For the month of November, there has been a depreciation of almost $1,089.60.
By deducting the expected residual value from the cost of the tractor and dividing the result by the total projected operational life in hours, let's first get the depreciation per hour:
A tractor's depreciation per hour is calculated by deducting the residual value from the purchase price, and multiplying the result by the number of hours the tractor will be in use.
[tex]\rm D = \dfrac {136,700 - 14,500} { 18,800}\\D = \$6.81[/tex]
Multiplying the depreciation per hour by the number of hours the tractor was used to get the depreciation for the month of November
[tex]D_m = 6.81 \times 160\\D_m = \$1,089.60[/tex]
Therefore, for the month of November, there has been a depreciation of almost $1,089.60.
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g at what rate is the diagonal of a cube increasing if its edges are increasing at a rate of 18.4 cm/s? (use decimal notation. give your answer to three decimal places.) rate is cm/s
The diagonal of a cube increasing at a rate of 31.869 cm/s.
It is given that edges are increasing at a rate of 18.4 cm/s.
We know the formula of diagonal of cube which is
D = [tex]\sqrt{3}[/tex] a
where a is the edge.
Now we will differentiate the diagonal equation with respect to time er get,
[tex]\frac{dD}{dt}[/tex] = [tex]\sqrt{3}[/tex] [tex]\frac{da}{dt}[/tex]
Given that edges are increasing at a rate of 18.4 cm/s, this means
[tex]\frac{da}{dt}[/tex] = 18.4 cm/s
Therefore
[tex]\frac{dD}{dt}[/tex] = [tex]\sqrt{3}[/tex] (18.4) cm/s
[tex]\frac{dD}{dt}[/tex] = 1.732(18.4) cm/s
[tex]\frac{dD}{dt}[/tex] = 31.869 cm/s
Hence the diagonal of a cube increasing at a rate of 31.869 cm/s.
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Use the marginal tax rate chart to answer the question.
Marginal Tax Rate Chart
Tax Bracket
Marginal Tax Rate
$0–$10,275
10%
$10,276–$41,175
12%
$41,176–$89,075
22%
$89,076–$170,050
24%
$170,051–$215,950
32%
$215,951–$539,900
35%
> $539,901
37%
Determine the effective tax rate for a taxable income of $63,425. Round the final answer to the nearest hundredth.
10%
14.67%
15.18%
22%
The effective tax rate for a taxable income of $63,42 using the marginal tax rate chart rounded to the nearest hundredth is 15.18%.
The correct answer option is option C
What is the effective tax rate?Income = $63,425 and marginal rates
Find tax payable amount:
Tax bracket $0 - $10,275Marginal rate = 10%Amount taxable = $10275 -$0
= $10275
Tax payable = 10% of 10275
= 0.1 × 10275
=$1027.5
Tax bracket $10,276 - $41,175Marginal rate = 12%
Amount taxable = $41,175 - $10,276
= $30899
Tax payable = 12% of 30899
= 0.12 × $30899
= $3707.88
Tax bracket $41,176 - $89,075Marginal rate = 22%Amount taxable = $89,075 - $41,176
= $22249
Tax payable = 22% of 22249
= 0.22 × $22,249
= $4894.78
Total tax payable amount = $10275 + $3707.88 + $4894.78
= $9630.16
Effective tax rate = (Total tax payable amount/ income) × 100
= ($9630.16 / $63,425) × 100
= 15.18%
Therefore, the effective tax rate for a taxable income of $63,425 is 15.18%.
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a triangular parcel of land has sides of lengths 590 feet, 980 feet and 1423 feet. a) what is the area of the parcel of land? area
The area of the parcel of land is 226934.799 square feet.
Given:
a triangular parcel of land has sides of lengths 590 feet, 980 feet and 1423 feet.
a).
