Sister's age will be equal to 12 and Kim's age is 24.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Consider that x is sister's age, Kim's age is twice that of her sister
Thus Kim's age = 2x
Kim’s age + Sister’s age = 36
The equation:
x + 2x = 36
Now solve the equation;
x + 2x = 36
3x = 36
x = 36 / 3
x = 12
Therefore, Kim's age = 2x = 2(12) = 24
Hence, Sister's age is 12 and Kim's age is 24.
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given a binary-class classification problem in which the class labels are binary, the dimension of feature is d, and each attribute can take k different values. please provide the numbers of parameters to be estimated with and without the simplifying assumption. please explain your answer. briefly justify why the simplifying assumption is necessary.
For binary class classification, assumptions are necessary in a way:
Given that
From Boyer Naive classifier,
We evaluate (ai | vj) is given below
(ai | vj) = n(e) + m(p) / n + m
Here,
m = equivalent sample size
n(e) = number of training examples
for which v = vj and a = ai
n(i) = number of training example for which v = vj
P = a prior estimate for P(ai | vj)
Here, we calculate that
P(SUV | yes), P(Red | yes), P(Domestic | yes)
P(SUV | no), P(Red | no), P(Domestic | no)
We evaluating this value like
yes:
RED : SUV: DOMESTIC:
n = 5 n = 5 n = 5
n(c) = 3 n(c) = 1 n(c) = 2
P = 0.5 P = 0.5 P = 0.5
m = 3 m = 3 m = 3
Therefore, with the above calculation we can justify that the simplifying assumptions are necessary in a binary class classification.
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The population of Kingsfield grew from 7,500 to 9,000
in one year. During the same time the population of
Queensville dropped from 32,000 to 25,600. Let the
original populations represent year 1. If these percentage
rates of decline and growth continue, during what year will
Kingsfield have a larger population than Queensville?
The time that it will take for Kingsfield to have a larger population than Queensville is given as follows:
3.58 years.
How to model the populations?The rates of decline and growth are constant, meaning that the populations for each town are modeled by exponential functions.
The rates for each town are given as follows:
Kingsfield: 9000/7500 = 1.2.Queensville: 25600/32000 = 0.8.Considering the initial population, the exponential functions for the population of each town after t years are given as follows:
Kingsfield: y = 7500(1.2)^t.Queensville: y = 32000(0.8)^t.Kingsfield will have a larger population than Queensville when:
[tex]7500(1.2)^t > 32000(0.8)^t[/tex]
Hence:
[tex]\left(\frac{1.2}{0.8}\right)^t > \frac{32000}{7500}[/tex]
(1.5)^t > 4.27
tlog(1.5) > log(4.27)
t > log(4.27)/log(1.5)
t > 3.58 years.
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in three to five sentences explain your understanding of the algorithm express the algorithm in either detailed pseudocode or in program code establish the running time complexity of the algorithm by explaining how you arrived at it.
An algorithm for navigating or searching through tree or graph data structures is called depth-first search. The algorithm begins at the root node (choosing an arbitrary node to serve as the root node in the case of a graph) and proceeds to investigate each branch as far as it can go before turning around.
Thus, the basic concept is to begin at the root or any other random node, mark that node, then advance to the next nearby node that is not marked. This process is repeated until there are no more adjacent nodes that are unmarked. Then go back and look for more unmarked nodes to cross. Print the path's nodes lastly.
To solve the issue, adhere to the instructions listed below:
Make a recursive function that accepts a visited array and the node's index.
