Answer:
68 miles
Step-by-step explanation:
The total distance can be determined from the fractions.
SolutionLet d represent the total distance of the race.
The distance running is 1/2d. The distance swimming is 1/4d. The remaining distance is 17 miles.
Remaining = total distance - distance running - distance swimming
17 mi = d -1/2d -1/4d = 1/4d . . . . . . . . use known fractions
68 mi = d . . . . . . . multiply by 4
The total distance of the race is 68 miles.
__
Additional comment
This would be a very difficult race. A typical "iron man" race has a swimming distance under 2.5 miles, less than 1/10 of the distance running. The biking distance is typically about 4 times the running distance of "only" 26 miles. An iron man race can take about 17 hours to complete.
This race has a 17-mile swimming segment, which would take a fast swimmer on the order of 8 hours, by itself. (This is 2.7 times the length of a "marathon" swim.) Here, the running distance is 34 miles, about 30% longer than a marathon.
In the regular octagon below, if AP = 12 cm. and BC = 19 cm, find its area.
First symmetrically cut the octagon to get 8 pieces. (So that you will get the idea that this polygon is divided into 8 triangles)
Then find the area of one of the triangles:
Area of Triangle = [tex]\frac{1}{2} * b* h[/tex]
A = [tex]\frac{1}{2}[/tex] × 12 × 19
A = 114 cm²
To find the area of the whole octagon shape:
A = 114 × 8 = 912 cm²
Hope it helps!
Answer:
Step-by-step explanation:
You cannot do this unless you are certain that P is the center of the octagon. I don't know if that's solvable from the information given. So I will make the assumption that P is the center.
Determine the midpoint of BC. Call it E. Draw a line from P to E. By symmetry EP = AP. BE = 1/2 * BC = 19/2 = 9.5 by construction
You have a trapezoid witch is 1/4 the area of the octagon. Three more trapezoids can fit into the octagon.
Formula
Area = (AP + BE)*PE / 2
Givens
AP = 12
BE = 9.5
PE = 12
Solution
Put the givens and constructions into the formula
Area = (12 + 9.5)*12/2
Area = 21.5 * 12/2
Area = 21.5 * 6
Area = 129
That's the area of one of the trapezoids. Multiply the area here by 4.
You get 516.
Question 10 of 10
The function F(x) = log5 x is decreasing.
A. True
B. False
SUBMIT
Answer: False
Step-by-step explanation:
The base is more than 1, so the function is increasing.
The surface areas of two similar cylinders are 6cm² and 54cm².
i. Find the scale factor for the enlargement.
ii. If the larger cylinder has height 12cm, how high is the smaller one?
iii. What is the ratio of their volumes?
Answer:
3, 4, 27
Step-by-step explanation:
1) Area scale factor = 9
Length scale factor = 3 because √9
2) 12/3 = 4
3) 3³ = 27
Is the function y = 3x4 - 1 linear or nonlinear?
the concentration of a drug in a patient's bloodstream t hours after the drug was administrated presented by the equation c(t) = 5t-t²+1 (in mg/mL). construct a table of values for c(t) for t=1,2,5,10. Round off answer to tree decimal places. use use the table to sketch a graph and interpret the result by giving the (a) domain, (b) range, (c) vertical asymptote, and (d) horizontal asymptote.
The graph of the function has no asymptotes.
The table of values of c(t)The function is given as:
c(t) = 5t - t² + 1
When t = 1, 2, 5, 10;
We have:
c(1) = 5(1) - 1² + 1 = 5
c(2) = 5(2) - 2² + 1 = 7
c(5) = 5(5) - 5² + 1 = 1
c(10) = 5(10) - 10² + 1 = -49
So, the table of values is
t c(t)
1 5
2 7
5 1
10 -49
See attachment for the graph of the function
The domain
From the question, we understand that t represents time.
