To factor the quadratic x^2 + 3x + 2, it can be written as (x + 1)(x + 2). The concept of infinity over infinity (∞/∞) is an indeterminate form in limits and usually requires further techniques to evaluate.
To factor x^2 + 3x + 2, you want to find two numbers that both add up to +3 (the coefficient of x) and multiply to +2 (the constant term). These numbers are +1 and +2. Thus, you can express the quadratic equation as a product of two binomials:
x^2 + 3x + 2 = (x + 1)(x + 2).
As for the concept of limits like ∞/∞, it commonly arises when evaluating the behavior of functions as the variable approaches infinity. It represents an indeterminate form which requires further algebraic manipulation or techniques such as L'Hôpital's rule to find a meaningful limit.
The cost of admission to Water World is $7.50. The owner wants to raise the admission cost. For every $1 increase in the admission cost, the number of visitors to the park will drop by 25 per day. Currently, an average of 225 people visit the water park each day. Find the amount by which the admission cost to the water park should be increased to obtain maximum income. 6. The path of the water fro
To maximize income for Water World, the admission cost should be increased by $0.75, calculated by finding the vertex of the quadratic equation representing the income as a function of price increase and visitor numbers.
Explanation:To find the amount by which the admission cost to Water World should be increased to obtain maximum income, we can create a quadratic equation to represent the income based on the number of visitors and admission cost.
Step 1: Define variables and equation
Let x represent the increase in dollars to the current admission cost of $7.50. The new admission cost would be (7.50 + x) dollars.
With each $1 increase, the number of visitors decreases by 25. The new average number of visitors per day would be (225 - 25x) visitors.
Step 2: Formulate the income
Income, I, is equal to the admission cost multiplied by the number of visitors, which is I = (7.50 + x)(225 - 25x).
Step 3: Expand and maximize the quadratic equation
I = 1687.5 - 187.5x + 225x - 25x² = -25x² + 37.5x + 1687.5. This is a quadratic equation that opens downward, meaning it has a maximum point at its vertex.
The formula for the x-coordinate of the vertex of a parabola y = ax² + bx + c is -b/(2a). In this scenario, a = -25 and b = 37.5.
Step 4: Find the vertex
The x-coordinate of the vertex (maximum income) is -37.5 / (2 × -25) = 0.75. Therefore, the admission cost should be increased by $0.75 to maximize income.
The measure of an angle exceeds 6 times its supplement by 5. find the measure of the angle
(y-2) = 3(×-1) what's the slope
If y varies directly as x, and y = - 4 when x=32, find why when x=3
simplify √18
A. 2√3
B. 2√9
C. 3√2
D. 9√2
The equation 4x+3y=24 represents a linear function in two variables. Identify the slope, x-intercept (zero), and y-intercept of this linear function.
PLEASE HELP ME!!!! WORTH 10 POINTS!!!
Write the equation of the line, in point-slope form. Identify the point (-2, -2) as (x1, y1). Use the box provided or the upload option to submit all of your calculations and final answer.
aiden currently has a balance of $4443.48 in an account he has held for 17 years he open the account with initial deposit of $2567 what is the simple interest rate on the account
Brittany borrowed 3 movies from the library. Each movie is almost 2 hours long. About how many hours of movies does Brittany have to watch?
There are 3 movies, and each movie is 2 hours long. Assuming that Brittany watches all three without breaks so the total time consumed watching all 3 movies is:
total hours = 3 movies * (2 hours / movie)
total hours = 6 hours
Create two expressions using the following criteria:
Include one expression that contains rational exponents that can be simplified further. Provide the simplified form to your instructor.
Include one expression that contains radicals that can be simplified further. Provide the simplified form to your instructor.
The Answer to the about question rational exponents and radicals is given below.
How to solve this question?To solve the first part Let us assume a expression (E) that contains rational exponents
E = 6² / ( 9[tex]\frac{2}{3}[/tex] × 3[tex]\frac{5}{3}[/tex] )
E = 6² / ( (3²)[tex]\frac{2}{3}[/tex] × 3[tex]\frac{5}{3}[/tex] )
E = 6² / ( 3[tex]\frac{4}{3}[/tex] × 3[tex]\frac{5}{3}[/tex] )
E = 6² / 3[tex]\frac{9}{3}[/tex]
E = 6² / 3³
E = 36/27 = 4/3
E = 4/3
To solve the second part Let us assume a expression (F) that contains radicals.
F = 10 × √(∛(59 +5))
F = 10 × √(∛64)
F = 10 × √(∛(4×4×4))
F = 10 × √4
F = 10 × √(2×2)
F = 10 × 2
F = 20
Thus we have simplified the expression that contains rational exponents and also the expression that contains radicals also.
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To simplify an expression with rational exponents, we multiply the exponents together. To simplify an expression with radicals, we can find the square root of the number.
Explanation:An expression with rational exponents that can be simplified further is:
To simplify this expression, we can use the rule that states when we raise an exponent to another exponent, we multiply the exponents together. Therefore, (161/4)3/2 = 161/4 * 3/2 = 163/8.
