The factored form of 12x²y - 6x² is 6x²(2y - 1).
How to factorise?The expression to be factorise is as follows: 12x²y - 6x².
Factorisation is the is defined as the breaking down of an entity . Factorisation simply implies we decompose the expression.
Therefore,
12x²y - 6x²
let's find the factors of 12x²y and 6x².
Hence, the factors are 6x²
12x²y - 6x² = 6x²(2y - 1)
Therefore, the factored form is 6x²(2y - 1)
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In ΔLMN, m = 450 inches, � m∠M=74° and � m∠N=41°. Find the length of l, to the nearest 10th of an inch
In the triangle LMN the length of the side l as per given measures of side and angles is equal to 42.4 inches ( nearest tenth )
In triangle LMN,
Let us consider side length opposite to ∠L, ∠M, and ∠N be l , m , and n respectively.
Measure of side m = 450 inches
Measure of ∠M = 74°
Measure of ∠N = 41°
Sum of all the angles in a triangle is equal to 180°
m ∠M + m ∠N + m ∠L = 180°
⇒ 74° + 41° + m ∠L = 180°
⇒ m ∠L = 180° - 115°
⇒ m ∠L = 65°
Using sine law of triangle we have,
sin L / l = sin M / m = sin N / n
⇒sin L / l = sin M / m
Substitute the value we get,
⇒ sin 65° / l = sin 74° / 450
⇒ l = sin 65° × ( 450 / sin 74°)
⇒ l = 0.9063 × ( 450 / 0.9613 )
⇒ l = 42.43 inches
⇒ l = 42.4 inches ( nearest tenth )
Therefore, the measure of the side length l in a triangle LMN is equal to 42.4 inches ( nearest tenth ).
The above question is incomplete, the complete question is:
In ΔLMN, m = 450 inches, m ∠M=74° and m ∠N=41°. Find the length of l, to the nearest 10th of an inch.
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Answer: 424.3
Step-by-step explanation: n ΔLMN, m = 450 inches, m∠M=74° and
m∠N=41°. Find the length of l, to the nearest 10th of an inch.
A.A.S.→Law of Sines
Plug in. Opposite sides go together. 450 sin, 65 sin 74 ≈ 424.2742 ≈ 424.3
l=
sin74
450sin65
≈424.2742≈424.3
to decide which thing of coffee is better value-for-money calculate the price per gram of a 250 g of coffee for 2949 stands and a 750 grams of coffee for $69.99
The second option has the better value-for-money.
Which coffe has the better value-for-money?To find the price per gram, you need to take the quotient between the cost and the mass for each case.
The first brand costs $29.49 for 250 grams, then the cost is:
c = $29.49/250g = $0.12 per gram.
The other brand costs $69.99 for 750 grams, then the cost per gram is:
C = $69.99/750g = $0.09 per gram
We can see that the second option has the better vale-for-money.
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16.0 meters Question 9(Multiple Choice Worth 2 points) (09.06 MC) 01.6 meters Sara's Kite flew 48 meters in the air. Tayjen's kite flew 5,860 centimeters in the air. How much higher was Tayjen's kite
Tayjen's kite flew 5,860 centimeters in the air then Tayjen's kite flew 10.6 meters higher than Sara's kite.
What is BODMAS?
BODMAS is an acronym used to remember the order of operations in arithmetic. The acronym stands for:
B - Brackets (or Parentheses)
O - Orders (exponents and roots)
DM - Division and Multiplication (performed left to right)
AS - Addition and Subtraction (performed left to right)
BODMAS provides a set of rules that dictate the order in which mathematical operations should be performed in an expression that contains multiple operations. It is important to follow the order of operations to ensure that the expression is evaluated correctly and consistently. For example, in the expression 5 + 3 x 2, if we follow the BODMAS rule, we first perform the multiplication (3 x 2) and then the addition (5 + 6), giving us the answer of 11. If we were to perform the addition first, we would get a different answer (5 + 3 = 8, and 8 x 2 = 16), which would be incorrect.
