Calculate the discriminant to determine the number of real roots of the quadratic equation y=x^2+3x−10.
A) no real roots
B) three real roots
C) one real root
D) two real roots
Answers
Hello!
x² + 3x - 10
The discriminant Δ is calculate by the formula: b² - 4ac
Δ = b² - 4ac
Δ = 3² - 4 * 1 * (-10) = 9 + 40 = 49
The discriminant is > 0 so there are two real roots.
Related Questions
If a cheetah travels 50 miles per day, how many feet per hour does the cheetah travel?
HELP FAST
Answers
26400 is what they travel in feet in a day divide that by 24 and that should be your answer
Evaluate Expression
Answers
Answer:
72
Step-by-step explanation:
a-3(b) where a=6 and b=-4
6-3(-4)
6(12)
= 72
What is the answer for 9x > 3
Answers
Answer:
X > 1/3
Step-by-step explanation:
Divide 9 by both sides, and you get x>3/9/ This can be simplified to x>1/3/
a coach must choose five starters from a team of 14 players.how many different ways can the coach choose the starters?
Answers
The coach can choose the starters from the team in 2002 in different ways.
How to calculate the number of different ways the coach can choose the starters from a team of 14 players?To calculate the number of different ways the coach can choose the starters from a team of 14 players, we can use the concept of combinations. The order of selection does not matter in this case.
The number of ways to choose a subset of k items from a set of n items is given by the combination formula:
C(n, k) = n! / (k!(n-k)!)
In this scenario, the coach needs to choose 5 starters from a team of 14 players. Therefore, we can calculate the number of ways using the combination formula:
C(14, 5) = 14! / (5!(14-5)!)
= 14! / (5!9!)
= (14 * 13 * 12 * 11 * 10) / (5 * 4 * 3 * 2 * 1)
= 2002
Therefore, the coach can choose the starters from the team in 2002 in different ways.
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Weighted Undirected Graph
Your task is to implement a Graph class, where every node is denoted by a string, and every edge has a weight. The class should allow the weight to be int.
The class should offer a reasonably effective suite of operations, including but not limited to:
Adding and removing nodes and edges.
The Code
You are provided with two files:
graph.h: this includes most of the basic definitions you will need. You should define data structures to represent a weighted undirected graph and implement the functions so that they can work correctly. You may add new includes, classes, functions, and/or variables to the class per your need, as long as they do not interfere with the existing definitions. You must NOT change the class name, template, parameters, or return types of functions.
graph.cpp: this includes a main function. You may write some code to test your data structures and function implementations for the class. This file will not be marked so you can do anything you like with it -- just ensure it does not cause any error. When the "run" button is pressed, it will compile and run main.cpp.
graph.h
#include
using namespace std;
template // the template allows the weight of an edge to take any numeric data type (denoted by T).
//Class of node to keep track of Vertex value and weight
class Graph {
public:
/* define your data structure to represent a weighted undirected graph */
Graph(); // the contructor function.
~Graph(); // the destructor function.
size_t num_vertices(); // returns the total number of vertices in the graph.
size_t num_edges(); // returns the total number of edges in the graph.
void add_vertex(const string&); // adds a vertex to the graph -- every vertex uses a string as its unique identifier.
bool contains(const string&); // checks if a vertex is in the graph -- returns true if the graph contains the given vertex; otherwise, returns false.
vector get_vertices(); // returns a vector of all the vertices in the graph.
void add_edge(const string&, const string&, const T&); // adds a weighted edge to the graph -- the two strings represent the incident vertices; the third parameter represents the edge's weight.
bool adjacent(const string&, const string&); // check if there is an edge between the two vertices in the graph -- returns true if the edge exists; otherwise, returns false.
vector> get_edges(); // returns a vector of all the edges in the graph -- each edge is represented by a pair of vertices incident to the edge.
vector get_neighbours(const string&); // returns a vector of all the vertices, each of which is directly connected with the given vertex by an edge.
