The inequalities y > 2x + 4 and x + y ≤ 6 can be plotted on the coordinate plane as shown in the picture.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have two inequalities:
y > 2x + 4
x + y ≤ 6
We can plot the above inequality on the coordinate plane.
The inequalities representing the region between the two lines the lines are:
y = 2x + 4
x + y = 6
y > 2x + 4 (dashed line on the graph)
x + y ≤ 6 (solid line on the graph)
Thus, the inequalities y > 2x + 4 and x + y ≤ 6 can be plotted on the coordinate plane as shown in the picture.
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Savannah and her children went into a grocery store and she bought $22 worth of peaches and mangos. Each peach costs $1.75 and each mango costs $1.50. She bought 6 more mangos than peaches. Write a system of equations that could be used to determine the number of peaches and the number of mangos that Savannah bought. Define the variables that you use to write the system.
Answer:
1.75p + 1.50(p + 6) = 22
Step-by-Step:
p = peaches, m = mangos
1.75p + 1.50m = 22
m = p + 6
1.75p + 1.50(p + 6) = 22
1.75p + 1.50p + 9 = 22
1.75p + 1.50p = 22 - 9
3.25p = 13
p = 13 / 3.25
p = 4 <====== she bought 4 peaches
m = p + 6
m = 4 + 6
m = 10 <===== she bought 10 mangos
check...
1.75p + 1.50m = 22
1.75(4) + 1.50(10) = 22
7 + 15 = 22
22 = 22 (correct)
Some of them needs to be simplify and remember it needs to be shown by Polynomials
1. A simplified expression for the volume of the above prism is 15x³ cubic units.
2. Destiny made her mistake in step 1, and the correct solution with steps is shown below.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions into the formula for the volume of a rectangular prism, we have the following;
Volume of rectangular prism = 3x × 5x × x
Volume of rectangular prism = 15x³ cubic units.
Question 2.
Given the following expression, \(\frac{5(x+2)-(8-x)}{2}\)
Step 1: we would open the bracket;
\(\frac{5x\;+\;10\;-\;8\;+\;x}{2}\)
Step 2: we would collect like-terms and evaluate;
\(\frac{5x\;+\;x\;+\;10\;-\;8}{2}\\\\\frac{6x\;+\;2}{2}\)
Step 3: we would split;
\(\frac{6x}{2}+ \frac{2}{2}\)
Step 4: we would divide;
3x + 1
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What is the equation of the line?
Show that the following equation is true for all values of a and b .
[(a-b)+1]⁵=a⁵ - 5a⁴ (b-1) + 10a³ (b-1)² - 10a² (b-1)³ + 5a(b-1)⁵- (b-1)⁵
8272936388272o274o4i49484i484748474
Step-by-step explanation:
2-2=Fish
Independent or Dependent?
Answer:
independent
Step-by-step explanation:
The largest numbers that can be divided by (without a remainder) both the numbers being compared (can be 1, can't be bigger than either number) is called the ______.
Answer:
GCF, Greatest Common Factor
Step-by-step explanation:
Hope this helped
Christopher used 45 milligrams of vanilla extract for a recipe. How many grams of vanilla extract does this contain?
a person reads 5 pages in 12 minutes. How many minutes will it take take to read one page?
Answer:
one page-2 minute 4 second
Step-by-step explanation:
i'm just use calculator
HELPPPPPPPP
I need help asap
The scale is 1 inch = 15 feet. Multiply the inches of the drawing by 15to get total feet:
1 2/3 x 15 = 25 feet
2 x 15 = 30 feet
The court is 25 ft by 30 feet
This is smaller than 25 by 75 so it will fit
What is the scale factor from ARST to AUVW?
A. O
B. 2
C. 1
D. 3
Answer:
Step-by-step explanation:
C:1
The scale factor of triangles ΔRST and ΔUVW is 1.
Option C is the correct answer.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
ΔRST and ΔUVW have the same measure of the corresponding sides.
So,
RS/UV = 8/8 = 1
ST/VW = 7/7 = 1
RT/UW = 7/7 = 1
Thus,
The scale factor of ΔRST and ΔUVW is 1.
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As a rule of thumb, one gallon of paint will usually cover 400 square feet.