Let a = 590 , b = 980, c = 1423 lengths
s = semi-perimeter
= 1/2(a+b+c)
= 1/2(590+980+1423)
= 1496.5
s-a = 1496.5-590
= 906.5
s-b = 1496.5-980
=516.5
s-c = 1496.5-1423
= 73.5
Heron's formula for area:
A = [tex]\sqrt{(s(s-a)(s-b)(s-c))}[/tex]
= √1496.5(906.5)(516.5)(73.5)
= √51499402997.4
≈ 226934.799
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If $2x-y=7,$ what is the value of $7-8x+4y$?
Answer:
[tex]7-8x+4y=-21[/tex]
Step-by-step explanation:
[tex]2x-y=7 \implies 8x-4y=28 \\ \\ \implies 7-8x+4y=7-28=-21[/tex]
You are facing north. You turn 45 degrees to your left. Take two steps forward. Turn 180 degrees. Turn 45 degrees to your right. Take one step back. Turn 90 degrees to your right. Which one of these statements is true?* You are facing the same direction you started. You are facing east. You are facing south. You are standing on the same spot you started out on. You are facing west.
Answer: Northeast - unless you are at the South Pole, in which case you are still facing North.
Step-by-step explanation
Sequence:
Facing North
90 degrees left = facing West
180 degrees right = facing East
reverse = facing West
45 degrees left = facing Southwest
reverse = facing Northeast
The average of 3 numbers is 19 two of the numbers are 17 and 24 what is the third number.
The required third number of the given triad is 16.
What is average?The average is characterized as the mean worth which is equivalent to the proportion of the amount of the quantity of a given arrangement of values to the complete number of values present in the set.
According to question:Given two number are 17 and 24.
Let the third number is x,
Average of three number is 19
17 + 24 + x/3 = 19
41 + x = 57
x = 16
Thus, the third number is 16.
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find the 3x3 matrix that corresponds to the composite transformation of a scaling by 2, a rotation of 90o about the origin
The 3x3 matrix after composite transformation of scaling by 2, a rotation of 90° about origin is [tex]\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right][/tex].
Let A=[tex]\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right][/tex] be a 3x3 matrix
scaling the matrix A by 2 then the result will be
[tex]2A=2\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right]\\\\=\left[\begin{array}{ccc}2a&2b&2c\\2d&2e&2f\\2g&2h&2i\end{array}\right][/tex]
now, rotating the resultant matrix by 90° in counterclockwise direction about the origin, we get
[tex]=\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right][/tex]
Thus, a 3x3 matrix after composite transformation of scaling by 2, a rotation of 90° about origin is [tex]\left[\begin{array}{ccc}2c&2d&2i\\2b&2e&2h\\2a&2d&2g\end{array}\right][/tex]
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In experiments in which participants manually tracked a complex pattern that consisted of two segments that were random patterns on every trial and one segment that was the same every trial, the results showed that the participants improved
more on the repeated segment than the two random segments, and reported they were not aware that one segment was the same on every trial.
For the given experiments , participants concluded that complexity is more on the random patterns on every trials compare to one segment that was same for every trial.
As given in the question,
Steps for the experiment where participants manually tracked a complex pattern which consists of two segments are as follow:
In first case : One segment consists of random patterns on every trial that is on every new trial there is new random pattern which participant has to follow.
In second case : Another segment consists of same pattern on every new trial.
After conducting experiment reports conclude that repeated segment with the same pattern present more improved result compare to random patterns. As participants were aware of the same segment on each new trial.
Therefore, given experiments of participants proves the complexity is more on the random patterns on every trials compare to one segment same for every trial.
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Select the graph that correctly displays the solution of the system of inequalities.
y> 2x²+x-3
y<-x² + 5x
By plotting the obtained solutions on the graph we get graph as below.
The given system of inequalities are y >2x²+x-3 and y <-x² + 5x.
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.