An expression with radicals that can be simplified further is:
To simplify this expression, we can find the square root of 32. The square root of 32 can be simplified as follows: √(32) = √(16 * 2) = √(16) * √(2) = 4√(2).
A quadratic equation is shown below: x2 − 8x 13 = 0 which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers?
a. subtract 5 from both sides of the equation
b. subtract 3 from both sides of the equation
c. add 5 to both sides of the equation
d. add 3 to both sides of the equation
Add 3 to both sides, so you will have
x^2 - 8x + 13 + 3 = 3
x^2 -8x + 16 = 3
And now the left side is a perfect square trinolmial: (x-4)^2.
A rectangular page is designed to contain 64 square inches of print. the margins at the top and bottom of the page are each 1 inch deep. the margins on each side are 1 1/2 inches wide. what should the dimensions of the page be so that the least amount of paper is used.
To find the dimensions of the page that will use the least amount of paper, we need to consider the total area of the page and subtract the area of the margins. Set up an equation to represent the given information and solve for the dimensions of the page.
Explanation:To find the dimensions of the page that will use the least amount of paper, we need to consider the total area of the page and subtract the area of the margins. Let's assume the width of the page is x inches. The total area of the page is then x(x+3) square inches (length times width). The area of the margins at the top and bottom is 2(x+3) square inches (width times depth), and the area of the margins on each side is 3(x) square inches (length times width). We can set up an equation to represent the given information: x(x+3) - 2(x+3) - 3(x) = 64. Simplifying this equation will give us the dimensions of the page that will use the least amount of paper.
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The circumference of a circle is 28 \pi inches, what is the length of the radius of this circle?
Answer: 14 inches
Step-by-step explanation:
We know that the circumference of a circle is given by :_
[tex]\text{Circumference}=2\pi r[/tex], where r is the radius of the circle.
Given : The circumference of a circle [tex]=28\pi\text{ inches}[/tex]
Then , the circumference of the circle is given by :-
[tex]28\pi=2\pi r\\\\\Rightarrow\ r=\dfrac{28}{2}=14[/tex]
Hence, the radius of circle = 14 inches.
What is the area of a parallelogram whose vertices are A(−12, 2) , B(6, 2) , C(−2, −3) , and D(−20, −3)
Final answer:
The area of the parallelogram with the given vertices is calculated using the base and height found from the coordinates, which yields an area of 90 square units.
Explanation:
The student wants to know the area of a parallelogram with given vertices A(-12, 2), B(6, 2), C(-2, -3), and D(-20, -3). To find this area, we can use the distance formula to calculate the lengths of adjacent sides and then find the product of one side's length and the absolute value of the other side's perpendicular height to it. First, we determine the lengths of sides AB and AD which are parallel to the x and y axes, respectively, thereby simplifying our calculations.
Side AB is horizontal, so we can find its length by the difference in x-coordinates: Length of AB = |xB - xA| = |6 - (-12)| = 18 units. Side AD is vertical, so its length is determined by the difference in y-coordinates: Length of AD = |yD - yA| = |(-3) - 2| = 5 units.
The area of the parallelogram is then the product of the base, AB, and the height, AD, which is equal to 18 units * 5 units = 90 square units.
The area of the parallelogram with given vertices is 90 square units, calculated by multiplying the base length AB (18 units) by the height AD (5 units).
Explanation:To find the area of a parallelogram with vertices A(−12, 2), B(6, 2), C(−2, −3), and D(−20, −3), we can calculate the base and the height of the parallelogram. Since points A and B lie on the same horizontal line (they have the same y-coordinate), AB can be considered as the base. To calculate the length of AB, we simply subtract the x-coordinate of A from that of B:
Base AB = xB - xA = 6 - (−12) = 18 units
Points B and C form one of the sides BC of the parallelogram, but because they do not form a vertical line, we cannot directly take BC as the height. Instead, point D has the same x-coordinate as point A which means line AD is vertical, and thus the height can be found by subtracting the y-coordinate of D from that of A:
Height AD = yA - yD = 2 - (−3) = 5 units
The area of a parallelogram is calculated as the product of its base and height:
Area = Base × Height = 18 units × 5 units = 90 square units
Therefore, the area of the parallelogram is 90 square units.
A school had an election where the candidates received votes in the ratio of 1:2:3. If the winning candidate received 210 votes, how many people voted in the election?
The number of people who voted in the election is 420 people
Based on the information given,
Winning candidate = 210 votes
Second candidate = 2 × 210/3 = 140 votes
Last candidate = 1 × 210/3 = 70 votes.
The number of people who voted in the election will be the addition of the total votes and this will be:
= 210 + 140 + 70
= 420 votes
Therefore, from the information given, the number of people who voted in the election is 420 people.
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Which functions have graphs that are steeper than the graph of f(x)=−3x2 ?
Select each correct answer.
j(x)=2x2
m(x)=4x2
g(x)=−4x2
k(x)=3x2
h(x)=−2x2
the answer would be:
g(X)
and
m(X)
it's correct i just did the quiz
Answer:
g(X)
and
m(X)
Step-by-step explanation:
HELP PLS ASAP
Al gets paid semimonthly. His gross pay for each pay period is $750. He has 18% withheld for taxes and 4% withheld for personal deductions. What is the amount of his annual net pay?