To compare the height of Sara's kite, which is measured in meters, with the height of Tayjen's kite, which is measured in centimeters, we need to convert Tayjen's kite's height to meters.
To do that, we divide the height of Tayjen's kite by 100, since there are 100 centimeters in a meter:
5,860 centimeters ÷ 100 = 58.6 meters
Now we can compare the heights of the two kites:
58.6 meters - 48 meters = 10.6 meters
Therefore, Tayjen's kite flew 10.6 meters higher than Sara's kite.
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Rashida measured the length of a beam to be 16 3/4
feet. The actual length of the beam is 17 1/2
feet.
What is the percent error in Rashida's measurement?
The percent error in Rashida's measurement while measuring the length of the beam is 4.29%.
What is meant by percent error?
The percent error is the distinction between the estimated value and the actual value in relation to the actual value. Percent errors show the magnitude of our measurement errors during an analysis procedure. We are getting close to the accepted or original value when the percent mistakes are smaller. The relative error is multiplied by 100 to get the percent error.
Given,
The actual length of beam = 17 and 1/2 feet = 17.5 feet
The measured length of beam = 16 and 3/4 feet = 16.75 feet
The formula to find the percent error is as follows:
Percent error = [tex]|\frac{Measured\ value - Actual\ value}{Actual\ value} | * 100[/tex]
= [tex]|\frac{16.75 - 17.5}{17.5} | * 100 =[/tex] 0.75/17.5 * 100 = 4.29%
Therefore the percent error in Rashida's measurement while measuring the length of the beam is 4.29%.
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The diagram shows three identical coins of
radius 1 cm.
Calculate the shaded area in the middle
of the diagram.
Complete the table below treat each row has a different problem.
Important : the last row is sector area (a)
The different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.
What is sector?The sector is essentially a section of a circle, and it may be described using the following three criteria:
The area of a disc that is surrounded by two radii and an arc is known as a circular sector.
The circle is divided into the Major Sector and the Minor Sector by a sector.
The region with a lesser extent is referred to as the Minor Sector, whereas the territory with a larger area is referred to as the Major Sector.
Given that,
Central angle = [tex]\frac{\pi}{6}[/tex].
The arc length is given as:
l = α/360 (2πr)
Where, α is the central angle.
Substitute the value of central angle we have:
l = (π/6)/360 2πr
l = 2π²r/ 2160
The sector area is given as:
A = α/360 πr²
A = (π/6)/360 πr²
A = π²r²/ 2160
Similarly, the arc length is given as:
l = π/3
Substituting the value of l in arc length we have:
π/3 = α/360 (2πr)
α = 360(π)/ 6πr
α = 60/r
The sector area is given as:
A = α/360 πr²
A = (60/r) 360 πr²
A = πr/60
Hence, the different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.
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A figure is dilated by a scale factor of 3 and is rotated 90° clockwise.
Complete the description of the transformations that will transform the image back into the original figure. Drag and drop each choice into the correct boxes to complete the sentences below.
Answer:
Answers are below ----v
Step-by-step explanation:
1. Clockwise
2. 3
3. (y, -x)
4. (3x,3y)
I need help. Please :(
Answer:
x-8
Step-by-step explanation:
the answer is x-8 correct answer x-8
A kangaroo hopped 3,5203,5203, comma, 520 yards to the lake with her baby in her pouch. She hopped the remaining 5,2805,2805, comma, 280 yards without her baby in her pouch.
How many miles did the kangaroo hop to the lake?
Answer:
so im a little confused 3,5203,5203, is not a proper number and there is not enought yards to make a full mile could you reword it?