Put x=0, 1, 2 and 3 in the given inequalities, we get
Now, with y >2x²+x-3
When x=0
y >2(0)²+0-3
y >-3
When x=1
y >2(1)²+1-3
y >0
When x=2
y >2(2)²+2-3
y >7
When x=2
y >2(3)²+3-3
y >18
With the inequalities y<-x²+5x
When x=0
y<-0²+5(0)
y<0
When x=1
y<(-1)²+5(1)
y<6
When x=2
y<(-2)²+5(2)
y<14
When x=3
y<(-3)²+5(3)
y<24
By plotting the obtained solutions on the graph we get graph as below.
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The um of firt 11 term of an A. P i 19 and the um of firt 19 term i 11. Find the um of the firt 30 term
The sum of the first 30 terms of this arithmetic expression (A.P) will be -30.
Let the first term of the Arithmetic progression be a
And the common difference of this progression be d
An be the nth term of the progression
Sn be the sum of the first nth term of the progression
As we know,
Sn = n/2( 2a + (n-1)d)
S11 = 11/2(2a + (11-1)d)
S11 = 11/2(2a + 10d) = 11(a + 5d)
As S11 = 19
Therefore, 19 = 11(a + 5d)
19 = 11a + 55d………….(i)
Again, S19 = 11 = 19/2 ( 2a + 18d )
11 =19( a + 9d)
11 = 19a + 171d………(ii)
Now, multiplying equation (i) by 19 and (ii) by 11 and then subtracting them, we get
361 = 209a + 1045d
121 = 209a + 1881d
240 = -836d
d = -240/836 = -60/209
Putting the value of d in equation (i), we get
11a - 55x60/209 = 19
11a = 3300/209 + 19
11a = 7271/209
a = 661/209
Therefore sum of first 30 terms are S30 = 30/2(2(661/209)+29(-60/209))
S30 = 15(1322/209 -1740/209) = 15 (-418/209) = 15(-2) = -30
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1. If f(x) = x + 3 and g(x) = x² + 2x - 3, find [gxf](x).
The answer is g(f(x)) =(x+6)(x+2)
From the question, we have
f(x) = x + 3 and g(x) = x² + 2x - 3
g(f(x)) = g(x + 3)
=(x + 3)² + 2(x + 3) - 3
=x² + 9+6x+2x+6-3
=x² + 8x+12
=x² + 6x+2x+12
=(x+6)(x+2)
The answer is g(f(x)) =(x+6)(x+2)
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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What is the remainder when x 2 2x 1 is divided by x 1?.
The remainder when x² + 2x + 1 is divided by x + 1 is 0.
Given,
The polynomial functions; x² + 2x + 1 and x + 1
We have to find the remainder when x² + 2x + 1 is divided by x + 1
Remainder theorem;-
Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder.
Here,
p(x) = x² + 2x + 1
g(x) = x + 1
Now,
x + 1 = 0
x = -1
Then,
p(-1) = -1² + 2 x -1 + 1 = 1 - 2 + 1 = - 1 + 1 = 0
That is,
The remainder when x² + 2x + 1 is divided by x + 1 is 0.
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What are the 4 types of linear functions?.
Answer: direct variation, slope-intercept form, standard form and point-slope form.
Step-by-step explanation:
What are the types of linear functions?
There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
What are basic linear functions?
Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
inductive or deductive all numbers divisible by 6 are also divisible by 3. 36 is divisible by 6. so, 36 is divisible by 3.
Answer:
deductive
Step-by-step explanation:
How many solutions does this linear system have Y =- 6x 2?.
The linear system of equation y =-6x+2 has infinitely many solutions.
The linear equation is y = -6x+2 .
Now for any value of x we find the value of y ,
at x=0 ,y = 2
at x=1 , y = -4
at x=-2 , y = 14
Hence there are infinitely many solutions on the line . All points on the straight line are solutions.
The collection of variable values in a linear equation that yields every feasible solution is referred to as the "solution of a linear equation." In order to model real-world issues, linear equations include unknown quantities as one or more variables.