}
graph.cpp
#include "graph.hpp"
PLEASE START IMPLEMENTING FUNCTIONS HERE
Graph::Graph() {}
Graph::~Graph() {}
size_t Graph::num_vertices() {
}
size_t Graph::num_edges() {
}
void Graph::add_vertex(const string& u) {
}
bool Graph::contains(const string& u) {
}
vector Graph::get_vertices() {
}
void Graph::add_edge(const string& u, const string& v, const T& weight) {
}
bool Graph::adjacent(const string& u, const string& v) {
}
Graph::get_edges() {
}
vector Graph::get_neighbours(const string& u) {
}
int main() {. //For testing
Graph g;
g.add_vertex("A");
g.add_vertex("B");
g.add_vertex("C");
g.add_vertex("D");
g.add_vertex("E");
g.add_vertex("F");
g.add_edge("A", "B", 7);
g.add_edge("A", "C", 2);
g.add_edge("C", "D", 4);
g.add_edge("C", "E", 8);
g.add_edge("B", "E", 10);
g.add_edge("A", "E", 6);
g.add_edge("B", "C", 3);
g.add_edge("B", "F", 5);
g.add_edge("E", "F", 10);
g.remove_edge("B", "C");
g.remove_vertex("F");
cout << "Number of vertices: " << g.num_vertices() << endl; // should be 5
cout << "Number of edges: " << g.num_edges() << endl; // should be 6
cout << "Is vertex A in the graph? " << g.contains("A") << endl; // should be 1 or true
cout << "Is vertex F in the graph? " << g.contains("F") << endl; // should be 0 or false
}
Answers
The given code provides a basic framework for implementing a Graph class that represents a weighted undirected graph. The class is designed to work with any numeric data type for the edge weights.
It supports operations such as adding and removing nodes and edges, checking for the presence of a vertex, retrieving the list of vertices and edges, and finding neighboring vertices.
To implement the Graph class, you would need to define appropriate data structures to represent the graph, such as adjacency lists or matrices. You can also use a combination of maps and vectors to store the vertices, edges, and their weights. The provided functions in the code, such as the constructor, destructor, and various member functions, should be implemented with the appropriate logic to manipulate and retrieve the graph data.
For testing purposes, the main function in the graph.cpp file demonstrates the usage of the Graph class. It creates a graph, adds vertices, adds weighted edges between them, removes an edge, and removes a vertex. Finally, it performs some queries to test the implemented functionality, such as retrieving the number of vertices and edges, checking if specific vertices exist in the graph, and printing the results.
The given code provides a starting point for implementing a Graph class that represents a weighted undirected graph. By implementing the necessary data structures and logic for the member functions, you can create a functional graph data structure that supports various operations on the graph.
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given the following information, the test statistic is n = 49, xbar= 50, s = 7, h0: m => 52 ha: m < 52 the test statistic for the above information is
Answers
In this scenario, we are given the following information: sample size (n) is 49, sample mean (P) is 50, sample standard deviation (s) is 7, null hypothesis (H₀) states that the population mean (μ) is greater than or equal to 52, and the alternative hypothesis (Hₐ) states that the population mean is less than 52.
The test statistic for this situation is the t-statistic, which measures the difference between the sample mean and the hypothesized population mean, taking into account the sample size and the sample standard deviation. It is used to assess the evidence against the null hypothesis. In this case, since the alternative hypothesis states that the population mean is less than 52, we have a left-tailed test. To calculate the t-statistic, we use the formula:
t = (P - μ) / (s / √n)
Plugging in the given values:
t = (50 - 52) / (7 / √49) = -2 / (7 / 7) = -2
Therefore, the test statistic for the provided information is -2. This value represents the standardized difference between the sample mean and the hypothesized population mean, accounting for the sample size and standard deviation. It indicates that the sample mean is 2 standard deviations below the hypothesized population mean of 52.
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Need help ASAP, will give Brainly!
Answers
Answer:
y=-5x+2
your welcomesss
Explanation:
Slope is negative five, then just add the y intercept
is this rational or irrational?
Answers
Answer:
rational
hope it helps.
I need help asap please
Answers
Answer: x > 7
Step-by-step explanation:
3 + 8x > 59
>> -3 -3
8x > 56
>> ÷8 ÷8
x > 7
A cabinet door is 19 inches tall and 5 inches wide.
What is its area?
Answers
Answer:
95
Step-by-step explanation:
19 x 5 = 95
Intersection of 2 lines form a
Answers
Answer:
i believe that`s called a linear pair. the opposite sides of the lines create matching angles.
IF YOU ANSWER CORRECTLY YOU GET BRAINLYYYYY
Answers
305-22.50= 282.50
hope it helps
how many nonnegative integers can be written of the form a7 * 3^7 a2 * 3^6 where ai {1, 0, -1} amc
Answers
The non negative integers can be written of the form is 3281.
Given:
a7 * 3^7 a2 * 3^6 where ai {1, 0, -1}.
ai = 7,6,5,4,3,2,1,0
Total = 8
= \(3^{8}\) = 6561
= 6561 - 1 /2
= 6560/2
= 3280 is negative integers
Non negative or positive integers = 6561 - 3280 = 3281
Therefore the non negative integers can be written of the form is 3281.