Time cannot be negative i.e. t ≥ 0 The time does not exceed 5.2 i.e. t ≤ 5.2So, the domain is 0 ≤ t ≤ 5.2
The range
From the graph, the maximum of the graph is 7.25
So, the range is 0 ≤ f(t) ≤ 7.25
Asymptotes
From the graph, we can see that the graph has no asymptotes.
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A parent made x cupcakes for each of the 109 students in the fourth grade. Which expression could be used to determine the total number of cupcakes made?
109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade. This can be obtained by forming the algebraic expression for the given conditions.
Find the required expression:Algebraic expression is made up of numbers, operations and variables.Algebraic expression is true for all values of x. For example, 2x, 5x + 9 etc.
Given that,
A parent made x cupcakes for each of the 109 students in the fourth grade.
The total number of students in the class = 109
The number of cupcakes one student gets = 1 × x = x
⇒ The number of cupcakes 109 student gets = 109 × x = 109x
Hence 109x is the expression that could be used to determine the total number of cupcakes made given that a parent made x cupcakes for each of the 109 students in the fourth grade.
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Consider this quadratic equation. x2 3 = 4x which expression correctly sets up the quadratic formula to solve the equation?
The expression which correctly sets up the quadratic formula to solve the equation is (A) [tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex].
What is an expression?
In mathematics, an expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) Expressions are similar to phrases. A phrase in language may comprise an action on its own, but it does not constitute a complete sentence.To find which expression correctly sets up the quadratic formula to solve the equation:
Theory of quadratic equation - A quadratic equation is defined as any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.
An example of a quadratic equation in x is [tex]-4x^{2} +4=9x[/tex].
How to solve any quadratic equation using the Sridharacharya formula?
Let us represent a general quadratic equation in x, [tex]ax^{2} +bx+c=0[/tex] where a, b and c are coefficients of the terms.
According to the Sridharacharya formula, the value of x or the roots of the quadratic equation is -
[tex]x=\frac{-b+-\sqrt{(b)^{2}-4(a)(c) } }{2a}[/tex]
The given equation is [tex]x^{2} -4x+3=0[/tex]
Comparing with the general equation of quadratic equation, we get a = 1, b = -4 , c = 3.
Putting the values of coefficients in the Sridharacharya formula,
[tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex] which is (A).
Therefore, the expression which correctly sets up the quadratic formula to solve the equation is (A) [tex]\frac{-(-4)+-\sqrt[]{-4^{2}-4(1)(3) } }{2(1)}[/tex].
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The complete question is shown below:
Consider this quadratic equation. x^2+3=4x. Which expression correctly sets up the quadratic formula to solve the equation?
hey im pretty bad at this homework stuff can someone please help me answer all this
Answer:
Step-by-step explanation:
1. $135
2. a. no
b. $340
3. a. 33
b. $135*33= $4455+340= $4795
4. a. $7630 = 135v + 340
b. 135v + 340 = 7630
135v = 7290
v = 54 vacuums
A particle starts from rest at a fixed point A and moves in a straight line with an acceleration which, t seconds after leaving A, is given by a = 4t. After 2 seconds the particle reaches a point B and the acceleration then ceases. Find:
i) the velocity when the particle reaches B
ii) the distance AB
The particle moves on immediately with acceleration given by -3t, where t seconds is the time after the particle leaves A, until it comes to rest at a point C. Find:
iii) the value of t when the particle reaches C
(iv) the distance AC
(a) The velocity when the particle reaches B is 8 m/s.
(b) The distance between point A and B is 5.33 m.
(c) The value of t when the particle reaches C is 1.63 seconds.
(d) The distance AC is 8.7 m.
Velocity when the particle reaches BThe velocity when the particle reaches B is calculated as follows;
v = ∫a. dt
where;
v is velocitya is acceleration of the particlev = ∫(4t . dt)
v = 4t²/2
v = 2t²
v(2) = 2(2)²
v(2) = 8 m/s
Thus, the velocity when the particle reaches B is 8 m/s.