Step-by-step explanation:
(SAT Prep) Find the value of x.
it takes half of a yard of ribbon to make a bow how many bows can be made with 7 yards of ribbon
Answer:
14 bows
Step-by-step explanation:
.5 yards is need for one bow if you have 7 yards you have 14(.5) yards
easier way a half goes into 7, 14 times since 14 divide by two is 7
In ΔNOP, \overline{NP} NP is extended through point P to point Q, \text{m}\angle OPQ = (9x-19)^{\circ}m∠OPQ=(9x−19) ∘ , \text{m}\angle PNO = (2x+5)^{\circ}m∠PNO=(2x+5) ∘ , and \text{m}\angle NOP = (3x+16)^{\circ}m∠NOP=(3x+16) ∘. Find \text{m}\angle NOP. M∠NOP
The measure of angle NOP is found by solving an equation that is obtained by using the fact that the sum of the angles in a triangle is 180 degrees. The solution is m∠NOP to obtain the answer of 53.13 degrees.
In the problem, we are given a triangle NOP, where \overline{NP} is extended through point P to point Q. We are given the measures of three angles: m∠OPQ, m∠PNO, and m∠NOP.
We are asked to find the measure of angle NOP.To find the measure of angle NOP, we can use the fact that the sum of the angles in a triangle is always 180 degrees. So, we add up the measures of the three angles we know:
m∠OPQ + m∠PNO + m∠NOP = 180
We are given the measures of m∠OPQ, m∠PNO, and m∠NOP in terms of x. We substitute these values and get an equation in terms of x:
(9x-19) + (2x+5) + (3x+16) = 180
Simplifying the left side of the equation, we combine like terms:
14x + 2 = 180
We can then isolate x by subtracting 2 from both sides of the equation:
14x = 178
And then we can solve for x by dividing both sides of the equation by 14:
x = 12.71
Now that we know x, we can use it to find the measure of angle NOP, which is what we were asked to do. We substitute x = 12.71 into the equation for m∠NOP:
m∠NOP = 3x + 16 = 3(12.71) + 16 = 53.13
Therefore, the measure of angle NOP is 53.13 degrees.
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Match each pair of equivalent values.
1.
square root of 16
2. square of 8
3. 42
4. 12
5. √4
6. √144
k
16
1
4
2
64
12
Answer:
1 -
12 - ?
4 - square root of 16
64 -
16 -
2.828 - square root of 8
Step-by-step explanation:"
I need more terms to match them.
Write the expression as a square monomial
0.16x^2y^2
Answer: (____)^2
Answer:
0.0256x^4y^4
Step-by-step explanation:
1. The sum of two rational numbers is 5
6
. If one of the numbers is 7
36
,
find the other number.
Answer:
So, the rational number is [tex]\frac{52}{12}[/tex] .
Step-by-step explanation:
Let x be the other number.
We know ,
[tex]\frac{7}{36}[/tex] + x = [tex]\frac{5}{6}[/tex]
To find x, we need to convert both to have a common denominator.
So, if we multiply [tex]\frac{7}{36}[/tex] by [tex]\frac{10}{36}[/tex] ,
[tex]\frac{10}{1}[/tex] × [tex]\frac{7}{36}[/tex] + x = [tex]\frac{56}{10}[/tex]
After multiplication the fraction [tex]\frac{7}{36}[/tex] becomes [tex]\frac{70}{360}[/tex] .
[tex]\frac{70}{360}[/tex]+ x = [tex]\frac{56}{10}[/tex]
Now we have common denominator of 360in both fraction,
Now,
we can simplify the equation ,
[tex]\frac{70}{360}[/tex] + x = [tex]\frac{56}{10}[/tex]
70 + 360x = 56 × 36
2520 + 360x = 2016
504 + 360x = 2016
360x = 1512
x = [tex]\frac{1512}{360}[/tex]
=[tex]\frac{52}{12}[/tex]
So, the rational number is [tex]\frac{52}{12}[/tex] .
what is the value of y?
Answer:
y = 43
Step-by-step explanation:
47° , y and 90° lie on the straight line AB and sum to 180° , that is
47 + y + 90 = 180
y + 137 = 180 ( subtract 137 from both sides )
y = 43
John and Mary are building towers out of lego bricks. John used fewer than 18 bricks for his
tower. Mary used twice as many bricks as John. What is the greatest number of bricks Mary
could have used?
Answer:
34 bricks is the greatest amount Mary could have used
Step-by-step explanation:
Here is some information about some temperatures in Great Britain in January.