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(3ab - 6a)^2 is the same as
2(3ab - 6a)
True or false?
Answers
False. The expression \((3ab - 6a)^2\) is not the same as 2(3ab - 6a).
The expression\((3ab - 6a)^2\) is not the same as 2(3ab - 6a).
To simplify \((3ab - 6a)^2\), we need to apply the exponent of 2 to the entire expression. This means we have to multiply the expression by itself.
\((3ab - 6a)^2 = (3ab - 6a)(3ab - 6a)\)
Using the distributive property, we can expand this expression:
\((3ab - 6a)(3ab - 6a) = 9a^2b^2 - 18ab^2a + 18a^2b - 36a^2\)
Simplifying further, we can combine like terms:
\(9a^2b^2 - 18ab^2a + 18a^2b - 36a^2 = 9a^2b^2 - 18ab(a - 2b) + 18a^2b - 36a^2\)
The correct simplified form of \((3ab - 6a)^2 is 9a^2b^2 - 18ab(a - 2b) + 18a^2b - 36a^2\).
The statement that\((3ab - 6a)^2\) is the same as 2(3ab - 6a) is false.
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Sasha needs to write a division expression for the fraction 9/14. She is not sure which number goes where. Help Sasha understand how to write a division expression from a fraction
Answers
To write a division expression from a fraction, identify the numerator, which is the dividend, while the denominator is the divisor.
What is a division expression?A division expression is an algebraic expression using the division operand (÷).
Algebraic expressions involve the combination of numbers, constants, values, and variables with mathematical operands.
The result of a division operation, which is one of the four basic mathematical operations, is known as the quotient.
Thus, we can conclude that the dividend is related to the numerator of the fraction just as the divisor is related to the denominator of the fraction.
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10. What is the length of
side a?
2
2.9.
36 cm
15cm
39 cm
a
Answers
Answer:
the answer is a=15cm
Step-by-step explanation:
c²=a²+b²
where c=Hypothenuse,a=adjacent, b=opposite
a²=c²-b²
a²=39²-36²
a²=1521-1296
a²=225
take Square root of both sides
a=15cm
a large mixing tank currently contains 100 gallons of water into which 5 pounds of sugar have been mixed . A tap will open pouring 10 gallons per minute of water into the tank at the same time sugar is poured into the tank at a rate of 1 pound per minute. Find the concentration ( pounds per gallon) of sugar in the tank after 12 minutes
Answers
After 12 minutes, the concentration of sugar in the tank is approximately 0.0773 pounds per gallon.
To find the concentration of sugar in the tank after 12 minutes, we need to consider the amount of sugar and water added during that time period.
The tank initially contains 100 gallons of water with 5 pounds of sugar mixed in. Over the course of 12 minutes, the tap pours in 10 gallons per minute of water and 1 pound per minute of sugar.
After 12 minutes, the total amount of water added is 10 gallons/minute * 12 minutes = 120 gallons. The total amount of sugar added is 1 pound/minute * 12 minutes = 12 pounds.
Therefore, the final volume of water in the tank is 100 gallons (initial) + 120 gallons (added) = 220 gallons.
To find the concentration of sugar in the tank after 12 minutes, we divide the total amount of sugar (5 pounds initial + 12 pounds added) by the final volume of water (220 gallons):
Concentration of sugar = (Total amount of sugar) / (Final volume of water)
= (5 pounds + 12 pounds) / 220 gallons
= 17 pounds / 220 gallons
Simplifying the expression, we get:
Concentration of sugar = 0.0773 pounds/gallon
Therefore, after 12 minutes, the concentration of sugar in the tank is approximately 0.0773 pounds per gallon.
It's important to note that in this scenario, we assume perfect mixing of the sugar and water in the tank. Also, the concentration of sugar may vary over time as more water and sugar are added.
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I need help asap with thissssssssssss
Answers
Answer:
D
Step-by-step explanation:
The domain is the x value which in this case would be the hours of training
Two equations are shown: I will give 40 pts if someone answers
Equation 1: (x – 12) = 12
Solve each equation.
Answers
Answer:
x and y both equal 24
what is the average size of a customer's bill at a restaurant that earns daily $3,250 for the meals that it sells to 200 customers? $32.50 $20.00 $16.25 $15.84
Answers
The average size of a customer's bill at a restaurant that earns daily $3,250 for the meals that it sells to 200 customers is $16.25. Therefore, the right answer is option (c).
The average or mean is calculated by taking the ratio of the total sum of the outcomes of an event to the frequency or the number of times the event occurs.
It can be written as \(\frac{n_1+n_2+.....+n_a}{a}\).
