Answer: 2.5 or 2 1/2
Step-by-step explanation:
One way: 1/2 x 5 = 5/2
5/2 = 2 1/2 = 2.5
Another way: 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 5/2 = 2 1/2 = 2.5
Nelson claims that when the length and the breadth of a rectangle change by +20% and -20% respectively, the area of the rectangle will remain unchanged. Do you agree? Explain your answer.
Answer: No, the area will not stay the same.
The new area is smaller than the old area.
========================================================
Explanation:
Let's look at an example.
Consider a 10 by 30 rectangle. Its area is 10*30 = 300 square units.
Now let's change the length and width.
Increase the "10" by 20% to get 10*1.20 = 12Decrease the "30" by 20% to get 30*(1-0.20) = 30*0.80 = 24The rectangle is now 12 by 24. The new area is 12*24 = 288 square units.
In summary:
old area = 300 square unitsnew area = 288 square unitsThis is one counterexample, of infinitely many, that proves the area does not stay the same. Instead, the area shrinks.
-----------------
This section will go over a more formal proof using algebra.
L = lengthW = widthold area = length*width = LW
Let's say the length increases by 20% and the width decreases by 20%.
L becomes 1.20L after the 20% increase.W becomes 0.80W after the 20% decrease (since 100%-20% = 80%)Then,
new area = (new length)*(new width)
new area = (1.20L)*(0.80W)
new area = (1.20*0.80)*(LW)
new area = 0.96*(LW)
new area = 0.96*(old area)
This shows that the new area is 96% of the old area. There has been a 4% reduction (since 100% - 96% = 4%)
Notice how 96% of 300 = 0.96*300 = 288. See the previous section above.
How much warmer is 92 than 40?
The temperature measure 92 is warmer than 40 by a measure of; 52.
By how much is 92 warmer than 40?It follows from the task content that it is required to be determined, how much warmer is 92 than 40.
Since the greater temperature measure is; 92 while the lesser is 40.
It can be concluded that the temperature difference is; 92 - 40 = 52.
Ultimately, the measure 92 is 52 warmer than 40.
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properties of rectangles assignment
The properties of a rectangle are;
A rectangle is seen as a type of quadrilateralThe opposite sides are parallel and also equal to each otherEach interior angle is equivalent to 90 degreesThe sum of all the interior angles is 360 degreesWhat is a rectangle?A rectangle is described as a quadrilateral shape with only two pairs of its sides equal.
The properties of a rectangle are given as;
A rectangle is seen as a type of quadrilateralThe opposite sides are parallel and also equal to each otherEach interior angle is equivalent to 90 degreesThe sum of all the interior angles is 360 degreesThe diagonals bisect each other at right angleBoth the diagonals are of the same lengthA rectangle with side lengths a and b has the perimeter that is equal to 2a+2b unitsA rectangle with side lengths a and b has the area that is given as ab sin 90 = ab square unitsA diagonal of a rectangle is also the diameter of its circumcircleLearn about rectangles at:
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The properties of a rectangle is listed below;
A rectangle is referred to as a quadrilateral
The diagram of a rectangle is attached
What are the properties of a rectangle?A rectangle is a 4 sided shape and also four vertices
A rectangle is referred to as a quadrilateral
The opposite sides of a rectangle is opposite and equal to each other
The diagonals of a rectangle are equal
The diagonals of a rectangle bisects each other
Each interior angle of a rectangle is equal to 90°
The sum of all the interior angles is equal to 360°
Therefore, a four sided quadrilateral with two opposite sides equal is a rectangle.
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There are 400 eighth graders at Wilson Middle SchoolIn the class president election, 296 students voted for Luke, 60 students voted Alice, and 44 students voted for Chris.who voted for luke
Answer: In the class president election at Wilson Middle School, 296 students voted for Luke.
Step-by-step explanation:
Solve for x
Show proofs
Help
The length of the rise x is 25.5
How to determine the value of the side length xFrom the question, we have the following parameters that can be used in our computation:
Length = 17
Angle = 27 degrees
The rise, x is then calculated using the following laws of tangent
tan(27) = 13/x
Make x the subject
So, we have the following representation
x = 13/tan(27)
Evaluate the expression
This gives
x = 25.5
Hence, the value of x is 25.5
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Tamara is buying balloons and streamers to decorate for a party. She wants to spend no more than $15 on decorations.
One package of balloons costs $4.50. Streamers are $1.50 per roll.
Tamara knows she will be buying at least 2 rolls of streamers.
