Answers
All the intersection points are determined as (-65, 0, 3.48).
What are the intersection points?To find the intersection points of the two given functions, we can set them equal to each other and solve for the values of x and y that satisfy the equation.
Setting y = 3x² + x - 10 equal to y = x³ + 6x² + d, we get:
3x² + x - 10 = x³ + 6x² + d
Rearranging this equation, we get:
x³ + 3x² - x + d - 10 = 0 ...........(1)
Now, since we are given that the two graphs intersect at x = -5, we can substitute x = -5 into equation (1) to find the value of d.
Substituting x = -5 into equation (1), we get:
(-5)³ + 3(-5)² - (-5) + d - 10 = 0
-125 + 3(25) + 5 + d - 10 = 0
75 + d - 10 = 0
65 + d = 0
d = -65
So the value of d is -65.
Now that we have the value of d, we can substitute it back into equation (1) to find the other intersection points.
Substituting d = -65 into equation (1), we get:
x³ + 3x² - x - 75 = 0 ...........(2)
Solve equation (2), using graphing system.
roots = (3.48, 0)
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Related Questions
Nick's new home had a purchase price of $145,500. He got a 30-year fixed mortgage for 75% of the purchase price. The interest rate on the loan is 3.15%. What is his monthly payment?
Answers
Nick's monthly mortgage payment is $482.16.
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To calculate Nick's monthly mortgage payment, we first need to find out the amount he borrowed from the bank, which is 75% of the purchase price:
$145,500 x 0.75 = $109,125
Next, we need to calculate the monthly interest rate. We can do this by dividing the annual interest rate (3.15%) by 12:
3.15% / 12 = 0.002625
Now we can use the following formula to calculate Nick's monthly payment:
M = P [ [tex]i(1 + i)^{n}[/tex] ] / [ [tex](1 + i)^{n}[/tex] – 1]
Where:
M = Monthly payment
P = Loan amount (principal)
i = Monthly interest rate
n = Number of payments (in months)
Plugging in the values we have:
M = $109,125 [ 0.002625 [tex](1 + 0.002625)^{360}[/tex] ] / [ [tex](1 + 0.002625)^{360}[/tex] – 1]
M = $482.16
Therefore, Nick's monthly mortgage payment is $482.16.
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3. Choose the best answer.
The ABC Ad Agency has two automotive tire chains as clients. This could lead to a(n)
A)conflict of interest
B)defect
C)stereotype
D)overworked staff
Answers
The correct option - A) conflict of interest is caused due to ABC Ad Agency has two automotive tire chains as clients.
Explain about the conflict of interest:A conflict of interest arises when a person's personal interests, such as those related to their family, friends, finances, or social standing, potentially impair their judgement, choices, or actions at work. Conflicts of interest are taken seriously enough by government organisations that they are governed.
Conflicts of interest happen most frequently when requirements and interests collide. Because of the nature of connections against policies of organisations or regulations of the federal and state levels, various forms of conflicts of interest may arise. Humans are prone to prejudice (having an unfair preference) due to trivial considerations like friendship, food, or flattery. They can also be persuaded to make a choice by the prospect of gaining money, status, or power.For the given data- The ABC Ad Agency has two automotive tire chains as clients.
This, could lead to a(n) conflict of interest.
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When two sample means are significantly different
Group of answer choices
The pooled variance estimate should not be used
The difference is too great to attribute to chance
The corresponding population means are significantly different
The difference is of practical importance
Answers
When two sample means are significantly different, "the difference is too great to attribute to chance".
What is statistical significance?The likelihood of finding a difference between two samples (such means or proportions) through pure chance is known as statistical significance. The likelihood of obtaining the observed difference if there were no actual difference between the associated population parameters is calculated to ascertain this. The difference is deemed statistically significant if the p-value is below a predetermined cutoff (often 0.05).
Significant difference between two sample means indicates that the likelihood of such a difference occurring by chance alone is low. If there is a true difference between the matching population means from which the samples were selected, it shows that the difference between the sample means is too large to be explained by chance.
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How does examining the answers to a question help you determine if the question is a statistical question?
Answers
As a statistical question is one that can be addressed using statistical methods or analysis, looking at the responses to a question can help identify whether it is a statistical question.
In order to provide a response to a question regarding a population or sample, statistical inquiries typically entail gathering and evaluating data. Consequently, a statistical question's responses would require some sort of data analysis or interpretation.
As a result, we can tell if a question is statistical by looking at the replies and seeing if it requires the use of statistical techniques and data analysis to answer.
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Find the gradients of lines A and B
Answers
The correct answer is (1,1) because both of the lines meet together at these numbers
simplify [Xn (X'nY)]'.
Answers
Answer:
(X'U'Y) + (XUY')
Step-by-step explanation:
Starting with [Xn(X'nY)]', we can use De Morgan's laws to simplify the expression:
[Xn(X'nY)]' = (Xn)' + (X'nY)'
Recall that Xn represents the logical operator "and", while X' represents "not X". Using these definitions, we can expand the expression:
(Xn)' + (X'nY)' = (X'U'Y) + (XUY')
where U represents the logical operator "or".
Therefore, [Xn(X'nY)]' simplifies to (X'U'Y) + (XUY').
A principal of $1500 is invested at 8.5% interest, compounded annually.
How much will the investment be worth after 14 years?
Use the calculator provided and round your answer to the nearest dollar.