STEP -1
// C++ program to print DFS traversal from
// a given vertex in a given graph
#include <bits/stdc++.h>
using namespace std;
// Graph class represents a directed graph
// using adjacency list representation
class Graph {
public:
map<int, bool> visited;
map<int, list<int> > adj;
// function to add an edge to graph
void addEdge(int v, int w);
// DFS traversal of the vertices
// reachable from v
void DFS(int v);
};
void Graph::addEdge(int v, int w){
adj[v].push_back(w); // Add w to v’s list.}
void Graph::DFS(int v)
{
// Mark the current node as visited and
// print it
visited[v] = true;
cout << v << " ";
// Recur for all the vertices adjacent
// to this vertex
list<int>::iterator i;
for (i = adj[v].begin(); i != adj[v].end(); ++i)
if (!visited[*i])
DFS(*i);
}
// Driver's code
int main()
{
// Create a graph given in the above diagram
Graph g;
g.addEdge(0, 1);
g.addEdge(0, 2);
g.addEdge(1, 2);
g.addEdge(2, 0);
g.addEdge(2, 3);
g.addEdge(3, 3);
cout << "Following is Depth First Traversal"
" (starting from vertex 2) \n";
// Function call
g.DFS(2);
return 0;
STEP- 2
Time complexity: O(V + E), where V is the number of vertices and E is the number of edges in the graph.
Auxiliary Space: O(V), since an extra visited array of size V is required.
Pseudocode:
Depth_First_Search(matrix[ ][ ] ,source_node, visited, value)
{
If ( sourcce_node == value)
return true // we found the value
visited[source_node] = True
for node in matrix[source_node]:
If visited [ node ] == false
Depth_first_search ( matrix, node, visited)
end if
end for
return false //If it gets to this point, it means that all nodes have been explored.
//And we haven't located the value yet.
}
final answer-
A tree data structure or a graph's vertices can be searched using a recursive technique called t. Beginning with the first node of graph G, the depth-first search (DFS) algorithm digs down until it reaches the target node, also known as the node with no children.
The DFS method can be implemented using a stack data structure due to its recursive nature. The DFS algorithm implementation procedure is comparable to that of the BFS algorithm.
The following describes how to implement DFS traversal step-by-step. -
Create a stack with all of the graph's vertices in it first.
Select whatever vertex you want to use as the first vertex in the traverse, and add it to the stack.
uses for the DFS algorithm
The following list of uses for the DFS algorithm includes:
The topological sorting can be implemented using the DFS algorithm.
It can be applied to determine the routes connecting two vertices.
It can also be used to find graph cycles.
DFS technique is also applied to puzzles with a single solution.
If a graph is bipartite or not, it can be determined using DFS.
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if ride cast birr 50 to pick up and 10 birr per km how much you go with birr1350
The distance the ride will go for birr 1350 is 130 kilometres.
How to find the distance the ride can go base on the amount?The ride cost birr 50 to pick up and 10 birr per km. The distance you can go with birr 1350 can be calculated as follows;
Let's use equation to represent the total amount spent on the distance covered.
Therefore,
let
x = total distance travelled in kilometresy = total amount in birrHence,
y = 50 + 10x
Therefore,
where
y = 1350
y = 50 + 10x
1350 = 50 + 10x
1350 - 50 = 10x
1300 = 10x
divide both sides by 10
x = 1300 / 10
x = 130 km
Therefore, the ride will go 130 km.
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The members of the senior class are planning a dance. They use the equation r=p n to determine the total receipts. What is n expressed in terms of r and p ?
1) n=r+p
2) n=r-p
3) n={p}/{r}
4) n={r}/{p}
1)
2)
3)
4)
The n expressed in terms of r and p is n=r/p.
How to solve the word problems?
Systems of linear equations must be used to solve some word problems. Here are some hints to help you determine when you need to create a system of linear equations in a word problem:
There are two separate numbers at play, such as the total number of adults and children, the total number of large boxes and little boxes, etc.Each quantity has a value attached to it, such as the cost of an adult or kid ticket, the number of products in a large box as compared to a small box, etc.You must frequently create two distinct linear equations in two variables in order to solve these issues.
So, it is expressed as:
r=pn
n=r/p
Hence, The n expressed in terms of r and p is n=r/p.
