The equation of the line of best fit is: y = -1.15x + 102.8 and Using the equation of the line of best fit, the predicted cost is: $62.55
What is the Equation of a Line of Best Fit?
The equation of a line of best fit is represented by the equation, y = mx + b, where m is the slope and b is the initial value.
1. Using two points, (72, 20) and (20, 80):
Slope (m) = change in y / change in x = (80 - 20)/(20 - 72) = 60/-52
Slope (m) = -1.15.
Substitute m = -3 and (a, b) = (72, 20) into y - b = m(x - a)
y - 20 = -1.15(x - 72)
y - 20 = -1.15x + 82.8
y = -1.15x + 82.8 + 20
y = -1.15x + 102.8
The equation of the best line of fit is y = -1.15x + 102.8.
2. Monthly heating cost, y, for a month with an average temperature of 35°F (x) will be calculated by substituting x = 35 into y = -1.15x + 102.8.
y = -1.15(35) + 102.8
y = 62.55
The predicted monthly cost is $62.55.
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which of the following is not a polynomial identity
Option B does not represent a polynomial identity.
What is a polynomial identity?Polynomial identities are equations that are true for all possible values of the variable. The polynomial identities are -
(x + y)² = x² + 2xy + y²(x – y)² = x² – 2xy + y²(x²– y²) = (x + y)(x – y)(x + a)(x + b) = x²+ (a + b)x + ab.(x + y + z)²= x² + y² + c² + 2xy + 2yz + 2zx.(x + y)³ = x³ + y³ + 3xy (x + y)(x – y)³ = x³ – y³ – 3xy (x – y)(x³ + y³) = (x + y)(x² – xy + y²)Given are the equations as shown in the image.
The equation that is not a polynomial identity is option B.
Therefore, Option B does not represent a polynomial identity.
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What are all the prime numbers between 36 and 50?.
What is the solution for Y =- 3x 8?.
The y-intercept is (0, 8).
The equation, y = mx + b, is the slope-intercept form of a straight line.
Here, x and y are the coordinates of the points, m is the gradient, and b is the intercept of the y-axis.
y = mx + b is the slope-intercept form of the equation of a straight line. In the equation y = mx + b, m is the slope of the line and b is the intercept.
The value of b is equal to y when x = 0, and m shows how steep the line is. The slope of the line is also called the gradient.
The y-intercept is what you get when you plug in x = 0
Similarly, the x-intercepts are what you get when you plug in y = 0
So, because we're finding the y-intercept, plug in 0 for x and solve for y.
Therefore, the y-intercept is (0, 8).
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A doctor's office is deciding between buying 2 different sized cups. The 2 cups are shown. 1.5 in 4 in. --2 in.--- 6 in. Before deciding which size cup to buy, they determine how much water each size cup can hold. How much more water, in cubic inches, can the larger cup hold than the smaller cup? Round your answer to the nearest hundredth. Use the pi key on your calculator for pi. (On the EOC, this problem specifically says - in cubic inches so you need to add that to your answer. EX. 5.81 cubic inches)
The water that the larger cup can hold more than the smaller cup, given the two cups is 15. 71 cubic inches
How to find the amount of water ?To find the amount of water, first find the volume of the cups using the volume of a cone formula. This formula is:
= Pi x r² x height of cone / 3
The amount of water the larger cup can hold is:
= Pi x 2² x 6 / 3
= 25. 13 cubic inches
The water in the smaller cup is:
= Pi x 1.5² x 4 / 3
= 9. 42 cubic inches
The difference is:
= 25. 13 - 9. 42
= 15. 71 cubic inches
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Whats 2/3 + 3/5 in fractions
Answer:
19/15
2/3+3/5
Multiply each by 3
10/15+9/15=19/15
[tex] = \frac{2}{3} + \frac{3}{5} \\ [/tex]
[tex] = \frac{2}{3} \times \frac{5}{5} + \frac{3}{5} \times \frac{3}{3} \\ [/tex]
[tex] = \frac{10}{15} + \frac{9}{15 \\ } [/tex]
[tex] = \frac{10 + 9}{15} \\ [/tex]
[tex] = \frac{19}{15} \\ [/tex]
[tex] = 1 \frac{4}{15} \\ [/tex]
A factory can produce two products x and y with a profit approximated by p=14x+22y-900.