Answers
The investment will be worth approximately $4468 after 14 years.
What is annual interest rate?Annual interest rate is the rate at which an investment or loan grows in value over the course of a year, expressed as a percentage. It represents the cost of borrowing or the return on investment over one year.
According to question:The following equation can be used to determine the future value of an investment using compound interest:
FV = P * (r/n + 1)(n*t)
Where:
FV is the investment's future value.
The principal is P. (initial investment)
The annual interest rate is represented by r,
The number of times the interest is compounded annually by n (expressed as a decimal).
t is the time (in years)
In this case:
P = $1500
r = 8.5% = 0.085
n = 1 (compounded annually)
t = 14
With these values entered into the formula, we obtain:
FV = 1500 * [tex](1 + 0.085/1)^(1*14)[/tex]
= $4467.56
Therefore, the investment will be worth approximately $4468 after 14 years.
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Graph the linear equation
5x -6y = 30 by following these steps:
Step 1: Find the x-intercept. Let y = 0 and solve for x.
x=
Answers
Answer:
Substitute 0 for the value of x and y.
5x - 6y = 30
5x - 6(0) = 30
5x = 30
The x-intercept is 6.
x = 6
(6, 0)
5x - 6y = 30
5(0) - 6y = 30
-6y = 30
y = -5
The y-intercept is -5.
(0, -5)
(The graph is in the picture)
Which function represents the inverse of function f?
= 3x + 5
O A. T (2)
O B.
O c.
O D.
=-3x - 5
x+ //
– ž
g(x) =
p(x) =
8(x) = 3z +5
x
Answers
The inverse function of f(x) = 3x + 5 is given as follows:
C. p(x) = 1/3x - 5/3.
How to obtain the inverse function?The function in the context of this problem is defined as follows:
f(x) = 3x + 5.
To obtain the inverse function, first we must exchange the variables x and y, hence:
y = 3x + 5
x = 3y + 5.
Now we must isolate the variable y, hence:
3y = x - 5
y = (x - 5)/3.
p(x) = 1/3x - 5/3.
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A baseball team has the starting and relief pitchers shown in the table. The manager selects a pitcher at random. Find the probability that the pitcher is left-handed.
Pitchers on Baseball Team (Table)
Pitchers Number
Left-handed starters 1
Right-handed starters 4
Left-handed relievers 2
Right-handed relievers 1
Answers
Okay, here are the steps to find the probability the randomly selected pitcher is left-handed:
1) There are 1 left-handed starter, 4 right-handed starters, 2 left-handed relievers and 1 right-handed reliever.
2) In total, there are 1 + 4 + 2 + 1 = 8 pitchers.
3) Of the 8 pitchers, 1 + 2 = 3 are left-handed.
4) So the probability the randomly selected pitcher is left-handed = (3/8) = 3/8 = 0.375
Therefore, the probability that the randomly selected pitcher from the team is left-handed is 0.375.
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NEED ASAP PLSS
The average weight per adult is 150 pounds, and the average weight per child is 40 pounds. Write an equation for the number of adults A and the number of children C the elevator can hold.
Answers
Let's assume that the elevator has a weight capacity of W pounds.
We can set up two equations to represent the number of adults (A) and the number of children (C) the elevator can hold:
Averaged weight per adult * Number of adults + Averaged weight per child * Number of children ≤ Weight capacity of the elevator
Using the given values, we can substitute:
150A + 40C ≤ W
This equation represents the weight limit of the elevator, where the sum of the weight of all adults and children inside the elevator cannot exceed W.
14. Type the correct answer in each box.
Answers
A41 represents the element at the line 4 and column 1, which is the same for B41.
When two matrices are added or subtract, we add or subtract the elements at the same position.
The elements are:
A41 = 7.B41 = 2.Hence:
(A - B)41 = 7 - 2 = 5.(A + B)41 = 7 + 2 = 9.When a matrix is multiplied by a constant, each element is multiplied by a constant, hence:
c41 = -3 x 5 = -15.d41 = -3 x 9 = -27.More can be learned about operations with matrices at https://brainly.com/question/16901354
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Différenciation implicit function containing product and quotient. d/dx (2y/5x)
Answers
Answer:
To differentiate the given expression, we will need to use both the product rule and the quotient rule.
Let's first rewrite the expression using the reciprocal identity for x:
2y/5x = 2y * (5x)^(-1)
Now we can use the product rule and the quotient rule to find the derivative with respect to x:
d/dx [2y * (5x)^(-1)] = 2y * d/dx[(5x)^(-1)] + (5x)^(-1) * d/dx[2y]
Using the chain rule, we can find the derivative of (5x)^(-1) with respect to x:
d/dx[(5x)^(-1)] = -1/(5x)^2 * 5 * (dx/dx)
d/dx[(5x)^(-1)] = -1/(5x)^2
Using the chain rule again, we can find the derivative of 2y with respect to x:
d/dx[2y] = 2 * (dy/dx)
Substituting these expressions back into the original equation, we get:
d/dx [2y/5x] = 2y * (-1/(5x)^2) + (5x)^(-1) * 2 * (dy/dx)
Simplifying this expression, we get:
d/dx [2y/5x] = -2y/(5x)^2 + 2/(5x) * (dy/dx)
Therefore, the derivative of 2y/5x with respect to x is -2y/(5x)^2 + 2/(5x) * (dy/dx).
