ASAP Please help and ThankyouThis graph shows how the total distance jack has walked depends on the number of trips he has made to school. What is the rate of change?
Answers
we will take two points on the line,
first is (0,2) and other is (1, 4)
the rate of change will be the slope of the line,
[tex]\begin{gathered} m=\frac{4-2}{1-0} \\ m=\frac{2}{1}=2 \end{gathered}[/tex]so the rate of the change is 2 km per trip
so the answer is 2
Related Questions
what value of c would complete the square for the following trinomials?
Answers
To find the value of c that will make the given expression a perfect square, we simply;
Step 1: Take the coefficient of x : that is, 6
Step 2: Divide the coefficient obtained in step 1 by 2: That is, 6/2 = 3
Step 3: Square the result in step 2: That is, 3^2 = 9
Hence, c = 9
The value of c in the first expression is 9.
Second Expression:
[tex]x^2-10x+c[/tex]Step 1: 10 ( Do not bother yourself with the negative sign, just pick the number 10)
Step 2: 10/2 = 5
Step 3: 5^2 = 25
so, c = 25
Third expression:
[tex]x^2+32x+c[/tex]Step 1: 32
Step 2: 32/2 = 16
Step 3: 16^2 = 256
So, c = 256
Fourth expression:
[tex]x^2-12x+c[/tex]Step 1: 12
Step 2: 12/2 = 6
Step 3: 6^2 = 36
So, c = 36
Last expression:
[tex]x^2+8x+c[/tex]Step 1: 8
Step 2: 8/2 = 4
Step 3: 4^2 = 16
so, c = 16
Determine which of the value(s), if any, must be excluded from the domain of the variable in the expression x^2/x^2+25Options:x=3,x=5,x=0,x=-5None
Answers
Given:
The expression is,
[tex]\frac{x^2}{x^2+25}[/tex]The domain of the function is values of independent variable for which expression is defined. Since expression is not defined when,
[tex]x^2+25=0[/tex]Sinece there is no real value of x for which denominator of expression,
[tex]x^2+25[/tex]is zero. So domain of the expression is,
[tex](-\infty,\infty)[/tex]So all values of x is included in the domain of the function. Thus answer is None.
Filling in Table (decreasing)Dependent QuantityA Helicopter flying at 3509 feet begins its descent. Itdescends at a rate of 41 feet per minuteIndependent Quantity0Complete the missing part of the tables, and make afunction that describes the Helicopter's decent133222Your answer: Not there yet, keep working3140Share with Class
Answers
(0,3509)
(1,3468)
(3,3386)
(7,3222)
(9,3140)
h=3509-41x
Explanation
Step 1
as we can see, the independent quantity is the time , and the dependent quantity is the heigth because it depends on the time.
then when time = o, t=o
[tex]0\Rightarrow3509\text{ ft}[/tex]after 1 minute the helicopter has descended 41 ft, then
when time = 1, t=1
[tex]\begin{gathered} heigth_1=3509-(1\cdot41) \\ heigth_1=3509-41 \\ heigth_1=3468 \\ (1,3468) \end{gathered}[/tex]when t=3
[tex]\begin{gathered} heigth_3=3509-(3\cdot41) \\ heigth_3=3509-123 \\ heigth_3=3386 \end{gathered}[/tex]when heigth=3222
[tex]\begin{gathered} \text{heigth}_x=3509-(x\cdot41) \\ 3222=3509-41x \\ \text{subtract 3509 in both sides} \\ 3222-3509=3509-41x-3509 \\ -287=-41x \\ \text{divide both sides by -41} \\ \frac{-287}{-41}=\frac{-41x}{-41} \\ 7=x \\ \text{hence}(7,3222) \end{gathered}[/tex]when heigth=3140
[tex]\begin{gathered} \text{heigth}_x=3509-(x\cdot41) \\ \text{3140}=3509-41x \\ subtract\text{ 3509 in both sides} \\ \text{3140-3509}=3509-41x-3509 \\ -369=-41x \\ \text{divide both sides by -41} \\ \frac{-369}{-41}=\frac{-41x}{-41} \\ 9=x \\ x=9,\text{then} \\ (9,3140) \end{gathered}[/tex]Step 2
now, the equation is
[tex]\begin{gathered} \text{Heigth}=3509-41x \\ h=3509-41x \\ \text{where} \\ h\text{ is the heigth in ft and t is the time in minutes} \end{gathered}[/tex]I hope this helps you
Bob grew 1,102 plants with 29 seed packets. With 94 seed packets, how many total plants can Bob have in his backyard? Assume the relationship is directly proportional.