The vertices of the feasible region are (0,100) (0,700) (400,500)
The minimum profit is (0,100) and the maximum profit is (400,500)
Given that, P=14x+22y-900 where p is the profit
y > x +100 y must exceed the production of x by at least 100 units
x+2y<1400
x>0
y>0
We cannot produce negative quantities
Substitute y = x+100 into x+2y <1400
x+2(x+100) < 1400
x+2x+200 <1400
3x+200<1400
Subtract 200 from each side
3x<1200
Divide by 3
x<400
y = x+100
y = 400+100
y = 500
(400,500)
y > x +100
when x=0 y > 100
x+2y <1400
0+2y <1400
2y <1400
y <700
When x=0 y = 700
a) The vertices of the feasible region are (0,100) (0,700) (400,500)
b) Maximum and minimum profit occur at the vertices.
P=14x+22y-900
P(0,100) = 14(0) +22(100)-900 =2200-900=1300
P(0,700) = 14(0) +22(700)-900 =15400-900=14500
P(400,500) = 14(400) +22(500)-900 =5600+11000-900=15700
Thus, The vertices of the feasible region are (0,100) (0,700) (400,500)
The minimum profit is (0,100) and the maximum profit is (400,500)
Complete question: A factory can produce two products, x and y, with a profit approximated by P=14x+22y-900. The production of y must exceed the production of x by at least 100 units. Moreover, production levels are limited by the formula x+2y<1400.
a) Identify the vertices of the feasible region.
b) What production levels yield the maximum profit, and what is the maximum profit?
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Find the coordinates of the circumcenter of AABC with vertices A (1, 0), B (8, -7), and
(7,-4).
The coordinates of the circumcentre P(x, y) of ΔABC with vertices A (1, 0), B (8, -7), and C(7,-4) is P(6.4, 1.6).
What is circumcentre?If there is a circle that encompasses all of the vertices of a polygon, it has a circumcenter that is the centre of the circle. The circumcentre and ensuing circumcircle of a triangle are both always distinct.
Let P(x, y) be the circumcentre
Then
PA = PB = PC
⇒PA² =PB² =PC²
Now, PA² = PB²
⇒ (x−1)² +(y−0)² =(x−8)² +(y+(-7))²
⇒ x = 8 − y
And, PB² = PC²
⇒ (x−8)² +(y+(-7))²= (x−7)² +(y−(-4))²
⇒ x = 24− 11y
Factor out x from both equations
8 − y = 24− 11y
10y = 24 - 8
10y = 16
y = 16/10
y = 1.6
For x
x = 8 − y
x = 8 − 1.6
x = 6.4
Thus, the coordinates of the circumcentre P(x, y) of ΔABC with vertices A (1, 0), B (8, -7), and C(7,-4) is P(6.4, 1.6).
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In the triangle below,
x = [ ? ] cm. Round to the
nearest tenth.
15 cm
35
90°
The value of side x for the right-angle triangle is 8.6 cm.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that the sides are Hypotenuse H = 15 cm, perpendicular = x, and the base is y.
The value will be calculated as,
x = [ sin(35) x 15 ]
x = 8.6 cm
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acide whether the two expressions are equivalent and explain your reasoning.
5x + 2-3x and 2x+2
3(x-1)+2 and 3x+2
4 (2x - 2) and -2 (4-4x)
Equivalent: Yes or No
Equivalent: Yes or No
Equivalent: Yes or No
Justification:
Justification:
Justification
When two expressions can be written similarly or when they can be combined into a single, simpler expression, they are said to be equivalent.
What is the best way to tell if two expressions are comparable to one another?
Let's evaluate each expression pair separately.
8. (n2+4)-n2 and 4n. (n2+4)-n2 = n2+ 4 - n2 = 4, which is not the same as 4n.
NOT THE SAME
9. The product of 3x + 5 and 2(x + 3) 2(x + 3) equals 2x + 6, not 3x + 5.
NOT THE SAME
10. 15 - 6x and 15(1 - 6x) (1 - 6x)
In other words, 15(1 - 6x) = 15 - 90x, which is not equal to 15 - 6x, is NOT EQUAL.
