Length of blue cloth is 60 inches , length of gold cloth is 48 inches and length of white cloth is 72 inches are greatest lenght of the pieces by greatest common factor.
What does "largest common factor" mean?
A group of numbers' greatest common factor (GCF) is the biggest factor that all the numbers have in common. For instance, the numbers 12, 20, and 24 share the components 2 and 4. Since four is the largest, we refer to the GCF of 12, 20, and 24 as four.a. As, the length of all pieces are equal, so for getting the greatest possible length of the pieces, we need to find GCF(greatest common factor) of 60, 48 and 72.
First we will factor out all three numbers completely
60 = 2 × 2 × 3 × 5
48 = 2 × 2 × 2 × 2 ×3
72 = 2 × 2 × 2 × 3 × 3
The common factors are: 2, 2 and 3
Thus the GCF = 2 × 2 × 3 = 12
So, the greatest possible length of the pieces without having any cloth left over will be 12 inches.
b. For finding the number of pieces for each color cloth, we will just divide the length of each cloth by 12. So
Number of pieces for blue cloth = 60/12 = 5
Number of pieces for gold cloth = 48/12 = 3
Number of pieces for white cloth = 72/12= 6
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What did lambert call the difference between the angle-sum of a triangle and 180 degrees?
Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.
Who is Lambert?Johann Heinrich Lambert (26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally referred to as either Swiss or French, who made significant contributions to mathematics, physics (particularly optics), philosophy, astronomy, and map projections. Lambert pioneered the use of hyperbolic functions in trigonometry. He also proposed theories about non-Euclidean space. Lambert is credited with being the first to demonstrate that is irrational by employing a generalized continued fraction for the function tan x. Euler believed the conjecture but was unable to prove it was irrational, and it is speculated that Aryabhata believed it as well in 500 CE. Lambert also developed theorems about conic sections that simplified the calculation of comet orbits.Lambert refers to the defect as the difference between the angle-sum of a triangle and 180 degrees.Therefore, Lambert calls the difference between the angle-sum of a triangle and 180 degrees the defect.
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B ABCD is a parallelogram and angle A< 90°. The height through the vertex D intersects the diagonal AC at point M. The height through vertex B intersects the diagonal AC at point N. Prove that MBND is a parallelogram.
MBND is a parallelogram as BN=MD and BN║MD.
A parallelogram is a quadrilateral whose both pair of opposite side are equal and parallel. Few examples of parallelograms are square, Rhombus and rectangle.
Given ABCD is a parallelogram and ∠A=90°
Now we have to prove that MBND is a parallelogram
Given BN⊥AC and DM⊥AC
Since BN and DM are both perpendicular to the same straight line AC then we cam say that BN║DM.
Again we know from the properties of parallelogram that the diagonal divides a parallelogram into two equal triangles.
Therefore the diagonal AC divides the parallelogram into two equal triangles ΔABC and ΔADC.
Now we know that the area of a triangle is given by [tex]\frac{1}{2}[/tex] ×base ×height .
Area of ΔABC =Area of ΔADC
Since BN⊥AC and DM⊥AC
∴[tex]\frac{1}{2}[/tex]×BN×AC=[tex]\frac{1}{2}[/tex]×DM×AC
This above equation can be simplified as
BN=MD
Hence BMND is a parallelogram as we know from the properties of parallelogram that when a pair of opposite sides are equal and parallel in a quadrilateral it is a parallelogram.
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an amusement park charges 18 dollars for 4 rides. how much will 7 rides cost
There are a total of 463,100 books in a library. What is the value of the exponet when this number is written in scientific notation?
Answer: 4.631*10^5
Step-by-step explanation:
463,100=
400,000+63,100=
4*100,000+(63,100/100,000)*100,000=
4*10^5+(631/1000)*10^5=
4*10^5+0.631*10^5=
(4+0.631)*10^5=4.631*10^5
If Kevin has a total of 81 hours of service, how many weeks has he volunteered?
If Kevin has a total of 81 hours of service, then he volunteered for 0.48 weeks.
As per the question statement, Kevin served as a volunteer for 81 hours.
We are required to find out the number of weeks, he volunteered his service.
To solve this question, we just need to know that a week consists of how many hours ?