Let x=
the number of packages of balloons
Let y=
the number of streamer rolls
Graph the system of inequalities and choose the region that represents the combinations of balloons and streamers that Tamara can purchase.
A graph of the system of inequalities is shown in the image attached below.
The region that represents the combinations of balloons and streamers that Tamara can purchase is the shaded region that contains the point (1, 3).
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of balloons and number of streamer rolls respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of packages of balloons.Let the variable y represent the number of streamer rolls.Since one package of balloons costs $4.50 and streamers are $1.50 per roll, and Tamara wants to spend no more than $15 on decorations, a linear inequality to describe this situation is given by:
4.50x + 1.50y ≤ 15.
Additionally, Tamara knows she will be buying at least 2 rolls of streamers;
y ≥ 2
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F(x)=4x+2 FIND THE INVERS SHOW WORK
Given To find Solution: First, we replace with and with : Now, we finally replace with Therefore, the inverse of is
Answer:y=(x-2)/4
Step-by-step explanation:
y=4x+2
4x=y-2
x=(y-2)/4
y=(x-2)/4
Match the following to their correct classification
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
4x+20
4x+20>40
4x+20=40
The option " Inequality " (3 of 3) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.
The correct classification of the terms is:
Expression; 4x+20
Inequality: 4x+20 > 40
Equation: 4x+20 = 40
What is an expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
Here, we have
Given: 4x+20
4x+20>40
4x+20=40
We have to find their correct classification.
We concluded from an expression that
When an expression has the "=", then the expression is an equation.
When an expression has any of the following signs">, <, >=, <= or != ", then the expression is an inequality.
When the expression is neither an equation nor an inequality, then it is just an expression.
Hence, the correct classifications are:
Expression; 4x+20
Inequality: 4x+20 > 40
Equation: 4x+20 = 40
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A letter in the word ACCEL is
chosen 50 times. results are
shown in the table below.
What is the theoretical probability of
choosing a C?
probability is calculated from the number of times an event happens, divided by the total number of trials in an actual experiment.
probability for choosing C = 7/50
Bonnie bakes a pan of brownies and cut them into 12 equal pieces after lunch 8/12 of the brownies are left her friends eat half of those brownies with dinner what fraction of the whole pan of brownies do they eat with dinner
Answer:
4/12
Step-by-step explanation:
8/12 ÷ 2 = 4/12
Answer: 1/3
Step-by-step explanation:
8/12 divided by 2 is 1/3
In order to ride a
roller coaster at the theme park, riders
must be at least 52 inches tall. Write
an inequality to show the
safe heights for riders.
The inequality to represent the height of roller coaster is x≥52.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that. in order to ride a roller coaster at the theme park, riders must be at least 52 inches tall.
Let the height be x.
Now, x≥52
Therefore, the inequality is x≥52.
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Please help! Make you brainliest and 15 points!
Answer:
b value is 3
rise = 3 run = -2
another point could be (2,0)
Step-by-step explanation:
If a matrix has a determinant of -13, does the matrix have an inverse (yes/no)?
Yes, The matrix does indeed have an inverse.
What do you understand by the matrix?A rectangular or square array of figures, characters, or expressions arranged in rows and columns is known as a matrix. In many different disciplines, including computer science, engineering, physics, and mathematics, matrices are frequently employed and Matrix representations of physical phenomena, such as the wave functions in quantum mechanics, are common in physics. To represent and simulate complicated systems, like circuits and control systems, engineers employ matrices. Matrix-based techniques are utilised in a variety of computer science applications, including image processing, computer graphics, and machine learning.
The elements of a matrix, which are often written with a rectangular bracket, can be used to symbolise it.
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Yes, the inverse of a matrix exists if the determinant of the matrix is -13.
What is a matrix?
Linear equations are expressed using matrices, which are ordered rectangular arrays of numbers. Columns and rows make up a matrix. Mathematical operations like addition, subtraction, and matrix multiplication can also be done on matrices. If there are m rows and n columns, the matrix is represented as m × n matrix. The inverse of a matrix is available only for square matrices.
Now the determinant is a value that is associated with a square matrix.
The product of all the elements in any row or column and their corresponding co-factors is the determinant of a matrix.
For an inverse matrix to exist, the determinant of the matrix should not be zero. This is because the determinant of the inverse matrix is the inverse of the determinant of the original matrix.
If the determinant is zero, then the determinant of the inverse matrix will be 1/0, which is undefined.
