∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel.
What are consecutive angles?A pair of angles formed on each side of the transversal when it interacts with two parallel lines are known as consecutive angles. The angles in the same region (either interior or exterior) on each of the parallel lines form consecutive angles pairs and are supplementary.
Given that, in a race, all members of a rowing team should keep the oars parallel to produce maximum speed, and m∠1 = 6x + 18 and
m∠2 = 9x+12, and x = 10.
Putting the value of x, we get,
m∠1 = 6x + 18 = 6*10 + 18 = 78°
m∠2 = 9x+12 = 9*10 + 12 = 102°
m∠1 + m∠2 = 180°
Therefore, ∠1 and ∠2 are consecutive angles pairs.
We can prove that oars are parallel by converse of consecutive angles theorem.
Hence, ∠ 1 and ∠ 2 are consecutive angles, the measures are 78° and 102° respectively and converse of consecutive angles theorem will prove the oars parallel
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In the figure, triangle LMN is similar to triangle PQR. Whats the length of PQ?
Simplify (4x to the power of 3) power of 2
The correct answer is: " 4096 x⁶ " .
Step-by-step explanation:
Given: [(4x)³] ² ; Simplify.
Method 1)
Note the following multiplication property of exponents:
⇒ (aᵇ)ᶜ = a⁽ᵇ*ᶜ⁾ ;
As such:
[ [(4x)³] ² = (4x)⁽²ˣ³⁾ = (4x)⁶ ;
Now; note the following property of exponents:
(ab)ᶜ = aᶜ * bᶜ ;
As such: (4x)⁶ = 4⁶ * x⁶ ;
Now; we can simplify 4⁶ ; by using a calculator:
→ 4⁶ = 4096 ;
Or: 4⁶ = 4 * 4 * 4 * 4 * 4 * 4 ;
= (4 * 4) * 4 * 4 * 4 * 4 ;
= 16 * 4 * 4 * 4 * 4 * ) ;
= (16 * 4) * 4 * 4 * 4 ;
= 64 * 4 * 4 * 4 ;
= (64 * 4) * 4 * 4 ;
= (126 * 4) * 4
= (256) * 4 ;
= 4096 .
_______
or: 4⁶ = 4 * 4 * 4 * 4 * 4 * 4 ;
= (4 * 4) * (4 * 4) * (4 * 4) ;
= 16 * 16 * 16 ;
= (16 * 16) * 16 ;
= (256) * 16 , = 4096.
_______
So: [(4x)³] ² = 4⁶ * x⁶ = 4096 x⁶ ;
_______
Method 2) Given: [(4x)³] ² ;
(4x)³ = 4x * 4x * 4x ;
[(4x)³]² = (4x * 4x * 4x)²
= (4x * 4x * 4x) * (4x * 4x * 4x) ;
= (4 * 4 * 4 * x * x * x * 4 * 4 * 4 * x * x * x ;
= 4 * 4 * 4 * 4 * 4 * 4 * x * x * x * x * x * x ;
⇒ (4 * 4 * 4 * 4 * 4 * 4) = 4⁶ = 4096 ; (see Method 1 above).
⇒ (x * x * x * x * x * x) = x⁶ ;
⇒ [(4x)³] ² = 4⁶ * x⁶ = 4096 x⁶ ;
_______
Method 3)
[(4x)³] ² = (4x)⁽²ˣ³⁾ = (4x)⁶ ;
(4x)⁶ = 4x * 4x * 4x * 4x * 4x * 4x ;
= 4 * 4 * 4 * 4 * 4 * 4 * x * x * x * x * x * x ;
= (4 * 4 * 4 * 4 * 4 * 4) * (x * x * x * x * x * x) ;
⇒ (4 * 4 * 4 * 4 * 4 * 4) = 4⁶ = 4096 ; [see Method 1 above].
⇒ (x * x * x * x * x * x) = x⁶ ;
⇒ [(4x)³] ² = 4⁶ * x⁶ = 4096 x⁶ .
_______
The correct answer is: " 4096 x⁶ " .
_______
Hope this is helpful.
Best wishes in your academic endeavors!
_______
Answer:
Simplify (4x to the power of 3) power of 2
Step-by-step explanation:
The school I go to tells me to do this:
(4x^3)^2
(4x^3)(4x^3)
(4)(4) - 16
(x^3)(x^3) - x^6 bc you add the exponents
16x^6 which is correct bc my teacher has checked us on that before in class bc we have had equations like that ^_^
which of the following is a probability sample?
a. Quota sample
b. Convenience sample
c. Cluster sample
d. Judgment sample
e. Snowball sample
The correct option is option (C) .