Distance ABx = ∫v
where;
x is the distance between A and Bx = ∫2t². dx
x = ²/₃t³
x(2) = ²/₃(2)³
x(2) = 5.33 m
Thus, the distance between point A and B is 5.33 m.
value of t when the particle reaches Cwhen the particle reaches point C, final velocity, vf = 0
vf = v + at
where;
v is the velocity at point0 = 8 - 3t(t)
0 = 8 - 3t²
3t² = 8
t² = 8/3
t² = 2.67
t = √(2.67)
t = 1.63 seconds
Distance between A and Cx = ∫vf
x = ∫(8 - 3t²)
x = 8t - t³
x(1.63) = 8(1.63) - (1.63)³
x(1.63) = 8.7 m
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Is anyone really good at math?
Answer: 12 cm
Step-by-step explanation:
[tex]\mathtt{Using\ the \ pythagorean \ theorem: \\}[/tex]
[tex]a^2+b^2=c^2, \\\ we\ can\ plug\ in\ values\ for\ a,\ b,\ and\ c[/tex]
[tex]L=a\ and\ M=b\ and\ N=c[/tex]
Therefore,
[tex]L^2+35^2=37^2\\L^2+1225=1369\\L^2=144\\\sqrt{L^2} =\sqrt{144} \\L=\pm12\\Taking\ only\ the\ positive\ answer,\ we\ get:\\\large\boxed{L = 12cm}[/tex]
We have: L² + M² = N²
=> L² = N² - M² = 37² - 35² = 144 = 12²
=> L = 12
ANSWER: B.12
OK done. Thank to me :3
Select the correct answer. what is the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11?
1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.
2. The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists at 0.531.
What is the probability that a person who exists older than 35 years contains a hemoglobin level between 9 and 11?Let the number of the person who is older than 35 years have a hemoglobin level between 9 and 11 be x.
From the given table it is clear that the total number of the person who is older than 35 years exists 162.
75+x+40 = 162
x+116 = 162
x = 162-116
x = 46
The number of people who are older than 35 years has a hemoglobin level between 9 and 11 exists at 46.
1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists
P = Probability who is older than 35 years has a hemoglobin level
between 9 and 11 / Person who exists older than 35
P = 46/162 = 0.284
The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.
2. Person who is older than 35 years has a hemoglobin level of 9 and above exists 46 + 40 = 86.
The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists
P = Probability who is older than 35 years has a hemoglobin level
between 9 and above / Person who is older than 35
P = 86/162 = 0.531.
The probability that a person who is older than 35 years has a hemoglobin level of 9 and above exists at 0.531.
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The following are the ages of 13 history teachers in a school district. 24, 27, 29, 29, 35, 39, 43, 45, 46, 49, 51, 51, 56 Notice that the ages are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
of
Given the triangle ABC at points A=(1,6) B=(-3,5) C=(7,1), and if the triangle is first reflected over the
y axis, and then over the x axis, find the new point A".
Select one:
O a. (1,-6)
Ob. (3,5)
Oc. (-1,-6)
O d. (1,6)
After reflected over the triangle the point a become A = (-1,-6). The option c is correct.
According to the statement
we have given that the a triangle ABC at the points A=(1,6) B=(-3,5) C=(7,1), and we have to find the points of a when the triangle is first reflected over the y axis.
So, For this purpose
we know that the when the triangle is at the x axis then the point A is A=(1,6).
But when the triangles reflected over the y - axis then the point A goes to the negative side of the graph. In other words whole of the triangle shift to the negative side of the graph. That's why the point become negative.
So, The option c is correct. After reflected over the triangle the point a become A = (-1,-6)
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Solve for x. You must show all your work to receive credit.
Step-by-step explanation:
since the 2 arc angles cover the full circle, we know their sum must be 360°.
so,
23x - 5 + 37x + 5 = 360
60x = 360
x = 6
and so the angle at V = 5×6 + 17 = 30+17 = 47°
Diego wants to paint his room purple. He bought one gallon of purple paint that is 30% red paint and 70% blue paint. Diego wants to add more blue to the mix so that the paint mixture is 20% red, 80% blue.