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what is the square root of -75 in simplified form
Answer:
5[tex]\sqrt{3}[/tex]i
Step-by-step explanation:
[tex]\sqrt{-5(5)(3)}[/tex] You can pull out a 5 and you are left with [tex]\sqrt{-1}[/tex] and [tex]\sqrt{3}[/tex].
The [tex]\sqrt{-1}[/tex] = 1
5[tex]\sqrt{3}[/tex] i
Answer: [tex]5\sqrt{3} i[/tex]
Step-by-step explanation:
The square root of -75 is not a real number, because it is not possible to find a real number that when squared results in a negative number.
In mathematics, the square root of a number is defined as the number that, when multiplied by itself, equals the original number. For example, the square root of 4 is 2, because 2 x 2 = 4. Similarly, the square root of 9 is 3, because 3 x 3 = 9.
However, it is not possible to find a real number that, when squared, results in a negative number. This is because any real number multiplied by itself is always positive, regardless of whether the original number was positive or negative. For example, the square of -2 is 4, because (-2) × (-2) = 4, which is a positive number.
Double however, complex numbers are used to represent numbers that have a non-zero imaginary component, such as the square root of -1. Complex numbers are written in the form a + bi, where a and b are real numbers and i represents the imaginary unit.
Therefore, the square root of -75 can be written in simplified form as [tex]5\sqrt{3} i[/tex], where [tex]i[/tex] is the imaginary unit. This represents a complex number with a real component of 0 and an imaginary component of [tex]5\sqrt{3}[/tex].
5. You use a line of best fit for a set of data to make a prediction about an unknown value. The
correlation coefficient for your data set is -0.993. How confident can you be that your
predicted value will be reasonably close to the actual value?
Answer: The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of -0.993 indicates a very strong negative relationship, which means that as one variable increases, the other variable decreases. This suggests that you can be quite confident that your predicted value will be reasonably close to the actual value.
A study is conducted to estimate the average difference in the cost of analyzing data using two different statistical packages. To do so, 15 data sets are used. Each is analyzed by each package, and the cost of the analysis is recorded. These observations result: (a) Find the set of difference scores subtracting in the order package I minus package II. (b) Find d and Sd(c) Find a 90% confidence interval on the mean difference in the cost of running a data analysis using the two packages.
The null hypothesis cannot be rejected.
Given that,
A study is done to determine the average cost difference between utilizing two different statistical tools to analyze data. 15 data sets are used to do this. Each program performs an analysis on each, and the cost of the analysis is noted.
To test if cost is same, we test mean difference of scores =0
H0: d=0
H0: d != 0
z0 = 0-(-05467) / 0.039976
= 1.367
z score for alpha = .05 is 1.96
Since, z0 < z score, we cannot reject the null hypotheses
Therefore, the null hypothesis cannot be rejected.
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The triangle and the rectangle below have the same area.
Calculate the value of w.
Show your working.
Answer:5 cm
Step-by-step explanation:
Answer: w=2.5cm
Step-by-step explanation:
when solving for a right triangle, you need to to the length multiplied by the width and then divided by two. You then get (6*5)/2=30/2=15.
When solving for a rectangle, it’s the same, but without dividing by two. But you need them to be equal, and you already have the measure six.
So 5/2=2.5 therefore w=2.5cm.
PLEASE HELP MEE!!
What is the inverse of the function shown?
The inverse of the function shown is (x + 5).
What is the inverse of the function?
A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as "[tex]f^{-1}[/tex]" or "[tex]F^{-1}[/tex]." Here, (-1) should not be confused with an exponent or a reciprocal.
Coordinates of the given line are (8,3) and (-2,-7)
The function of the given graph for two points form is
[tex]y-y_{1} = \frac{y_{2}-y_{1} }{x_{2} -x_{1}} (x-x_{1} )[/tex]
or, [tex]y-3 = \frac{-7-3 }{-2-8} (x-8 )[/tex]
or, y - 3 = x - 8
or, y = x -8 + 3 = x - 5
y = x - 5
To find the inverse, replace x with y and y with x then, we get
x = y - 5
y = x + 5
[tex]f^{-1}[/tex] = x + 5
Hence, the inverse of the function shown is (x + 5).