Cluster Sampling is a type of probability sampling and other options are non- probability sampling examples .
Sampling :
Sampling is defined as a technique that selects individual members or subsets from a population to help determine characteristics of the population as a whole.
Croach and Housden postulate that a sample is a finite number taken from a large group for testing and analysis, and that the sample can be taken as representative of the group as a whole.
There are two main types of sampling:
i) probability sampling
ii) Non-probability sampling
A) probability sampling:
It is defined as the sampling technique which researchers use a related method to draw probability theory samples from a larger population.
The most important requirement for probabilistic sampling is that everyone in the population has a known equal chance of being selected.
Probability Samples:
1. Stratified Sampling: Stratified sampling is a type of sampling technique that divides the total population into smaller groups or strata to complete the sampling process. Hierarchies are formed based on some common characteristics of demographic data.
2. Cluster Sampling: Cluster sampling is a probabilistic sampling technique in which researchers divide a population into multiple groups (clusters) for research purposes. Researchers then select random groups using simple sampling techniques for data collection and data analysis.
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Which digits are most important when determining that 8923 is greater than 8884
Answer:
hundreds would say the hundreds because they're both in the 8000s and you want to look at the first different digits ihni so i hope this helps
Step-by-step explanation:
A farmer wants to fence an area of 24 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be (in ft) in order to minimize the cost of the fence? smaller value ft larger value ft.
The lengths of the sides of the rectangular field in order to minimize the cost will be length = 6000 feet and width = 4000 feet .
In the question ,
it is given that ,
the area that farmer need to fence = 24 million square feet
let the length of field be [tex]=[/tex]"x" and
let the width of rectangular field be [tex]=[/tex]"y" .
So , the area of the rectangular field = x.y = 24
So , y = 24/x .
given that the field is divided into half ,
So , the required fencing will be
S = 2x + 3y
Substituting y = 24/x in the equation,
we get ,
S = 2x + 3(24/x)
S = 2 + 72/x
Differentiating the equation "S [tex]=[/tex] 2 [tex]+[/tex] 72/x" with respect to "x" ,
dS/dx = 2 - 72/x²
to minimize the cost of fencing , we equate ds/dx to 0 ,
we get
2 - 72/x² = 0
x² = 36 million feet
x² = 36000000
x = 6000 feet
and y = 24/x = 24million/6000
= 24000000/6000
= 4000 feet
Therefore , The length of the rectangular field is 6000 feet and the width of the rectangular field is 4000 feet .
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Point K is located at (-5,-5) on the coordinate plane. Point K is reflected over the y-axis to create point K. What ordered pair describes the location of K'?
The reflection of the point K across the y-axis is (5, -5)
How to determine the image of the reflection?From the question, the point is given as:
Point K = (-5, -5)
Rewrite this point as
K = (-5, -5)
The transformation is given as
Reflection across the y-axis
Mathematically, this transformation can be represented as
(x, y) = (-x, y)
So, we have
K' = (5, -5)
Hence, the image of the reflection is (5, -5)
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Answer:
(5, -5)
Step-by-step explanation:
The other guy is 100% right!
There are three roses and eight daisies in a vase what is the ratio of all flowers in the vase to daisies???what is the ratio of roses to all flowers in the vase ???
Answer:
11:8
3:11
Step-by-step explanation:
The total is 11 (3+ 8)
Given 49−−√=7, which of the following statements is true?
The correct statement regarding the sentence square root of 49 = 7 is given as follows:
C. 7 is the length of the side of a square whose area is 49.
How to obtain the area and the perimeter of a square?
Considering a square of side length s, we have that the area and the perimeter of the square are given as follows:
In the context of this problem, the expression is given as follows:
square root of 49 = 7.
For a square with area of 49 units squared, the side length is obtained as follows:
s² = 49
s = square root of 49
s = 7.
Which means that option C is the correct option.
Missing InformationThe problem is given by the image shown at the end of the answer.
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What is an equation of the line that passes through the points (-1, 3) and (-2,-1)?
Answer: y = 4x + 7
Step-by-step explanation:
It's a line, so the formula is y = mx + b.
(x₁, y₁) = (-1, 3)(x₂, y₂) = (-2, -1)Slope(m): [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}} =\frac{-1-3}{-2-(-1)} =\frac{-4}{-1} =4[/tex]
Y-intercept(b):
[tex]y=4x+b\\3=4(-1)+b\\3=-4+b\\b=3+4=7\\[/tex]
Therefore, y = mx + b = 4x + 7.