Answers
If the relation between number of plants and the number of seed packets is directly proportional and x is the number of plants can Bob have for 94 seed packets, you can write;
[tex]\frac{x}{94}=\frac{1102}{29}[/tex]By solving for x in the previous expression and simplifying, you get:
[tex]\begin{gathered} x=\frac{1102}{29}\cdot94 \\ x=3572 \end{gathered}[/tex]Hence, Bob could have 3572 plants if he uses 29 seed packets.
I need help with this. Find the value ( s ) of x and y.
Answers
Answer:
x = 10
y = 71 degrees
Explanation:
Let's go ahead and find x as shown below;
[tex]\begin{gathered} 38+(7x+1)=(10x+9)\text{ (external angle is equal sum of opposite interior angles)} \\ 7x-10x=9-38-1 \\ -3x=-30 \\ x=\frac{-30}{-3} \\ \therefore x=10 \end{gathered}[/tex]To find y, we need to know that;
[tex]\text{Angle}(7x+1)=7(10)+1=^{}71^{\circ}[/tex]So let's call the third angle z. Let's go ahead and find z;
[tex]\begin{gathered} 38+71+z=180\text{ (sum of angles in a triangle)} \\ z=180-71-38 \\ \therefore z=71 \end{gathered}[/tex]Therefore y = 71 degrees (vertically opposite angles and equal)
The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. A flashlight is projecting a triangle onto a wall, as shown below. A The original triangle and its projection are similar. What is the missing length n on the projection? O 35 0224 10 40
Answers
We can see that the scale factor from the smaller triangle to the projected triangle is 2.
Multiply each length of the original triangle by the scale factor, to obtain the side lengths of the second triangle:
15 x 2 = 30
15x 2 = 30
20 x 2 = 40
answer : 40
Sketch the graph of the equation Y=2x^2-10x+9
Answers
Solution:
The equation is given below as
[tex]y=2x^2-10x+9[/tex]Step 1:
We will figure out the y-intercept by putting x=0
[tex]\begin{gathered} y=2x^{2}-10x+9 \\ y=2(0)^2-10(0)+9 \\ y=9 \\ (0,9) \end{gathered}[/tex]Step 2:
Calculate the vertex of the graph using the formula below
[tex]\begin{gathered} y=2x^2-10x+9 \\ x=-\frac{b}{2a},b=-10,a=2,c=9 \\ x=\frac{-(-10)}{2(2)}=\frac{10}{4}=\frac{5}{2} \\ \\ y=2(\frac{5}{2})^2-10(\frac{5}{2})+9 \\ y=2(\frac{25}{4})-25+9 \\ y=\frac{25}{2}-16 \\ y\frac{=25-32}{2} \\ y=-\frac{7}{2} \end{gathered}[/tex]Hence,
The vertex of the equation is
[tex](\frac{5}{2},-\frac{7}{2})[/tex]Using a graphing calculator, we will have the graph be
Solve fort.-t = 9(t – 10)t=Stuck? Watch a video or us
Answers
We are to solve for t in the equation given
To do this, we have to expand the bracket
Expanding, we have
-t = 9(t-10)
-t = 9t - 90
Collecting the like terms, we have
90 = 9t + t
90 = 10t
Dividing both sides by 10 to get t, we have
[tex]\begin{gathered} t=\frac{90}{10} \\ t=9 \end{gathered}[/tex]Therefore the value of t is 9.