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A salesperson works at a car dealership and earns $20 per hour plus a $100 bonus for each car sold. The salesperson sells 8 cars and earns a minimum of $1,400 this week.
Which inequality represents the possible number of hours, x, the salesperson works this week?
Responses
100x+20≥1,400, where x≥13.8
100 x + 20 ≥ ≥ 1 , 400 , where x ≥ ≥ 13.8
100x+20≤1,400, where x≤13.8
100 x + 20 ≤ ≤ 1 , 400 , where x ≤ ≤ 13.8
20x+800≥1,400, where x≥30
20 x + 800 ≥ ≥ 1 , 400 , where x ≥ ≥ 30
20x+800≤1,400, where x≤30
The inequality which represents the possible number of hours , x, the salesperson works this week is 20x + 800 ≥ 1400 where x ≥ 30,
using equation formation steps.
What is an equation ?
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
For instance, 3x + 5 = 14 is an equation.
Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
In given que,
minimum earning = $1400
The possible number of hours = x
No. of cars sold = 8
Price earned by sold cars = $800
Price earned per hour =$20
Price earned for x hours = $20x
So, the total amount = 20x + 800
The equation become 20x + 800 ≥ 1400
Solving inequality que,
20x >= 600
x ≥ 30
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Solve for x in the triangle. Round your answer to the nearest tenth.
Answer: 2.795
Step-by-step explanation:
[tex]cos 56= \frac{x}{5}[/tex]
Annette's Floral Shop has a charge account with Southern Flowers, a wholesaler where she
buys her floral supplies. This month, Annette has purchased 16 dozen roses at $30.96 per
dozen, 40 dozen chrysanthemums at $17.80 per dozen, and 20 dozen tulips at $21.10 per
dozen. In her state, Annette must pay a 6% sales tax on all orders. At the end of the month,
what is the balance on Annette's charge account?
Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.
What is Percentage ?The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
use the unitary approach.by adjusting the fraction's denominator to 100.It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
1 dozen of Rose costs = $30.96
1 dozen of chrysanthemums costs = $17.80
1 dozen of of tulips costs = $ 21.10
Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips
= 16 * 30.96 + 40 * 17.80 + 20 *21.10
= $1629.36
There is a 6% sales tax on all order = 6% of 1629.36 = $ 97.76
Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.
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Total balance in Annette's charge account is $1727.12 with 6% of tax on all order.
What is Percentage ?
The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.
Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:
Use the unitary approach.
by adjusting the fraction's denominator to 100.
It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary technique.
1 dozen of Rose costs = $30.96
1 dozen of chrysanthemums costs = $17.80
1 dozen of of tulips costs = $ 21.10
Total Spending = 16 dozens of roses + 40 dozen of chrysanthemums + 20 dozens of tulips
= 16 * 30.96 + 40 * 17.80 + 20 *21.10
= $1629.36
There is a 6% sales tax on all order = 6% of 1629.36 = $ 97.76
Total balance in Annette's charge account is $ 97.76 + 1629.36 = $1727.12.
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What is the equation of the circle shown on the graph
The equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.
What is an equation of a circle?
A circle can be characterized by its centre's location and its radius's length.
Let the center of the considered circle be at the (h, k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
The center of the circle is at (-2, 1) and the radius of the circle is 2 units. Then the equation of the circle will be
(x - (-2))² + (y - 1)² = 2²
(x + 2)² + (y - 1)² = 2²
(x + 2)² + (y - 1)² = 4
Hence, the equation of the circle shown on the graph is (x + 2)² + (y - 1)² = 4.