A. $7,200
B. $14,040
C. $15,300
D. $15,600
Please explain your answer THANKS
What is 372 rounded to the nearest 100
The number 372 rounded to the nearest 100 would be 400.
When you round a number to a certain digit, you have to check the value of the digit before the place you want to round off to.
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
Here, the question said nearest hundred, so I had to look at the value in the tens place which is 7.
Hence, we round up to the next hundred.
So, we get;
372 rounded to the nearest 100 is 400.
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1 more than two-thirds of a is b
A store sells self-serve frozen yogurt sundaes the function C(w) represents the cost, in dollars, of a sundae weighing w ounces. An appropriate domain for the function would be
A. Integers
B. Rational numbers
C. nonnegative integers
D. nonnegative rational numbers
Answer:
D.Non negtaive rational numbers.
Step-by-step explanation:
Given
A store sells self serve frozen yogurt and weight of yogurt taken in ounces.
The function C(w) represents the cost , in dollars .
The given yogurt can be measured in gram or kilogram or ounces etc.
The quantity of yogurt can not be negative because quantity is always a positive number . So it can not be a negative number
The quantity is defined as the amount of any material or substance .
The quantity is always a positive number . It can not be negative value of a number.
Here, the quantity is taken in ounces so it is a positive number .
The quantity of any material can be natural number or positive rational number .
Hence,the domain for the function C(w) are non negative rational numbers.
An appropriate domain for the function would be non negtaive rational numbers .
Therefore, the correct answer is option D.
Question B please, working out as well please
Find the density function of y = ez , where z ∼ n(µ, σ2). this is called the lognormal density, since log y is normally distributed.
Y = e^2 -> ln y = z [e^2 > 0 -> y > 0]
Fy (y) = P (Y ≤ y)
= P (e^2 £ y)
= P (Z ≤ ln y)
= Fx (ln y)
Differentiating, fy (y) = 1/y fz (ln y)
= 1/y * [(1 / σ sqrt of 2π) e^(1/2 ((ln y - µ)/a)^2)] , y > 0
Which is the required density function of y = e^2
Final answer:
The student needs to find the density function for y = e^z where z is normally distributed. The density function of a normally distributed variable y is determined by its mean (µ) and variance (σ²). Probabilities can be found using a standard normal distribution table, the z-score transformation, and the PDF equation for a normally distributed variable.
Explanation:
The student is asking to find the density function of y = ez, where z follows a normal distribution with mean μ and variance σ2, denoted as z ~ N(μ, σ2). This transformation results in a lognormally distributed variable since the logarithm of y is normally distributed.
The Probability Density Function (PDF) of a normally distributed random variable y is given by the equation:
f(x) = (1/(σ√(2π))) * e-(x-μ)²/2σ²
If z has a standard normal distribution z ~ N(0, 1), you can find the cumulative probability using the cumulative probability distribution function (CDF), also denoted as Φ(z). To find probabilities for z, such as in the case of finding z0.01 = 2.326, you can use a z-table, a calculator, or computer software.
Conversion of x to a z-score is performed using the formula z = (x - μ) / σ. This transformation allows us to use the table for the standard normal distribution to find associated probabilities.
WILL GIVE BRAINLIEST- 20 POINTS
(answers must be right before i pick)
FAST!!
y=-1/2–x + 4
x + 2y=–8
How many solutions does this linear system have?
one solution: (8, 0)
one solution: (0, 8)
no solution
infinite number of solutions
please help
Answer:
No solution.Step-by-step explanation:
Given system of linear equations:
y=-1/2x + 4 and
x + 2y=-8.
Let us convert second equation in slope intercept form too.
x + 2y=-8
Subtracting x from both sides, we get
x -x+ 2y=-8-x
2y = -x-8
Dividing both sides by 2, we get
2y/2 = -x/2-8/2
y = -1/2 x - 4.
Let us find slope and y-intercept of each of the equation.
Slope-intercept form of a linear equation is y = mx+b, where m is the slope and b is y-intercept.
On comparing first equation y=-1/2x + 4 by slope-intercept form y = mx+b slope is -1/2 and y-intercept is 4.
For the second equation y = -1/2 x - 4 slope is -1/2 and y-intercept is -4.
Note: Slopes of both equations are same but y-intercepts are different.So, the lines would be parallel and would not cut at any point.So, the system of equation would not have any solution.Therefore, correct option is 3rd option:
No solution.the temperature at noon was -3 degrees. by 10pm on the same day was the temperature increased by 5.4 . what was the temperature at 10 pm?
show that |3+10|=|3|+|10|
8P + 2 > 3P - 15 can u guys solve please
I need help math please what's the answer
What is the missing leg length of the hypotenuse 23 and the other leg is 11??
The length of a rectangle is 10 feet less then 4 times the width the perimeter is 50 feet. Find the length and the width
In isosceles pqr with base , pq = 2x + 3, and pr = 9x - 11. what is the value of x?