The locations where the lines or planes used to illustrate the linear equations intersect or meet are known as the solutions. The set of values for each variable in a system of linear equations is known as the solution set.
Disclaimer: the complete question is :
How many solutions does this linear system have Y =- 6x + 2?.
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case sales price per unit variable costs per unit total fixed costs break-even in units 1 $20 $16 $40,000 2 25 5 5,000 3 30 81,000 9,000 4 4 48,000 8,000
Case 1: Break-even units are 10000
Case 2: Fixed cost is $1,00,000
Case 3: Variable cost is $20
Case 4: The sale price is $15
Break-even in units = Fixed cost/Selling price - Variable cost
Case 1:
Sales price = $20
Variable cost = $16
Fixed cost = $40,000
Break-even point = 40000/20-16
= 10000 units
Case 2:
Sales price = $25
Variable cost = $5
Break-even units = 5000
Finding fixed cost:
5000 = Fixed cost/25-5
Fixed cost = 5000* 20
= 1,00,000
Case 3:
Sales price = $29
Fixed cost = 81000
Break-even units = 9000
Finding variable cost:
9000 = 81000/29-variable cost
2,61,000 - 9000*Variable cost = 81000
Variable cost = 20
Case 4:
Variable cost = $9
Fixed cost = $48000
Break-even units = 8000
Finding sales price:
8000 = 48000/Sales price - 9
8000*Sales price - 72000 = 48000
Sale price = $15
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70 pupils in a sports centre are surveyed. The pupils can only use the swimming pool and the gym. 28 pupils use the swimming pool and the gym. 48 pupils use the swimming pool. 39 pupils use the gym. Find the probability to select a pupil that uses neither the swimming pool nor the gym.
The probability that a pupil uses neither pool nor gym is 11/70
What is Probability?Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6.
Number of pupil that can use pool and gym = 28
Number of people that can use pool = 48
Number of people that can use gym = 39
Number of people that can use pool only = 48 - 28 which is 20
Number of people that can use gym only = 39 - 28 = 11
Total number of persons that can use either pool, gym or both = 20 + 11 + 28 which is 59
Number of people that cannot use either or both of the facilities = 70 - 59 which is 11.
Probability = required outcome / possible outcome
Required outcome = 11
possible outcome = 70
Probability = 11/70
In conclusion, the probability that a pupil uses neither swimming pool nor gym is 11/70
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Prove the theorem by first setting up a one-to-one correspondence between permutations of nn objects with nini indistinguishable objects of type ii, ii=1, 2, 3, ..., kk, and the distributions of nn objects in kk boxes such that nini objects are placed in box ii, ii=1, 2, 3, ..., kk and then applying that the number of different permutations of nn objects, where there are n1n1 indistinguishable objects of type 1, n2n2 indistinguishable objects of type 2, ...., and nknk indistinguishable objects of type kk is n!n1!n2!...nk!n1!n2!...nk!n!.Theorem: The number of ways to distribute nn distinguishable objects into kk distinguishable boxes so that nini objects are placed into box ii, ii=1,2,...,kk, equals
In every distribution of k boxes containing n distinct objects, where box i receives ni. Let Si stand for the set that includes those ni identifiable items for i = 1, 2,..., k.
Given,
he collection of objects can be expressed equivalently as k, i = 1 Si has the following object types: left| S 1 |right| = n 1S number of items of type 1, left |S2| right| = n 2S number of objects of type 2, and so on.
In this case, type i denotes objects that fit into box i and are therefore interchangeable. By simply permuting these sets, one can obtain all conceivable distributions of objects. kS I 1, 2, and S i
The number of distribution options is equal to the number of these permutations for i=1, 2,..., k.
n!/(n₁!,n₂!...nₐ!)
That is,
In every distribution of k boxes containing n distinct objects, where box i receives ni. Let Si stand for the set that includes those ni identifiable items for i = 1, 2,..., k.