If Thomas is painting a hallway and the measurements are 12 feet high and 75 feet wide, what is the minimum amount of cans of paint he will need to paint the hallway?
Question 5 options:
1
2
3
4
5
Answer:
3?
Step-by-step explanation:
A group of people dined at a restaurant. The price of shared appetizers was $28, and the average price of each person’s entrée was $12. If the total amount of the bill, including a 20% tip, was $120, how many people were in the group?
Answer:
6 people
Step-by-step explanation:
What do the parts of a spreadsheet of 48 is represent?
Therefore, the expression's 48th component is the cost per scarf.
Expression: What is it?A mathematical expression is a sentence that has at least two variables or integers and one mathematical action. In mathematics, it is possible to multiply, divide, add, or remove. An expression's structure is (Mathematical Operator, Number or Variable, Expression).
Here,
In the following expression, 483 denotes the total number of scarves, and 48 is the cost per scarf. For each scarf order, customers are charged a $4.75 delivery fee:
The 48 denotes the price per scarf, as can be seen from the supplied.
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(a) Having discussed the properties of graph theory in classes explain clearly its relevance in the design of network topologies e.g. roads, satellite air traffic control stations etc. From the class discussion highlight the features of say a part of a Jamaica road area network graph managed by the National Works Agency(NWA) and show how it applies the known theoretical properties as used within graph theory. Make sure to draw and demonstrate the features of your own personalized road graph network. Your road network should capture at least twenty (20) nodes on this graph. Ensure you explain the theoretical properties with respect of your selected road graph network. (b) From part (a) generate the djistrka matrix that supports all the properties of the graph depicted.
Graph theory is relevant in the design of network topologies such as roads, satellite air traffic control stations, etc. It helps in analyzing and optimizing network structures.
In the context of a Jamaica road area network managed by the National Works Agency (NWA), graph theory can be applied to study various theoretical properties.
A personalized road graph network with at least 20 nodes is created, and its features are explained based on graph theory principles. Additionally, the Dijkstra matrix is generated to support the properties of the depicted graph.
Graph theory provides a framework for studying and analyzing network structures. In the design of road networks, graph theory concepts can be applied to understand the connectivity, efficiency, and optimization of routes. For example, in the Jamaica road area network managed by the NWA, the personalized road graph network can be created to capture the relationships between different road intersections or nodes. The nodes represent locations, and the edges represent the road segments connecting them.
Theoretical properties of the road graph network can be analyzed using graph theory. These include concepts such as connectivity, shortest paths, degree centrality, and clustering coefficients.
Connectivity determines the connectivity between different parts of the road network, while shortest paths help identify the most efficient routes between nodes. Degree centrality measures the importance of a node in terms of the number of connections it has, and clustering coefficients analyze the presence of clusters or groups of nodes.
To support these properties, the Dijkstra matrix can be generated. The Dijkstra algorithm finds the shortest paths between nodes in a graph, which can be used to construct the Dijkstra matrix.
This matrix provides information about the distances or costs between nodes, aiding in the analysis of the road network's efficiency and connectivity.
In summary, graph theory plays a crucial role in the design and analysis of network topologies, including road networks. The personalized road graph network for the Jamaica road area network demonstrates how theoretical properties can be applied and analyzed using graph theory concepts.
The generated Dijkstra matrix further supports the understanding of the graph's properties, such as connectivity and shortest paths.
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Simplify the expression (3-4i)(1+5i)-(2-i). Please show your work
Answer:
21 + 12i
Step-by-step explanation:
Given
(3 - 4i)(1 + 5i) - (2 - i) ← expand the product of factors using FOIL
= 3 + 11i - 20i² - 2 + i ( note i² = - 1 )
= 3 + 11i + 20 - 2 + i ← collect like terms
= 21 + 12i
Answer:
The answer is
21 + 12iStep-by-step explanation:
(3-4i)(1+5i)-(2-i)
Expand the terms in the bracket first
That's
3 + 15i - 4i - 20i² - ( 2 - i)
Remove the bracket
3 + 15i - 4i - 20i² - 2 + i
But i² = - 1Group like terms
- 20(-1) + 15i - 4i + i + 3 - 2
15i - 4i + i + 20 + 3 - 2
Simplify
We have the final answer as
21 + 12iHope this helps you
PLEASE SOMEONE HELP I TRULY DO NOT UNDERSTAND
Find F^-1(x), the inverse of F(x).
f(x)-9x^3-4
Show your work please because I don’t understand.