In the given question, the sum of the customer bill is given as $3,250.
And the number of customers served is given to be 200.
Therefore, the average size of a customer's bill is calculated by \(\frac{3250}{200}\)
Which turns out to be $16.25.
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The answer is $16.25. To find the average size of a customer's bill, you would divide the total earnings by the number of customers.
$3,250 / 200 customers = $16.25 per customer.
To find the average size of a customer's bill at the restaurant, you need to divide the total daily earnings by the number of customers. Here's a step-by-step explanation:
1. The restaurant earns $3,250 daily from the meals it sells.
2. The restaurant serves 200 customers daily.
Now, calculate the average bill size:
3. Divide the total daily earnings ($3,250) by the number of customers (200).
$3,250 ÷ 200 = $16.25
The average size of a customer's bill at the restaurant is $16.25.
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The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary)
15, 30, 60,...
Find the 6th term.
Answers
Answer:
960
Step-by-step explanation:
60× 2
120×2
240×2
480 ×2 = 960
The average of a sample of high daily temperature in a desert is 114 degrees F, a sample standard deviation or 5 degrees F, and 26 days were sampled. What is the 90% confidence interval for the average temperature? Please state your answer in a complete sentence, using language relevant to this question.
Answers
In a sample of 26 days from the desert, the average of the high daily temperature is 114 degrees F, and the sample standard deviation is 5 degrees F.
To determine the 90% confidence interval for the average temperature, we can use the t-distribution as follows:To find the critical value of t, we can use the t-table. Since our sample has n = 26, the degrees of freedom (df) are n - 1 = 25. At a confidence level of 90%, with 25 degrees of freedom, the critical t-value is 1.708.The standard error of the mean is calculated as s / sqrt(n), where s is the sample standard deviation and n is the sample size. Therefore, the 90% confidence interval for the average temperature is (114 - 1.67, 114 + 1.67), or (112.33, 115.67) degrees F.
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i need help with this one! asap please!
Answers
Answer:
D. 60
Step-by-step explanation:
Height = constant / width
30 = c / 2
2* 30 = 60
c = 60
12 = c / 5
12 * 5 = 60
c = 60
10 = c / 6
10 * 6 = 60
c = 60
Simplify.
3(x + 4) plzzz answer
Answers
Answer:
3x+12
Step-by-step explanation:
When we multipy 3 with (x+4) it becomes 3x+12
Answer:
3x+12
Step-by-step explanation:
3(x+4)
3*x=3.....keep the x with 3 because x just represents 1
3*4=12
so your answer should be
3x+12
hope this helps :)
a rectangular garden has a length that is twice its width. the dimensions are increased so that the perimeter is doubled and the new shape is a square with an area of 3600 square feet. what was the area of the original garden, in square feet?
Answers
The area of the original garden is 7200 square feet.
Given,
a rectangular garden has a length that is twice its width. the dimensions are increased so that the perimeter is doubled and the new shape is a square with an area of 3600 square feet.
we are asked to determine the area of the original garden = ?
let the width be x
and the length be 2x
area of the square = 3600 sq feet
Perimeter of the rectangle = 2(l+b)
⇒ 2(2x+x)
⇒ 2(3x)=6x
area of square = a²
a² = 3600
a = √3600
a = 60
now we get the width = 60
length = 2(60)
= 120
Now calculate the area of the rectangle:
= l×b
= 60 × 120
= 7200
hence we get the area as 7200 square feet.
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what percentage of variation is explained by the regression line
Answers
The coefficient of determination is 0.233, then 23.3% of the variation in the data about the regression line is explained.
The coefficient of determination, represented by R2, is a measure of how much of the variation in the data is explained by the regression line. It is calculated by squaring the correlation coefficient, R.
If the coefficient of determination is 0.233, then the percentage of the variation in the data about the regression line that is explained is 23.3%. This is calculated by multiplying the coefficient of determination by 100 to convert it to a percentage.
In other words, 23.3% of the variation in the data is explained by the regression line, and the remaining 76.7% of the variation is unexplained.
It is important to note that the coefficient of determination does not indicate causation, but rather the strength of the relationship between the independent and dependent variables.
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Complete question is below
if the coefficient of determination is 0.233, what percentage of the variation in the data about the regression line is explained?
The percentage of variation explained by the regression line is measured by the coefficient of determination (R-squared).
In regression analysis, the coefficient of determination (R-squared) is used to measure the percentage of variation in the dependent variable that is explained by the regression line.
R-squared ranges from 0 to 1, where 0 indicates that the regression line explains none of the variation and 1 indicates that the regression line explains all of the variation. It is a measure of how well the regression line fits the data points.