1. How much blue paint should Diego add? Test the following possibilities: 0.2 gallons, 0.3 gallons, 0.4 gallons, 0.5 gallons.
0.2 gallons
0.2 gallons,
0.3 gallons
0.3 gallons,
0.4 gallons
0.4 gallons,
0.5 gallons
0.5 gallons,
BoldItalicUnderlineImage (12 image limit)Increase indentDecrease indentFormula keypadUndoRedoBullet listNumbered list
Edit imageView imageDelete image
2. Write an equation in which x
represents the amount of paint Diego should add.
3. Check that the amount of paint Diego should add is a solution to your equation.
idrk but I hope you have a good day and good luck with ur answer
Complete the proofs, ASAP!!! (Geometry)
1) [tex]\triangle ABC[/tex] with [tex]\overline{AC} \cong \overline{BC}[/tex], [tex]\overline{AB} \parallel \vec{CE}[/tex] (given)
2) [tex]\angle A \cong \angle B[/tex] (base angles theorem)
3) [tex]\angle A \cong \angle 1[/tex] (corresponding angles theorem)
4) [tex]\angle B \cong \angle 2[/tex] (alternate interior angles theorem)
5) [tex]\angle 1 \cong \angle 2[/tex] (transitive property of congruence)
6) [tex]\vec{CE}[/tex] bisects [tex]\angle BCD[/tex] (if a ray splits an angle into two congruent parts, it is a bisector)
The given decimal is 0.571
Convert the decimal into fraction :
Write down the decimal divided by1
:
0.571
1
Multiply both top and bottom by1000
:
0.571
1
×1000
1000
=571
1000
Don't answer this.
A, B, and C are equal in length; each one is 4.47 units long. ABC is an isosceles triangle since two of its sides are congruent.
The information given that A, B, and C are equal in length; each one is 4.47 units long illustrates that the angle is an equilateral triangle.
Secondly, when two of its sides are congruent, then the triangle is an isosceles triangle.
How to illustrate the information?It should be noted that an equilateral triangle simply means the triangle tht had equal shape and angles. Here, since A, B, and C are equal in length; each one is 4.47 units long illustrates that the angle is an equilateral triangle.
Secondly, when two of its sides are congruent, then the triangle is an isosceles triangle. On such triangle, two out of the three sides are equal.
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Given 8 different toppings to choose from, how many 3-topping pizzas are possible?
Answer:
336 ways
Step-by-step explanation:
Use nPk which is [tex]\frac{n!}{(n-k)!}[/tex]. This is [tex]\frac{8!}{5!}[/tex]. This becomes 8×7×6 as the 8! and 5! cancel out. 8×7×6 is 336.
Total number of possible 3-topping pizzas are 336 ways.
How do you calculate the number of possible ways something can be arranged?In more general terms, if we have n items total and want to pick k in a certain order, we get: n! / (n – k)! And this is the permutation formula: The number of ways k items can be ordered from n items: P(n,k) = n (n – k)!
Given that,
Total number of items n = 8
number of picking item k = 3
Now,
p(n,k) = [tex]\frac{n!}{(n -k)!}[/tex]
p(8,5) = [tex]\frac{8!}{(8 -3)!}[/tex]
= [tex]\frac{8!}{5!}[/tex]
= [tex]\frac{8.7.6.5! }{5! }[/tex]
= 8 × 7 ×6
p(8,5) = 336 ways
Hence, Total number of possible 3-topping pizzas are 336 ways.