So, as long as the determinant is not equal to zero, the inverse matrix exists.
Therefore the inverse of a matrix exists if the determinant of the matrix is -13.
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Can someone please help me with this question
40 degrees Is the answer.
Hope this helps mate.
PLs give brainliest
Answer:
40
80 + (16x-4) + (9x +4) =180
x=4
BAC = (9*4+4)
BAC = 40
What is the value of 205 pounds in kg
The conversion from pounds (lb) to kilograms (kg) is determined by multiplying the weight in pounds by 0.45359237. The formula to convert pounds to kilograms is kg = lb x 0.45359237.
To calculate the weight of 205 pounds in kilograms, the calculation is as follows: kg = 205 lb x 0.45359237 = 92.98 kg.Therefore, the weight of 205 pounds is equal to 92.98 kilograms. This calculation can also be used to convert any weight in pounds to its equivalent in kilograms. For example, to convert 500 pounds to kilograms, the calculation would be: kg = 500 lb x 0.45359237 = 226.79 kg.This calculation can be used to convert any weight in pounds to its equivalent in kilograms. It is important to remember that the formula must be used correctly and that all units must be consistent. It is also essential to ensure that the result is rounded to the correct number of decimal places for accuracy.
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HELP HELP HELP HELP HELP HELP
We would expect to see around 200 fewer accidents per year among 16-year-old drivers in your state if the proposal to increase the permit period from 6 to 12 months is implemented.
What is an estimation?Estimation is the process of determining an estimate or approximation, which is a value that can be used for a specific purpose even when the input data is incomplete, uncertain, or unstable.
It is difficult to predict exactly how many fewer accidents would occur as a result of increasing the time a driver must hold a learner's permit from 6 to 12 months. However, there is evidence to suggest that longer permit periods can result in fewer accidents, as novice drivers have more time to gain experience under supervision before obtaining a full license.
According to research by the Insurance Institute for Highway Safety, increasing the permit period from 6 to 12 months could lead to a 20% reduction in crash rates among 16-year-old drivers.
Assuming this reduction holds true in your state, we can estimate the number of accidents that would be prevented by multiplying the current number of accidents involving 16-year-old drivers (let's assume 1,000 per year) by 20%, or 0.2. This gives us an estimated reduction of 200 accidents per year.
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Patrice's credit card has an APR of 11%, calculated on the previous monthly
balance, and a minimum payment of 2%, starting the month after the first
purchase. Her credit card record for the last 7 months is shown in the table
below.
End of
month
1
456734
Previous
balance
$0.00
$3900.00
$3857.75
$3815.96
$3774.62
$3733.73
$3693.28
New
charges
$3900.00
$0.00
$0.00
$0.00
$0.00
$0.00
$0.00
Payment
received
$0.00
$78.00
$77.16
$76.32
$75.49
$74.67
$73.87
Finance
charges
$0.00
$35.75
$35.36
$34.98
$34.60
$34.23
$33.86
Principal
paid
$0.00
$42.25
$41.79
$41.34
$40.89
$40.45
$40.01
New
balance
$3900.00
$3857.75
$3815.96
$3774.62
$3733.73
$3693.28
$3653.27
How much of the $3900 charge]that Patrice made during the first month has
been paid off?
The amount of the $ 3, 900 charge that Patrice has made after paying off the first month is $ 246.73.
How to find the amount ?To find the amount that Patrice has paid out of the $ 3, 900 charge to the credit card, look at the principal payments made since that day. Add them all up to get the amount paid from the charge.
The amount paid from the charge is :
= 42. 25 + 41. 79 + 41. 34 + 40. 89 + 40. 45 + 40. 01
= $ 246.73
In conclusion, out of the $ 3, 900 charge, Patrice has paid $ 246. 73.
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A rectangle has a length of 19 inches and a
vidth of 15 inches. What is the perimeter
of the rectangle?
The perimeter is
inches.
Answer:
Step-by-step explanation:
So when solving for the perimeter you need to add up all the sides. So 15 + 15 = 30 and 19 + 19 = 38. So 38 + 30 = 68 inches. So there is your answer. 68 inches is the perimeter.
You have 71/2 minutes to complete three rock climbing walls do you normally climb each wall in 155 seconds do you have enough time to climb all three walls.
In order to finish the task in the allotted time, you would therefore need to ascend more quickly or decide to only climb the first two walls.