11. (y + y + 2 + y) + 3y and 6y + 2 (y + y + 2 + y) + 3y equals y+y+y+y +2 + 3y, which equals 3y + 2 + 3y and 6y + 2.
It is equivalent to the other phrase.
EQUIVALENT
12. 8y - 3 + 10y and 3 (6 - 1)
8y - 3 + 10y = 8y + 10y - 3 = 18y - 3 3(6 - 1) = 3(5) = 15
Both of the expressions are incompatible.
NOT THE SAME.
Only the expressions shown in position 11 are equivalent.
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What is the quotient 3x3 10x2 10x 4 )/( x 2?.
After solving, the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2) is 3x^2 + 4x + 2.
In the question, we have to find the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2).
The polynomial is 3x^3 + 10x^2 + 10x + 4.
We have to divide the given equation by x + 2 to find the quotient.
Four operations, namely divide, multiply, subtract, and bring down, can be used to break down the division process into phases.
1: Find the appropriate integer to use as the divisor for the given number.
2: Multiply the integer (quotient) and divisor to obtain the amount to be deducted from the payout.
3: Deduct the amount from the dividend.
4: Bring down the balance and any additional digits from the dividend in step four.
5: Continue the procedure outlined above until the remainder equals zero or less than the divisor.
x+2 ) 3x^3 + 10x^2 + 10x + 4 ( 3x^2 + 4x + 2
3x^3 + 6x^2
- -
___________
4x^2 + 10x
4x^2 + 8x
- -
______________
2x + 4
2x + 4
- -
____________
0
Hence, the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2) is 3x^2 + 4x + 2.
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The complete question is:
What is the quotient (3x^3 + 10x^2 + 10x + 4) ÷ (x + 2)?
The figure shows a line graph and two shaded triangles that are similar:
Which statement about the slope of the line is true?
A.) It is 1/6 throughout the line.
B.) It is 6 throughout the line.
C.) The slope from point O to point A is 1/6 times the slope of the line from point A to point B.
D.) The slope from point O to point A is six times the slope of the line from point A to point B.
Answer: A). It is 1/6 throughout the line
Step-by-step explanation:
work out the answer to these simultaneous equations
y=4x
y=x² - 12
-2x -y=6
-2x +8y=-30
Answer : -4
explained:
you would have to sub 2 from -2x and -30(-30 - 2 = -32) to get x by it self then divide 8 by 8(equals) x then divide -32 with 8 = -4
your welcome!
Julia parcourt 1200 km par mois en voiture. Elle possède
une voiture à essence qui consomme 6 L d'essence par 100 km.
Je raisonne
Pour réduire son impact écologique et économiser,
Julia s'informe sur les voitures hybrides. Elle apprend
qu'une voiture hybride consommerait
d'essence de moins que sa voiture actuelle.
Si le prix d'un litre d'essence est de 1,30 $ pendant
toute l'année, combien Julia économiserait-elle
en essence par année si elle remplaçait sa voiture
actuelle par une voiture hybride?
Answer:
Julia parcourt 1200 km par mois en voiture, donc elle parcourt 1200 x 12 = 14400 km par an.
Sa voiture actuelle consomme 6 L d'essence par 100 km, donc elle consomme 6/100 x 14400 = 864 L d'essence par an.
Si elle remplaçait sa voiture actuelle par une voiture hybride qui consomme moins d'essence, elle économiserait 864 L d'essence par an.
Si le prix d'un litre d'essence est de 1,30 $, alors Julia économiserait 864 x 1,30 = 1129,20 $ par an si elle remplaçait sa voiture actuelle par une voiture hybride.
Unit 4 Lesson 5 Cumulative Practice Problems
1. The table shows the monthly revenue of a business rising exponentially since it
opened an online store.
(f)0
(f)3
months since online monthly revenue
store opened
in dollars
0
1
3
4
6
72,000
90,000
112,500
a. Describe how the monthly revenue is growing.
b. Write an equation to represent the revenue, R, as a function of months, m, since
the online store opened.
c. Find the monthly revenue 1 month after the online store opened. Record the
value in the table. Explain your reasoning.
d. Explain how we can use the value of R(1) to find R(4).
The company's monthly revenue rises by 8% on a monthly basis.