If 6s = 24, does 6s ÷ 6 = 24 ÷ 6? Why or why not?
Answer:
Yes.
Step-by-step explanation:
if 6s=24, s = 4 because 6 x 4 = 24
so
6s divided by 6 = 24 divided by 6 because 6 x s = 24
SOO
24 divided by 6 = 24 divided by 6
HELP ME ASAP!! PLEASEEE I GOTTA SUBMIT THIS IN 6 MINUTES
The domain and range of the function is given by D:{x|∞<x<∞} and
R:{y|∞<y<∞}
In the given graph we can see that the graph is of straight line .
We know that the straight line graph of the function is of the form
y = mx + c
Now we can say that the graph of the given function is of that form.
The graph passes through (-7,0) and (-5,3)
Slope of the line= 3 / 2
Equation of the line is
y-3 = -3/2(x+5)
or, 2y+3x+9 = 0
Here the domain will be all possible values of x and range will be all possible values of y.
Domain : {x|∞<x<∞}
Range : {y|∞<y<∞}
A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.
A is the domain and B is the co-domain if a function f: A →B exists that maps every element in A to an element in B. 'b', where (a,b) R, provides the representation of an element 'a' under a relation R.
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A bobsled team is practicing runs on a track, Their first run takes 4.85 minutes. On each of the two runs, the team's time changes by -5 1/2% compared to the previous time.
A- What was the team's time, rounded to the nearest hundredth of a minute on their final run?
B- Explain how you check your answer for reasonableness.
Answer:
A. 4.33 minutes
B. it will be about 11% less than the initial time (4.85 -0.54)
Step-by-step explanation:
You want to know the team's final time if it decreases by 5 1/2% on each of two runs after their initial run time of 4.85 minutes. And you want to know how to check the answer for reasonableness.
A. Final runIf the time decreases by 5.5% on each run, it is multiplied by (1 -5.5%) = 0.945 on each run. The time after 2 more runs will be ...
(4.85 min)(0.945)(0.945) ≈ 4.33 min
The team's time on the final run was about 4.33 minutes.
B. Reasonableness checkFor small percentages, the product of small percentage changes is nearly the same as the sum of the percentage changes. That is, two changes by -5.5% will be about the same as a change of 2 × (-5.5%) = -11%.
Of course a decrease of 11% is a decrease of 10% and another decrease of 1%. This makes the estimated time be ...
4.85 -0.485 -0.0485 ≈ 4.85 -0.54 = 4.31
The estimate is a larger change than the actual change, so the computed value of 4.33 is judged to be reasonable. (The actual effect of two -5.5% changes is about a -10.7% change.)
__
Additional comment
This "add the percentages" is a suitable way to check the reasonableness of all sorts of problems involving percent changes, including problems involving investments or loan interest.
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Which of the following numbers is a composite number? A. 31 B. 47 C. 43 D. 33
Given m and n are parallel lines. 1 is a transversal.
Which of the following angles are congruent to <5? Select ALL that apply
Answer: Angles 1, 3, 7
Step-by-step explanation:
∠7 is vertical to ∠5
∠1 is corresponding to ∠5
∠3 is opposite interior angle of ∠5, it is also vertical to ∠1
Which of the following is an equation for the constant of proportionality? A k=y+xk=y+x B k=yxk=yx C k=xyk= y x D k=y−xk=y−x E k=yxk= x y
An equation for the constant of proportionality is (b) y = kx
How to determine the constant of proportionality?From the question, we have the options to represent the given parameters
An equation that represents a constant of proportion passes through the origin
So, we have the following points
(x, y) = (0, 0) and (x, y)
The slope (k) is then calculated as
Slope = (y₂ - y₁)/(x₂ - x₁)
So, we have
k = (y - 0)/(x - 0)
Evaluate the difference
k = y/x
Make y the subject
y = kx
Hence, the constant of proportionality has an equation of (b) y = kx
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a manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting. it is believed that the machine is underfilling the bags. a 9 bag sample had a mean of 441 grams with a standard deviation of 25. a level of significance of 0.025 will be used. assume the population distribution is approximately normal. determine the decision rule for rejecting the null hypothesis. round your answer to three decimal places.
The null and alternative hypothesis are H0 : μ = 444; Ha : μ < 444.
In the given question we have to determine the decision rule for rejecting the null hypothesis.
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 444 gram setting.