We can proceed with the facts that a week consists of 7 days and each day consists of 24 hours. Therefore, a week consists of [tex](24*7)=168[/tex] hours, of which, Kevin volunteered for 81 hours.
Therefore, as per the unitary method, we get that,
168 hours make 1 week, then
1 hour makes [tex](\frac{1}{168})[/tex] weeks, and
81 hours make [tex](\frac{81}{168})=0.48[/tex] weeks approximately.
Unitary Method: This is a technique for solving a problem where first, we find the value of a single unit, and then find the necessary value by multiplying the single-unit value.To learn more about Unitary Method, click on the link below.
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Can someone give me the answer of D??
Answer:
Corrected - didn't see the 10 to the negative 2 in the denominator at first - sorry)
8000
Step-by-step explanation:
Simplify
5.12 x 10 ^6/ 1.6 X 10 ^5 X (.4 X 10^-2)
Do the math
3.2 x 10/.04 x 1- ^-2)
Simplify
8 X 10^3
Simplify
8000
k) pq (r² + 1) - r (p² + q²)
Answer:
pqr²−p²r−q²r+pq
Step-by-step explanation:
Let's simplify step-by-step.
pq(r²+1)−r(p²+q²)
Distribute:
=(pq)(r²)+(pq)(1)+−p²r+−q²r
=pqr²+pq+−p²r+−q²r
=pqr²−p²r−q²r+pq
The kinetic energy k of an object varies jointly with its mass m and its velocity v. The formula to kinetic energy is K = 1/2mv^2. Rearrange the formula to write the mass m in terms of K and v, where v is not equal to 0.
(I will rate brainliest if only right)
The mass m in terms of K and v is expressed as m= 2K/v^2
Subject of formulaThe subject of formula is a way of representing a variable in terms of other variables.
Given the equation below;
K = 1/2mv^2
Make m the subject of the formula
2K = mv^2
Divide both sides by v^22K/v^2 = mv^2/v^2
2K/v^2 = m
Swap
m= 2K/v^2
Hence the mass m in terms of K and v is expressed as m= 2K/v^2
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find x: -3 = 4x - 12x^2 + 7x^3
Answer:
x = 0.3384663
Step-by-step explanation:
The graph of y=
-2x²5x+2 is drawn below
Draw a suitable line to solve -2x² - 5x + 2 = -5
Answer:
x = 1 and x = -3.5
Step-by-step explanation:
y = -2x² -5x + 2
-2x² -5x + 2 = -5
which means y = -5
Draw the line on y = -5 like the green line in the attached file
and see where this line intersects with the graph
the values are:
x = 1 and x = -3.5
Answer:
Draw a line at y = -5.
x ≈ -3.5
x ≈ 1
Step-by-step explanation:
Given equation:
[tex]y = -2x^2 - 5x + 2[/tex]
This is the equation of the graphed parabola.
To solve the equation [tex]-2x^2 - 5x + 2 = -5[/tex] draw a line at y = -5 and find the points of intersection of the two graphed equations.
From inspection of the graph, the x-values of the points of intersection are:
x ≈ -3.5x ≈ 1Solving algebraically
Add 5 to both sides of the equation:
[tex]\implies -2x^2-5x+2+5=-5+5[/tex]
[tex]\implies -2x^2-5x+7=0[/tex]
Factor out -1 from the left side:
[tex]\implies -1(2x^2+5x-7)=0[/tex]
Divide both sides by -1:
[tex]\implies 2x^2+5x-7=0[/tex]
Find two numbers that multiply to -14 and sum to 5: 7 and -2
Rewrite b as the sum of these two numbers:
[tex]\implies 2x^2+7x-2x-7=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(2x+7)-1(2x+7)=0[/tex]
Factor out the common term (2x + 7):
[tex]\implies (x-1)(2x+7)=0[/tex]
Apply the zero-product property:
[tex](x-1)=0 \implies x=1[/tex]
[tex](2x+7)=0 \implies x=-\dfrac{7}{2}=-3.5[/tex]
Martin wants to clean his swimming pool.
He hired a cleaning machine to do this job.
The cost of hiring the cleaning machine was
£35.54 for the first day,
then £18.25 for each extra day.
Estimate how much it would cost to rent the machine for 4 days.
Help plssss
Answer:
90.29
Step-by-step explanation:
I did math
4a + 2b - 12ax + 15b = -40x - 52. What is a and b
Answer:
a = 10/3 and b = -196/51.