What is an exponential function?The mathematical formula f (x) = an x denotes an exponential function. a constant known as the function's base and a variable called x are present.
Any function whose constant is raised to the power of an input is said to be exponential.
An exponential function looks like this:
[tex]$y=a b^x$[/tex]
Where:
A stands for the starting point.
B is equal to 1 plus the rate r.
The following ordered pair can be seen in the table.
(x,y) = {(0,72000) (3,90000)}
The result is:
[tex]$90000=72000 \times b^3$[/tex]
Subtract 72000 from both sides.
[tex]$1.25=b^3$[/tex]
Take the cube's two side roots.
[tex]$b=\sqrt[3]{1.25}$$b=1.08$[/tex]
Observe that:
[tex]$b=1+r$[/tex]
The result is:
[tex]$1+r=1.08$[/tex]
Take 1 away from each side.
r= 0.08
Describe as a percentage
r= 8%
As a result, the company's monthly revenue increases by 8%.
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2. A lemonade recipe calls for cup of lemon juice for every cup of water.
a. Use the table to answer these questions.
i. What does x represent?
ii. What does y represent?
iii. Is there a proportional relationship between x and y?
b. Plot the pairs in the table in a coordinate plane.
X
1
2
3
4
y
4
1
2
3
²14
1
Answer: a. i. In this context, x represents the number of cups of water.
ii. In this context, y represents the number of cups of lemon juice.
iii. Yes, there is a proportional relationship between x and y. The recipe states that for every cup of water, there should be one cup of lemon juice. This means that as the amount of water increases, the amount of lemon juice also increases in the same proportion.
b. To plot the pairs in the table in a coordinate plane, we can use the values of x and y as the coordinates. For example, the first pair (x=1, y=4) would be plotted at the point (1, 4) on the coordinate plane. Similarly, the second pair (x=2, y=1) would be plotted at the point (2, 1), and so on.
Please note that the table provided with X, Y and ²14,1 is incorrect, it is not possible to plot these values in a coordinate plane as the values are not valid.
Step-by-step explanation:
I need help with this. Please don't rush and take your time.
Answer:
The correct answer is B.
Which equation represents the graph?
Answer:D y=-2x-1
Step-by-step explanation:
To solve this problem, we first need to look at the direction of the line to determine whether the slope is positive or negative. Since the left portion of the line is Quadrant 2 and the right portion in quadrant 4, the slope will be negative. Anytime the line looks like \ it will be negative, while / is positive. This immediately eliminates answers A and C. Now, our next order of business is to find the slope of the line. To do this, we need to pick two points on the line and use the equation (y2-y1)/(x2-x1). Any points on the line will work, so even if you do not use the same as me, you still should get the same answer (this is a good way to check!)
point 1: (-2,3)
point 2: (0,-1)
(-1 - 3) / (0 - -2) = (-1 - 3) / (0 + 2) = -4/2 = -2
Since the slope is -2, we know the answer is d. Hope this helps
What is the distance between the pair of points 2 3 and 4 1?.
The distance between given pair of points ( 2, 3 ) and ( 4, 1) is equal to
2√2.
As given in the question,
Given pair of points is represented by the coordinates
( x₁ , y₁ ) = ( 2, 3 )
( x₂ , y₂ ) = ( 4, 1 )
Standard formula to find the distance between two pair of points is :
= √( y₂ - y₁ )² + (x₂ - x₁ )²
Substitute the values to get the distance between two pair of points we have,
= √ ( 1 - 3 )² + ( 4 - 2 )²
= √ 2² + 2²
= √4 + 4
= √8
= 2√2 units.
Therefore, the distance between the given pair of points is equal to 2√2.
The above question is incomplete , the complete question is:
What is the distance between the pair of points (2, 3) and (4, 1) ?
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How many solutions does Y =- 3x 7 have?.
The equation, Y = - 3x + 7 has infinitely many solutions.
Here we are given the equation y = - 3x + 7.
Now this equation has 2 variables. when an equation has 2 variables, there must be at least 2 equations for the system to have a unique solution, hence the given equation cannot have 1 unique solution.
If we plot this equation on the graph we will see that it makes a never-ending line.
Here for every value of x, we get a different value of y, which can be easily seen in the graph.
Therefore we cannot conclude that this will have no solution. Hence since there can be infinite possible answers to the above equation, this has infinitely many solutions.