What do the two definitions of "minute" mean?The Latin term minute, which means "small," is the root of both the adjective instant (my-NOOT), which denotes something that is incredibly small, and the substance minute (MIN-it), which denotes 60 seconds of time. Although the two terms have different pronunciations, they both refer to small sizes.
We can compute the overall time needed to scale all three barriers and compare it to the time available, which is 71/2 minutes or 450 seconds, to determine if you have enough time.
One wall takes 155 seconds to scale, so climbing three walls would take:
3 walls x 155 seconds per wall = 465 seconds
You wouldn't have enough time to scale all three walls inside the allotted time restriction because 465 seconds is longer than the amount of time that is accessible, which is 450 seconds.
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in a triangle ABC, E and F are mid points of equal sides AB and AC of triangle ABC. Show that BF = CE
BF=CE in a triangle ABC, E and F are mid points of equal sides AB and AC of triangle ABC.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given E and F are mid point of equal sides AB and AC of triangle ABC
In ΔABF and ΔACE
AB=AC (given )
∠A=∠A (common angle )
The side FA is equal to EA
If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent
∴ΔABF≅ΔACE (SAS rule)
∴BF=CF ( Corresponding parts of Congruent triangles.)
Hence, in a triangle ABC, E and F are mid points of equal sides AB and AC of triangle ABC then BF=CE.
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how many zeros in a million
Answer:
There are 6 zeros in one million.
Step-by-step explanation:
1000000 (one million)
6 zeros
A loan of $25,000 has an annual simple interest rate of 5.5%. The total cost of the loan is $38,750. How much total interest will you pay?
The solution is, total interest will you pay is $13750.
What is Subtraction?Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
here, we have,
given that,
A loan of $25,000 has an annual simple interest rate of 5.5%.
The total cost of the loan is $38,750.
so, total interest will you pay = $(38750 - 25000)
= $13750
Hence, The solution is, total interest will you pay is $13750.
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In the figure, the person is 5 ft tall and his shadow is 4 ft long. The tree's shadow is 22 ft long.
What is the height of the tree? Show all your work.
Answer: The height of the tree is approximately 44 ft.
Step-by-step explanation: Step 1: Calculate the ratio of the person's height to the length of their shadow.
Person's Height: 5 ft
Length of Shadow: 4 ft
Ratio: 5 ft/4 ft = 1.25
Step 2: Use the ratio to calculate the length of the tree's shadow.
Length of Tree's Shadow: 22 ft
Ratio: 1.25
Calculation: 22 ft/1.25 = 17.6 ft
Step 3: Multiply the length of the tree's shadow by the ratio to calculate the tree's height.
Length of Tree's Shadow: 17.6 ft
Ratio: 1.25
Calculation: 17.6 ft x 1.25 = 22 ft
Answer: The height of the tree is approximately 44 ft.
Two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.
Which Postulate or Theorem is stated above?
Question 1 options:
Polygon Similarity Postulate
Polygon Congruence Postulate
Angle-Angle Similarity Postulate
Side-Side-Side Similarity Theorem
Side-Angle-Side Similarity Theorem
Angle-Angle Similarity Postulate states that two polygons are similar if and only if they have two corresponding angles that are congruent.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Given that two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.
The statement above is the Angle-Angle Similarity Postulate, which states that two polygons are similar if and only if they have two corresponding angles that are congruent.
Hence, Angle-Angle Similarity Postulate states that two polygons are similar if and only if they have two corresponding angles that are congruent.
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Answer:
Angle-Angle Similarity Postulate
Step-by-step explanation:
9tailsminato9.
What are the math topics covered in the grade 6 math worksheets?
The math topics covered in the grade 6 math worksheets are algebra,geometry,measurement, number operation.
1. Number sense and operations: This includes understanding numbers, fractions, decimals, and integers, as well as performing operations with them.
2. Algebra: This includes understanding algebraic expressions and equations, and using them to solve problems.
3. Geometry: This includes understanding basic geometric concepts, such as lines, angles, and shapes, and using them to solve problems.
4. Measurement: This includes understanding measurement concepts, such as length, area, and volume, and using them to solve problems.
5. Data analysis and probability: This includes understanding basic concepts of statistics, such as mean, median, and mode, and using them to analyze data and make predictions.
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i need help :) if any of you know how to do this I would appreciate it.
Step-by-step explanation:
So in order to find out how much he needs to sell, let's find out what the target is. We do that by working options A.
