tannyy, has the same retirement plan, saving 55,500 at the end of each year and retiring once he hits 31,500,000. However, Tommys account is expected to grovide an annual retum of 9.6%. How much sooner can Tommy retire? 4 years 2 years 7 vears 5 years 6 years
To find out how much more Tommy's account will be worth after 25 years, we need to calculate the future value of his account after 25 years at a 7.6% annual interest rate.
We can use the formula:
FV = PV x (1 + r)^n
where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years.
Here, PV = $55,500 (annual contribution) x 25 (years) = $1,387,500. r = 7.6%, and n = 25.
So,FV = $1,387,500 x (1 + 0.076)^25= $186,514.
To find out how much John must contribute annually to retire at the same time as Tommy, we need to calculate the present value of his contributions and compare it to Tommy's account balance after 25 years, which is $186,514.
We can use the formula:PV = FV / (1 + r)^n
where PV is the present value, FV is the future value, r is the annual interest rate, and n is the number of years.
Here, FV = $1,500,000, r = 7.6%, and n = 25.
So,PV = $1,500,000 / (1 + 0.076)^25= $335,131.
John's present value after 25 years is $335,131.
He needs to contribute an additional amount to reach the goal of $1,500,000.
So,John's annual contribution = (goal - present value) / [(1 + r)^n - 1]= ($1,500,000 - $335,131) / [(1 + 0.076)^25 - 1]= $11,695.
To find out how long it will take John to reach the goal of $1,500,000, we can use the formula: n = log(FV/PV) / log(1 + r)
where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. Here, FV = $1,500,000, PV = $55,500 (annual contribution), r = 7.6%.
So,n = log($1,500,000 / $55,500) / log(1 + 0.076)= 36.95 years. years
.To find out how much sooner Tommy can retire, we need to calculate the number of years it will take him to reach $1,500,000 at a 9.6% annual interest rate.
We can use the formula:n = log(FV/PV) / log(1 + r)where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years.
Here, FV = $1,500,000, PV = $55,500 (annual contribution), r = 9.6%.
So,n = log($1,500,000 / $55,500) / log(1 + 0.096)= 32.95 years. Tommy will retire 5 years sooner than John (37 years - 32 years = 5 years).
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If Sally's utility function is U=6(q1)0.5+q2, what is her Engel curve for q2 ? Let the price of q1 be p1, let the price of q2 be p2, and let income be Y. Sally's Engel curve for good q2 is Y=. (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcu E.g., a subscript can be created with the _character.)
The Engel curve for good q2, given Sally's utility function U=6(q1)0.5+q2, is Y= (6(q1)0.5) / p2.
To derive the Engel curve, we need to find the relationship between income (Y) and the quantity consumed of good q2. In Sally's utility function, the first term represents the utility she receives from consuming q1, and the second term represents the utility she receives from consuming q2.
To find the Engel curve for q2, we need to hold q1 constant and vary Y. We can do this by solving the utility function for q1 and substituting it into the income equation.
Rearranging the utility function, we have (q1)0.5 = (U - q2) / 6. Substituting this into the income equation Y = p1q1 + p2q2, we get Y = p1(U - q2) / 6 + p2q2.
Simplifying further, we have Y = (p1U - p1q2) / 6 + p2q2.
Rearranging the terms, we get Y = (p1U + 6p2q2 - p1q2) / 6. Finally, we can factor out q2 from the numerator to obtain Y = (6(q1)0.5) / p2.
Therefore, the Engel curve for good q2 is Y = (6(q1)0.5) / p2, where Y represents income, q1 is the quantity consumed of good q1, and p2 is the price of good q2.
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5(x+1)-x=3(x-1)+7 no solutions one solution and what does x equal or all numbers are solutions.
Answer:
There is only one solution to this equation 5(x+1)-x=3(x-1)+7, which is x = -1.
What is linear equation ?
A linear equation is an algebraic equation that represents a straight line on a graph. It is a polynomial equation of the first degree, which means that the highest power of the variable in the equation is one. Linear equations can be written in the form
\(y = mx + b\)
where y and x are variables,
m is the slope of the line
b is the y-intercept.
Step-by-step explanation:
Given linear equation is 5(x+1)-x=3(x-1)+7
To solve the equation, we can simplify and collect like terms on each side:
5(x+1) - x = 3(x-1) + 7
5x + 5 - x = 3x - 3 + 7 // Distribute the 5 and 3
4x + 5 = 3x + 4 // Simplify by combining like terms
x = -1 // Subtract 3x from both sides, then subtract 5 from both sides
Therefore, x = -1 is the solution to the equation.