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Correct Question
How many solutions does Y = - 2x + 3 have?
Find (−7z−4)−(−3z+1) .
Answer:
[tex] \sf \: -4z - 5 [/tex]
Step-by-step explanation:
Given expression,
→ (-7z - 4) - (-3z + 1)
Let's simplify the expression,
→ (-7z - 4) - (-3z + 1)
→ -7z - 4 + 3z - 1
→ (-7z + 3z) + (-4 - 1)
→ (-4z) + (-5)
→ -4z - 5
Hence, the answer is -4z - 5.
express the following as a ratio in it's simplest form: 48 seconds: 1 minute
Answer:
4:5
Step-by-step explanation:
We know that 1 minute is equals to 60 seconds.
So the ratio is now:
48 seconds : 60 seconds
We need to simplify the ratio in its simplest form. 12 goes into both 48 and 60 so:
48/12 = 4 seconds
60/12 = 5 seconds
So the ratio 48 seconds: 1 minute in its simplest form is:
4 seconds : 5 seconds
Please help !!
Consider the line y = -2-4x.
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Slope of a perpendicular line:
Slope of a parallel line:
For the line y = -2-4x, the slope of a line parallel to this line is -4 and the slope of a line perpendicular to this line is 1/4.
What is slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The equation for the line is - y = -2 - 4x.
The slope of a line is represented by the coefficient of the x term. In this case, the slope of the line y = -2 - 4x is -4.
The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. The negative reciprocal of -4 is 1/4.
So, the slope of a line perpendicular to y = -2 - 4x is 1/4.
The slope of a line parallel to a given line is the same as the slope of the given line.
So the slope of a line parallel to y = -2 - 4x is -4.
Therefore, the parallel and perpendicular slope is -4 and 1/4 respectively.
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A bulk food store sells two types of trail mix that are a combination of nuts, chocolate, and dried fruit. One of the trail mixes is 75% nuts, and the other is 35% nuts. A customer puts in a special order for 10 pounds of trail mix that is 60% nuts. How much of each trail mix should be combined to create the special order trail mix?
The amount of each trail mix that should be combined to create the special order trail mix are:
6.25 pounds of the trial that contains 75% nuts.
3.75 pounds of the trial that contains 35% nuts.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
Trial mix A = x
= 75% nuts.
Trial mix B = y
= 35% nuts
Now,
Two equations are:
x + y = 10 _____(1)
x = 10 - y _____(2)
0.75x + 0.35y = 10 x 0.60 ______(3)
Substituting (2) in (3)
0.75 (10 - y) + 0.35y = 6
7.5 - 0.75y + 0.35y = 6
7.5 - 6 = 0.75y - 0.35y
1.5 = 0.40y
y = 1.5/0.40
y = 3.75
Now,
x = 10 - 3.75
x = 6.25
Thus,
6.25 pounds of the trial that contains 75% nuts.
3.75 pounds of the trial that contains 35% nuts.
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please help me. i have no idea what to do
Answer:
F
Step-by-step explanation:
(x + 2)² + (y - 3)² = 37
intersection points with the x-axis means that their y-values are 0 !
that is the whole trick, as I am sure you experienced already with lines and y-intersects (x = 0) and x-intersects (y =0).
so, we need to solve for x, when y = 0 :
(x + 2)² + (-3)² = 37
x² + 4x + 4 + 9 = 37
x² + 4x - 24 = 0
the solution to a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (-4 ± sqrt(4² - 4×1×-24))/(2×1) =
= (-4 ± sqrt(16 + 96))/2 = (-4 ± sqrt(112))/2 =
= (-4 ± sqrt(16×7))/2 = (-4 ± 4×sqrt(7))/2 =
= -2 ± 2×sqrt(7)
x1 = -2 + 2×sqrt(7)
x2 = -2 - 2×sqrt(7)
so, F is the right answer.
(PLEASE HELP QUICKLY) Aiden and his children went into a grocery store and he bought $14 worth of apples and bananas. Each apple costs $1.75 and each banana costs $0.70. He bought a total of 14 apples and bananas altogether. By following the steps below, determine the number of apples, x, and the number of bananas, y, that Aiden bought.