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10. use the division algorithm to divide 116 by 3, and then, based on your work, determine which of the following statements is true. (a) q
By using the division algorithm to divide 116 by 3 will be 38.
The given integers a and b are 116 and 3 respectively.
Let q be the counter variable and r be the variable to store the new dividend after each loop.
Division algorithm,
If a<b
return 0;
else
q = 0;
r = a;
repeat
q = q+1;
r = r-b;
until r<b;
return q, r;
Working:
116 is not less than 3, implies
r = 116 -3 = 113
q = 0+1=1
Repeating until we get q = 38, r = 2 = a
2<3, hence returns q = 38, r =2
The question is incomplete, the complete question is:
use the division algorithm to divide 116 by 3, and then, based on your work, determine which of the following statements is true.
(a) q = 39 (b) q =32 (c) q = 38
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To cater a holiday banquet, Food Service LLC agrees to buy one hundred pumpkin pies from Great Desserts Inc. To be enforceable, the agreement must be in writing if the pies cost at least
$500
In order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies from great desserts inc. to be enforceable, the agreement must be in writing if the pies cost at least $500.
What is an Agreement?
This refers to the legally binding contract that exists between two or more entities where the terms of the contract have been drawn up and the terms have been agreed upon by all parties involved, subject to certain conditions before it can be enforceable.
Hence, we can see that in order to cater a holiday banquet, food service LLC agrees to buy one hundred pumpkin pies and because they are a limited liability company, there needs to be a minimum threshold and this can be done, if the cost of the pies is at least $500.
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Express in a single log term
The simplified form of the given logarithmic expression as required in the task content bis Choice B; 2log8.
What is the simplified form of the expression as a single log term?It follows from the task content that the simplified form of the logarithmic expression is to be determined as a single log term.
On this note, since the given expression is;
2log2 + 2log4
It follows from factorisation that we have;
2 ( log 2 + log 4 )
Therefore, the expression in the parentheses can be simplified as a single log term using the sum of logarithms law as follows;
= 2 ( log ( 2 × 4 ) )
= 2 log 8.
Ultimately, the answer choice which represents the simplified form of the expression as a single log term is; Choice B; 2 log 8.
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What is the image of (10,-6) after a dilation by a scale factor of 1/2 centered at the origin?
The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).
What is dilation?
A dilation is a function f from a metric space M into itself that, for any points x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is a positive real number. Such a dilatation is a resemblance of the space in Euclidean space.
Here, we have
Given
The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin.
We have to find the image after dilation.
The coordinates of an image (-10,-6), dilating the coordinate by 1/2 means reducing the image by multiplying each coordinate by the factor of 1/2.
Image = (1/2(-10), 1/2(-6))
Image = (-5,-3)
Hence, the image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).
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PLEASE ANSWERE ASAP
If BC = 16.7 ft, what is AY?
Answer:
Since YA=AX, XB=BZ, ZC=CY, it follows that A, B and C are the midpoints of the sides TX, XZ, ZY. AB, BC, AC are parallel to the sides and equal to their half. In fact, AB = YC=ZC. Therefore BC=AY.)
Good luck;)
Step-by-step explanation:
I need help with my math homework
Answer:
Read explanation :)
Step-by-step explanation:
Activity 1: When it says direction it refers to the tiles going horizontal and vertical for example the 4 and 9 going vetical to make vertical you must first add 4 + 9 which equals 13 then add a 2 under the 9 so it equals 15. And for 8 and 4 horizontal you must add 8 + 4 which equals 12 so add a three in between the 8 and 4 and for the 7 there is a two on the right of it so add 7 + 2 to equal 9 then add 6 to equal 15 then add a 1 in between the 8 and the 6 to equal 15 and add the 5 in the middle.
Activity 2: On the addition table on the left side of the table the number is the number you add to the number on top for example: the 2 at the top of the table plus the 6 on the same vertical line going down so it would be 2 + 6 which equals 8 as it tells you the answer and for 7 on the left side of the table and 3 at the top of the table with the vertical line would be 7 + 3 which equals 10.