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What is the greatest common factor of 33 and 39
Answer:3
Step-by-step explanation:
Answer:
since 3 is the largest of these common factors the gcf of 33 and 39 would be 3
11) The difference of two numbers is 3. Their sum is 23. What are the numbers?
Answer:
Step-by-step explanation:
ill try this one in a few minutes for you.
What do you mean by data type?
Answer:
A data type is an attribute associated with a piece of data that tells a computer system how to interpret its value
Step-by-step explanation:
Data types categorize data and specify its nature, amount characteristics, and behavior. It decides how data is handled within a computer system in terms of storage and manipulation.
Data types categorize data and specify its nature, characteristics, and behavior. It is a crucial part of every data structure and computer language. Primitive data types and complex data types are the two basic divisions of data types. Basic types like numbers, characters, booleans, and strings are examples of primitive data types. Arrays, objects, and records are examples of sophisticated data types that are more complex. Data types specify how information is handled and stored by computer systems. Size, precision, and range are a few examples of the unique qualities that each data type possesses. The arithmetic, comparison, and logic operations that can be carried out on the data are also determined by the data types.
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Evaluate this exponential expression.
A. 63
OB. 66
C. 19
D. 207
6 (4+2)2-32
Answer:To evaluate the exponential expression 6(4+2)² - 32, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
First, we simplify the expression inside the parentheses:
4 + 2 = 6
Next, we square the result:
6² = 36
Now, we substitute the squared result back into the expression:
6(36) - 32
Next, we perform the multiplication:
6 * 36 = 216
Finally, we subtract 32:
216 - 32 = 184
Therefore, the value of the given exponential expression 6(4+2)² - 32 is 184.
HELP ME WITH THIS PLEASE HUURRYY
Answer:
the answer would be A, 78.52
Step-by-step explanation:
Help ASAP please thank u
Answer:
(A). F(x) = (x+1)^2
Step-by-step explanation:
If you replace x with the values of the axis, you get all the coordinates of the graph.
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What is the coefficient of the third term in this expression?
–
5–2t3–4t3u3+8v
The coefficient of the third term in the given expression is -4
Determining the coefficient of a term in an expressionFrom the question, we are to determine the coefficient of the third term in the given expression.
A coefficient is the numerical value that is written along with a variable or it is multiplied by the variable.
The given expression is
5 – 2t3 – 4t3u3 + 8v
This can be properly written as
5 - 2t³ - 4t³u³ + 8v
The third term in this expression is - 4t³u³
In this term, the numerical value that is written along with the variable is -4
Hence, the coefficient is -4
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in the following pseudocode which uses recursion to find the factorial of a number, which is the base case?factor(n - 1)n * factor(n - 1)n
The base case in the given pseudocode is factor(0).
The pseudocode is using recursion to find the factorial of a number. In each recursive call, the function is subtracting 1 from the given number (n - 1) and then multiplies it with the result of the recursive call for n - 1. The base case is the condition that stops the recursion and provides a result.
In this case, the base case is a factor(0). When the input number reaches 0, the recursion stops, and the function returns 1. This is because the factorial of 0 is defined as 1.
So, when the base case is reached, the recursion unwinds, and the factorial value is calculated by multiplying the current number (n) with the result of the previous recursive call (factor(n - 1)).
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PLEASE HELP ME!!!ITS DUE TODAY!!
PONLE QUE ES A LA MIERDA IEUFJEUNFUF
Answer:
17.28 is around
23.76 is the area
Step-by-step explanation:
You are testing H0: μ = 0 against Ha: μ > 0 based on an SRS of 16 observations from a Normal population.
What values of the t statistic are statistically significant at alpha = 0.005 level?
Any t statistic greater than 2.947 would be considered statistically significant at the 0.005 level, leading to the rejection of the null hypothesis H0: μ = 0 in favor of the alternative hypothesis Ha: μ > 0.
To determine the values of the t statistic that are statistically significant at alpha = 0.005 level when testing H0: μ = 0 against Ha: μ > 0 based on an SRS of 16 observations from a Normal population, you should follow these steps:
1. Determine the degrees of freedom (df): Since you have an SRS of 16 observations, the df = 16 - 1 = 15.
2. Identify the alpha level: In this case, alpha = 0.005.
3. Use a t-distribution table or software to find the critical t value corresponding to the given alpha level and df: For df = 15 and a one-tailed test with alpha = 0.005, the critical t value is approximately 2.947.