For example, if the R-squared value is 0.75, it means that 75% of the variation in the dependent variable is explained by the regression line, while the remaining 25% is unexplained.
Therefore, the percentage of variation explained by the regression line can be determined by the R-squared value.
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See screenshot below.
Answers
Using system of linear equations he will require 20kg of 15% copper and 30kg of 70% copper to produce an alloy of 48% in 50kg
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables.
To solve this problem, we need to write a system of linear equations and find the equivalent amount of the metal required to make the desired amount of the alloy.
0.15x + 0.7y = 0.48(50) ..eq(i)
0.15x + 0.7y = 24 ...eq(i)
x + y = 50 ...eq(ii)
solving equation (i) and (ii)
x = 20, y = 30
He needs 20kg of 15% copper and 30kg of 70% copper to get 48% of 50kg of alloy.
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Eiko is wearing a magic ring that increases the power of her healing spell by 30 % 30%30, percent. Without the ring, her healing spell restores � HH health points. Which of the following expressions could represent how many health points the spell restores when Eiko is wearing the magic ring?
Answers
The expression 1.3H represents the relationship between the number of health points restored by Eiko's healing spell with and without the magic ring.
H represents the number of health points restored by the spell without the ring. The expression 0.3H represents the additional 30% increase in the power of the spell due to the magic ring, as the ring increases the spell's power by 30%.
Adding the two, H + 0.3H, gives us the total number of health points restored by the spell with the magic ring, which is equal to 1.3 times the number of health points restored by the spell without the ring.
So, when Eiko is wearing the magic ring, her healing spell restores 1.3 times as many health points as without the ring, represented by the expression 1.3H.
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A thick cable, 60 ft long and weighing 180 lb, hangs from a winch on a crane. Compute in two different ways the work done if the winch winds up 25 ft of the cable.
Write a function for the weight of the remaining cable after x feet has been wound up by the winch.
Estimate the amount of work done when the winch pulls up Δx ft of cable.
Answers
To compute the work done when the winch winds up 25 ft of the cable, we can use two different methods: the work-energy principle and the integral of force.
Method 1: Work-Energy Principle
The work done is equal to the change in potential energy. In this case, the potential energy is due to the weight of the cable. The formula for potential energy is PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the change in height.
Given:
Length of the cable (h) = 60 ft
Weight of the cable (m) = 180 lb
Change in height (Δh) = 25 ft
Using the formula, the work done is:
Work = PE = mgh = (180 lb)(32.2 ft/s^2)(25 ft)
Method 2: Integral of Force
The work done can also be calculated by integrating the force over the distance. The force acting on the cable is equal to its weight.
Given:
Weight of the cable (w) = 180 lb
Change in length (Δx) = 25 ft
To write a function for the weight of the remaining cable after x feet has been wound up by the winch, we can express it as a linear function. The weight of the cable is proportional to the length remaining. Let's assume the initial length of the cable is L ft.
Weight of remaining cable = w - (w/L) * x
To estimate the amount of work done when the winch pulls up Δx ft of cable, we can use the integral of force formula:
Work = ∫(w - (w/L) * x) dx
Integrating this expression over the interval [0, Δx] will give us an estimation of the work done.
Please note that numerical values are needed to provide a specific estimation of the work done when Δx ft of cable is pulled up.
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Consider the following data for a dependent variable y and two independent variables, x1 and x2 ; for these data SST = 15,128.4, and SSR = 14,141.7.
x 1 x 2 y
29 13 95
46 10 109
24 18 112
51 16 179
41 5 94
51 19 176
75 8 170
36 13 118
59 13 142
76 16 211
Round your answers to three decimal places.
a. Compute R2 .
b. Compute Ra 2 .
c. Does the estimated regression equation explain a large amount of the variability in the data?
SelectYesNoItem 3
Answers
Based on the equation in the question , the R2 would be 0.934.
To compute R2, we need to use the formula:
R2 = SSR / SST
Given that SSR = 14,141.7 and
SST = 15,128.4,
We can substitute these values into the formula:
R2 = 14,141.7 / 15,128.4
R2 ≈ 0.934
b. To compute Ra2, we need to subtract R2 from 1:
Ra2 = 1 - R2
Substituting the value of R2 we calculated in part a:
Ra2 ≈ 1 - 0.934
Ra2 ≈ 0.066
c. A large R2 value indicates that the estimated regression equation explains a large amount of the variability in the data.
In this case, R2 is approximately 0.934, which means that the estimated regression equation explains about 93.4% of the variability in the data.
So, the answer is "Yes".
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