$19 for 40 hours
[tex]40 \times 19 = 760[/tex]
Now that we have 760, we know this amount is 8%. Next we setup a ratio
[tex] \frac{760}{x} = \frac{8\%}{100\%} [/tex]
We cross multiply
[tex]8x = (760)(100)[/tex]
[tex]8x = 76000[/tex]
Last but not least, we divide by 8 on both sides
[tex]x = 9500[/tex]
Yvette is saving money to buy holiday gifts. She will save the money she makes at her part-time job. However, she borrowed $25 from her sister that she has to pay back before she can start saving.
This relationship can be shown by a linear function. Below is a table showing how many hours Yvette has worked (input), and how much money she's saved (output).
Hours Worked (x) Amount Saved (y)
0 -$25
4 $14
8 $53
12 $92
16 $131
Which of the following statements are true regarding the graph of this linear function? Select all that apply.
Group of answer choices:
A. The slope of the line, 25, is the amount of money she makes per hour of work.
B. The slope of the line, 9.75, is the amount of money she starts with having worked 0 hours.
C. The y-intercept of the line, 0, is the amount of money she starts with, since she's worked 0 hours.
D. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.
E. The slope of the lines, 9.75, is the amount of money she makes per hour of work.
The slope of the line is 9.75 and the y-intercept is -25.
What is a linear function?
Two distinct but related concepts are referred to by the phrase "linear function": A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.
Here, we have
Given: Yvette is saving money to buy holiday gifts. She will save the money she makes at her part-time job. However, she borrowed $25 from her sister which she has to pay back before she can start saving.
Let the linear function that models the given situation be y = ax + b. Here, a and b are constants. We can use this information to find the values of a and b.
We put x = 0 and y = -25 into y = ax + b
b = -25
Substitute the value of b into y = ax + b
y = ax -25...(1)
Now we put x = 4 and y = 14 in equation(1) and we get
14 = 4a - 25
4a = 39
a = 9.75
Substitute the value of a in equation (1):
y = 9.75x - 25
Compare the above function with the slope-intercept form of a line y = mx + c
m = 9.75, c = -25
Hence, the slope of the line is 9.75 and the y-intercept is -25.
A. From the previous calculations, it is clear that the slope of the line is 9.75. Hence, the first statement is not true.
B. From the given table, it is known that person Y had started working with -25 dollars. Clearly, 9.75 is the slope of the line, but it does not represent the initial amount that person Y had at x = 0. Hence, the second statement is not true.
C. From the previous calculations, it is clear that the y-intercept is -25, not 0. Hence, the third statement is not true.
D. From the previous calculations and the given table, it is clear that the y-intercept is -25, and it does represent the initial amount that person Y had at x = 0. Note that the y-intercept is negative as the person has borrowed 25 dollars from her sister. Hence, the fourth statement is true.
E. From the previous calculations, it is clear that the slope of the line is 9.75. It is known that the slope of a line represents the rate of change in the value of y with respect to x. So, it can be concluded that 9.75 represents the amount that person Y earns per hour. Hence, the fifth statement is true.
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Jack spends 1 1/2times as long on his homework as Jill.
Last week, Jill spent 6 3/4hours doing homework.
How long did Jack spend doing homework?
Answer:
10.125 hours
Step-by-step explanation:
We can convert 6 3/4 hours into minutes by multiplying it by 60
this equals 405. Jill spent 405 minutes doing homework.
Jack spent 1 1/2 times as long on his homework as Jill (1 1/2 is equivalent to 1.5)
We can multiply 1.5 x 405 and get 607.5 which means Jack spent 607.5 minutes doing homework
607.5 minutes is equivalent to 10.125 hours.
Help its due today
A.1. Look at the labels of the graph. What are the units for the point ? (3 pts)
B. 2. What is the unit rate for the graph in terms of centimeters/minute? Explain how you found the unit rate. (3 pts)
_________ cm per 1 min
The units are 8 minutes, 28 centimeters.
The unit rate of the graph is 3.5 centimeters/minute
How to determine the units for the point?
A unit rate is defined as the rate for one of something. For example, if 10 oranges cost $50, the unit rate will be $50/10 = $5 i.e. $5 for one orange.
The 8 belongs to the time axis, so the unit is minute (min). The 28 belongs to the water level axis, so the unit is centimeters (cm).
The unit rate of the graph is time divided by the water level. That is:
unit rate = 28/8 = 3.5 centimeters/minute
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Which number has 57 as a multiple?
Answer:
What are the multiples of 57? The first 10 multiples of 57 are 57, 114, 171, 228, 285, 342, 399, 456, 513 and 570
Step-by-step explanation:
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