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(ITS DUE IN 30 MINUTES)Frigidia is a colony in Antarctica. The colony is 1,000 square kilometers in size. Currently, 30,000 people live there. Last year, 10,000 children were born and 2,000 people immigrated. 20,000 people died and 5,000 emigrated. It is believed that the island could support up to 50 people per square kilometer.
The current growth rate is ___.
43%
-43%
4.3 %
-4.3%
The current growth rate of the island is given as follows:
-43%.
How to calculate the growth rate?The first step in calculating the growth rate is obtained the increases and the decreases in the population, as follows:
Increases: 10,000 births + 2,000 people immigrating = 12,000.Decreases: 20,000 deaths + 5,000 people emigrating = 25,000.The total change is obtained by the subtraction of the increases by the decreases, as follows:
Total change = 12,000 - 25,000 = -13,000
Then the growth rate, as a percentage, is obtained by the division of the total change of -13,000 by the initial population of 30,000 and then multiplied by 100%, as follows:
-13,000/30,000 x 100% = -43%.
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Mr. Lee deposited $450 into a savings account that earns 5% compound interest, compounded annually for 2 years. What is the total amount that Mr. Lee will have in his account at the end of 2 years?
Answer:
Okay, I've never learned about this before but I want to help and I think I get it. Again, I'm not very sure about this. $472.50
Step-by-step explanation:
I took one percent of 450 and mutiplied that by five to get 22.5
22.5 + 450 = 472.50 making THAT answer.
When there is a problem with Solver being able to find a solution, many times it is an indication of a(n)
When Solver is unable to find a solution to a problem, it can be an indication of various issues. One possible cause is that the problem may be too complex for Solver to solve within the given constraints.
In such cases, it may be necessary to adjust the problem parameters or seek alternative solutions. Another possible cause of Solver's inability to find a solution could be due to incorrect input data. This can lead to inconsistent or contradictory constraints, making it impossible for Solver to arrive at a feasible solution. Lastly, Solver may fail to find a solution due to numerical errors or limitations in the algorithm used. These issues can arise when dealing with large datasets or highly non-linear problems. In any case, when Solver is unable to find a solution, it is important to carefully examine the problem and its parameters, and consider alternative approaches. Sometimes, a small adjustment to the input data or constraints can make all the difference in arriving at a successful solution. In such cases, Solver may struggle to find an accurate or optimal solution. Ill-conditioned problems typically involve numerical instability or poor scaling, while infeasible problems occur when the given constraints cannot be satisfied simultaneously. It is crucial to analyze and refine the problem to enable Solver to find a viable solution effectively. When there is a problem with Solver being unable to find a solution, it often indicates the presence of a(n) ill-conditioned or infeasible problem.
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When fingerprinting a person who is missing fingers, what are the two notations you should use on the fingerprint card
Fingerprinting is a technique used by forensic experts and crime scene investigators to identify individuals based on their unique fingerprints. Fingerprints are unique to each individual and have distinct ridge patterns that are used to identify individuals.
It is an effective way of identifying people because fingerprints remain the same throughout a person's life, unlike other physical characteristics.
When fingerprinting a person who is missing fingers, two notations that should be used on the fingerprint card are "amputation" and "absent." The notations on the fingerprint card should indicate that the fingers are missing due to amputation or absence.
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When fingerprinting a person missing fingers, the two notations that should be used on the fingerprint card are tented arch for a missing middle finger and amputation notation for a completely missing finger.
Explanation:When fingerprinting a person who is missing fingers, two notations should be used on the fingerprint card:
Tented arch: If the person is missing the middle finger, the missing finger should be notated as a tented arch. This means that the ridges of the fingertip start on one side of the finger and end on the other, creating a tent-like shape.Amputation: If a person is missing a finger completely, the notation should indicate the specific finger that is missing and the level of the amputation, such as 'Amputation of left index finger at the proximal phalanx'.Learn more about Fingerprinting here:https://brainly.com/question/34652657
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What is the Volume and surface area of a cone with a diameter of 18ft and a slant height of 30ft
Answer:
A cone with a diameter of 18ft and a slant height of 30ft
Using Pythagorean theorem, the height is calculated by:
H = sqrt(18^2 - (30/2)^2) = 9.95
The surface area:
A = lateral surface area + base
A = pi x radius x slant height + pi x radius^2
A = pi x (30/2) x 18 + pi x (30/2)^2 = ~1555.1 (ft2)
The volume:
V = base x height x (1/3)
V = pi x radius^2 x height
V = pi x (30/2)^2 x 9.95 = 7033.2 (ft3)
Hope this helps!