[tex]\mu_{0}[/tex] = 444
A 9 bag sample had a mean of 441 grams with a standard deviation of 25.
A level of significance of 0.025 will be used.
There have claim that the machine is underfilling the bags.
So , the null and alternative hypothesis are
H0 : μ = 444
Ha : μ < 444
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the length of the longer leg of a right triangle is 25 cm more than seven times the length of the shorter leg. the length of the hypotenuse is 26 cm more than seven times the length of the shorter leg. find the side lengths of the triangle.
The side lengths of the triangle is 17, 144, 145
Let x be the length of the short leg
The length of the longer leg of a right triangle is 25 cm more than seven times the length of the shorter leg
The length of the long leg is 25 + 7x
The length of the hypotenuse is 26 cm more than seven times the length of the shorter leg.
The length of the hypotenuse is 26 + 7x
(26 + 7x)² = (25 + 7x)² + x²
676 + 364x + 49x² = 625 + 350x + 49x² + x²
0 = x² -14x - 51
0 = (x - 17)(x + 3)
{-3, 17}
Length cannot be negative.
The length of the long leg is 25 + 7x = 25 + 7(17) = 144
The length of the hypotenuse is 26 + 7x = 26 + 7(17) = 145
Therefore, the side lengths of the triangle is 17, 144, 145
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Sami made $23,400 last year in income from his job. He worked 30 hours per week and worked all 52 weeks of the year, What was his hourly pay
rate?
Sami made !
per hour and $
per week.
So, lets think about the information we are given.
Sammy earns 23,400 in a given year.
In a year, he works 52 weeks.
Per week, he works 30 hours.
Find hours -> find pay.
To find hours, multiply number of weeks by hours
52 * 30 = 1560
He works 1560 hours per year.
To find hourly income, divide total money per year by hours per year. He makes 15 dollars per hour.
Find $ per week.
Hourly rate by hours per week
15 * 30 =450 per week
Hope this helps :)
Answer:
Sami had an hourly pay rate of $15 an hour
Step-by-step explanation:
Multiply 52 by 30 and you get 1,560, this is the total number of hours sami worked in a year.
If Sami made $23,400 in one year and worked 1,560 hours, you divide the total amount of hours work and total amount of money made to get an hourly pay rate of $15 an hour.
What is the quotient of (-168) + (-14) + (-3)? Pls help me
A: -36
B: -4
C: 4
D: 36
Answer: B: -4
Step-by-step explanation: -168/-14 = 12
12/-3 = -4
Please solve the question below
Through proportionality, we find out that the value of [tex]y[/tex] is 25/4 when [tex]x[/tex] is doubled, 25/9 when [tex]x[/tex] is tripled, 25/36 when [tex]x[/tex] is increased to 5 times its original value, 1 when [tex]x[/tex] is increased by 5 times its original value, and 400 when [tex]x[/tex] is reduced by 75%.
It is given to us that -
[tex]y[/tex] is inversely proportional to [tex]x^{2}[/tex]
This implies that -
[tex]y[/tex] ∝ [tex]\frac{1}{x^{2} }[/tex]
[tex]= > y=\frac{k}{x^{2} }[/tex] ----- (1)
where, [tex]k[/tex] = Constant of proportionality
It is also given to us that for a particular value of [tex]x[/tex], [tex]y[/tex] is 25.
From equation (1) and from the above statement, it can be said that -
[tex]x^{2} =\frac{k}{y} \\= > x^{2} =\frac{k}{25}\\= > x=\frac{\sqrt{k} }{5}[/tex] ------ (2)
Now, we have to find out the value of [tex]y[/tex] when [tex]x[/tex] -
a) is doubled
=> [tex]x_{1} = 2x[/tex] ---- (3)
Using equation (3) in equation (1),
[tex]= > y=\frac{k}{(x_{1}) ^{2} }\\= > y=\frac{k}{(2x)^{2} }\\= > y=\frac{k}{4x^{2} }[/tex]---- (4)
Substituting the value of [tex]x[/tex] from equation (2) in equation (4), we have
[tex]y=\frac{k}{4x^{2} }\\= > y=\frac{k}{4(\frac{\sqrt{k} }{5} )^{2} } \\= > y=\frac{25k}{4k}\\ = > y=\frac{25}{4}[/tex]
Thus, the value of [tex]y[/tex] is 25/4 when [tex]x[/tex] is doubled.