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how do you calculate this
Answer:
y = - 2x - 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line
m = [tex]\frac{-1-1}{0-(-1)}[/tex] = [tex]\frac{-2}{0+1}[/tex] = [tex]\frac{-2}{1}[/tex] = - 2
the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = - 2x - 1 ← equation of line
If f(x) = 3x + 1 and f^-1 = x-1/3 , then the ordered pair of f(3) =
Answer:
10
Step-by-step explanation:
f(x) = 3x + 1
f^-1 = x-1/3 , it is known as inverse function.
f(3)= 3*3 +1
=9+1
=10
To find inverse,
x=3x + 1
y=3x+1
Exchanging the position or x and y
x=3y+1
x-1=3y
.•. y=x-1/3
A ship travels due west for 94 miles. It then travels in a northwest direction for 119 miles and ends up 173
miles from its original position. To the nearest tenth of a degree, how many degrees north of west (x) did it
turn when it changed direction? Show your work.
Using the law of cosines, the ship turned 72 degrees northwest when it changed direction.
What is the law of cosines?The law of cosines states that we can find the side c of a triangle as follows:
c² = a² + b² - 2abcos(C)
In which:
C is the angle opposite to side c.a and b are the lengths of the other sides.For this problem, the parameters are given as follows:
a = 94, b = 119, c = 173.
Hence the internal angle C is found as follows:
c² = a² + b² - 2abcos(C)
173² = 94² + 119² - 2 x 94 x 119cos(C)
22327cos(C) = -6932
cos(C) = -6932/22327
C = arccos(-6932/22327)
C = 108º.
The turning angle is the outside angle, which is supplementary with C, hence:
T = 180 - C = 180 - 108 = 72º.
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Ekaete collected 12 raffle tickets. Roseline collected twice as many. How many raffle tickets did they collect in all?
Answer:
36
Step-by-step explanation:
12 times 2 which is 24 then u add 12 cause it's the amount they have together so you get 36
Lesson 1.6 Multiply by 1-digit numbers.
estimate then find the product
(only the circled ones)
The multiplication shows that the answers will be:
1. 3744
2. 8244
3. 3630
4. 2616
5. 20772
6. 7820
7. 3916
8. 3521
9. 21285
10. 54162
11. 4548
12. 2091
13. 17128
14. 55692
15. $895
16. 4300 miles
How to calculate the value?1. 416 × 9 = 3744
2. 1374 × 6 = 8244
3. 726 × 5 = 3630
4. 872 × 3 = 2616
5. 2308 × 9 = 20772
6. 1564 × 5 = 7820
7. 4 × 979 = 3916
8. 503 × 7 = 3521
9. 5 × 4257 = 21285
10. 6018 × 9 = 54162
11. 758 × 6 = 4548
12. 3 × 697 = 2091
13. 2141 × 8 = 17128
14. 7 × 7956 = 55692
15. From the information given, the cost of each ticket is $179. Also, there are 5 people that are flying.
Therefore, the total cost will be:
= $179 × 5
= $895
16. Also, for the second question, since the distance between the two cities is 2150 miles. The exact distance will be:
= 2150 × 2
= 4300 miles.
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Given the linear regression equation, y^=134. 63−2. 79x. What is the predicted value of y^ when x=45? (round answer to two decimal places, example: 3. 45)
Answer:
9.08
Step-by-step explanation:
To find the predicted value of y, put the x-value where x is in the equation and do the arithmetic.
Substitution[tex]\hat{y}=134.63-2.79x\qquad\text{given}\\\\\hat{y}=134.63-2.79(45) = 134.63-125.55\qquad\text{use 45 for x}\\\\\boxed{\hat{y}=9.08}\qquad\text{simplify}[/tex]
what do I check off
Answer:
E. >
Because 65 is greater than 56.
Sami cuts out a rectangle that has a perimeter of 48 inches and a length of 13 inches. they cut out another rectangle that is the same length and twice as wide. what is the perimeter of the new rectangle?
Answer:
70 inches
Step-by-step explanation:
the width of the original rectangle:
48/2 - 13 = 24 - 13 = 11
the new rectangle:
length: 13
width: 2(11) = 22
perimeter: 2(13+22) = 2(35) = 70
The perimeter of the new rectangle is 70 inches.