Maximum Temp (°C) Minimum Temp (°C)
-8
-1
0
Glasgow
Cardiff
Exeter
b)
2
6
8
a) Which city is warmest in January?
How much colder is the minimum temperature in Glasgow
than the minimum temperature in Cardiff?
Exeter
c) Which city has the biggest difference between the maximum
and minimum temperatures?
°C
Determine whether the underlined value is a parameter or a statistic. In a championship football game, a quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns.Is the value a parameter or a​ statistic?
A quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. The value "59%" is a statistic.
In this scenario, a sample of the quarterback's passes was taken during the championship football game, and the completion percentage was calculated based on that sample. Since the percentage was calculated based on a sample, it is a statistic. A parameter, on the other hand, is a value that describes a characteristic of an entire population. For example, if we were to consider the completion percentage of all quarterbacks in the league, then the mean or median completion percentage would be a parameter because it would describe a characteristic of the entire population of quarterbacks. In summary, statistics are values that describe a characteristic of a sample, while parameters are values that describe a characteristic of a population.
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Complete Question
Determine whether the underlined value is a parameter or a statistic. In a championship football game, a quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. Is the value a parameter or a statistic?
Discussion topic
read this article discussing the value of specific polling results in us presidential elections.
your thoughts about the
article, in particular, comment about what surprised you or what you
thought might be interesting to understand more deeply. Also comment about any
statistical
discussion or information that you are now better able to understand because of your
background in statistics.
give
Overall, the article has given me a deeper appreciation for the role that statistics plays in the political landscape.
One statistical discussion that stood out to me was the concept of margin of error. This is a measure of the accuracy of a poll and is calculated by taking into account the sample size and the variability in responses. I now have a better understanding of how pollsters use this measure to determine the reliability of their results.
Additionally, the article highlighted the importance of understanding statistical significance, which refers to the likelihood that a particular result occurred by chance. This is an essential concept in statistics that helps to determine whether a particular result is reliable or not.
It has also emphasized the need to interpret polling data with caution and to be mindful of the potential for errors and biases.
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select the most correct statement below that describes the differences between type 1 and type 2 hypervisors?
A type 1 hypervisor functions as a compact operating system and runs directly on the host's hardware, but a type 2 hypervisor operates as a software layer on operating system, similar to other computer programs.
Which is the safer hypervisor, type 1 or type 2, and why that is more superior?
Native hypervisors are a safer solution. They are not dependent on the underlying OS, unlike hosted hypervisors. If you are attacked, the bare-metal hypervisor will improve your chances (Type 1). Because of this reliance, the type 2 server loses efficiency, performance, and speed. A Type 1 hypervisor operates directly on the hardware of the host computer. These hypervisors interface directly with the host computer's CPU, RAM, and physical storage, making them typically quicker and more effective than Type 2 hypervisors. eliminate the requirement to travel through the OS layer.
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Shape ABCD is a rectangle.
C is the point with coordinates (0,-8)
The equation of the straight line through A and B is 2y + x = 4. Find the equations of the lines
DC, AD and BC.
Equation of line DC is y = -1/2 x - 8
Equation of line AD is y = 2x + 2
Equation of line BC is y = 2x - 8
How to find the equation of the linesThe equation of the line 2y + x = 4 is arranged in slope intercept form to have
y = -x/2 + 2
The slope is -1/2
with a slope of -/2 and points (0, -8) line DC is written as
y - -8 = -1/2 (x - 0)
y + 8 = -1/2 x
y = -1/2 x - 8
Equation of line AD
line AD is a perpendicular line to line DC hence the slope is negative reciprocal of the slope of line DC
slope = 2
point A(0, 2) line AD is written as
y - 2 = 2 (x - 0)
y - 2 = 2x
y = 2x + 2
Equation of line BC
line BC is a parallel to line AD hence the slopes are equal
slope = 2
point C (0, -8) line AD is written as
y - - 8 = 2 (x - 0)
y + 8 = 2x
y = 2x - 8
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The Jacob family plans to attend a concert. An
adult ticket (a) is $7.50 each and a child's ticket (c)
is $5.00 each. Mr. Jacob purchased a total of 11
tickets for a total of $65. How many of each kind of
ticket was purchased?