Determine three ways to have a total of 14 apples and bananas
Answer:
6 apples and 5 bananas
Step-by-step explanation:
x + y = 11
x = 11 - y
1.75x + 0.70y = 14
1.75(11 - y) + 0.7y = 14
19.25 - 1.75y + 0.7y = 14
5.25 = 1.05y
y = 5
x = 11 - 5 = 6
Answer: 4 apples and 10 bananas
Step-by-step explanation:
Consider: a=apple, b=bananas
1) a + b = 14 // 14 total of apples and bananas
a = 14 - b
2) 1.75a + 0.70b = $14 // $14 worth of apple and bananas
3) Substituting 1) in 2):
1.75(14 - b) + 0.70b = 14
24.5 - 1.75b + 0.70b = 14
b = 10.5 / 1.05
b = 10
4) Substituting 3) in 1):
a = 14 - 10
a = 4
The box-and-whisker plot below represents some data set. What is the value of the upper quartile?
The value of the upper quartile is 65.
In the box plot, what is the upper quartile?The lower quartile, which is represented by the left border of the box, is the value that the first 25% of the data falls within. 25% of the data are to the right of the upper quartile value, which is indicated by the upper quartile at the right border of the box.
The left whisker represents the bottom 25% of the data, the left half of the box represents the second 25%, the right half of the box represents the third 25%, and the right whisker represents the top 25%.
The value of the upper quartile is 65.
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Help pleaseee!! I need it done before Monday
In point-slope form, the equation of the line through the indicated points is y - 2 = -4/3. ( x - 4 ).
What is the formula for the line passing through the specified points?Y - Y1 = m is the line's equation in point slope form (x – x1).As a result, the equation for a line passing through the origin and having a slope of m is given by y - 0 = m(x = 0), which equals y = mx. Given the information in the query;
A Point (4, 2)
x₁ = 4
y₁ = 2
B Point (1, 6)
x₂ = 1
y₂ = 6
We start by figuring out the line's slope.
Slope m is equal to (y2 - y1)/(x2 - x1)
Slope: m = (6 - 2) ( 1 - 4 )
(4)/ Slope m ( -3)
Slope m=-4/3
Then, simplify the point slope formula y - y1 = m(x - x1) using the slope -4/3 and point (4,2).
y - y₁ = m(x - x₁)
y - 2 = -4/3( x - 4 ) ( x - 4 )
As a result, y - 2 is the equation of the line in point-slope form that passes through the indicated places.
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Help me write a simplified expression for the perimeter of a square, please.
Answer:
12x² - 40
Step-by-step explanation:
The perimeter of a two-dimensional shape is the distance all the way around the outside.
As a square has four sides of equal length, the perimeter of a square is four times the length of one side.
[tex]\begin{aligned}\textsf{Perimeter}&=4(3x^2-10)\\&=4 \cdot 3x^2+4 \cdot (-10)\\&=12x^2-40\end{aligned}[/tex]
Answer:
Perimeter of square = 12x² - 40
Step-by-step explanation:
Perimeter of square formula,
→ P = 4 × Side
→ [ P = 4a ]
Now the perimeter of square is,
→ P = 4 × (3x² - 10)
→ P = 4(3x²) - 4(10)
→ P = (4 × 3)x² - 40
→ [ P = 12x² - 40 ]
Hence, perimeter is 12x² - 40.
Four students were asked to convert the polar coordinates (4, 11pi/6) to a complex number using technology. Select the correct work.
The complex number z = (4, 11π / 6) in rectangular form is z = 2√3 - i 2 (z = 3.464 - i 2). (Correct choice: C)
How to convert a complex number into rectangular formHerein we find a complex number in polar form, whose definition is shown below:
[tex]z = r\cdot e^{i\,\theta}[/tex]
Likewise,
z = (r, θ)
Where:
r - Normθ - Direction, in radians.This number is equivanlent to the following expression in rectangular form:
z = a + i b
Where:
a = r · cos θ
b = r · sin θ
If we know that r = 4 and θ = 11π / 6, then the complex number in rectangular form is:
a = 4 · cos (11π / 6)
a = 2√3
b = 4 · sin (11π / 6)
b = - 2
The rectangular form of complex number z = (4, 11π / 6) is the number z = 2√3 - i 2.
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