Step-by-step explanation:
4a + 2b - 12ax + 15b = -40x - 52
Equating coefficients of x:
-12ax = -40x
-12a = -40
a = 40/12
= 10/3.
Equating constants:
4a + 2b + 15b = -52
4a + 17b = -52
Substituting a = 10/3:
40/3 + 17b = -52
17b = -52 - 40/3
b = (-52 - 40/3) / 17
= (-156/ 3 - 40/3) / 17
= -196 / 51
tyler wants to buy a new game system that costs $240 tyler has already saved $32 but he needs to make a plan so he can save the rest of the money he needs he decided to save the same amount of money x dollars each month for the next four months, write an equation that helps tyler determine the amount of money he must save each month, solve the equation to find the amount of money he must save each month to meet his goal of buying a new game system
Answer: He must save $52 per month
Step-by-step explanation: 240-32= 208/4= 52
An observation deck extends 454 feet out above a valley. The deck sits 404 feet above the valley floor. If an object is dropped from the observation deck, its height h in feet, after t seconds, is given by
h=-16² +404. How long will it take for the object to be 4 feet above the valley floor?
Answer:4.12
Step-by-step explanation:
Can you determine any purpose why these concepts are present in the pictures?
The purpose why these concepts are present in the pictures is to develop imagination power among students.
As you imagine more, your mind becomes stronger and you have greater mental control. Innovation requires a strong imagination. If you succeed in what you set out to do, the same individuals who now accuse you of daydreaming will begin to aspire to be like you. Keep your aspirations high and your imagination expanding.
Imagination is a potent brain stimulant because it forces you to think differently than most people do. Your imagination can help you come up with scenarios that most effectively handle difficulties, even though your brain might classify them as being unexpected.
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Find the value of x such that the data set has the given mean.
100, 122, 107, 115, 107, x; mean 108
X=
(Type an integer or a decimal.)
Sh
The value of x is 108. If the mean of the data set 100, 122, 107, 115, 107, x is 108.
According to the given question.
We have a data set 100, 122, 105, 115, 107, x .
Also, the mean of the data set is 108.
As we know that, mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Therefore, the mean of the data set 100, 122, 105, 115, 107, x is given by
Mean = [100 + 122 + 107 + 115+ 107 + x]/6
⇒ 108 × 6 = (551 + x)
⇒ 648 = 551 + x
⇒ x = 648 - 551
⇒ x = 97
Hence,the value of x is 108. If the mean of the data set 100, 122, 107, 115, 107, x is 108.
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1. true or false. if false, correct the statement to make it true. explain ur reasoning
If f(x) = x³, then -4f(x - 1) + 2 can be written as -4(x3 − 1) + 2
pls!!!! asap!!!
Answer: False
The correct expression is -4(x-1)^3+2
====================================================
Work Shown:
[tex]f(x) = x^3\\\\f(x-1) = (x-1)^3\\\\-4f(x-1) = -4(x-1)^3\\\\-4f(x-1)+2 = \boldsymbol{-4(x-1)^3+2}\\\\[/tex]
So the error is with the stuff in the parenthesis. Instead of (x^3-1) it should be (x-1)^3
Side note: (x-1)^3 expands to x^3-3x^2+3x-1
Solve for t.
|-3t - 1| - 3 = 3
Answer:
32028464937583748374
Seventh grade > Z.2 Scale drawings: word problems 84H
Carmen drew a scale drawing of a house and its lot. In real life, the lawn in the backyard is
72 meters long. It is 24 millimeters long in the drawing. What is the scale of the drawing?
1 millimeter :
Submit
You've won a new
meters
Tutorial
Qu
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00
The scale of the drawing is in the ratio of 1 millimeter : 3 meter
In this, we need to find the ratio that is 1millimeter:x meter where x is the original scaling of the plot.
We have been given that
24 millimeters = 72 meters
Now we have to find how many meters is equal to 1 millimeter which will find out by the unitary method.
Thus, 24 millimeters = 72 meters
1 millimeter = 72/24 meter
1 millimeter = 3 meter
Hence the scale of the drawing is 1 millimeter : 3 meter
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(Type exponential notation with positive exponents.)
The correct answer to the exponential expression which is as given in the task content is; 8³.