Your Welcome Hope This Helps You.
Cole has c oatmeal cookies. He lets 5 of his friends share them fairly. Write an expression that shows how many cookies each friend gets.
An expression that shows number of cookies each friend got is c/5.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Given that, Cole has c oatmeal cookies. He lets 5 of his friends share them fairly.
Total number of cookies =c
Sharing among 5 friends
Number of cookies each friend got =Total number of cookies/5
= c/5
Therefore, an expression that shows number of cookies each friend got is c/5.
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Suppose the heights of 18-year-old men are approximately normally distributed, with mean 69 inches and standard deviation 6 inches. If a random sample of fifteen 18-year-old men is selected, what is the probability that the mean height x is between 68 and 70 inches? (Round your answer to four decimal places.)
The probability that the mean height x is between 68 and 70 inches is found as 37.28%.
What is meant by the term z score?The z-score effectively represents the standardized distance in units of "number standard deviations" between the raw score (procured from a population assuming a normal distribution) as well as the population mean.The z-score is written as follows:
z = (x - μ)/σ
In which,
x = between 68 and 70 inches.
μ = mean 69 inches
σ = standard deviation 6 inches
Put the values in the formula,
Probability that the mean height x is between 68 and 70 inches
P(68 < x < 70) = (68 - 69 / 6) < z < (70 - 69 / 6)
P(68 < x < 70) = (-0.16) < z < (0.16)
P(68 < x < 70) = 0.4364 - 0.0636
P(68 < x < 70) = 0.3728
P(68 < x < 70) = 37.28%
Thus, the probability that the mean height x is between 68 and 70 inches is found as 37.28%.
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Question 1
Two months ago, a car dealership sold 30 red cars and 120 cars that were not red. Last
month the car dealership sold a total of 200 cars. Tarik predicts that the dealership sold
45 red cars last month. Do you think this is a reasonable prediction? Explain.
Answer:
Yes this is a resendable prediction
Step-by-step explanation:
t=10-x identify to dependent and independent variable
Answer: t is the dependent variable and x the independent variable
Step-by-step explanation: t is the dependent variable it depends upon the values of x that we put in.
x is the independent variable as we can use whatever values we want for x it is not affected by t
Two angles form a linear pair, the sum of one angle plus 27 is equal to two times the sum of the other angle
The pair of Linear angles are 51° and 129°.
What are Linear Angles:When two lines intersect at a point then they will form two linear angles. The sum of angles of a linear pair is always equal to 180°. Such angles are also known as supplementary angles.
In other words, if the sum of two adjacent angles is 180° then the pair of angles are said to be Linear Angles.
Here we have
Two angles form linear angles
Let x and y be the two angles
=> x + y = 180 ------ (1) [ since both are linear angles ]
Given that the sum of one angle plus 27 is equal to two times the sum of the other angle
=> x + 27 = 2y
=> x = (2y - 27) ---- (2)
Substitute (2) in (1)
=> 2y - 27 + y = 180
=> 3y = 153
=> y = 153/3
=> y = 51
Now substitute y = 51 in (1)
=> x + 51 = 180
=> x = 180 - 51
=> x = 129
The pair of Linear angles are 51° and 129°.
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=420(1.04)^x
4% is the percentage rate of increase or decrease in exponential function.
What exactly makes a function exponential?
A mathematical function using the following formula is an exponential function: f (x) = an x. where an is a constant known as the function's base and x is a variable.
The transcendental number e, or roughly 2.71828, is the most often encountered exponential-function base.
We have,
y = 420( 1.04)ˣ
The equation represents exponential growth because the growth factor is greater than 1.
The general form equation is
y(x)= a(1-r)^x such that r is the growth percent.