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x d and y d are two points in d-dimensional euclidean space. the euclidean distance between x and y is: be the region inside the d-dimensional hypersphere with radius r, centered at the origin. the volume of s is the gamma function that we saw earlier in class when talking about the beta distribution.
The calculation of the separation between two locations on a plane is done using the Euclidean distance formula. This equation estimates the separation between two places.
[tex]d = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} }[/tex]
Our perception of space is frequently incorrect in high dimensions since it was created in two and three dimensions. Think about randomly distributing 100 points into a unit square. The range [0, 1] is used to produce each coordinate independently and evenly at random.
Choose a point, calculate the distances between it and every other point, and then chart the distribution of those distances. The points are then uniformly generated at random in a 100-dimensional unit cube when the dimension is increased. Around an average distance, the distribution of distances becomes concentrated.
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se strong induction to show that every natural number can be expressed as the sum of distinct powers of 2. (for exam- ple, 21
It is proved that every natural number can be expressed as the sum of distinct powers of 2 using strong induction.
What is natural number?Natural numbers are those in mathematics that are utilized for counting and ordering. Cardinal numbers are those used for counting, while ordinal numbers are those used for ranking. The positive integers, also referred to as non-negative integers, are a subset of the natural numbers. A few examples are 1, 2, 3, 4, 5, 6,.... In other words, the set of all whole numbers other than 0 (i.e., 23, 56, 78, 999, 100202, etc.) is known as the natural numbers.
Here,
The statement is obviously true for n=0.
Assume that we are given an n≥1 and that it is true for all m with 0≤m<n.
When n=2^m then m<n and therefore m=∑k2^pk with finitely many pk, all of them different. It follows that n=∑2^(pk+1) with all pk+1 different.
When n=2^(m+1) with an m as before then n=2^0+∑k2^(pk+1) with all pk+1 different and different from 0.
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John read the quarter of the time that tom read. Tom read only two-fifth of the time that sasha read. Sasha read twice as long as mike. If mike read 5 hours, how long did john read?.
The required read time taken by the John in the given question is 2 hours.
How ratio help us to solve this problem?A ratio can be characterized as the relationship or examination between two quantities of a similar unit to check how greater is one number than the other one.
According to question:Sasha read = 2(mike read)
given, mike read 5 hours
Then, Sasha = 10 hours
Similarly,
Tom read = (Sasha read)2/5
Tom read = 4 hours
Now, john read = (Tom read)/4 = 4/2
John read = 2 hours
Thus, read time of John is 2 hours.
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what is a perpendicular
Answer:
at an angle of 90° to a given line, plane, or surface.
"dormers and gables that extend perpendicular to the main roofline
Step-by-step explanation:
How do you determine if a graph crosses or touches the x-axis?.
Answer:The zeros of a function f correspond to the x-intercepts of its graph. If f has a zero of odd multiplicity, its graph will cross the x-axis at that x value. If f has a zero of even multiplicity, its graph will touch the x-axis at that point.
you have weekly store-level unit sales data as well as binary promotion information about if the product was on display or not. you run a linear regression model (yunit.sales
~ xdisplay.promotion. This means that the promotion has a positive effect on unit sales, and the model can accurately predict unit sales based on whether the promotion is present or not.
What are regression models?Regression models are statistical models that are used to forecast a continuous result information based on one or more predictor variables. These models are employed to comprehend how the predictor and outcome variables relate to one another as well as to forecast the result variable. In disciplines like economics, finance, and psychology, regression models are frequently employed to forecast variables like future sales or psychological health. Regression models can be either linear or nonlinear, and they can also have numerous predictor variables. These models typically include an intercept and a slope for each predictor variable, which are used to calculate the predicted outcome.
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:
Ethan needs to add together two whole numbers
and wants to estimate the answer first.
He rounds both numbers to 1 significant figure,
which gives him 300 and 600, and adds them
together to get an estimate of 900.