:)
For the word KANGAROOS, if a letter is selected at random, what is the probability
that it is a vowel?
Answer:
4/9 or 44.4%
Step-by-step explanation:
If a=6 and b=24 what is (a+b) b is squared
Answer:
the correct answer is 582
Answer:
582
Step-by-step explanation:
B²= base×base
The base is 24
24 ×24 = 576
When you add 6 to 576 you get 582.
I hope this is correct. Sorry if it is wrong.
−7 + 3(8n − 8) = 8(7 + 3n) please show work
Answer:
Step 1: Simplify both sides of the equation.
−7+3(8n−8)=8(7+3n)
−7+(3)(8n)+(3)(−8)=(8)(7)+(8)(3n)(Distribute)
−7+24n+−24=56+24n
(24n)+(−7+−24)=24n+56(Combine Like Terms)
24n+−31=24n+56
24n−31=24n+56
Step 2: Subtract 24n from both sides.
24n−31−24n=24n+56−24n
−31=56
Step 3: Add 31 to both sides.
−31+31=56+31
0=87
Answer:
There are no solutions.
Step-by-step explanation:
What is the area and perimeter of a circle (-4,2) (-3,4)
Step-by-step explanation:
Let radius of circle is r=18 units
Perimeter of full circle is given by 2πr
Thus, perimeter of three quarters circle is given by,
( ¾ × 2πr) + (2 × r)
The perimeter of this "circle" would be:
( ¾ × 2 × π × 18) + (2 × 18) = 27π + 36 ≈ 120.78 m
A candy store uses 10. 3 grams of sugar each hour. How many grams of sugar will the store use in 10 hours?
The candy store will use 103 grams of sugar in 10 hours.
To find out how many grams of sugar the store will use in 10 hours, we can simply multiply the amount of sugar used in one hour (10.3 grams) by the number of hours (10).
To solve the problem, we use a simple multiplication formula: the amount used per hour (10.3 grams) multiplied by the number of hours (10) to find the total amount of sugar used in 10 hours.
We can interpret this problem using a rate equation: the rate of sugar usage is 10.3 grams/hour, and the time period is 10 hours. Multiplying the rate by the time gives the total amount of sugar used.
So the calculation would be:
10.3 grams/hour x 10 hours = 103 grams
Therefore, the candy store will use 103 grams of sugar in 10 hours.
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Standard Form to Scientific Notation:
5.8 x 107 =
Answer:
just move the decimal a 107 times and add 0's
Step-by-step explanation:
Solve 1. At a concert, a band sold t-shirts for $18 and hats for $12. They sold 60 t-shirts and hats combined for a total of $870. How many t-shirts did they sell? How many hats?
Answer:
25 t-shirts and 35 hats were sold
Step-by-step explanation:
Here, we want to calculate the number of hats and the number of t-shirts sold.
Let the number of hats be h and the number of t-shirts be t
The sum of both is 60;
Mathematically;
h + t = 60 •••••••••••(i)
The total revenue from selling h hats at $12 per one is 12 * h = $12h
The total revenue from selling t t-shirts at $18 per one is 18 * t = $18t
So the addition of this gives the total;
12h + 18t = 870 ••••••••(ii)
From i, h = 60-t; substitute this into ii
12(60-t) + 18t = 870
720 -12t + 18t = 870
720 + 6t = 870
6t = 870 -720
6t = 150
t = 150/6
t = 25
From the substitution;
h = 60-t
h = 60-25
h = 35
Answer:
48 hats
Step-by-step explanation:
im not sure if this is the right answer but i hope this helps
What type of triangle has an exterior angle that is obtuse at to vertices?
A mechanic charges $60 to inspect your heater, plus $70 per hour to work on it. You owe the mechanic a total of $410. Write and solve an equation to find the amount of time h (in hours) the mechanic works on your heater.
Answer:
($410 - $60) / $70 = 5
After subtracting the $60 base fee, you can just divide the hours paid for by the hourly wage and find out how many hours were worked. Hope this helps!