b) is tripled
=> [tex]x_{2}=3x[/tex] ---- (5)
Using equation (5) in equation (1),
[tex]= > y=\frac{k}{(x_{2} )^{2} } \\= > y=\frac{k}{(3x)^{2} } \\= > y=\frac{k}{9x^{2} }[/tex]------ (6)
Substituting the value of [tex]x[/tex] from equation (2) in equation (6), we have
[tex]y=\frac{k}{9x^{2} }\\= > y=\frac{k}{9(\frac{\sqrt{k} }{5} )^{2} } \\= > y=\frac{25k}{9k} \\= > y=\frac{25}{9}[/tex]
Thus, the value of [tex]y[/tex] is 25/9 when [tex]x[/tex] is tripled.
c) increased to 5 times its original value
[tex]x_{3}= x+5x\\= > x_{3}=6x[/tex]
From equation (2),
[tex]x_{3}=6x\\= > x_{3}=6(\frac{\sqrt{k} }{5} )\\= > x_{3}=\frac{6\sqrt{k} }{5}[/tex]----- (7)
Using equation (7) in equation (1),
[tex]y=\frac{k}{(x_{3}) ^{2} } \\= > y=\frac{k}{(\frac{6\sqrt{k} }{5} )^{2} } \\= > y=\frac{25k}{36k} \\= > y = \frac{25}{36}[/tex]
Thus, the value of [tex]y[/tex] is 25/36 when [tex]x[/tex] is increased to 5 times its original value.
d) increased by 5 times its original value
[tex]x_{4}=5x\\= > x_{4}=5(\frac{\sqrt{k} }{5}) \\= > x_{4}=\sqrt{k}\\[/tex]------ (8)
Using equation (8) in equation (1),
[tex]= > y=\frac{k}{(x_{4}) ^{2} }\\= > y=\frac{k}{(\sqrt{k} )^{2} } \\= > y=1\\[/tex]
Thus, the value of [tex]y[/tex] is 1 when [tex]x[/tex] is increased by 5 times its original value.
e) reduced by 75%
[tex]= > x_{5}= x-(\frac{75}{100} )x\\= > x_{5}=\frac{100x-75x}{100}\\ = > x_{5}=\frac{25x}{100} \\= > x_{5}=0.25x[/tex]
Substituting the value of [tex]x[/tex] from equation (2) in the above equation,
[tex]x_{5}=0.25x\\= > x_{5}=0.25(\frac{\sqrt{k} }{5} )\\= > x_{5}=0.05\sqrt{k}[/tex]----- (9)
Using equation (9) in equation (1),
[tex]= > y=\frac{k}{(x_{5}) ^{2} }\\= > y=\frac{k}{(0.05\sqrt{k}) ^{2} } \\= > y= \frac{1}{0.0025}\\ = > y= 400[/tex]
Thus, the value of [tex]y[/tex] is 400 when [tex]x[/tex] is reduced by 75%.
Therefore, through proportionality, we find out that the [tex]y[/tex] is 25/4 when [tex]x[/tex] is doubled, 25/9 when [tex]x[/tex] is tripled, 25/36 when [tex]x[/tex] is increased to 5 times its original value, 1 when [tex]x[/tex] is increased by 5 times its original value, and 400 when [tex]x[/tex] is reduced by 75%.
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Triangle ABC ~ Triangle DEF. Triangle ABC has
side lengths of 7, 9, and II. Triangle DEF has side
lengths of 17.5, 22.5, and x. Find the length of the
longest side of triangle DEF
192.5 the length of the longest side of triangle DEF .
What do you mean by congruent?
It is claimed that two figures are "congruent" if they can be positioned exactly over one another. Both the shape and size of the bread slices are same if you lay one slice on top of the other. Congruent refers to having precisely the same shape and size.Triangle ABC ~ Triangle DEF.
SO, both triangle sides are equal .
7/17.5 = 9/22.5 = 11/x
1/17.5 = 11/x
x = 11 * 17.5
x = 192.5
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8 8.3 8.8.3
a)
How many sticks would be in pattern number 6?
b) How many sticks would be in pattern number n?
if aaron tunes into his favorite radio station at a randomly selected time, there is a 0.20 probability that a commercial will be playing.
About 20% of the time Aaron tunes in to his favored station, there will be a commercial playing.
Given info;
The assumption is that over a significant number of days, 20% of the time he tunes in to his favorite station, an ad will be playing. This is based on the idea of relative frequency.
The relative frequency of event A, which is calculated by dividing the number of desired outcomes by the total outcomes, will be off over a large number of experiments, according to the likelihood of an outcome A of a%.