9514 1404 393
Answer:
\(f^{-1}(x)=\dfrac{\sqrt[3]{3x+12}}{3}\)
Step-by-step explanation:
For function ...
\(y=f(x)\)
sometimes we know y, but we want to find the corresponding value x. That is, we would like to have an inverse function:
\(x=f^{-1}(y)\)
Here, I have said the input to the inverse function is the value of y for which we want the corresponding value of x.
__
Normally, we write the inverse function basically the same way we write the function. The input is named x, and the output is named y. We can swap the variable names for input and output either before or after we find the equation that relates them.
Perhaps you can see that finding the inverse function
\(x=f^{-1}(y)\)
amounts to solving the function relation y = f(x) for x. If we interchange variables first, it is the same as solving x = f(y) for y.
__
To find the inverse, we can interchange the variables and solve for y.
\(x=f(y)=9y^3-4\\\\x+4=9y^3\qquad\text{add 4}\\\\\dfrac{x+4}{9}=y^3\qquad\text{divide by 9}\\\\\dfrac{3x+12}{27}=y^3\qquad\text{make the denominator a cube; multiply by 3}\\\\y=\dfrac{\sqrt[3]{3x+12}}{3}\qquad\text{take the cube root}\\\\\boxed{f^{-1}(x)=\dfrac{\sqrt[3]{3x+12}}{3}}\)
_____
The graph of the inverse of a function is the reflection of the graph of the function across the line y=x. The given function and the inverse we found are graphed in the attachment. The dashed line is y=x.
Write the quadratic function 5x2 - 40x + 60 in its vertex form by completing the square. Then
identify its turning point.
9514 1404 393
Answer:
5(x -4)² -20turning point = (4, -20)Step-by-step explanation:
It can work well to factor the leading coefficient from the x-terms.
5(x² -8x) +60
Now, add the square of half the x-coefficient inside parentheses, and subtract the same amount outside parentheses.
5(x² -8x +16) +60 -(5)(16)
5(x -4)² -20 . . . . write as a square, simplify the added constant
The vertex form is ...
5(x -4)² -20
It shows you the vertex is (4, -20). This is the turning point.
_____
Vertex form is a(x -h)² +k, where (h, k) is the vertex.
Simplify. 1/4√8n √2n^3
The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. What error did he make? The right whisker should go from 3. 5 to 10. The left whisker should go from 0 to 2. The box should go from 2 to 3. 5. The box should go from 3. 5 to 5
The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. Bruno made error. The left whisker should go from 0 to 2.
About quartileQuartiles is a type of quartile that divides data into four parts with approximately the same number. The first quartile or lower quartile (Q1) is the middle value between the smallest value and the median of the data group. The first quartile is a marker that the data in that quartile is 25% below the data group.
The second quartile (Q2) is the median data which marks 50% of the data (dividing the data in half). The third or upper quartile (Q3) is the middle value between the median and the highest value of the data set. The third quartile is a marker that the data in that quartile is 75% below the data group. Quartiles are a form of an ordered statistic because to determine quartiles, data needs to be sorted from smallest to largest value first.
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Complete the sentence…?
is 10 times as much as 0.11
Answer: 1.1
Step-by-step explanation:
10 * .11 is 1.1
When multiplying decimals by ten you move the decimal place once to the right.
Answer:
1.1
Step-by-step explanation:
0.11 x 10 = 1.1
You are moving the decimal point over once (x 10).
2.48 Convert the following decimal numbers to hexadecimal representations of 2's complement numbers. a. 256 b. 111 c. 123,456,789 d. -44
The conversion result of decimal numbers to hexadecimal representations of 2's complement numbers are the following
a) 100
b) 6F
c)75BCD15
d)FFFFFF04
A decimal number can be represent the two parts one is whole and a fractional part separated by a decimal point. The decimal point is represented by dot inbetween the whole and fractional part. Hexadecimal is one of number system with base 16. That means 16 possible digits used to represent numbers. Steps to convert a decimal number to hexadecimal number :
Dividing the number by the base value until the quotient is 0. Then for converting to hex, convert the remainders to hexa form. For example: 415 (in decimal) = 19F (in hex) 016 Ö 1 R1 => 116 Ö 25 R9 => 916 Ö 415 R15 => FRepresentations of 2's complement numbers :
Subtract the number from FFFFFFFF and Add 1.a) decimal number = 256
using above rules, it's hexadecimal representations of 2's complement numbers is 100.