A grocery store surveys its customers and asks them to indicate (a) how many times they go to the grocerystore in a typical month, (b) their age (in years), (c) whether or not they have ever had to wait in line at thegrocery store more than 10 minutes, (d) the product they purchase most often at the grocery store, and (e)how long (in years) they have shopped at this particular grocery store. We would consider the customer'sage in years to be aand whether or not the customer has had to wait in linemore than 10 minutes to be aO numerical variable; categorical variableO categorical variable; categorical variableO numerical variable; numerical variableO explanatory variable; response variableO categorical variable; numerical variable
Answers
The age in years is a numerical variable because it can be listed in ascending or descending order. while whether or not the customer has had to wait in line more than 10 minutes is a categorica
ARITHMETIC AND ALCEBRA REVIEWWord problem on optimizing an area or perimeter
Answers
region 1 will require the most paint
Explanation:length of tape = 24 ft
perimeter of the region to be painted = 24 ft
The region is rectangular, so we will apply the area of rectangle and perimeter to find the width.
perimeter = 2(length + width)
Area = length × width
We have 3 different regions with different lengths
For region 1:
length = 6 ft
from the formula for perimter, we can find the width:
perimeter = 2(length + width)
perimeter/2 = length + width
[tex]\text{width = }\frac{perimeter\text{ }}{2}-\text{ length}[/tex]width for region 1 = 24/2 - 6 = 12 - 6
width = 6
Area = 6 × 6 = 36 ft²
For region 2:
length = 7 ft
width = 24/2 - 7 = 12 - 7
width = 5 ft
Area = 7 × 5 = 35 ft²
For region 3:
length = 8 ft
width = 24/2 - 8 = 12 - 8
width = 4 ft
Area = 8 × 4 = 32 ft²
b) The region that will require the most paint is the one that has the highest area. The higher the area, the larger the amount of paint that will be needed.
From calculations above, the highest area is 36 ft²
Hence, the region that will require the most paint is region 1
12 Stefanie is painting her bedroom. She can paint 12 1/3 square feet in 1/5 of an hour. How many square feet can she paint in one hour?
Answers
stephanie can paint 12 1/3 square feet in 1/5 of an hour. So,
[tex]undefined[/tex]Name the quadrant in which each of the point lies. (-2,5)
Answers
The quadrants have the following division.
Since the points (-2, 5) is located on the negative side of the x-axis, and in the positive side of the y axis, it belongs to the second quadrant.
The answer is quadrant II
What is the M and B forX = 5M=B=
Answers
ANSWER
m = undefined
b = doesn't exist
EXPLANATION
x = 5 is a vertical line where in all points x is 5. Therefore, if we use the formula for the slope:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]The denominator will always be 0. Since we can't divide by 0, the slope is undefined.
Since it's a vertical line, there's no y-intercept. This is because the y-intercept is the value of y when x = 0 and in a vertical line x has always the same value: in this case, 5.
Which tree is growing faster?Tree 2Tree 1 is growing 2 week 2 4 6 8 10inches every week. inches5 10 15 20 25tallHint: First calculate the unit rate for Tree 2.Enter the number that belongs in the numerator.Unit Rate[?]=inches/week
Answers
Calculating the unit rate for Tree 2 we have the following
[tex]\text{Unit Rate }=\frac{5\text{ inches}}{2\text{ week}}\text{ }=\frac{10\text{ inches}}{4\text{ week}}\text{ }=\frac{15\text{ inches}}{6\text{ week}}[/tex]When simplified the unit rate is
[tex]\frac{5}{2}\text{ inches/week}[/tex]This is 2.5 inches per week. Compared to Tree 1,
select all of the trips that would take 5 hours 1. Drive 40 miles per hour between Bend and Portland, which are 200 miles apart 2. Take a train going 50 miles per hour from Martinez to Dunsmuir, which are 259 miles apart 3. Walk 4 miles per hour to school, wh6is 1.75 miles apart
Answers
Answer:
1. Yes
2. No
3. No.
Explanation:
The amount of time taken on a trip is equal to the distance travelled divided by the speed.
[tex]\text{time taken = }\frac{dist\text{ travelled }}{\text{speed}}[/tex]1. The drive from Bend to Portland is 200 miles and the speed is 40 miles per hour; therefore, the time taken is
[tex]\text{time taken = }\frac{200}{40}=5\text{ hours.}[/tex]2. The drive from Martinez to Dunsmuir is 259 and the speed is 50 miles per hour; therefore, the time taken is
[tex]\text{time taken = }\frac{259\text{ miles}}{50\text{ mile per hour}}\text{ = 5.18 hours}[/tex]3.