1 + r = 1.04
r = 0.04 ⇒ 4%
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Given the ellipse with equation substitute the x-values from the table into the equation to obtain y-values, rounded to the nearest integer.
The value of y when X value is -1 would be = -5
What is substitution equation method?The substitution equation method is the method of solving equation whereby a value is being simplified and substituted into the second equation to obtain the next unknown value.
From the given equation:
(x-2)²/16 - (y-4)²/9 = 1
Take X = -1 and substitute X for -1 into the given equation,
(-1-2)²/16 - (y-4)²/9 = 1
9/16 - (y-4)²/9 = 1
(y-4)²/9 = 9/16- 1
(y-4)²/9 = -7/16
Cross multiply
(y -4)² = 9(-7)/16
y²+16 = -63/16
16(y²+16) = -63
16y²+256 = -63
16y² = -319
y² = -319/16
y² = -20
y= -√20
y = -4.5
y = -5
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Isosceles trapezoid ABCD is shown.
A
B
D
C
Which three statements are correct?
ZBAC ZCAD
ZACD ZACB
ZADC ZBCD
AD
AB
AC
BC
CD.
BD
ہے
From the given Isosceles trapezoid ABCD, the three correct statements are:
∠ADC ≅ ∠BCD
AD ≅ BC
AC ≅ BD
What is Isosceles trapezoid?An isosceles trapezoid is a trapezoid with equal base angles and hence equal left and right side lengths.
Particularly in isosceles trapezoids, there are unique correlations. "Equal legs" is what the term "isosceles" denotes. Non-parallel sides on isosceles trapezoids have the same lengths. The "legs" are another name for these equal sides.
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. A triangle with two congruent sides is referred to as being isosceles, in other words.
Thus, three correct statements are -
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Question In △XYZ, A is the midpoint of XY¯¯¯¯¯¯¯¯, B is the midpoint of YZ¯¯¯¯¯¯¯, and C is the midpoint of XZ¯¯¯¯¯¯¯¯. AC = 7, AB = 5, and XY = 24. What is the perimeter of △XYZ? Enter your answer in the box. Perimeter = units
The perimeter of triangle XYZ is 48 units
What is the perimeter of a triangle?
The total of a triangle's sides equals the triangle's perimeter. The space encircled by a triangle's three sides is known as its area.
Here, we have
In The triangle XYZ
A is the midpoint of XY
B is the midpoint of YZ
AB = 1/2 XZ
AB = 5 units
Substitute the value of XZ in AB
5 = 1/2 × XZ
XZ = 10 units
B is the midpoint of YZ
C is the midpoint of XZ
BC = 1/2 XY
XY = 24 units
BC = 1/2 × 24 = 12 units
A is the midpoint of XY
C is the midpoint of XZ
AC = 1/2 YZ
AC = 7
7 = 1/2 YZ
YZ = 14
The perimeter of a triangle = the sum of the lengths of its sides
Perimeter ΔXYZ = XY + YZ + ZX
Perimeter ΔXYZ = 24 + 14 + 10
Hence, the perimeter of triangle XYZ is 48 units
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7. Multiply the
polynomials.
(2x³ + 4x² − 5x)(x³ + 2x - 1)
2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).
Define multiplication.Multiplication in elementary algebra is the process of figuring out what happens when a number is multiplied by itself. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication.
Given
Polynomial
(2x³ + 4x² − 5x)(x³ + 2x - 1)
Multiplying by distributive method,
2x³(x³ + 2x - 1) + 4x²(x³ + 2x - 1) - 5x(x³ + 2x -1)
2x⁶ + 4x⁴ - 2x³ + 4x⁵ + 2x³ - 4x² - 5x⁴ + 10x² - 5x
Adding polynomials with same powers
2x⁶ + 4x⁵ + 4x⁴ - 5x⁴ - 2x³ + 2x³ - 4x² + 10x² - 5x
2x⁶ + 4x⁵ - x⁴ + 6x² - 5x
2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).
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