Answer:Mr. Jacob purchased 7 adult tickets at $7.50 each, and 4 child tickets at $5.00 each, for a total of 11 tickets at a cost of $65.
Step-by-step explanation:
SOLVING EQUATIONS Solve the equation. Check your solution.
49. b+7+12=30
The Serenity and the Mystic are sail boats. The Serenity and the Mystic start at the same point and travel away from each other in opposite directions. The Serenity travels at 14 mph and the Mystic travels at 21 mph. How far apart will they be in 3 hours?
Answer:
Step-by-step explanation:d = 14t + 21t = 35t
So, after 3 hours, the distance between the boats will be:
d = 35 * 3 = 105 miles
Therefore, the Serenity and the Mystic will be 105 miles apart after traveling for 3 hours.
PLEASE SOLVE
the graphs of y=px+w and y=rx+s are perpendicular and p=100|r|. Find the values of p and r
P=_
R=_
Answer:
Step-by-step explanation:
-Identity the measures of the reference angle for 521°.
-Identify the measure of the largest negative angle co-terminal with 521°
The reference angle would be 155 degrees.
What is reference angle?An angle's reference angle is the measure of the smallest, positive, acute angle formed by the terminal side of the angle and the horizontal axis.
The positive reference angles have terminal sides that lie in the first quadrant and can be used as models for angles in other quadrants.
The reference angle is acute angle, it must be < 90°.
The terminal side lies in Quadrant II.
The positive measure is:
=180-25
=155°.
And the negative measure is:
= 155-360
= -205°.
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solve the equations y=2x+56 and y=9x
The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).
What is the solution to the equation?The possible value of the variables that satisfy the equation which is known as the solution of the equation.
The equations are given below.
y = 2x + 56 ....1
y = 9x ....2
From equations 1 and 2, then we have
9x = 2x + 56
7x = 56
x = 8
Then the value of the variable 'y' is given as,
y = 9(8)
y = 72
The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).
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If the sum of 3 consecutive numbers is 114 find the numbers? WILL MARK BRAINLIEST!:)
If the sum of 3 consecutive even numbers is 114, we can represent the numbers as x, x+2, and x+4.
The sum of the three numbers is:
x + (x+2) + (x+4) = 3x + 6
We know that the sum is 114, so we can set up the equation:
3x + 6 = 114
Subtracting 6 from both sides gives:
3x = 108
Dividing both sides by 3 gives:
x = 36
Therefore, the three consecutive even numbers are 36, 38, and 40.
Answer:
37, 38, 39
Step-by-step explanation:
let the 3 consecutive numbers be
n , n + 1 , n + 2
then summing and equating to 114
n + n + 1 + n + 2 = 114
3n + 3 = 114 ( subtract 3 from both sides )
3n = 111 ( divide both sides by 3 )
n = 37
n + 1 = 37 + 1 = 38
n + 2 = 37 + 2 = 39
the 3 consecutive numbers are 37 , 38 , 39
Suppose your home is located at (0, 0) on a coordinate plane. The school is located 5 miles west of your home. The playground is 3 miles south of the school. What is the shortest distance, in miles, between your home and the playground? Round your answer to the nearest tenth
The shortest distance is 5.83 miles as we calculate this by distance formula.
A distance formula is a formula used to find the distance between any two points only if the coordinates are known. These coordinates can be on the x-axis, y-axis, or both. Suppose we have two points, P and Q, in the XY plane. Point P has coordinates (x1,y1) and Q has coordinates (x2,y2). Then the formula for the distance PQ between two points is:
PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])
The school is located 5 miles west of your home the co ordinate is (-5,0)
The playground is 3 miles south of the school so co - ordinate is (0,-3)
shortest distance = PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])
√([tex]5^{2} +3^{2}[/tex]) = √34
=5.830 miles
And this Question also can be do by right angle triangle method
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