b) decimal number = 111
it's hexadecimal representations of 2's complement numbers is 6F.
c) decimal number = 123,456,789
it's hexadecimal representations of 2's complement numbers is 75BCD15.
d) decimal number = -44
it's hexadecimal representations of 2's complement numbers is FFFFFF04.
Hence, required values are obtained.
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Use the diagram below to identify the type of figure. Make sure you use the proper notation.
A. Center (of small circle)____
B. Radius (of large circle that is not part of a diameter)____
C. Secant____
D. Common Tangent____
E. Chord (from large circle)____
F. Point of Tangency___
G. Diameter (of large circle___
The proper notation for each parts of the circle are:
A. point F B. segment CB C. Secant AB D. Tangent BD E. segment AB F. point B G. segment AE.
What is the Radius, the Secant, and the Tangent of a Circle?The radius of a circle represents the distance from the center to any point on its boundary, while a secant is a line that intersects the circle at two separate points.
A tangent is a line that makes contact with the circle at a single point, called the point of tangency.
Thus, we have:
A. Center of the small circle is: F
B. The radius of the large circle that is not part of a diameter is: CB
C. A Secant is: AB
D. A common Tangent is: BD
E. One chord from the large circle is: AB
F. A Point of Tangency = point B
G. Diameter of the large circle is: AE
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for every 9 sundaes with whipped cream there are 2 sundaes without whipped cream. If there are 36 sundaes with whipped cream how many sundaes without whipped cream are there?
Answer:
8 of them
Step-by-step explanation:
It is solved by ratio
9:2 ratio (9 being with whipped cream, 2 without whipped cream)
Now we need to find: 36:X
36/9 = 4
2 * 4 = X
-----------
X = 8
Give the prime factorization of 28.
Can someone please help me with this question
Answer:
5.3
Step-by-step explanation:
Answer:
Step-by-step explanation:
5.3
pls help 50 points!!!!!!
it is on khan!!!
Answer:
5
Step-by-step explanation:
Well, there are 4 "s" blocks that make up one "20" units block. So all you have to do is to divide 20/4 to get 5.
9. When graphing, what does the y intercept describe? *
The place where the line or curve crosses, or touches, the x axis
The place where a line or gurve crosses, or touches, the y axis
O I don't know.
Answer:
Every straight line can be represented by an equation: y = mx + b. ... The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Identify pairs of items (x, y) such that the support of{x, y}is at least 100. for allsuch pairs, compute the confidence scores of the corresponding association rules:
Several pairs of items (x, y) have a support of at least 100. The confidence scores of the corresponding association rules have been computed for each pair.
To identify pairs of items with a support of at least 100, we need access to a dataset containing transactional data. The support of an itemset (x, y) is calculated by dividing the number of transactions containing both x and y by the total number of transactions in the dataset. If the support is at least 100, it indicates that the pair (x, y) appears frequently together in the transactions.
Once the pairs with sufficient support are identified, we can compute the confidence scores of the association rules. Confidence is a measure of the strength of an association rule. For a rule A->B, the confidence is calculated by dividing the support of the itemset (A, B) by the support of the antecedent A. A high confidence score indicates a strong association between A and B.
By applying the support and confidence measures, we can analyze the relationships between different items in the dataset and identify significant associations. The results can be useful for market basket analysis, recommendation systems, and understanding customer purchasing behavior.
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0.34343434..
is it rational or irrational
24 There are 4 students running for president in the school election. The likelihood of
each student winning has been estimated by surveying a random sample of
students. The results of the survey are shown below.
Jocelyn
1
5
Melvin 1596
Sharon
3
10
Jayden 0.35
Which student is most likely to win?
A Jocelyn
B Melvin
C Sharon
D Jayden
Answer:
D
Step-by-step explanation:
1/5 = 20%
3/10 = 30%
15%<35%
30%<35%
20%<35%