The distance to the school is 1.75 miles and the speed is 4 miles per hour; therefore, the time taken is
[tex]\text{time taken = }\frac{1.75\text{ miles}}{4\text{ miles per hour }}=0.4375\text{ hours. }[/tex]Hence, the only trip that takes 5 hours is trip 1.
A rocket is fired from the ground at an angle of 1.12 radians. Suppose the rocket has traveled 440 yards since it was launched. Draw a diagram and label the values that you know.How many yards has the rocket traveled horizontally from where it was launched?____ yards What is the rocket's height above the ground? ____yards
Answers
ANSWER
• Horizontal distance it traveled: ,191.7 yards
,• Height above ground: ,396 yards
EXPLANATION
Diagram:
The height, the horizontal distance and the distance traveled form a right triangle.
Since we know the angle, we can find both x and y. The distance traveled is the hypotenuse of the triangle, y is the opposite side to the known angle and x is the adjacent side:
[tex]\sin (1.12)=\frac{y}{440}\Rightarrow y=440\cdot\sin (1.12)=440\cdot0.9=396[/tex][tex]\cos (1.12)=\frac{x}{440}\Rightarrow x=440\cdot\cos (1.12)=191.7[/tex]how do I find out whether an infinite geometric series converges and how do I find its sum. for example:6+3+3/2+3/4+...
Answers
We are given the following infinite geometric series
[tex]6+3+\frac{3}{2}+\frac{3}{4}+\cdots[/tex]The general form of an infinite geometric series is given by
[tex]a_1+a_1r+a_1r^2+a_1r^3+\cdots[/tex]Where a1 is the first term and r is the common ratio.
The first term is equal to 6
The common ratio is the division of any two consecutive numbers in the infinite geometric series.
[tex]\frac{3}{6}=\frac{1}{2}[/tex]You can also take any other two consecutive numbers in the series and you will get the same common ratio.
[tex]\frac{\frac{3}{2}}{3}=\frac{3}{2}\cdot\frac{1}{3}=\frac{3}{6}=\frac{1}{2}[/tex]As expected, we still got the same common ratio as before.
How do I find out whether an infinite geometric series converges?
An infinite geometric series converges if the absolute value of the common ratio is less than 1.
[tex]\begin{gathered} |r|<1 \\ \frac{1}{2}<1 \\ 0.5<1 \end{gathered}[/tex]Since the absolute value of the common ratio is less than 1, the infinite geometric series converges.
How do I find its sum?
The sum of this infinite geometric series is given by
[tex]S=\frac{a_1}{1-r}[/tex]Substitute the values of first term a1 and common ratio r.
[tex]S=\frac{6}{1-\frac{1}{2}}=\frac{6}{\frac{1}{2}}=6\cdot\frac{2}{1}=12[/tex]Therefore, the sum of this infinite geometric series is 12.
The ratio of the amount of money Rachel saved to the amount of money Timothy saved was12 : 13. After Timothy spent $27, Rachel had 3 times as much as Timothy,A. How much did Rachel save?b How much did they save altogether at first?
Answers
For a)
Before
Rachel : Timothy
12 : 13
After
Rachel : Timothy
3 : 1
In order to have the same amount for Rachel
12: 4
Timothy
13units -4 units =9 units
9units=$27
1 unit=27/9
1unit = $3
For Rachel
Rachel saved $36
b)
Total units at first =12+13=25
If 1units is $3
25 units is 3x25
25 units is $75
They saved together 75
ANSWER
Rachel saved $36
They saved together 75
Find the probability of X less than or equal to 2X 0 1 2 3P(x) 0.12 0.67 0.19 0.020.980.790.020.19
Answers
Step 1:
Probability of x less than or equal to 2.
[tex]\begin{gathered} \text{Probability of x less than or equal to 2 = 0.12 + 0.67 + 0.19} \\ =\text{ 0.98} \end{gathered}[/tex]Step 2:
Final answer
= 0.98
P(E') = P(F) = 0.6 and P(E n F) = 0.24:a. Write down P(E).b. Explain how you know E and F:i are independentii are not mutually exclusivec Find P(E u F').