What is the greatest possible difference
between his estimate and the true answer to the
addition?
The required greatest difference between the estimate and the true value is 45.
Given that,
Ethan needs to add together two whole numbers and wants to estimate the answer first. He rounds both numbers to 1 significant figure, which gives him 300 and 600 and adds them together to get an estimate of 900.
The rounding of values is superseding a number with an inexact value that has a more ephemeral, more uncomplicated, or more direct representation.
Here,
For the estimated number 900, the least number that can be rounded to the number 900 is 855,
Now,
Difference = 900 - 855 = 45
Thus, the required greatest difference between the estimate and the true value is 45.
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Where is the outlier in a data set?.
Answer:
It is data outside what you would expect.
Step-by-step explanation:
An example would be if I asked everyone is a class how many dogs they dad living with them. I would expect to get answers like 0, 1, 2, 3 or 4. If someone answered 115 that would be be an outlier, it is outside all of the data that I have collected.
In triangle ABC points X and Z are in AB and Y is on AC such that XY and BC are parallel and ZY and XC are parallel. If AZ=8, ZX=4, then what is XB?
If length of AZ=8 units and the length of ZX=4, then the length of the side XB is 6 units
Consider the triangle ABC
The points X and Y are on the line AB and Y is on the line AC
The lines XY and BC are parallel
Therefore
AX / XB = AY / YC
Similarly, the lines ZY and XC are parallel
AZ / ZX = AY / YC
Therefore the the proportion will be
AX / XB = AZ / ZX
The length of the line AX = AZ + ZX
= 8 + 4
= 12 units
Then the proportion will be
12 / XB = 8 / 4
Cross multiply the terms
12 × 4 = 8 × XB
XB = (12 × 4) / 8
XB = 48 / 8
XB = 6 units
Hence, the length of the side XB is 6 units
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Find the values of x and y. Y= 3x+29
Answer:
x= 37 , y= 143
Step-by-step explanation:
okay so to start out we must write an equation in order to find the angles of a parallelogram.
2x+2y=360 (the angles of a parallelogram always equal 360 degrees)
next, since we know that the angle for y is "y+3" we can substitute this into the equation
2x+2(y+3)=360
next, since it is given that y=3x+29 we can now substitute that into the equation
2x+2[(3x+29)+3]=360
now, SOLVE!
[tex]2x+2[(3x+29)+3]=360 \\2x+2(3x+32)=360 \\2x+6x+64=360\\8x+64=360\\8x=296\\x=37[/tex]
okay, now we know that x=37 degrees so now we must find y. this can be done by substituting 37 into (3x+29)+3 or simply, 3x+32
[tex]y=3x+32\\y=3(37)+32\\y=111+32\\y=143[/tex]
don't forget to check your work!
2(37)+2(143)=360
there you go! so x= 37 degrees and y= 143 degrees
Does an X or y-axis scale have to always start at zero?.
No, X or y-axis scale does not have to always start at zero. In a line chart, it's OK to start the axis at a number other than zero
Define axis.A line that is used to take or mark measurements is known as an axis in mathematics. Two crucial axes of the coordinate plane are the x and y axes. A horizontal number line is the x-axis, while a vertical number line is the y-axis. The coordinate plane is created by the perpendicular intersection of these two axes.
Given,
No, X or y-axis scale does not have to always start at zero.
A line chart encodes data using location (x, y coordinates), whereas a bar chart represents data using length. In a line chart, it's OK to start the axis at a number other than zero despite many claims that they are always misleading since this minute difference influences how a reader utilizes the chart.
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What is 18 ÷ 2/3.
What is -5/6÷9/10.
THESE ARE TWO SEPARATE QUESTIONS. 60 points because they are 2. If you figure them both out I will give Big Brain.
Answer:
18 ÷ 2/3 = 27
-5/6 ÷ 9/10 = -0.925