When he dials into his preferred station, there is a 0.2 probability that a commercial will start playing.
The conclusion is that over a long number of days, an advertisement will be playing about 20% of the time he tunes in to his preferred station.
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HELP GIVING BRAINILEST
Answer:
A: AC/AE = BC/BD
What is the average of the following equations? X + 3, 2x - 4, 3x - 6, 2x - 5, and 2x.
Please show your work. I will give you 50 points. I have 6 of these questions I need help with very badly. Thank you!!
The average of the given 5 equations is; x' = 2x - 1.6
What is the average of the equations?In mathematics, average is also called the mean and it has the formula as;
x' = ∑fx/∑f
Now, we are given the equations as;
x + 3, 2x - 4, 3x - 6, 2x - 5, and 2x.
Thus;
∑fx = x + 3 + 2x - 4 + 3x - 6 + 2x - 5 + 2x
∑fx = 10x - 8
The number of expressions given is 5 and so ∑f = 5
Thus;
x' = (10x - 8)/5
x' = 2x - 1.6
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helppppppppppp plssssssssssssssssssssssssssss
Answer:
answer is 5
Step-by-step explanation:
Simplify the following expression.
(14x + 9y) + (41x + 27y)
Answer:
55x+36y
Step-by-step explanation:
1. Group similar terms: 14x+41x+9y+27y
2. Add: 55x+36y
What is the correct way to break 12 into parts and multiply each part by 67
O 12 *610 2+2.6=20+12 = 32
O 12*6 10-6+2-6=60+12=72
O 12*6 1.6+2-6=6+12= 18
O 12 *6 10 2+10-6-20+60=80
According to algebra, we can break 12 into parts such that each X value when multiplied by 6 gives a total of 72. Thus, the 2nd option is correct.
Divide the quantity "12" into parts (the number of parts is not specified) and multiply each part by 6.
If you don't want to divide 12, the straight forward way is to simply multiply 12 by 6. 12 x 6 = 72
If we decompose 12 into 12 parts,
X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂
In this case X₁ represents the first unit of the number 12. X₂ represents the second unit of the number 12. X₁₂ represents the last unit of the number 12. Therefore, X₁ + X₂ + X₃ + X₄ + X5 + X₆ + X₇ + X₈ + X₉ + X₁₀ + X₁₁ + X₁₂ = 12
Each X value is the number 1. There are 12 locations and each case has its own identity. Multiplying each X value by 6 gives a total of 72.
According to algebra, we can break 12 into parts such that each X value when divided by 6 gives a total of 72. Thus, the 2nd option is correct.
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If a farmer wants his irrigation system to cover an area of 2 square miles, and his
sprinkler rotates through 50 degrees, what is the diameter of his circular field to the
nearest hundredth of a mile?
The diameter of his circular field is 18miles
What is sprinkler?
A sprinkler irrigation system is a tool used to irrigate (water) lawns, gardens, golf courses, and other areas. They are also utilised for cooling and dust control in the air. Sprinkler irrigation is a technique for applying water in a way that is similar to rainfall: it is controlled. Pumps, valves, pipes, as well as sprinklers are just a few of the possible components of the network used to distribute the water. Sprinklers for irrigation can be used in residential, commercial, and agricultural settings. Both sandy soil and uneven terrain with insufficient water supply can benefit from it. The rotating nozzle-topped perpendicular pipes are linked to the main pipeline at regular intervals. Water leaks from the rotating nozzles when it is pressurised and forced through the main pipe.
The irrigation sprinkler in this instance is angled.
θ = 50 = 50 π/ 180 rad.
It mists a sphere-shaped area.
A = 2/(2 miles).
If the sprinkler's length is
miles, L. It will be watered within the circle's radius.
Hence,
L^2 = A when divided by two in radians.
⇒ L = √ (2 A / θ)
= √ [(2 x 2 x 180) /40 π]
≈ 18 miles
Hence, The diameter of his circular field is 18 miles
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2. Use the areas of the two identical squares to explain why 5² + 12² = 13² without
doing any calculations.
The equation can be proved by taking Pythagorean Triplets into consideration, therefore 5^{2} + 12^{2} = 13^{2}
What are Pythagorean Triplets?
The "Pythagorean Triple" is a collection of three positive numbers, a, b, and c, that satisfy the following rule:
a^{2} + b^{2} = c^{2}
From the figure two in the attached image it can be very well observed that 5,12 and 13 are making a pythagorean triplets, therefore it can be said 5^{2} + 12^{2} = 13^{2}
Hence Proved.
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