What is Area of Rectangle?The area of Rectangle is length times of width.
The perimeter of a rectangle is given by the formula P = 2(l + w)
where P is the perimeter, l is the length, and w is the width.
The first rectangle has a perimeter of 48 inches and a length of 13 inches.
48 = 2(13 + w)
24 = 13 + w
w = 11
So the first rectangle has a length of 13 inches and a width of 11 inches.
The second rectangle has the same length of 13 inches and twice the width of the first rectangle, which means it has a width of 22 inches.
P = 2(13 + 22)
= 2(35)
= 70
Therefore, the perimeter of the new rectangle is 70 inches.
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Please help.
Match the graph of the function with the function rule.
The exponential function represented on the graph is defined by the following rule:
[tex]y = 3 \times 2^x[/tex]
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
a is the initial value, which is also the y-intercept, that is, the value of y when x = 0.b is the rate of change.From the graph, we get that when x = 0, y = 3, hence the initial value is of a = 3. Then the temporary definition is:
[tex]y = 3b^x[/tex]
Also from the graph, when x = 1, y = 6, hence we can apply to the definition to find b.
[tex]6 = 3b^1[/tex]
3b = 6
b = 2.
Hence the function is:
[tex]y = 3 \times 2^x[/tex]
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Find two consecutive numbers such that the sum of four times the first and triple the second is 157. (linear function)
So, 22, 23 are the two numbers.
What is linear and polynomial function?There are two distinct but related ideas that are referred to as linear functions: A polynomial function of degree 0 or 1 is referred to as a linear function in calculus and related fields if its graph is a straight line.
Consecutive numbers are preceding and following, hence we need two numbers so that
X+1=Y
or
X- Y = -1
In addition, we are aware of
4x + 3y = 157
Let's increase the top equation by 3 times.
We get
3x - 3y = -3
Then we combine that with the bottom equation.
4x + 3y = 157
7x= 154
x = 22
Afterward, we substitute x into the initial equation,
22+1 = 23
So, 22, 23 are the two numbers.
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i need help with my algebra assignment
Answer:
[tex]Question 1\\1+i\\-1-i\\Question 2\\\\-1+i\\1-i[/tex]
Step-by-step explanation:
Complex Numbers:
Complex numbers can generally be expressed in the form: [tex]a+bi[/tex] where a and b are both real numbers, with the a part representing the real part of the complex number, and the bi representing the imaginary part.
We can also graph these numbers using the complex plane. The complex plane has the real axis where the x-axis would normally be, and the imaginary axis where the y-axis would normally be. So by this definition the "a" is what determines the horizontal position or the position on the real axis and the "b" is what determines the vertical position or the position on the imaginary axis.
I attached a diagram of the complex plane, and it's essentially the same as a normal graph, with a=x, and b=y.
Question 1:
So when a complex number lies above the real-axis, that means the imaginary part is greater than 0. When a complex numbers lies to the right of the imaginary axis, that means the real part is greater than 0.
This means we have the form: [tex]a+bi \text { where } a > 0 \text{ and } b > 0[/tex]. You can literally plug in any number for a and b, so long as it fits this. For example we can just do: [tex]1+i[/tex]
So when a complex number lies below the real-axis, that means the imaginary part is less than 0. when a complex numbers lies to the left of the imaginary axis, the real part is less than 0.
This means we have the form: [tex]a+bi \text { where } a < 0\text{ and }b < 0[/tex]. You can plug in any real number that lies within this restriction. An example would be:
[tex]-1-i[/tex]
Question 2:
Above real axis and to the left of the imaginary axis means: b>0 and a<0. So we can plug in any number into the standard form that fits this restriction. an example would be: [tex]-1+i[/tex]
Below real axis and to the right of the imaginary axis means: b<0 and a>0. So we can plug in any number into the standard form that fits this restriction. An example would be: [tex]1-i[/tex]