Based on the given task content, Gina's error from her workings is dividing the bases of the exponent.
Exponential notationThe bases of exponential expression, if same, should be taken as one.If the bases of exponential notation are entirely different, then it should be simplified.In indices, Division between two different expressions simply means Subtraction of powers.Multiplication means addition of powersGina's working:
8^12 / 8^9
= 0^12 / 0^9
The Correct workings:
8^12 / 8^9
= 8^(12-9)
= 8³
So therefore, the correct answer to the exponential expression which is given in the above expression is 8³.
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So, the area is square units.
The area of a triangle is 4 square units.
Given that, the coordinates of the triangle ABC are A(4, 3), B(5, 1) and C(1, 1).
We need to find the area of a triangle ABC.
What is the area of a triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
The base of the triangle = |5-1|=4
From vertices, A(4, 3) to the base the distance is 2 units at the vertice (4, 1)
So, the height of the triangle = 2 units
Now, the area of a triangle ABC = 1/2 × 4 × 2 = 4 square units.
In the given solution the height of a triangle is wrongly calculated.
Therefore, the area of a triangle is 4 square units.
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Can someone help me with these so I can finish my math ??
1. -23 + 14 + (-33)
2. -7 + (-19) + 32
3. 102 + (-345) + 234
4. -78 + (-56) + 679
5. 178 + (-129) + 96
6. -312 + (-154) + 283
7. -14 + (-32)
8. -50 + 35
9. -81 + (-11)
10. 121 + (-232)
Answer:
Step-by-step explanation:
1. -42
2. 6
3. -9
4. 545
5. 145
6. -183
7. -46
8. -15
9. -92
10. -111
(3-x)² what is the standard form
Answer:
here is my answer........
Step-by-step explanation:
(3-x)^2 = 9 - 3x - 3x + X2
= X2 - 6x +9
what is the least number that must be subtracted from 3793 for getting a perfect square
Answer:
Step-by-step explanation:
So the nearest perfect square to 3793 is 3721. Hence, the least number that must be subtracted from 3793 to get a perfect square = 3793 - 3721 = 72.
Answer:
ABBCBAAHSHSHDHEEHDHSHHH74737477382
11. A population of bacteria triples every week in a laboratory. The number of
bacteria is modeled by the expression 900 3*, where x is the number of weeks
after a scientist measures the population size. When x = -2, what does the value
of the expression represent?
Answer:
Step-by-step explanation:
Let x represent the number of weeks a population of the bacteria increases. Then, we have the number of bacteria is molded by the expression of 900*3^x. By, the given expression and when we assigned a value of x=2. Then we have 900*3² .
Evaluate the expression when b = -2 and x = 4.
b-3x
Answer:
- 14
Step-by-step explanation:
You can substitute the given values into the expression.
b - 3x
= -2 - 3(4)
= -2 - 12
= - 14
Hope this helped! ^^
Answer:
give the other person the brainliest the answer is -14
Step-by-step explanation:
11 Write as a power of 5
125²
If a lawnmower has a cost price of $2500 and was sold for $2895 what is the percentage profit
The profit percentage for the lawn owner is 15.8%
Profit Percentage:
Profit means, if the selling price of a product is more than its cost price, there is a profit earned in the transaction.
So, it can be calculated as,
Profit = Selling Price - Cost Price
The formulas for profit percentage is,
Profit percentage(P%) = (Profit /Cost Price) × 100
Given,
Here we need to find the profit percentage, If a lawnmower has a cost price of $2500 and was sold for $2895.
Based on the question,
We know that,
Cost Price = $2500
Selling Price = $2895
So, the profit is,
profit = $2895 - $2500
profit = $395
Now, the profit percentage is calculated by apply the values on the formula,
profit percentage (P%) = (395/2500) x 100
Therefore,
P% = 395/25
P% = 15.8%
Therefore, the profit percentage for the lawn owner is 15.8%.
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If f(x) = 24x + 24, find the instantaneous rate of change of f(x) at x = 6
Answer:
168
Step-by-step explanation:
You'd plug 6 in for x
f(x) = 24x + 24
f(6) = 24(6) + 24
f(6) = 144 + 24
f(6) = 168
Please help me solve this please
Answer:
Step-by-step explanation:
what is the question>