Answers
Answer:
Explanations:
Given the following probability values:
P(E') = 0.6
P(F) = 0.6
P(E n F) = 0.24
a) The probability of E [P(E)] is expressed according to the formula;
[tex]\begin{gathered} P(E)=1-P(E^{\prime}) \\ P(E)=1-0.6 \\ P(E)=0.4 \end{gathered}[/tex]b) For the events E and F to be independent, the product of their individual proban
On June 10, Trudy Polanski deposited $1260 in a savings account that pays 5.5% interest compounded daily. How much interest will the money earn in 60 days?
Answers
The answer will be $32,893.43 compound interest will the money earn in 60 days.
What is compound interest?
The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.
When the amount compounds quarterly, it means that the amount compounds 2 times, n=12. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:
A = P (1 + r/12)^12t
A = 1260(1+5.5/12) ^12
A = $32,893.43
Hence the interest will be $32,893.43.
Learn more about compound interest, by the following link
https://brainly.com/question/24274034
#SPJ1
A card is chosen from a standard deck, thena month of the year is chosen. Find theprobability of getting a face card and June. use the counting principle to find each probability
Answers
1) Gathering the data
1 face card out of one deck: 12 /52
1 month of the year: 1/12
2) In Probability, The counting principle says we can multiply two
events
The question, says the probability of getting a face card
We have 12 face cards in a deck so, using the counting principle:
P( face card and June) = 12/52 *1/12 =1/52
Jamie cut a rope into thirds.He used two of the pieces to make a swing
Answers
The complete length of the rope would be represented by 1
If he cut the rope into thirds, it means that each length woiuld be 1/3.
Given that he used two of the pieces to make a swing, it means that the length used in making the swing is
1/3 + 1/3 = 2/3
The left over rope is 1/3
Also, he used equal lengths of the left over rope on four picture frames. It means that the length used on each picture frame is
1/3 divided by 4
= 1/3 * 1/4 = 1/12
Thus, the fraction of the original rope that he used for each picture frame is 1/12. Option B is correct
A store had 896 swimsuits that were marked to sell at $40.99. Each suit was marked down $17.90. Find the reduced price using the formula M=S-N, where M is the markdown, S is the original selling price, and N is the reduced price. The reduced price is?
Answers
Let us assumed that each of the swimsuit is marked to sell at $40.99, and each suit was marked down $17.90 (given).
With the given formula below, we solve for the reduced price
[tex]M=S-N[/tex][tex]\begin{gathered} M=\text{ \$17.90(given)} \\ S=\text{ \$40.99(given)} \\ N=\text{reduced price} \end{gathered}[/tex]Substitute the value of M and S in the given formula to solve for N as shown below:
[tex]\begin{gathered} 17.90=40.99-N \\ 17.90+N=40.99-N+N \\ 17.90+N=40.99 \\ 17.90+N-17.90=40.99-17.90 \\ N=23.09 \end{gathered}[/tex]Hence, the reduce price is $23.09
Determine whether the function is linear. If it is, State the rate of change.Question 8
Answers
Question 8.
Given the table:
x -7 -5 -3 -1 0
y 11 14 17 20 23
To determine if the function is linear, let's calculate to see if the rate of change is constant.
The x-values need to have a constant rate of change and the y-values need to have a constant rate of change.
If the function has a constant rate of change, then the functioncan be said to be linear.
To calculate the rate of change, we have:
[tex]\begin{gathered} x2-x1=-5\text{ - (-7) = -5 + 7 = 2} \\ \\ x3-x2=-3-(-5)=-3+5=2 \\ \\ x4-x3=-1-(-3)=-1+3=2 \\ \\ x5-x4=0-(-1)=0+1=1 \\ \\ We\text{ can se}e\text{ the x-values do not have a constant rate of change} \end{gathered}[/tex][tex]\begin{gathered} y2-y1=14-11=3 \\ \\ y3-y2=17-14=3 \\ \\ y4-y3=20-17=3 \\ \\ y5-y4=23-20=3 \\ \\ \text{The y-values have a constant rate of change} \end{gathered}[/tex]Since the x-values do not have a constant rate of change that means the function is not linear.
ANSWER:
The table does not represent a linear function
Simplify.
Radical sign 45x
9
Answers
Answer:
20.12461179
Step-by-step explanation
Determine the equation of the line that goes through the point (4, 4) with -1/4 slope. Enter your answer in slope-intercept form.Enter EquationPls see picture
Answers
The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m represents slope
c represents y intercept
From the information given,
m = - 1/4
the line passes through the point (4, 4). This means that
x = 4, y = 4
We would find c by substituting m = - 1/4, x = 4 and y = 4 into the slope intercept equation. We have
4 = - 1/4 * 4 + c
4 = - 1 + c
Adding 1 to both sides of the equation,
4 + 1 = - 1 + 1 + c
c = 5
By substituting m = - 1/4 and c = 5 into the slope intercept equation, the equation of the line is
y = - x/4 + 5
A.bMicah used the wrong sign for b in the formula x = -2aO B. Micah should have evaluated the function with x = 0 to find they-coordinate.O C. Micah did not use the correct order-of-operations dividing 47.5 by21 -9.5)OD. Micah should have found a positive value when he simplified the-9.5(2.5)2 term.The correct vertex is(Type an ordered pair.)
Answers
Answer
- Micah's mistake in calculating the vertex is that he used the wrong sign for b in using (-b/2a) to calculate the x-coordinate of the vertex.
The correct vertex is (-2.5, 122.375).
Explanation
The quadratic equation is
y = -9.5x² - 47.5x + 63
It is evident that Micah's mistake in calculating the vertex is that he used the wrong sign for b in using (-b/2a) to calculate the x-coordinate of the vertex.
To no calculate the correct vertex,
a = -9.5
b = -47.5
c = 63
x = (-b/2a)
[tex]\begin{gathered} x=-\frac{b}{2a} \\ x=-\frac{-47.5}{2\times-9.5} \\ x=-\frac{-47.5}{-19} \\ x=-2.5 \end{gathered}[/tex]We can hen substitute this for x in the quadratic equation to get the corresponding y-coordinate for the vertex.
y = -9.5x² - 47.5x + 63
y = -9.5(-2.5)² - 47.5(-2.5) + 63
y = -9.5 (6.25) + 118.75 + 63
y = -59.375 + 118.75 + 63
y = 122.375
Hence, the vertex is (-2.5, 122.375)
Hope this Helps!!!
In the figure below, find each of the following.A right triangle has a vertical side labeled "3.00", a horizontal side labeled "4.00" that goes rightwards from the bottom of the vertical side, and a hypotenuse labeled "5.00" that goes down and right from the top of the vertical side to the right of the horizontal side. The top left interior angle of the triangle is an acute angle and the bottom right interior angle is an acute angle .(a) the length of the side opposite (b) the length of the side adjacent to (c) cos()(d) sin()(e) tan()
Answers
Given
To find:
a) The length of the side opposite
(b) The length of the side adjacent to
(c) cos()
(d) sin()
(e) tan()
Explanation:
It is given that,
That implies,
(a) The length of the side opposite is 3.00.
(b) The length of the side adjacent to is 3.00.
(c) cos()
[tex]\begin{gathered} \cos(\theta)=\frac{adjacen\text{t }side}{hypotenuse} \\ =\frac{4.00}{5.00} \\ =\frac{4}{5} \\ =0.8 \end{gathered}[/tex](d) sin()
[tex]\begin{gathered} \sin(\varphi)=\frac{opposite\text{ }side}{hypotenuse} \\ =\frac{4.00}{5.00} \\ =\frac{4}{5} \\ =0.8 \end{gathered}[/tex](e) tan()
[tex]\begin{gathered} \tan(\varphi)=\frac{opposite\text{ }side}{adjacent\text{ }side} \\ =\frac{4.00}{3.00} \\ =\frac{4}{3} \\ =1.33 \end{gathered}[/tex]Complete the following equation. Your answers will be algebraic expressions. (a+bi)^2= _____ + 2abiHint: think of i as an ordinary variable and then replace i^2 with -1.
Answers
The given expression is:
[tex](a+ib)^2[/tex]Expand to get:
[tex]\begin{gathered} (a+ib)^2=a^2+i^2b^2+2abi \\ =a^2-b^2+2abi \end{gathered}[/tex]The value is as above since it is given that i^2=-1.
So the expansion is:
[tex](a+ib)^2=a^2-b^2+2abi[/tex]The blank should be:
[tex]a^2-b^2[/tex]